Plus One Economics Chapter Wise Questions and Answers Chapter 9 Uses of Statistical Methods

Students can Download Chapter 9 Uses of Statistical Methods Questions and Answers, Plus One Economics Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examinations

Kerala Plus One Economics Chapter Wise Questions and Answers Chapter 9 Uses of Statistical Methods

Plus One Economics Uses of Statistical Methods One Mark Questions and Answers

Question 1.
An essential part of a project report is
(i) Objectives
(ii) Methodology
(iii) Analysis
(iv) All the above
Answer:
(iv) All the above

Plus One Economics Chapter Wise Questions and Answers Chapter 9 Uses of Statistical Methods

Question 2.
Data collection is covered under which part of a project works?
(i) Statement of the problem
(ii) Methodology
(iii) Analysis
(iv) Conclusion
Answer:
(ii) Methodology

Plus One Economics Uses of Statistical Methods Two Mark Questions and Answers

Question 1.
List the statistical tools you use for the analysis of data collected.
Answer:
The following statistical tools can generally be used for the analysis of data collected

  • Measure of central tendency
  • Standard deviation
  • Coefficient of variation
  • Regression
  • Correlation

Plus One Economics Uses of Statistical Methods Three Mark Questions and Answers

Question 1.
Explain the steps towards making a project report.
Answer:
The following are the steps towards making a project report

  1. Identifying a problem or area of study
  2. Choice of target group
  3. Collection of data
  4. Organization and presentation of data
  5. Analysis and interpretation 0 Conclusion
  6. Bibliography

Plus One Economics Chapter Wise Questions and Answers Chapter 9 Uses of Statistical Methods

Question 2.
Write down the features of a good questionnaire.
Answer:
The features of a gdb questionnaire are mentioned
below.

  1. The questionnaire should not be too long.
  2. The number of questions should be as minimum as possible.
  3. The series of questions should move from general to specific.
  4. The questions should be precise and clear.
  5. The questions should not be ambiguous, to enable the respondents to answer quickly, correctly and clearly.
  6. If possible ask ‘yes’ or ‘no’ questions.
  7. The question should not be a leading question, which gives a clue about how the respondent should answer.
  8. The question should not indicate alternatives to the answer.

Plus One Economics Uses of Statistical Methods Five Mark Questions and Answers

Question 1.
Prepare a questionnaire to study the socio-economic conditions of students in your class.
Answer:
Questionnaire to study the socio-economic conditions

1. Name
2. Sex
3. Age
4. Class
5. The community to which you belong to
6. Details of family members:
Plus One Economics Chapter Wise Questions and Answers Chapter 9 Uses of Statistical Methods img1
7. Monthly income of the family

  • below 1000
  • between 1000 and 5000
  • between 5000 and 10000
  • above 10000

8. Do you live in the
a) rental house b) own house

9. Is your house electrified
a) yes b) no

Plus One Economics Chapter Wise Questions and Answers Chapter 9 Uses of Statistical Methods

10. Do you subscribe to the newspaper at home
a) yes b) no

11. Details of amenities at home:

  • cooking gas
  • television
  • bicycle
  • washing machine
  • motorcar
  • scooter
  • refrigerator
  • others

Plus One Economics Chapter Wise Questions and Answers Chapter 8 Index Numbers

Students can Download Chapter 8 Index Numbers Questions and Answers, Plus One Economics Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examinations

Kerala Plus One Economics Chapter Wise Questions and Answers Chapter 8 Index Numbers

Plus One Economics Index Numbers One Mark Questions and Answers

Question 1.
Which of the following is known as cost of living index?
(a) Consumers price index
(b) Wholesale price index
(c) Industrial production index
(d) All the above
Answer:
(a) Consumers price index

Question 2.
Index number can be calculated for ……….
(a) Price
(b) Quantity
(c) Volume
(d) All the above
Answer:
(d) All the above

Question 3.
In 2017 the price of oil increased by 30% compared to 2010. Identify the base year and the current year.
Answer:
Base year 2010, Current year 2017

Plus One Economics Chapter Wise Questions and Answers Chapter 8 Index Numbers

Question 4.
Which of the following indicates the changes in general price level?
(a) Consumers price index
(b) Wholesale price index
(c) Industrial production index
(d) All the above
Answer:
(b) Wholesale price index

Question 5.
An index number which accounts for the relative importance of the items is known as
(a) weighted index
(b) simple aggregative index
(c) simple average of relatives
(d) all the above
Answer:
(a) weighted index

Question 6.
In most of the weighted index numbers the weight pertains to
(a) base year
(b) current year
(c) both base and current year
(d) none of these
Answer:
(b) current year

Question 7.
The impact of change in the price of a commodity with little weight in the index will be
(a) small
(b) large
(c) uncertain
(d) none of these
Answer:
(a) small

Question 8.
A consumer price index measures changes in
(a) retail prices
(b) wholesale prices
(c) producers prices
(d) none of these
Answer:
(a) retail prices

Question 9.
The item having the highest weight in consumer price index for industrial workers is
(a) Food
(b) Housing
(c) Clothing
(d) all the above
Answer:
(a) Food

Plus One Economics Chapter Wise Questions and Answers Chapter 8 Index Numbers

Question 10.
In general, inflation is calculated by using
(a) wholesale price index
(b) consumer price index
(c) producers’ price index
Answer:
(a) wholesale price index

Question 11.
What is the other name of the consumer price index?
Answer:
The other name of the consumer price index is price deflator of income.

Question 12.
What is base period?
Answer:
Base period is the reference period with which the current period is compared.

Plus One Economics Index Numbers Two Mark Questions and Answers

Question 1.
Index numbers are very useful in deflating. Explain.
Answer:
Index numbers are very useful in deflating. They are very useful adjusting original data into real values. For example, money wages can be adjusted for price changes to find out the level of real wages.

Question 2.
Write down the uses of the wholesale price index.
Answer:
The wholesale price index number indicates the change in the general price level. The uses of the wholesale price index are noted down below.

  1. With the help of the wholesale price index, we can estimate the future demand and supply situations
  2. It helps in forecasting future prices
  3. It is used to measure the rate of inflation
  4. It can be used to eliminate the effect of change in price on aggregates such as national income, capital formation, etc.

Question 3.
Define index number.
Answer:
An index number is a statistical device for measuring changes in the magnitude of a group of related variables.

Question 4.
Mention the formula of ‘simple aggregative’ method?
Answer:
\(P_{01}=\frac{\sum P_{1}}{\Sigma P_{0}} \times 100\)
Here,
ΣP = Total of current year’s prices of different commodities.
ΣP0 = Total of base year’s prices of different commodites.

Question 5.
Give utility of index numbers.
Answer:

  1. Index numbers simplify the facts
  2. It is helpful to policymakers
  3. It makes comparative study easy
  4. It helps to study the general trend

Question 6.
Write a short note on Sensex.
Answer:
Sensex is the short form of Bombay Stock Exchange Sensitive Index with 1978 – 79 as base. The value of Sensex is with reference to this period. It consists of 30 stocks represented by 13 sectors of the economy. If Sensex rises, it indicates that the market is doing well and investors expect better earnings on their investment.

Plus One Economics Chapter Wise Questions and Answers Chapter 8 Index Numbers

Question 7.
Consumer price indices are of great useful because of various reasons. What are they?
Answer:

  1. They determine the purchasing power of money.
  2. They are helpful in the determination of real wages.
  3. They are helpful in wage negotiations and wage contracts.
  4. They help in deflating income and value series in national accounts.
  5. They help the government in formulation of wage policy, price policy, rent control and making general economic policies.

Plus One Economics Index Numbers Three Mark Questions and Answers

Question 1.
Name some important index number in use.
Answer:
some important index number in use are mentioned below.

  • Consumer price index
  • Wholesale Price Index
  • Industrial production index
  • Producer Price Index
  • Index number of agricultural production

Question 2.
Construct an index number for 1991 taking 1990 as base year.
Plus One Economics Chapter Wise Questions and Answers Chapter 8 Index Numbers img1
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 8 Index Numbers img2
It shows when compared to 1990 the general price level in 1991 increased by 20%.

Plus One Economics Chapter Wise Questions and Answers Chapter 8 Index Numbers

Question 3.
Point out the desirable properties of the base year.
Answer:
The desirable properties of base year are:

  • The base year should be a normal year.
  • Extreme values should not be selected as base period.
  • It should not belong to too far in the past.

Plus One Economics Index Numbers Four Mark Questions and Answers

Question 1.
What are the limitations of index numbers?
Answer:
The limitations of index numbers are mentioned below.

  • Index numbers are not fully true.
  • They do not help in international comparison.
  • They are prepared with certain specific objectives.
  • It is difficult to collect retail prices. So, index numbers based on wholesale prices may be misleading.

Question 2.
“Index number is used in economics for policymaking” substantiate.
Answer:
Wholesale price index number (WPI), consumer price index number (CPI) and industrial production index (IIP) are widely used in policymaking.

1. Consumer index number (CPI) or cost of living index numbers are helpful in wage negotiation, formulation of income policy, price policy, rent control, taxation and general economic policy formulation.

2. The wholesale price index (WPI) is used to eliminate the effect of changes in prices on aggregates such as national income, capital formation, etc.

3. WPI is widely used to measure the rate of inflation. Inflation is a general and continuing increase in prices. If inflation becomes sufficiently large, money may lose its traditional function as a medium of exchange and as a unit of account. Its primary impact lies in lowering the value of money.

4. CPI are used in calculating the purchasing power of money and real wage.

5. Index of industrial production gives us a quantitative figure about the change in production in the industrial sector.

6. Agricultural production index provides us a ready reckoner of the performance of agricultural sector.

7. Sensex is a useful guide for investors in the stock market. If the sensex is rising, investors are optimistic of the future performance of the economy. It is an appropriate time for investment.

Plus One Economics Index Numbers Five Mark Questions and Answers

Question 1.
Certain important issues should be kept in mind while constructing an index number”. Do agree? Substantiate your answer.
Answer:
Yes, certain important issues should be kept in mind, while constructing an index number. Those issues are mentioned below

1. You need to be clear about the purpose of the index. The calculation of a volume index will be inappropriate when one needs a value index.

2. Besides this, the items are not equally important for different groups of consumers when a consumer price index is constructed. The rise in petrol price may not directly impact the living condition of the poor agricultural labourers.

Thus the items to be included in any index have to be selected carefully to be as representative as possible. Only
then you will get a meaningful picture of the change.

3. Every index should have a base. This base should be as normal as possible. Extreme values should not be selected as base period. The period should also not belong to too far in the past. The comparison of between 1993 and 2005 is much more meaningful than a comparison between 1960 and 2005.

Many items in a 1960 typical consumption basket have disappeared at present. Therefore, the base year for any index number is routinely updated.

4. Another issue is the choice of the formula, which depends on the nature of question to be studied. The only difference between the Laspeyres index and Paasche’s index is the weights used in these formulae.

5. Besides, there are many sources of data with different degrees of reliability. Data of poor reliability will give misleading results. Hence, due care should betaken in the collection of data. If primary data are not being used, then the most reliable source of secondary data should be chosen.

Plus One Economics Chapter Wise Questions and Answers Chapter 8 Index Numbers

Question 2.
Explain various types of index numbers.
Answer:
Some Important Index Numbers
1. Consumer price index:
Consumer price index (CPI), also known as the cost of living index, measures the average change in retail prices. The CPI for industrial workers is increasingly considered the appropriate indicator of general inflation, which shows the most accurate impact of price rise on the cost of living of common people.

2. Wholesale price index:
The wholesale price index number indicates the change in the general price level. Unlike the CPI, it does not have any reference consumer category. It does not include items pertaining to services like barber charges, repairing, etc.

3. Industrial production index:
The index number of industrial production measures changes in the level of industrial production comprising many industries. It includes the production of the public and the private sector. It is a weighted average of quantity relatives. In India, it is currently calculated every month with 1993 – 94 as the base.

4. Index number of agricultural production:
The index number of agricultural production is a weighted average of quantity relatives. Its base period is the triennium ending 1981 – 82. In 2003 – 04 the index number of agricultural production was 179.5.

It means that agricultural production has increased by 79.5 percent over the average of the three years 1979 – 80, 1980 – 81 and1981 – 82. Foodgrains have a weight of 62.92 percent in this index.

5. Producer Price Index:
The producer price index number measures price changes from the producers’ perspective. It uses only basic prices including taxes, trade margins, and transport costs.

Plus One Economics Chapter Wise Questions and Answers Chapter 7 Correlation

Students can Download Chapter 7 Correlation Questions and Answers, Plus One Economics Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examinations

Kerala Plus One Economics Chapter Wise Questions and Answers Chapter 7 Correlation

Plus One Economics Correlation One Mark Questions and Answers

Question 1.
Who developed rank correlation co-efficient.
(i) Karl Pearson
(ii) Karl Marx
(iii) Spearman
(iv) None of the above
Answer:
(iii) Spearman

Question 2.
If r= +1, if shows:
(i) Positive correlation
(ii) Perfect positive correlation
(iii) No correlation
(iv) Rank correlation
Answer:
(ii) Perfect positive correlation

Question 3.
If ‘r’ is positive the two variables will more in
(i) Opposite direction
(ii) Inverse direction
(iii) Same direction
(iv) None of the above
Answer:
(iii) Same direction

Plus One Economics Chapter Wise Questions and Answers Chapter 7 Correlation

Question 4.
Which of the following correlation can be used to measure numerically only leniar relationship between two variables?
(i) Karl Pearsons coefficient of correlation
(ii) Spearman correlation
(iii) Rank correlation
(iv) None of the above
Answer:
(i) Karl Pearsons coefficient of correlation

Question 5.
The unit of correlation coefficient between height in feet and weight in kgs is
(i) kg/feet
(ii) percentage
(iii) non-existent
Answer:
(iii) non-existent

Question 6.
The range of simple correlation coefficient is
(i) 0 to infinity
(ii) minus one to plus one
(iii) minus infinity to infinity
Answer:
(ii) minus one to plus one

Question 7.
If rxy is positive the relation between X and Y is of the type.
(i) When Y increases X increases
(ii) When Y decreases X increases
(iii) When Y increases X does not change
Answer:
(i) When Y increases X increases

Question 8.
If rxy = 0 the variable X and Y are
(i) linearly related
(ii) not linearly related
(iii) independent
Answer:
(ii) not linearly related

Question 9.
Of the following three measures which can measure any type of relationship
(i) Karl Pearson’s coefficient of correlation
(ii) Spearman’s rank correlation
(iii) Scatter diagram
Answer:
(iii) Scatter diagram

Question 10.
If precisely measured data are available the simple correlation coefficient is
(i) more accurate than rank correlation coefficient
(ii) less accurate than rank correlation coefficient
(iii) as accurate as the rank correlation coefficient
Answer:
(iii) as accurate as the rank correlation coefficient

Question 11.
Define correlation.
Answer:
Correlation studies and measures the direction and intensity of relationship among variables.

Plus One Economics Chapter Wise Questions and Answers Chapter 7 Correlation

Question 12.
Write the formula for calculating correlation.
Answer:
1. Karl Pearson’s coefficient of correlation
\(r=\frac{\sum x y}{\sqrt{\sum x^{2} \times \sum y^{2}}}\)

2. Spearman’s Rank correlation coefficient
\(R=1-\frac{6 \Sigma D^{2}}{N\left(N^{2}-1\right)}\)

Plus One Economics Correlation Two Mark Questions and Answers

Question 1.
Can r lie outside the -1 and 1 range depending on the type of data?
Answer:
No, r cannot lie outside -1 and 1 range depending on the types of data. It lies between minus one and plus one.

Question 2.
Indicate the kind of relationship between X and Y, if the points of the scatter diagram tend to cluster about.

  1. A straight line sloping upward.
  2. A straight line sloping downward.

Answer:

  1. A straight line sloping upward: it is the case of positive correlation.
  2. A straight line sloping downward: it is the case of negative correlation.

Question 3.
Name the correlation mentioned in the graph.
Plus One Economics Chapter Wise Questions and Answers Chapter 7 Correlation img1
Answer:
(a) Positive correlation
(b) Negative correlation
(c) No correlation
(d) Perfect positive correlation
(e) Perfect negative correlation

Question 4.
Give two examples each for positive and negative correlation.
Answer:
1. Positive Correlation

  • Relation between price and supply
  • Relation between height and weight

2. Negative Correlation

  • Relation between price and demand
  • Sale of woolen garment and day temperature

Plus One Economics Chapter Wise Questions and Answers Chapter 7 Correlation

Question 5.
What are perfect correlations? Give examples.
Answer:
Perfect correlation is that where changes in two related variables are exactly proportional. It is of two types:
a) Positive perfect correlation and
b) Negative perfect correlation
There is perfect positive correlation between the two variables of equal proportional changes are in the same direction. It is expressed as +1. If equal proportional changes are in the reverse direction. Then there is negative perfect correlation and it is described as -1.
Plus One Economics Chapter Wise Questions and Answers Chapter 7 Correlation img2

Question 6.
Show in scatter diagram the following.

  1. Positive correlation
  2. Negative correlation

Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 7 Correlation img3

Plus One Economics Correlation Three Mark Questions and Answers

Question 1.
Interpret the values for as 1, -1 and 0.
r=1 r = -1 r = 0
Answer:
r as 1 means that there is perfect positive relationship between two variables r as -1 means that there is perfect negative relationship between two variables r as 0 means that there lack correlation between two variables

Question 2.
List some variables where accurate measurement is difficult.
Answer:
The following are some variables where accurate measurement is difficult.

  • Secularism
  • Honesty
  • Beauty
  • Impartiality
  • Patriotism

Question 3.
State the nature of relationship.

  1. sale of woolen garments and the day temperature
  2. amount of rainfall and yield of crop
  3. the colour of dress and intelligence of the lady

Answer:

  1. negative correlation
  2. positive correlation
  3. no correlation

Question 4.
Write down the merits of scatter diagram.
Answer:
Merits of scatter diagram are pointed out below:

  1. It is a very simple method of studying correlation.
  2. Just a glance of the diagram will show the relationship.
  3. It indicates whether the relationship is positive or negative.

Question 5.
Construct a flow chart showing the methods of measuring correlation?
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 7 Correlation img4

Question 6.
Illustrate positive correlation and negative correlation.
Answer:
Correlation is commonly classified into negative and positive correlation.
The correlation is said to be positive when the variables move together in the same direction. When the income rises, consumption also rises. When income falls, consumption also falls. For instance, sale of ice-cream and temperature move in the same direction.

The correlation is negative when they move in opposite directions. When the price of apples falls its demand increases. When the prices rise its demand decreases. When you spend more time in studying, chances of your failing decline. These are instances of negative correlation. The variables move in opposite direction.

Question 7.
Calculate the coefficient of correlation from the following data.
Plus One Economics Chapter Wise Questions and Answers Chapter 7 Correlation img5
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 7 Correlation img6

Plus One Economics Chapter Wise Questions and Answers Chapter 7 Correlation

Question 8.
The following are the ranks obtained by 10 students in two subjects. Calculate Spearman’s rank correlation.

Rank of StatisticsRank of Economics
12
24
31
45
53
69
77
810
96
108

Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 7 Correlation img7

Question 9.
Calculate coefficient of correlation using the following data.
Plus One Economics Chapter Wise Questions and Answers Chapter 7 Correlation img8
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 7 Correlation img9

Plus One Economics Correlation Five Mark Questions and Answers

Question 1.
What do you mean by Spearman’s rank correlation coefficient? Point out the situations where it is used. Also, bring about its usefulness.
Answer:
Spearman’s rank correlation was developed by the British psychologist C.E. Spearman. It is used when the variables cannot be measured meaningfully as in the case of price, income, weight, etc. The ranking may be more meaningful when the measurements of the variables are suspect.

There are also situations when you are required to quantify qualities such as fairness, honesty, etc. Ranking may be a better alternative to the quantification of qualities. Moreover, sometimes the correlation coefficient between two variables with extreme values may be quite different from the coefficient without the extreme values. Under these circumstances, rank correlation provides a better alternative to simple correlation.

Rank correlation coefficient and simple correlation coefficient have the same interpretation. Its formula has been derived from simple correlation coefficient where individual values have been replaced by ranks. These ranks are used for the calculation of correlation. This coefficient provides a measure of linear association between ranks assigned to these units, not their values. It is the Product Moment Correlation between the ranks.

Plus One Economics Chapter Wise Questions and Answers Chapter 7 Correlation

Question 2.
“Correlation Coefficient has certain essential properties”-substantiate.
Answer:
Correlation Coefficient has certain essential properties as discussed below.
1. r has no unit. It is a pure number. It means units of measurement are not part of r. r between height in feet and weight in kilograms, for instance, is 0.7.

2. A negative value of /-indicates an inverse relation. A change in one variable is associated with change in the other variable in the opposite direction. When price of a commodity rises, its demand falls. When the rate of interest rises the demand for funds also falls. It is because now funds have become costlier.

3. If r is positive the two variables move in the same direction. If/”= 0 the two variables are uncorrelated. There is no linear relation between them. However other types of relationships may be there.

4. If r = 1 or r = -1 the correlation is perfect. The relation between them is exact.

5. A high value of r indicates strong linear relationship. Its value is said to be high when it is close to+1 or-1.

6. A low value of r indicates a weak linear relation. Its value is said to be low when it is dose to zero.

7. The value of the correlation coefficient lies between minus one and plus one, -1 < r < +1. If, in any exercise, the value of r \s outside this range indicates error in calculation.

8. The value of r is unaffected by the change of origin and change of scale. Given two variables X and Y let us define two new variables.

Question 3.
Illustrate the following ideas in scatter diagrams.
i. Positive correlation
ii. Perfect positive correlation
iii. Negative correlation
iv. Perfect negative correlation No correlation
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 7 Correlation img10
Plus One Economics Chapter Wise Questions and Answers Chapter 7 Correlation img11
Plus One Economics Chapter Wise Questions and Answers Chapter 7 Correlation img12

Plus One Economics Chapter Wise Questions and Answers Chapter 6 Measures of Dispersion

Students can Download Chapter 6 Measures of Dispersion Questions and Answers, Plus One Economics Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examinations

Kerala Plus One Economics Chapter Wise Questions and Answers Chapter 6 Measures of Dispersion

Plus One Economics Measures of Dispersion One Mark Questions and Answers

Question 1.
Find out the measure of dispersion from the following.
Answer:
(i) Range
(ii) Mean deviation
(iii) Standard deviation
(iv) All the above
Answer:
(iv) All the above

Question 2.
Variance is equal to:
(i) SD
(ii) SD²
(iii) √SD
(iv) SD/2
Answer:
(ii) SD²

Question 3.
Lorenz curve is used to measure
Answer:
(i) Literacy rate
(ii) Unemployment
(iii) Inequality
(iv) None of these
Answer:
(iii) Inequality

Plus One Economics Chapter Wise Questions and Answers Chapter 6 Measures of Dispersion

Question 4.
Which is the graphical method of determining dispersion?
(i) Range
(ii) Q.D
(iii) S.D
(iv) Lorenz curve
Answer:
(iv) Lorenz curve

Question 5.
Which among the following is not an absolute measure of dispersion?
(i) Range
(ii) Co-efficient of variation
(iii) Mean deviation
(iv) Standard deviation
Answer:
(ii) Co-efficient of variation

Question 6.
Which of the following is the most widely used measure of dispersion?
(i) Range
(ii) Standard deviation
(iii) Mean deviation
(iv) Quartile deviation
Answer:
(ii) Standard deviation

Question 7.
Which of the following is useful in comparing the variability of two or more distributions?
(i) Lorenz Curve
(ii) Standard deviation
(iii) Mean deviation
(iv) Quartile deviation
Answer:
(iii) Mean deviation

Question 8.
Which of the following is not based on all the values?
(i) Mean deviation from mean
(ii) Mean deviation from median.
(iii) Range
(iv) Standard deviation
Answer:
(iii) Range

Question 9.
Mean deviation
(i) is least when calculated from median and higher when calculated from mean.
(ii) is least when calculated from mean and higher when calculated from median.
(iii) same when calculated from median and mean.
(iv) cannot be calculated either from median or mean.
Answer:
(i) is least when calculated from median and higher when calculated from mean.

Plus One Economics Chapter Wise Questions and Answers Chapter 6 Measures of Dispersion

Question 10.
Mention the purpose for which Lorenz Curve is drawn.
Answer:
Lorenz curve is drawn for the presentation of inequality (or dispersion)

Plus One Economics Measures of Dispersion Two Mark Questions and Answers

Question 1.
Which measure of dispersion is the best and how?
Answer:
Standard deviation is the best measure of dispersion. Because it possesses most of the characteristics of an ideal measure of dispersion.

Question 2.
Range is not based on all the values. Do you agree? Substantiate.
Answer:
Yes, I agree with the statement that range is not based on all the values. It is simply the difference between the largest (L) and the smallest value (S) in a distribution. Therefore, range cannot be considered as a good measure of dispersion.

Question 3.
Give two limitations of range.
Answer:
Given below two limitations of range.

  1. range is unduly affected by extreme values
  2. range is not based on all values.

Question 4.
Differentiate between range and interquartile range.
Answer:
Range is the difference between the value of extreme while interquartile range is the difference between quarter extreme values of the series.

Question 5.
Some measures of dispersion depend upon the spread of values whereas some calculate the variation of values from a central value. Do you agree?
Answer:
Yes, I agree with this statement. Range and quartile deviation measure the dispersion by calculating the spread within which the values lie. That is they de-pend.on the spread of values. On the other hand, mean deviation and standard deviation calculate the variation of value from a central value.

Plus One Economics Chapter Wise Questions and Answers Chapter 6 Measures of Dispersion

Question 6.
Write the merits and demerits of mean deviation.
Answer:
1. Merits

  • It is based on all observations
  • It is less affected by extreme items
  • It is easy to calculate & simple to understand

2. Demerits

  • It ignores + signs
  • It is difficult to compute when
  • or median comes infraction.

Plus One Economics Measures of Dispersion Three Mark Questions and Answers

Question 1.
Calculate coefficient of standard deviation from the following information SD = 22.4, Mean = 159
Answer:
Coefficient of standard deviation = \(\frac{\mathrm{SD}}{\bar{x}} \times 100\)
\(=\frac{22.4}{159} \times 100=0.14 \times 100=14\)

Question 2.
Following are certain measures of dispersion. Classify them into absolute measures and relative measures.
{Range, Coefficient of variation, Mean Deviation, Coefficient of Quartile Deviation, coefficient of Range, Standard deviation}
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 6 Measures of Dispersion img1

Question 3.
Find odd ones out and justify your answer.

  1. range, quartile deviation, mode, standard deviation
  2. scatter, spread, variation, correlation
  3. Range, Mean Deviation, coefficient of variation, Standard deviation.

Answer:

  1. Mode. Others are methods of studying measures of dispersion.
  2. Correlation. Others are different expressions of dispersion.
  3. Coefficient of variation. Others are absolute measures of dispersion.

Question 4.
Calculate the coefficient of variation, if,
Number of Boys = 72
Average Height = 68
The variance of distribution = 9
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 6 Measures of Dispersion img2

Question 5.
Point out features of good measure of dispersion.
Answer:
The features of a good measure of dispersion are pointed out below:

  • It should be easy to understand
  • It should be simple to calculate
  • It should be rigidly defined
  • It should be based on all observations
  • It should not be affected by extreme values

Plus One Economics Chapter Wise Questions and Answers Chapter 6 Measures of Dispersion

Question 6.
The size of landholdings of 5 persons are given below:

IndividualsLand in acres
A1.5
B3.0
C0.5
D6.0
E2.0

 

  1. Analyse the data by measuring the dispersion using the easiest method.
  2. What are the drawbacks of that method?

Answer:
1. Range is the simplest method of studying dispersion.
Range = L – S
where L = Largest item
S = Smallest item
Range = 6 – 0.5 = 5.5 acres
2.

  • It is not based on each and every item of the distribution.
  • It is subject to fluctuations from sample to sample.
  • It cannot be computed in case of open-end classes.

Question 7.
If the sum of 10 values is 100 and the sum of their square is 1090, find the coefficient of variation.
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 6 Measures of Dispersion img3

Plus One Economics Measures of Dispersion Four Mark Questions and Answers

Question 1.
In a town, 25% of the persons earned more than Rs 45,000 whereas 75% earned more than 18,000. Calculate the absolute and relative values of dispersion.
Answer:
We get the following information from the above.
Q1 = Rs. 18000 and Q3 = Rs. 45000
Absolute measure of dispersion (quartile deviation)
= Q3 – Q1/2 = 45000 – 18000/2
= Rs. 13500
Relative measure of dispersion (coefficient of Q. D)
= Q3-Q1/Q3 + Q1
= 45000 -18000 / 45000 + 18000
= 27000/63000
= 3/7
= 0.43

Question 2.
What do you mean by dispersion? Name the important methods of measuring dispersion.
Answer:
Dispersion is the extent to which values in a distribution differ from the average of the distribution.
To quantify the extent of the variation, there are certain measures namely:

  1. Range
  2. Quartile Deviation
  3. Mean Deviation
  4. Standard Deviation
  5. Lorenz curve

Question 3.
Mention the merits of standard deviation.
Answer:
Merits of standard deviation are:

  1. It is rigidly defined
  2. It is based on all observations
  3. It takes algebraic signs in consideration
  4. It serves the basis of other measures like correlation.

Question 4.
The number of telephone calls received at an exchange in 245 successive one-minute intervals are shown in the following frequency distribution. Compute the mean deviation about the median.

No. of callsFrequency
014
121
225
343
451
540
639
712

Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 6 Measures of Dispersion img4

Plus One Economics Chapter Wise Questions and Answers Chapter 6 Measures of Dispersion

Question 5.
The coefficient of variation of two series are 58% and 69% and their standard deviation are 21.2 and 15.6. Calculate their mean.
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 6 Measures of Dispersion img5

Question 6.
Calculate the standard deviation.

MarksFrequency
20 – 403
40-806
80-10020
100-12012
120-1409

Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 6 Measures of Dispersion img6

Plus One Economics Measures of Dispersion Five Mark Questions and Answers

Question 1.
Match the following.

AB
Measures of dispersionKarl Pearson
Standard deviationSD2
Graphical methodSD/mean x 100
VarianceAverage of the second order
Quartile deviationSemi-interquartile range
Coefficient of variationLorenz curve

Answer:

AB
Measures of dispersionAverage of the second order
Standard deviationKarl Pearson
Graphical methodLorenz curve
VarianceSD2
Quartile deviationSemi-inter quartile range
Coefficient of variationSD/mean x 100

Plus One Economics Measures of Dispersion Eight Mark Questions and Answers

Question 1.
What do you mean by Lorenz curve? Give the steps required in the Construction of the Lorenz Curve.
Answer:
The measures of dispersion discussed so far give a numerical value of dispersion. A graphical measure called Lorenz Curve is available for estimating dispersion. In constructing a Lorenz curve, the following steps are involved.

  1. Calculate class mid-points and find cumulative totals
  2. Calculate cumulative frequencies
  3. Express the grand totals and convert the cumulative totals in these columns into percentages,
  4. Now, on the graph paper, take the cumulative percentages of the variable on Y-axis and cumulative percentages of frequencies on X-axis. Thus each axis will have values from ‘0’to ‘100’.
  5. Draw a line joining Co-ordinate (0, 0) with (100,100). This is called the line of equal distribution
  6. Plot the cumulative percentages of the variable with corresponding cumulative percentages of frequency.
  7. Join these points to get the curve OAC.

Plus One Economics Chapter Wise Questions and Answers Chapter 6 Measures of Dispersion

Question 2.
Calculate

  1. standard deviation and
  2. mean deviation

from the following data.
X = 7, 9, 18, 11, 10, 8, 17, 13, 11, 16
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 6 Measures of Dispersion img7
1. Standard deviation
\(s=\sqrt{\frac{\sum d^{2}}{N}}\)
\(=\sqrt{\frac{134}{10}}=3.66\)

2. Median deviation
\(M D=\frac{\Sigma|d|}{N}=\frac{32}{10}=3.2\)

Question 3.
The following table gives the distribution of income of 100 families in a village. Calculate standard deviation.

IncomeNo. of Families
0-100018
1000-200026
2000-300030
3000 – 400012
4000 – 500010
5000 – 60004

Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 6 Measures of Dispersion img8

Question 4.
Write down the formula for finding out various measures of dispersion.
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 6 Measures of Dispersion img9
Plus One Economics Chapter Wise Questions and Answers Chapter 6 Measures of Dispersion img10
Plus One Economics Chapter Wise Questions and Answers Chapter 6 Measures of Dispersion img11

Plus One Economics Chapter Wise Questions and Answers Chapter 5 Measures of Central Tendency

Students can Download Chapter 5 Measures of Central Tendency Questions and Answers, Plus One Economics Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examinations

Kerala Plus One Economics Chapter Wise Questions and Answers Chapter 5 Measures of Central Tendency

Plus One Economics Measures of Central Tendency One Mark Questions and Answers

Question 1.
The midpoint of the class ‘5-10’ is:
(i) 5
(ii) 7.5
(iii) 10
(iv) 15
Answer:
(ii) 7.5

Question 2.
Mode is equal to:
(i) 3 median – 2 mean
(ii) 2 median – 3 mea
(iii) 3 median – 3 mean
(iv) 3 median -1 mean
Answer:
(i) 3 median – 2 mean

Question 3.
Which of the following is a positional average?
(i) Mean
(ii) Median
(iii) Mode
(iv) All the above
Answer:
(ii) Median

Question 4.
Which of the following divides the data into four equal parts?
(i) decile
(ii) percentile
(iii) quartiles
(iv) none of the above
Answer:
(iii) quartiles

Plus One Economics Chapter Wise Questions and Answers Chapter 5 Measures of Central Tendency

Question 5.
Which of the following is the most commonly used average?
(i) Arithmetic Mean
(ii) Median
(iii) Mode
(iv) Percentile
Answer:
(i) Arithmetic Mean

Question 6.
Mode can be graphically located by means of
(i) bio diagram
(ii) pie diagram
(iii) histogram
(iv) ogive
Answer:
(iii) histogram

Question 7.
The most suitable average for qualitative measurement is
(i) Arithmetic mean
(ii) Median
(iii) Mode
(iv) Geometric mean
(v) None of the above
Answer:
(ii) Median

Question 8.
Which average is affected most by the presence of extreme items?
(i) median
(ii) Mode
(iii) Arithmetic mean
(iv) Geometric mean
(v) Harmonic mean
Answer:
(iii) Arithmetic mean

Question 9.
The algebraic sum of deviation of a set of n values from A.M. is
(i) n
(ii) 0
(iii) 1
(iv) None of the above
Answer:
(ii) 0

Question 10.
The average value of a given variable is known as ____
Answer:
A.M

Question 11.
Total of given variables can be depicted by _____
Answer:
Σx

Question 12.
Common factor is depicted by ____
Answer:
‘c’

Plus One Economics Chapter Wise Questions and Answers Chapter 5 Measures of Central Tendency

Question 13.
A.M should be
(i) Simple
(ii) Based on all items
(iii) Rigidly defined
(iv) All the above
Answer:
(iv) All the above

Question 14.
Median is the _____ value in a series.
Answer:
Middle.

Question 15.
Q3 represents ____ Quartile.
Answer:
Middle.

Question 16.
_____ is the division of the series into 100 equal parts.
Answer:
Percentiles.

Question 17.
\(\left(\frac{N+1}{10}\right)^{t h}\) is used to calculate _____.
Answer:
Deciles

Question 18.
Value of median is equal to _____Answer:
Answer:
II Quartile – 50th percentile, 5th Decile

Question 19.
Pick out the odd one out and Justify.
Arithmetic mean, Median, Standard deviation, Mode
Answer:
Standard deviation. Others are measures of central tendency.

Plus One Economics Chapter Wise Questions and Answers Chapter 5 Measures of Central Tendency

Question 20.
Which average would be suitable in the following cases?

  1. Average size of readymade garments.
  2. Average intelligence of students in a class.
  3. Average production in a factory per shift.
  4. Average wages in an industrial concern.
  5. When the sum of absolute deviations from average is least.
  6. When quantities of the variable are in ratios.
  7. In case of open-ended frequency distribution.

Answer:

  1. Mode
  2. Median
  3. Mode or median
  4. Mode or median
  5. Mean
  6. Mode or mean
  7. Median

Plus One Economics Measures of Central Tendency Two Mark Questions and Answers

Question 1.
Name the types of positional averages.
Answer:
Positional averages are median and mode.

Question 2.
Explain weighted Arithmetic mean
Answer:
When calculating Arithmetic means it is important to assign weights to various items according to their importance. The arithmetic mean calculated with the relative importance to different items is known as weighted arithmetic mean.

Question 3.
Give the special features of arithmetic mean.
Answer:
It is interesting to know and useful for checking your calculation that the sum of deviations of items about arithmetic mean is always equal to zero. Symbolically, S (X-X) = 0.However, arithmetic mean is affected by extreme values. Any large value, on either end, can push it up or down.

Question 4.
If median and mean of distribution are respectively 18.8 and 20.2. What would be its made?
Answer:
Mode = 3 Median – 2 Mean
= 3 × 18.8 – 2 × 20.2
= 56.4 – 40.4 = 16

Plus One Economics Chapter Wise Questions and Answers Chapter 5 Measures of Central Tendency

Question 5.
Mention two demerits of median.
Answer:

  1. Median is not based on all observations
  2. It cannot be given for further mathematical treatment

Question 6.
Give the formulae of median in all series
Answer:
Formulae of Median
Plus One Economics Chapter Wise Questions and Answers Chapter 5 Measures of Central Tendency img 1

Question 7.
If median is 15 and mean is 17, calculate mode?
Answer:
Mode = 3 median – 2 mean
= 3 × 15 – 2 × 17
= 45 – 34 = 11

Question 8.
Can there be a situation where mean, median and mode are equal?
Answer:
Yes. Mean, median and mode will be equal when all given variables are the same.

Question 9.
Mark the missing value of the following data. The mean marks are 10.05.
5, 6, 7, 8, 12, ?, 15, 17, 18, 3, 10 5, 10, 12, 15, 11, 13, 1
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 5 Measures of Central Tendency img 2

Plus One Economics Measures of Central Tendency Three Mark Questions and Answers

Question 1.
What is the relative position of arithmetic mean, median and mode?
Answer:
Relative position of arithmetic mean, median and mode can be understood from the following narration. Suppose we express,
Arithmetic Mean = Me
Median = Mi
Mode = Mo
The relative magnitude of the three is
Me>Mi>Moor
Me<Mi<Mo
That is the median is always between the arithmetic mean and the mode.

Question 2.
Write down the advantages of median.
Answer:
Merits of median:

  • It is easy to understand
  • It is not affected by extreme values It can be graphically determined
  • It is suitable in case of open-end classes
  • It is suitable for qualitative measurement

Plus One Economics Chapter Wise Questions and Answers Chapter 5 Measures of Central Tendency

Question 3.
Write the merits of mode.
Answer:
Merits of mode

  • It is easy to understand and simple to calculate
  • It is not affected by extreme values
  • It can be graphically determined
  • It is suitable in case of open-end classes.

Question 4.
Complete the following

  1. ………………. divides the series into two equal parts
  2. The central tendency based on all values is …………..
  3. The average which can be determined through ogive is ………

Answer:

  1. median
  2. mean
  3. median

Question 5.
The mean mark of 60 students in section A are 40 and mean mark if 40 student in section B is 35. Calculate the combined mean of all the students.
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 5 Measures of Central Tendency img 3

Plus One Economics Measures of Central Tendency Four Mark Questions and Answers

Question 1.
Point out important features of a good average.
Answer:
The important features of a good average are given below.

  1. It should be easy to understand
  2. It should be simple to calculate
  3. It should be rigidly defined
  4. It should be based on all observations
  5. It should not be affected by extreme values.
  6. It should be capable for further statistical calculations.

Question 2.
Following information pertains to the daily income of 150 families. Calculate the arithmetic mean.
Plus One Economics Chapter Wise Questions and Answers Chapter 5 Measures of Central Tendency img 4
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 5 Measures of Central Tendency img 5

Plus One Economics Chapter Wise Questions and Answers Chapter 5 Measures of Central Tendency

Question 3.
Calculate the median from the following data.

XF
0-105
10-208
20-3010
30-4014
40-503

Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 5 Measures of Central Tendency img 6

Plus One Economics Measures of Central Tendency Five Mark Questions and Answers

Question 1.
Comment whether the following statements are true or false.

  1. The sum of deviation of items from median is zero.
  2. An average alone is not enough to compare series.
  3. Arithmetic mean is a positional value.
  4. The upper quartile is the lowest value of top 25% of items.
  5. Median is unduly affected by extreme observations.

Answer:

  1. False
  2. True
  3. False
  4. True
  5. False

Question 2.
There are three types of averages. Name them. Also, give appropriate definitions.
Answer:
There are several statistical measures of central tendency or “averages”. The three most commonly used averages are:

  • Arithmetic Mean
  • Median
  • Mode

1. Arithmetic mean:
Arithmetic mean is the most commonly used measure of central tendency. It is defined as the sum of the values of all observations divided by the number of observations

2. Median:
Median is that positional value of the variable which divides the distribution into two equal parts, one part comprises all values greater than or equal to the median value and the other comprises all values less than or equal to it. The Median is the “middle” element when the data set is arranged in order of the magnitude.

3. Mode:
The word mode has been derived from the French word “la Mode” which signifies the most fashionable values of distribution because it is repeated the highest number of times in the series. Mode is the most frequently observed data value. It is denoted by Mo.

Plus One Economics Chapter Wise Questions and Answers Chapter 5 Measures of Central Tendency

Question 3.
What are the merits and demerits of arithmetic mean?
Answer:
1. Merits

  • It is simple to calculate
  • It is regidly defined
  • It is easy to understand
  • It is based on all observations

2. Demerits

  • It is affected by extreme values.
  • It cannot be calculated in open-end series.
  • It cannot be determined graphically.
  • It may sometimes give misleading results.

Plus One Economics Measures of Central Tendency Eight Mark Questions and Answers

Question 1.
Prepare a list of peculiarities of median, quartiles, and percentiles.
Answer:
1. Median

  • The arithmetic mean is affected by the presence of extreme values in the data.
  • If you take a measure of central tendency which is based on middle position of the data, it is not affected by extreme items.
  • Median is that positional value of the variable which divides the distribution into two equal parts, one part comprises all values greater than or equal to the median value and the other comprises all values less than or equal to it.
  • The Median is the middle element when the data set is arranged in order of the magnitude.

2. Quartiles

  • Quartiles are the measures that divide the data into four equal parts; each portion contains equal number of observations. Thus, there are three quartiles.
  • The first Quartile (denoted by Q1) or lower quartile has 25% of the items of the distribution below it and 75% of the items are greater than it.
  • The second Quartile (denoted by Q2) or median has 50% of items below it and 50% of the observations above it.
  • The third Quartile (denoted by Q3) or upper Quartile has75% of the items of the distribution below it and 25% of the items above it.
  • Thus, Q1 and Q3 denote the two limits within which central 50% of the data lies.

3. Percentiles

  • Percentiles divide the distribution into hundred equal parts, so you can get 99 dividing positions denoted by P1 P2, P3, ………., P99.
  • P50 is the median value.
  • If you have secured 82 percentile in a management entrance examination, it means that your position is below 18 percent of total candidates appeared in the examination.

Plus One Economics Chapter Wise Questions and Answers Chapter 5 Measures of Central Tendency

Question 2.
The daily sales of car of 20 distributing companies is given below. Calculate:

  1. Median, upper quartile and lower quartile.
  2. Interpret the result obtained.

 

Daily SalesNo. of Companies
0-201
20-403
40-609
60-805
80-1002
20

Answer:
1.
Plus One Economics Chapter Wise Questions and Answers Chapter 5 Measures of Central Tendency img 7
Plus One Economics Chapter Wise Questions and Answers Chapter 5 Measures of Central Tendency img 8
Plus One Economics Chapter Wise Questions and Answers Chapter 5 Measures of Central Tendency img 9
2. The median divides the values into two equal parts. Lower quartile (Q1) divides the values into 1/4 and upper quartile (Q3) divides the values into 3/4.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 9 Small Business

Students can Download Chapter 9 Small Business Questions and Answers, Plus One Business Studies Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examination

Kerala Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 9 Small Business

Plus One Small Business Two Mark Questions and Answers

Question 1.
Define small scale industries.
Answer:
Small scale industry:
A small scale industrial undertaking is defined as one in which the investment in fixed assets of plant and machinery does not exceed rupees one crore.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 9 Small Business

Question 2.
State the features of cottage industries.
Answer:
Cottage industries:
cottage industries are characterised by certain features:

  1. These are organised by individuals, with private resources.
  2. Normally use family labour and locally available talent.
  3. The equipment used is simple.
  4. Capital investment is small.
  5. Produce simple products, normally in their own premises.
  6. Production of goods using indigenous technology.

Plus One Small Business Three Mark Questions and Answers

Question 1.
Discuss the problems faced by small scale industries. (3)
Answer:
Problems of small business:
Small businesses are faced with the following problems:

  1. Small scale industries find it difficult to get adequate finance from banks and other financial institutions.
  2. They are not able to get quality raw materials at reasonable prices.
  3. Small business is generally operated by people who may not have all the managerial skills required to run the business.
  4. Small business firms cannot afford to pay higher salaries to the employees. So productivity per employee is relatively low and employee turnover is generally high.
  5. Small business depends excessively on middlemen for marketing the products. Middlemen exploit them by paying low price and delayed payments.
  6. Small business organization uses outdated technology to produce products. So they cannot compete with global enterprises with low quality products.
  7. Due to lack of marketing skills or lack of demand, many small business firms have to operate below full capacity.
  8. Use of outdated technology results low productivity and uneconomical production.
  9. Small-scale units find it very difficult to compete .with the product of multinational companies which are comparatively very cheap and of better quality
  10. Other important problems are poor project planning, inefficient management, transportation problems, lack of power, and lack of adequate warehousing, etc.

Plus One Small Business Four Mark Questions and Answers

Question 1.
Write short note on

  1. NSIC
  2. DIC (4)

Answer:
1. National Small Industries Corporation (NSIC):
This was set up in 1955 to promote, aid and foster the growth of small scale units in India.
Functions of NSIC :

  • It supplies imported machines and raw materials to small scale industries on easy hire-purchase schemes.
  • It exports the products of small units.
  • It provides technology to small scale Industries.
  • Helps in up-gradation of technology
  • Provides advisory service
  • Developing software technology parks and technology transfer centres.

2. The District Industries Centers (DICs):
DICs were established in May 1978. District Industries Centers is the institution at the district level which provides all the services and support facilities to the entrepreneurs for setting up small and village industries. Identification of suitable schemes, preparation of feasibility reports, arranging for credit, machinery and equipment, provision of raw materials and other extension services are the main activities undertaken by these centers.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 9 Small Business

Question 2.
What measures has the government taken to solve the problem of finance and marketing in the small scale sector? (4)
Answer:
Government assistance to small Industries and Small Business:
Institutional Support:
1. National Bank for Agriculture and Rural Development (NABARD):
NABARD was set up in 1982 to promote integrated rural development.
Functions of NABARD:

  • It provides financial support to small Industries, cottage and village industries and agriculture.
  • It provides counseling and consultancy services.
  • It also organises training and development programme for rural entrepreneurs.

2. The Rural Small Business Development Centre (RSBDC):
It aims at providing management and technical support to current and prospective micro and small entrepreneurs in rural areas. RSBDC has organized several programmes on rural entrepreneurship, skill upgradation workshops, training programmes, etc.

3. National small Industries Corporation (NSIC):
This was set up in 1955 to promote, aid and foster the growth of small scale units in India.
Functions of NSIC :

  • It supplies imported machines and raw materials to small scale industries on easy hire-purchase schemes.
  • It exports the products of small units.

4. Small Industries Development Bank of India (SIDBI):
SIDBI was set up in 1980. SIDBI is the main financial Institution for financing and development of small Business in India.
Functions of SIDBI:

  • Helps SSI unit for modernization and technology upgradation by providing loan
  • Meet working capital requirements of SSI.

5. The National Commission for Enterprises in the Unorganised Sector (NCEUS):
The NCEUS was constituted in September, 2004.
The objectives of NCEUS:

  • To recommend measures for improving the productivity of small enterprises
  • To generate more employment opportunities in rural areas

6. Rural and Women Entrepreneurship Development (RWED):
RWE provides the following services:

  • Creating a business environment that encourages initiatives of rural and women entrepreneurs.
  • Enhancing the human and institutional capacities required to foster entrepreneurial dynamism and enhance productivity.
  • Providing training manuals for women entrepreneurs and training them.
  • Rendering all types of advisory services.

7. World Association for Small and Medium Enterprises (WASME):
It is the only International Non-Governmental Organisation of micro, small and medium enterprises based in India, which set up an International Committee for Rural Industrialisation. Its aim is to develop an action plan model for sustained growth of rural enterprises.

There are several schemes to promote the non-farm sector initiated by the Government of India, i.e. IRDP, PMRY, TRYSEM, JRY, Development of Women and Children in Rural Areas (DWCRA) etc.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 9 Small Business

8. Scheme of Fund for Regeneration of Traditional Industries (SFURTI):
To make the traditional industries more productive and competitive, the Central Government set up a fund with₹100 crores.
The main objectives of the scheme are as follows:

  • To develop clusters of traditional industries in various parts of the country
  • To make traditional industries competitive, profitable and sustainable
  • To create employment opportunities in traditional industries.

9. The District Industries Centers (DICs):
DICs were established in May 1978. District Industries Centers is the institution at the district level which provides all the services and support facilities to the entrepreneurs for setting up small and village industries.

Identification of suitable schemes, preparation of feasibility reports, arranging for credit, machinery and equipment, provision of raw materials and other extension services are the main activities undertaken by these centers.

Plus One Small Business Five Mark Questions and Answers

Question 1.
What are the incentives provided by the Government for industries in backward and hilly areas? (5)
Answer:
Incentives:
The incentives offered by the government to develop backward areas are:

  1. Availability of land at concessional rate.
  2. Supply power at a concessional rate of 50% or exempt such units from payment in the initial years.
  3. Water is supplied on a no-profit, no-loss basis or with 50 percent concession or exemption from water charges for a period of 5 years.
  4. All union territories, industries are exempted from sales tax,
  5. Most states have abolished octroi.
  6. Units located in backward areas get scarce raw materials at concessional rates.
  7. Subsidy of 10-15% for building capital asset. Loans are offered at concessional rates.
  8. Some states encourage setting up of industrial estates in backward areas.
  9. Exemption from paying taxes for 5 or 10 years is given to industries established in backward, hilly and tribal areas.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 9 Small Business

Question 2.
Small scale industrial sector has an important role in Indian economy. To meet the financial and developmental needs of small business in India a separate bank had been set up. (5)

  1. Give the name of the bank.
  2. What are its major functions?

Answer:
1. SIDBI: Small Industries Development Bank of India (SIDBI). SIDBI was set up in 1980. SIDBI is the main financial Institution for financing and development of small Business in India.

2. Functions of SIDBI:

  • Helps SSI unit for modernisation and technology upgradation by providing loan
  • Meet working capital requirements of SSI.
  • Provides means forthe rehabilitation of sick units
  • Provides service like leasing, hire purchase, venture capital financing etc.
  • Provide equity support to small entrepreneurs.

Plus One Small Business Six Mark Questions and Answers

Question 1.
Describe the role of small business in rural India. (6)
Answer:
Role of small business in Rural India:

  1. Cottage and rural industries provide employment opportunities in the rural areas especially for the traditional artisans and the weaker sections of society.
  2. It prevents migration of rural population to urban areas in search of employment.
  3. Small business helps to eradicate poverty, income inequalities, etc in rural area.
  4. Small scale industries are powerful instrument for the accelerated industrial growth and creating productive employment in rural and backward areas.

Plus One Small Business Eight Mark Questions and Answers

Question 1.
How do small scale industries contribute to the socio-economic development of India? (8)
Answer:
Role of small business in India:

  1. Small industries are labour intensive and less capital intensive. They generate more number of employment opportunities.
  2. The share of product from small industries is 45% of total export from India. So it earn valuable foreign exchange.
  3. Small scale Industries produces a wide variety of goods e.g. readymade garments, stationery, soaps, leather goods, plastic and rubber goods.
  4. The contribution of small industries to the balanced regional development of the country is very significant.
  5. Small industries provide ample opportunity for entrepreneurship.
  6. It enjoys the advantage of low cost of production because they used local resources in their product.
  7. Due to the small size of the organisation, quick and timely decisions can be taken without consulting many people.
  8. Small industries are best suited for the products which are designed according to the taste, needs and preferences of the customers.
  9. Small industries maintain good personal relations with both customers and employees.

Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Students can Download Chapter 13 Probability Questions and Answers, Plus Two Maths Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Plus Two Maths Probability Three Mark Questions and Answers

Question 1.
Determine P(E/F). A die is thrown three times, E: ‘4 appears on the third toss’, F: ‘6 and 5 appears respectively on the two tosses’.
Answer:
n(S) = 63 = 216
E = {( 1, 1, 4), (1, 2, 4), (1, 3, 4)……….(1, 6, 4),
(2, 1, 4), (2, 2, 4), (2, 3, 4)……..(2, 6, 4),
(3, 1, 4), (3, 2, 4), (3, 3, 4)……..(3, 6, 4),
(4, 1, 4), (4, 2, 4), (4, 3, 4)…….(4, 6, 4),
(5, 1, 4), (5, 2, 4), (5, 3, 4)……..(5, 6, 4),
(6, 1, 4), (6, 2, 4), (6, 3, 4)……..(6, 6, 4)}
F = {(6, 5, 1), (6, 5, 2), (6, 5, 3), (6, 5, 4), (6, 5, 5), (6, 5, 6)}
⇒ E ∩ F = {(6, 5, 4)}
P(F) = \(\frac{6}{216}\) and P(E ∩ F) = \(\frac{1}{216}\)
Then, P(E/F) = \(\frac{P(E \cap F)}{P(F)}=\frac{\frac{1}{216}}{\frac{6}{216}}=\frac{1}{6}\).

Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Question 2.
Determine P(E/F). Mother, Father and son lineup at random for a photograph.
E: ‘Son on one end’, F: ‘ Father in middle.
Answer:
Let Mother-M, Father-F and Son-S.
n(S) = 3! = 6
E = {SMF, SFM, MFS, FMS},
F = {MFS, SFM}
⇒ E ∩ F = {SFM, MFS}
P(F) = \(\frac{2}{6}\) = \(\frac{1}{3}\) and P(E ∩ F) = \(\frac{2}{6}\) = \(\frac{1}{3}\)
Then, P(E/F) = \(\frac{P(E \cap F)}{P(F)}=\frac{\frac{1}{3}}{\frac{1}{3}}=1\).

Question 3.
A black and a red dice are rolled

  1. Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.
  2. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

Answer:
We have, n(S) = 36
1. E = Event of 5 on black die.
E = {(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)}
P(E) = \(\frac{6}{36}\) = \(\frac{1}{6}\)
F = Getting a sum greater than 9.
F = {(4, 6), (5, 5), (6, 4)(5, 6), (6, 5), (6, 6)}
⇒ E ∩ F = {(5,5), (5,6)}
P(E ∩ F) = \(\frac{2}{36}\)= \(\frac{1}{18}\)
Therefore the required probability
P(E/F) = \(\frac{P(E \cap F)}{P(F)}=\frac{\frac{1}{18}}{\frac{1}{6}}=\frac{1}{3}\).

2. E = Event of a number less than 4 on red die.
E = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3),
(3, 1), (3, 2), (3, 3), (3, 1), (3, 2), (3, 3),
(5, 1), (5, 2), (5, 3), (6, 1), (6, 2), (6, 3)}
P(E) = \(\frac{18}{36}\) = \(\frac{1}{2}\)
F = Getting a sum 8.
F = {(4, 4), (5, 3), (3, 5)(2, 6), (6, 2), (6, 6)}
⇒ E ∩ F = {(5, 3),(6, 2)}
P(E ∩ F) = \(\frac{2}{36}\)= \(\frac{1}{18}\)
Therefore the required probability
P(E/F) = \(\frac{P(E \cap F)}{P(E)}=\frac{\frac{1}{18}}{\frac{1}{2}}=\frac{1}{9}\).

Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Question 4.
An instructor has a question bank consisting of 300 easy True/False questions, 200 difficult true/False questions, 500 easy multiple choice questions, and 400 difficult multiple choice questions. If a question is selected from the test question bank, what is the probability that it will be an easy question given that it is a multiple choice question?
Answer:
Describe the events as follows
E: ‘getting an easy question.’
F: ‘getting a multiple choice question.’
Total Questions = 300 + 200 + 500 + 400 = 1400
n(F) = 500 + 400 = 900, n(E ∩ F) = 500
P(F) = \(\frac{900}{1400}=\frac{9}{14}\), P(E ∩ F) = \(\frac{500}{1400}=\frac{5}{14}\)
Therefore the required probability
= P(E/F) = \(\frac{P(E \cap F)}{P(F)}=\frac{\frac{5}{14}}{\frac{9}{14}}=\frac{5}{9}\).

Question 5.
Two cards are drawn at random without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.
Answer:
Describe the events as follows
B1: ‘getting a black card in the first draw.’
B2: ‘getting a black card in the second draw.’
P(B1) = \(\frac{26}{52}\) = \(\frac{1}{2}\)
When the first event is executed and since no replacement is allowed, the remaining total number of cards become 51 and black cards become 25.
P(B2/B1) = \(\frac{25}{51}\)
Therefore the required probability
P(B1 ∩ B2) = P(Bl) × P(B2/B1) = \(\frac{1}{2} \times \frac{25}{51}=\frac{25}{102}\).

Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Question 6.
If P(A) = \(\frac{6}{11}\), P(B) = \(\frac{5}{11}\) and P(A ∪ B) = \(\frac{9}{11}\) Find

  1. P(A ∩ B)
  2. P(A/B)
  3. P(B/A)

Answer:
1. P(A ∩ B) = P(A) + P(B) – P(A ∪ B)
Plus Two Maths Probability 3 Mark Questions and Answers 1

2. P(A/B)
Plus Two Maths Probability 3 Mark Questions and Answers 2

3. P(B/A)
Plus Two Maths Probability 3 Mark Questions and Answers 3

Question 7.
Events A and B are such that P(A) = \(\frac{1}{2}\), P(B) = \(\frac{7}{12}\) and P(not A or not B) = \(\frac{1}{4}\) State whether A and B are independent.
Answer:
P(not A or not B) = \(\frac{1}{4}\) ⇒ \(P(\bar{A} \cup \bar{B})=\frac{1}{4}\)
Plus Two Maths Probability 3 Mark Questions and Answers 4
We have, P(A) × P(B) = \(\frac{1}{2} \times \frac{7}{12}=\frac{7}{24}\)
Therefore, P(A ∩ B) ≠ P(A) × P(B)
Hence A and B are not independent.

Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Question 8.
Consider two events such that P(A) = \(\frac{1}{2}\), P(A ∪ B) = \(\frac{3}{5}\) and P(B) = p. Find p, if A and B are independent events.
Answer:
If A and B are independent then
P(A ∩ B) = P(A) × P(B)
We have,
P(A ∪ B) = P(A) + P(B) – P(A) × P(B)
Plus Two Maths Probability 3 Mark Questions and Answers 5

Question 9.
One card is drawn at random from a well shuffled pack of 52 cards. In which of the following cases are the events E and F independent? (3 scores each)

  1. E: ‘the card drawn is a spades.’
    F: ‘the card drawn is an ace.’
  2. E: ‘the card drawn is a black.’
    F: ‘the card drawn is a king.’
  3. E: ‘the card drawn is a king or a queen.’
    F: ‘the card drawn is queen or a jack.’

Answer:
1. P(E) = \(\frac{13}{52}=\frac{1}{4}\), P(F) = \(\frac{4}{52}=\frac{1}{13}\)
There is only one card which is an ace of spade.
P(E ∩ F) = \(\frac{1}{52}\)
We have,
P(E) × P(F) = \(\frac{1}{4} \times \frac{1}{13}=\frac{1}{52}\) = P(E ∩ F)
Hence E and F are independent events.

2. P(E) = \(\frac{26}{52}=\frac{1}{2}\), P(F) = \(\frac{4}{52}=\frac{1}{13}\)
There are two king of black.
P(E ∩ F) = \(\frac{2}{52}\) = \(\frac{1}{26}\)
We have,
P(E) × P(F) = \(\frac{1}{2} \times \frac{1}{13}=\frac{1}{26}\) = P(E ∩ F)
Hence E and F are independent events.

3. There are 4 king and 4 queen cards
P(E) = \(\frac{8}{52}\) = \(\frac{2}{13}\),
There are 4 queen and 4 jack cards.
P(F) = \(\frac{8}{52}\) = \(\frac{2}{13}\)
There 4 queen common for both.
P(E ∩ F) = \(\frac{4}{52}\) = \(\frac{1}{13}\)
We have,
P(E) × P(F) = \(\frac{2}{13} \times \frac{2}{13}=\frac{4}{169}\) ≠ P(E ∩ F)
Hence E and F are not independent events.

Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Question 10.
A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin’ and B be the event ‘3 on the die’. Check whether A and B are independent events or not.
Answer:
P(A) = \(\frac{1}{2}\) and P(B) = \(\frac{1}{6}\)
When a coin and die are tossed the sample space will be as follows.
S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}
Here head and 3 come only once.
⇒ P(A ∩ B) = \(\frac{1}{12}\)
P(A) × P(B) = \(\frac{1}{2} \times \frac{1}{6}=\frac{1}{12}\) = P(A ∩ B)
Hence A and B are independent.

Question 11.
Rani and Joy appear in an interview for two vacancies in the same post. The probability of Rani’s selection is \(\frac{1}{7}\) and that of Joy’s selection is \(\frac{1}{5}\) .What is the probability that

  1. Rani will not be selected? (1)
  2. Both of them will be selected? (1)
  3. None of them will be selected? (1)

Answer:
1. Let Rani’s selection be the event A and Joy’s selection be the event B.P(Rani will not be selected)
Plus Two Maths Probability 3 Mark Questions and Answers 6

2. P(Both of them will be selected)
P(A ∩ B) = P(A).P(B) = \(\frac{1}{7} \cdot \frac{1}{5}=\frac{1}{35}\).

3. P(None selected)
Plus Two Maths Probability 3 Mark Questions and Answers 7

Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Question 12.
Find the probability distribution of number heads in two tosses of a coin.
Answer:
S = {HH, HT, TH, TT}
Let X denotes the random variable of getting a head. Then X can take values 0, 1, 2.
P(X = 0) = P(no heads) = P({TT})
= P(T) × P(T) = \(\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}\)
P(X = 1) = P(one heads)
= P({HT, TH})
= P(H) × P(T) + P(T) × P(H)
= \(\frac{1}{2} \times \frac{1}{2}+\frac{1}{2} \times \frac{1}{2}=\frac{1}{2}\)
P(X = 2) = P(two heads) = P({HH})
= P(H) × P(H) = \(\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}\)
The required Probability Distribution is
Plus Two Maths Probability 3 Mark Questions and Answers 8

Question 13.
Ten eggs are drawn successively with replacement from a lot containing 10% defective eggs. Find the probability that there is at least one defective egg.
Answer:
Let X denotes the random variable of number of defective eggs in the 10 eggs drawn.
Clearly X has a Binomial Distribution with n = 10 and p = 10% = \(\frac{1}{10}\), q = 1 – p = \(\frac{9}{10}\)
⇒ P(X = x) = 10Cxq10-xpx = 10Cx\(\left[\frac{9}{10}\right]^{10-x}\left[\frac{1}{10}\right]^{x}\)
P(at least 1 defective egg) = P(X ≥ 1)
1 – P(X = 0) = 1 – 10C0\(\left[\frac{9}{10}\right]^{10}=1-\frac{9^{10}}{10^{10}}\).

Plus Two Maths Probability Four Mark Questions and Answers

Question 1.
In a hostel 50 % of the girls like tea, 40 % like coffee and 20% like both tea and coffee. A girl is selected and random.

  1. Find the probability that she likes neither tea nor coffee. (2)
  2. If the girl likes tea, then find the probability that she likes coffee. (1)
  3. If she likes coffee then find the probability she likes tea. (1)

Answer:
Let T denotes the set of girls who like tea and C denotes who like coffee.
1. P(T) = 50% = \(\frac{1}{2}\); P(C) = 40% = \(\frac{2}{5}\);
P(T ∩ C) = 20% = \(\frac{1}{5}\)
P(T ∪ C) = 1 – P(T ∪ C)
= 1 – {P(T) + P(C)-P(T ∩ C)}
\(=1-\left\{\frac{1}{2}+\frac{2}{5}-\frac{1}{5}\right\}=\frac{3}{10}\).

2.
Plus Two Maths Probability 3 Mark Questions and Answers 9

3.
Plus Two Maths Probability 3 Mark Questions and Answers 10

Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Question 2.
A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale.
Answer:
For the box to be approved all the three oranges should be selected from the 12 good ones. Since the events are executed without replacement the number for good oranges and total oranges reduce by one on each draw.
O1: ‘getting a good orange in the first draw.’
O2: ‘getting a good orange in the second draw.’
O3: ‘getting a good orange in the third draw.’
P(good orange in the first draw) =P(O1)= \(\frac{12}{15}\) = \(\frac{4}{5}\),
P(good orange in the second) = p(O2/O1) = \(\frac{11}{14}\),
P(good orange in the third)
= P(O3/(O1 ∩ O2)) = \(\frac{10}{13}\)
Therefore the required probability
= P(O1 ∩ O2 ∩ O3)
= P(O1)P(O2/O1)P(O3/(O1 ∩ O2))
\(=\frac{4}{5} \times \frac{11}{14} \times \frac{10}{13}=\frac{44}{91}\).

Question 3.
Let two independent events A and B such that P(A) = 0.3, P(B) = 0.6. Find

  1. P(A and B)
  2. P(A and not B)
  3. P(A or B)
  4. P (neither A nor B)

Answer:
1. P(A and B) = P(A ∩ B) = P(A) × P(B)
= 0.3 × 0.6 = 0.18.

2. P(A and not B) = P(A ∩ \(\bar{B}\)) = P(A) × P(\(\bar{B}\))
= 0.3 × 0.4 = 0.12.

3. P(A or B) = P(A ∪ B)
= P(A) + P(B) – P(A ∩ B)
= P(A) + P(B) – P(A) × P(B)
= 0.3 + 0.6 – 0.3 × 0.6 = 0.72.

4. P(neither A nor B) = \(P(\bar{A} \cap \bar{B})\)
= P(\(\bar{A}\)) × P(\(\bar{B}\)) = 0.7 × 0.4 = 0.28.

Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Question 4.
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that

  1. both balls are red.
  2. the first ball is a black and the second is red
  3. one of them is black and the other red.

Answer:
Describe the events as follows.
Black-B and Red-R.n(S) = 18,
P(B) = \(\frac{10}{18}\) = \(\frac{5}{9}\) and P(R) = \(\frac{8}{18}\) = \(\frac{4}{9}\)
Since the event is executed with replacement, is independent.
1. P( both ball is red) = P(R) × P(R)
= \(\frac{4}{9} \times \frac{4}{9}=\frac{16}{81}\).

2. P( first black and second red) = P(B) × P(R)
= \(\frac{5}{9} \times \frac{4}{9}=\frac{20}{81}\).

3. P( one of them is a black and the other red)
= P(B) × P(R) + P(R) × P(B)
\(=\frac{5}{9} \times \frac{4}{9}+\frac{4}{9} \times \frac{5}{9}=\frac{40}{81}\).

Question 5.
Bag 1 contains 3 red and 4 black balls while another Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the Bags and it is found to be red. Find the probability that it was from Bag II.
Answer:
Describe the events as follows.
A: ‘getting a defective ball’.
E1: ‘choosing Bag I.’
E2: ‘choosing Bag II.’
P(E1) = P(E2) = \(\frac{1}{2}\)
P(A/E1) = P (drawing a red ball from Bag I) = \(\frac{3}{7}\)
P(A/E2) = P (drawing a red ball from Bag II) = \(\frac{5}{11}\)
P (a ball from Bag II, being given that it is red)
Plus Two Maths Probability 4 Mark Questions and Answers 11

Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Question 6.
A Bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One ball of the two Bag is drawn at random and the ball is drawn the Bag is found to be red. Find the probability that the ball is drawn from first Bag.
Answer:
Describe the events as follows.
A: ‘getting a red ball’.
E1: ‘choosing Bag I.’
E2: ‘choosing Bag II.’
P(E1) = P(E2) = \(\frac{1}{2}\)
P(A/E1) = P (a red ball from Bag I) = \(\frac{4}{8}\) = \(\frac{1}{2}\)
P(A/E2) = P (a red ball from Bag II) = \(\frac{2}{8}\) = \(\frac{1}{4}\)
P (a ball from Bag II, being given that it is red)
Plus Two Maths Probability 4 Mark Questions and Answers 12

Question 7.
In a factory which manufactures blots, machines A, B, and C manufacture respectively 25%, 35%and 40% of the bolts. Of their outputs 5%, 4% and 2%are defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it is manufactured by the machine B?
Answer:
Describe the events as follows.
A: ‘getting a defective bolt’.
E1: ‘choosing machine A.’
E2: ‘choosing machine B.’
E3: ‘choosing machine C.’
P(E1) = 0.25, P(E2) = 0.35, P(E3) = 0.4
P(A/E1) = P
(a defective bolt from machine A)
= 5% = 0.05
P(A/E2) = P
(a defective bolt from machine B)
= 4% = 0.04
P(A/E3) = P
(a defective bolt from machine C)
= 2% = 0.02
P (a bolt from machine B, being given that it is defective)
= P(E2/A)
Plus Two Maths Probability 4 Mark Questions and Answers 13

Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Question 8.
Suppose 5% of men and 0.25% of women have hair grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume there are equal number males and females.
Answer:
Describe the events as follows.
A: ‘person is grey haired’.
E1: ‘choosing man.’
E2: ‘choosing woman.’
P(E1) = P(E2) = \(\frac{1}{2}\)
P(A/E1) = P (a grey haired person from men)
= 5% = 0.05
P(A/E2) = P (a grey haired person from women) = 0.25% = 0.0025
P(selecting a male, being given that it is grey haired)
Plus Two Maths Probability 4 Mark Questions and Answers 14

Question 9.
An Insurance company insured 2000 scooter drivers, 4000 car drivers, and 6000 truck drivers. The probabilities of an accident are .01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?
Answer:
Describe the events as follows.
A: ‘accident happens’.
E1: ‘choosing Scooter driver.’
E2: ‘choosing Car driver.’
E3: ‘choosing Truck driver.’
Total drivers = 2000 + 4000 + 6000 = 12000
Plus Two Maths Probability 4 Mark Questions and Answers 15
P(A/E1) = P
(accident of a Scooter driver) = 0.01
P(A/E2) = P
(accident of a Car driver) = 0.03
P(A/E3) = P
(accident of a Truck driver) = 0.15
P (accident happens, given that it is a Scooter driver).
= P(E1/A)
Plus Two Maths Probability 4 Mark Questions and Answers 16

Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Question 10.
A factory has two machines A and B. Past record shows that machine A produced 60% of the items of output and machine B produced 40% of the items. Further, 2% of the items produced by machine A and 1% produced by machine B were defective. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that it was produced by machine B?
Answer:
Describe the events as follows.
A: ‘getting a defective item.’
E1: ‘choosing machine A.’
E2: ‘choosing machine B.’
P(E1) = 60% = 0.6, P(E2) = 40% = 0.4
P(A/E1) = P (a defective from machine A) = 2% = 0.02
P(A/E2) = P (a defective from machine B) = 1% = 0.01
P (a defective from machine B)
Plus Two Maths Probability 4 Mark Questions and Answers 17

Question 11.
Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 or 4 she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1, 2, 3 or 4 with the die?
Answer:
Describe the events as follows.
A: ‘getting exactly one head.’
E1: ‘she getting 5 or 6.’
E2: ‘she getting 1, 2, 3 or 4.’
When a die is thrown the sample space is{1, 2, 3, 4, 5, 6}
P(E1) = \(\frac{2}{6}\) = \(\frac{1}{3}\), P(E2) = \(\frac{4}{6}\) = \(\frac{2}{3}\)
When she gets 5 or 6, throws a coin 3 times. Then sample space is {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
P(A/E1) = P (one head given that 5 or 6 happened)
\(\frac{3}{8}\)
When she gets 1, 2, 3 or 4, throws a coin once. Then sample space is {H, T}
P(A/E2) = P
(one head given that 1, 2, 3 or 4 happened)
\(\frac{1}{2}\)
P (She gets exactly one head threw 1, 2, 3 or 4)
Plus Two Maths Probability 4 Mark Questions and Answers 18

Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Question 12.
Vineetha and Reshma are competing for the post of school leader. The probability Vineetha to be elected is 0.6 and that of Reshma is 0.4 Further if Vineetha is elected the probability of introducing a new pattern of election is 0.7 and the corresponding probability is 0.3 if Resma is elected. Find the probability that the new pattern of election is introduced by Reshma.
Answer:
Let E1 and E2 be the respectively probability that Vineetha and Reshma will be elected. Let Abe the probability that a new pattern of election is introduced.
P(E1) = 0.6; P(E2) = 0.4
P(A|E1) = 0.7; P(A|E2) = 0.3
Plus Two Maths Probability 4 Mark Questions and Answers 19

Question 13.
Find the probability of number of doublets in three throws of a pair of dice.
Answer:
Let X denotes the random variable of getting a Doublet. Possible doublets are (1, 1),(2, 2),(3, 3),(4, 4),(5, 5),(6, 6).
Then X can take values 0, 1, 2, 3.
P(getting a doublet) = \(\frac{6}{36}\) = \(\frac{1}{6}\)
P(not getting a doublet) = \(\frac{30}{36}\) = \(\frac{5}{6}\)
P(X = 0) = P(no doublet) = \(\frac{5}{6} \times \frac{5}{6} \times \frac{5}{6}=\frac{125}{216}\)
P(X = 1) = P(one doublet and 2 non-doublets)
Plus Two Maths Probability 4 Mark Questions and Answers 20
P(X = 2) = P(2 doublet and 1 non-doublets)
Plus Two Maths Probability 4 Mark Questions and Answers 21
P(X = 3) = P(3 doublet) = \(\frac{1}{6} \times \frac{1}{6} \times \frac{1}{6}=\frac{1}{216}\)
The required Probability Distribution is
Plus Two Maths Probability 4 Mark Questions and Answers 22

Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Question 14.
Find the probability distribution of the number of white balls drawn when three balls are drawn one by one without replacement from a bag containing 4 white and 6 red balls.
Answer:
Let X denotes the random variable of number of white balls. Clearly X can take values 0, 1, 2, 3. Describe the events as follows.
W: ‘getting white ball.’
R: ‘getting red ball.’
P(X=0) = P(no white balls)
= P(RRR)= \(\frac{6}{10} \times \frac{5}{9} \times \frac{4}{8}=\frac{5}{30}\)
P(X=1) = P(1white, 2red balls)
= P(WRR) + P(RWR) + P(RRW)
Plus Two Maths Probability 4 Mark Questions and Answers 23
P(X=2) = P(2white, 1 red balls)
= P(WWR) + P(RWW) + P(WRW)
Plus Two Maths Probability 4 Mark Questions and Answers 24
P(X=3) = P(3white)
P(WWW) = \(\frac{4}{10} \times \frac{3}{9} \times \frac{2}{8}=\frac{1}{30}\)
The required Probability Distribution is
Plus Two Maths Probability 4 Mark Questions and Answers 25

Question 15.
Two dice are thrown simultaneously. If X denotes the number of sixes, find expectation of X. Also find the variance.
Answer:
Let X denotes the random variable of getting a 6. Clearly X can take values 0, 1, 2.
P(X = 0) = P(non-six, non-six) = \(\frac{5}{6} \times \frac{5}{6}=\frac{25}{36}\)
P(X = 1) = P((six, non-six),(non-six, six))
Plus Two Maths Probability 4 Mark Questions and Answers 26
P(X = 2) = P(six, six) = \(\frac{1}{6} \times \frac{1}{6}=\frac{1}{36}\)
The required Probability Distribution is
Plus Two Maths Probability 4 Mark Questions and Answers 27
Variance = σ2 = E(X2) – [E(X)]2
Plus Two Maths Probability 4 Mark Questions and Answers 28

Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Question 16.
A random variable X has the following probability distribution
Plus Two Maths Probability 4 Mark Questions and Answers 29
Determine

  1. k
  2. P(X < 3)
  3. P(X > 6)
  4. P(0 < X < 3)

Answer:
1. We know that sum of the probabilities is = 1
0 + k + 2k + 2k + 3k + k2 + 2k2 + 7k2 + k = 1
10k2 + 9k – 1 = 0
(k + 1)(10k – 1) = 0; k= -1 or k = \(\frac{1}{10}\)
(negative value cannot be accepted).

2. P(X < 3) = P(0) + P( 1) + P(2)
0 + k + 2k + 2k = 3k = \(\frac{3}{10}\).

3. P(X < 3) = P(7) = 7k2 + k
Plus Two Maths Probability 4 Mark Questions and Answers 30

4. P(0 < X < 3) = P(1) + P(2) = k + 2k = 3k = \(\frac{3}{10}\). Question

Question 17.
(i) P(A) = \(\frac{7}{13}\); P(B) = \(\frac{9}{13}\); (A ∩ B) = \(\frac{4}{13}\), then P(A/B) is
(a)  \(\frac{9}{4}\)
(b)  \(\frac{16}{13}\)
(c)  \(\frac{4}{9}\)
(d)  \(\frac{11}{13}\)
(ii) Probability of solving a specific problem independently by A and B are \(\frac{1}{2}\) and \(\frac{1}{3}\) respectively. If both try to solve the problem independently, then
(a) Find the probability that the problem is solved. (2)
(b) Find the probability that exactly one of them solve the problem. (1)
Answer:
(i) (c) \(\frac{4}{9}\)

(ii)
Plus Two Maths Probability 4 Mark Questions and Answers 31
P(Problem is solved)
= P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
Plus Two Maths Probability 4 Mark Questions and Answers 32

(iii) P(Exactly one of them solve)
Plus Two Maths Probability 4 Mark Questions and Answers 33

Plus Two Maths Probability Six Mark Questions and Answers Question

Question 1.
(i) A and B are two events such that P(A) = \(\frac{1}{5}\) and P(A ∪ B) = \(\frac{2}{5}\) Find P(B) if they are mutually exclusive
(a) \(\frac{1}{5}\)
(b) \(\frac{2}{5}\)
(c) \(\frac{3}{5}\)
(d) \(\frac{4}{5}\)
(ii) A box contains 3 red and 4 blue balls. Two balls are drawn one by one without replacement. Find the probability of getting both balls red.
(iii) Three cards are drawn successively without replacement from a pack of 52 cards. What is the probability that first two cards are queen and the third is king.
Answer:
(i) (a) \(\frac{1}{5}\).

(ii) Let A be the event that the first ball drawn is red and B be the event of drawing red ball in the second draw
P(A) = \(\frac{3}{7}\)
Probability of getting one red ball in the second draw = P(B/A) = \(\frac{2}{6}\) = \(\frac{1}{3}\). P(A ∩ B) = P(A).P(B/A)
\(=\frac{3}{7} \times \frac{1}{3}=\frac{1}{7}\).

(iii) Let Q denote the event that the card drawn is Queen and K denote the event of drawing a King
P(Q) = \(\frac{4}{52}\), P(Q/Q) = \(\frac{3}{51}\)
P(K/QQ) is the probability of drawing the third card is a king
P(K/QQ) = \(\frac{4}{50}\)
P(QQk) = P(Q)P(Q/Q)P(K/QQ)
\(=\frac{4}{52} \cdot \frac{3}{51} \cdot \frac{4}{50}=\frac{2}{5525}\).

Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Question 2.
60 shirts of different colours are on sale. If one shirt is chosen at random.
Plus Two Maths Probability 4 Mark Questions and Answers 34

  1. What is the probability that it is red? (1)
  2. What is the probability that it is plain and extra-large? (1)
  3. What is the probability that it is small, given that it is blue? (2)
  4. If A is the event ‘the shirt is medium’ and B is the event ‘the shirt is blue’. Are the events A and B independent? (2)

Answer:
1. P(Red) = \(\frac{8+8+2+4}{60}=\frac{11}{30}\).

2. P (Plain and extra-large) = \(\frac{4+5}{60}=\frac{3}{20}\).

3. P(small/blue)
Plus Two Maths Probability 4 Mark Questions and Answers 35

4.
Plus Two Maths Probability 4 Mark Questions and Answers 36
∴ Not independent.

Question 3.
From a box containing balls numbered from, 1 to 100, one ball is drawn at random. The events X and Y are as follows. X: A perfect square is drawn. Y: An even number is drawn.

  1. Find P(X) and P(Y). (2)
  2. Compute P (X/Y). (2)
  3. Are X and V independent? Justify. (2)

Answer:
Perfect square numbered balls are
1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
Therefore, there are 10 perfect square numbered balls, 50 even numbered balls and 5 perfect square even numbered balls.
1. P(X) = \(\frac{10}{100}=\frac{1}{10}\), P(Y) = \(\frac{50}{100}=\frac{1}{2}\)
P (Even perfect square number) = P (X ∩ Y) \(\frac{50}{100}=\frac{1}{20}\).

2. P(X/Y)
= P(Drawing a perfect square numbers from even numbers) = \(\frac{5}{50}=\frac{1}{10}\).

3. We have, P (X ∩ Y) = \(\frac{1}{20}=\frac{1}{10} \times \frac{1}{2}\)
= P(X).P(Y).
Therefore X and Y are independent events.

Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Question 4.
(i) The probability of three mutually exclusive events A, B, and C are given by 2/3, 1/4, 1/6 respectively. Is this statement ________ (1)
(a) true?
(b) false?
(c) cannot be said?
(d) data not sufficient?
A husband and wife appear in an interview for two vacancies in the same post. The probability of husband’s selection is 1/7 and that of wife’s selection is 1/5. What is the probability that
(ii) Only one of them will be selected? (3)
(iii) None will be selected? (2)
Answer:
(i) (b) Probability should be less than or equal to 1.
Here A, B, C are mutually exclusive.
Then,
P(A ∪ B ∪ C) = P(A) + P(B) + P(C) = \(\frac{2}{3}+\frac{1}{4}+\frac{1}{6}=\frac{26}{24}>1\)
∴ statement is false.

(ii) H – Event of husband selected,
W – Event of wife selected
Plus Two Maths Probability 4 Mark Questions and Answers 37

(iii) P (None of them will be selected)
Plus Two Maths Probability 4 Mark Questions and Answers 38

Question 5.
(i) Find P(A∩B) if A and B are independent events with P(A) = \(\frac{1}{5}\) and P(B) = \(\frac{5}{8}\)
Plus Two Maths Probability 4 Mark Questions and Answers 39
(ii) An unbiased die is thrown twice. Let the event A be getting prime number in the first throw and B be the event of getting an even number in the second throw. Check the independence of the events A and B. (3)
(iii) The probability of solving a problem independently by A and B are \(\frac{1}{3}\) and \(\frac{1}{4}\) respectively. Find the probability that exactly one of them solves the problem. (2)
Answer:
(i) (c) \(\frac{1}{8}\).

(ii) P(A) = \(\frac{18}{36}\) = \(\frac{1}{2}\)
P(B) = \(\frac{18}{36}\) = \(\frac{1}{2}\)
P(A∩B) = P( prime number in first throw and even number in the second throw)
Plus Two Maths Probability 4 Mark Questions and Answers 40
∴ A and B are independent events.

(iii)
Plus Two Maths Probability 4 Mark Questions and Answers 41
Probability of exactly one of them solves the problem = P(A)P(B’) + P(B)P(A’)
Plus Two Maths Probability 4 Mark Questions and Answers 42

Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Question 6.
(i) A set of events E1 + E2,…….En are said to be a partition of the Sample Space, then which of the following conditions is always not true (1)
(a) E1∪ E2 ∪……..∪ En = S,
(b) E1 ∩ En = Φ,
(c) P(E1) > 0,
(d) P(E1) ≥ P(En)
(ii) A person has undertaken a business. The probabilities are 0.80 that there will be a crisis, 0.85 that the business will be completed on time if there is no crisis and 0.35 that the business will be completed on time if there is a crisis. Determine the probability that the business will be completed on time. (2)
(iii) A box contains 5 red and 10 black balls. A ball is drawn at random, its colour is noted and is returned to the box. More over 2 additional balls of the colour drawn are put in the box and then a ball is drawn. What is the probability that the second ball is red? (3)
Answer:
(i) P(E1) ≥ P(En).

(ii) Let A be the event that the business will be completed on time and B be the event that there will be a crisis
P(B) = 0.80
P(no crisis) = P(B’) = 1 – P(B) = 0.20
P(A/B) = 0.35 P(A/B’) = 0.85
By theorem on total probability
P(A) = P(B)P(A/B) + P(B’)P(A/B’)
= 0.8 × 0.35 + 0.2 × 0.85 = 0.45.

(iii) Let a red ball be drawn in the first attempt P(drawing a red ball) = \(\frac{5}{15}=\frac{1}{3}\)
If two red balls are added to the box, then the box contains 7 red balls and 10 black balls
P(drawing a red ball) = \(\frac{7}{17}\)
Let a black ball be drawn in the first attempt P(drawing a black ball) = \(\frac{10}{15}=\frac{2}{3}\)
If two black balls are added to the box, then the box contains 5 red and 12 black balls
P(drawing a red ball) = \(\frac{5}{17}\)
Probability of drawing the second ball red is
Plus Two Maths Probability 4 Mark Questions and Answers 43

Question 7.

  1. Bag I contains 5 red and 6 black balls. Bag II contains 7 red and 5 black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from bag I. (3)
  2. A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being diamond. (3)

Answer:
1. Let E1 be the event of choosing Bag I and E2 be the event of choosing Bag II
A be the event of drawing a red ball
Plus Two Maths Probability 4 Mark Questions and Answers 44

2. Let E1 be the event of choosing a diamond and E2 be the event of choosing a non diamond card
A be the event that a card is lost
Plus Two Maths Probability 4 Mark Questions and Answers 45
When a diamond card is lost, there are 12 diamond cards in 52 cards. Then
Plus Two Maths Probability 4 Mark Questions and Answers 46
When a non diamond card is lost, there are 13 diamond cards in 51 cards. Then
Plus Two Maths Probability 4 Mark Questions and Answers 47

Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Question 8.
(i) If X denotes number of heads obtained in tossing two coins. Then which of the following is false (1)
(a) X(HH) = 2
(b) X(HT) = 1
(c) X(TH)= 0
(d) X(TT) = 0
(ii) Find the probability distribution of the number of tails in the simultaneous toss of two coins. (2)
(iii) A coin is tossed so that the head is 3 times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails. (3)
Answer:
(i) (c) X(TH)= 0.

(ii) Sample space is S = {HH, HT, TH, TT}
Let X denote the number of tails, then
X(HH) = 2, X(HT) = 1, X(TH) = 1, X(TT) = 0
Therefore X can take the values 0, 1 or 2
P(HH) = P(HT) = P(TH) = P(TT) = \(\frac{1}{4}\)
P(X = 0) = \(\frac{1}{4}\) P(X = 1) = \(\frac{1}{2}\) P(X = 2) = \(\frac{1}{4}\)
Then the Probability distribution is
Plus Two Maths Probability 4 Mark Questions and Answers 48

(iii) Let the probability of getting a tail in the biased coin be x.
P(T) = x P(H) = 3x
P(T) + P(H) = 1 ⇒ x + 3x = 1 x = \(\frac{1}{4}\)
P(T) = \(\frac{1}{4}\) P(H) = \(\frac{3}{4}\)
Let X denote the random variable representing the number of tails
P(X = 0) = P(HH) = P(H).P(H) = \(\frac{9}{16}\)
P(X = 1) = P(HT) + P(TH)
Plus Two Maths Probability 4 Mark Questions and Answers 49
P(X = 2) = P(TT) = P(T).P(T) = \(\frac{1}{16}\)
Then the Probability distribution is
Plus Two Maths Probability 4 Mark Questions and Answers 50

Question 9.
If a fair coin is tossed 10 times, find the probability of

  1. Exactly 6 heads. (2)
  2. At least 6 heads. (2)
  3. At most 6 heads. (2)

Answer:
Let X denotes the random variable of number of heads in an experiment of 10 trials.
Clearly X has a Binomial Distribution with
n = 10 and p = \(\frac{1}{2}\) ⇒ P(x) = nCxqn-x Px
Plus Two Maths Probability 4 Mark Questions and Answers 51
1. P(x = 6)
Plus Two Maths Probability 4 Mark Questions and Answers 52

2. P(at least 6 heads) = P(X ≥ 6)
= P(X = 6) + P(X = 1)+P(X = 8)
Plus Two Maths Probability 4 Mark Questions and Answers 53

P(at most 6 heads) = P(X ≤ 6)
= P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0)
Plus Two Maths Probability 4 Mark Questions and Answers 54
Plus Two Maths Probability 4 Mark Questions and Answers 55

Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Question 10.
Five cards are drawn successively with a replacement from a pack of 52 cards. What is the probability that

  1. All the 5 cards are spades? (2)
  2. only 3 cards are spade? (2)
  3. none is a spade? (2)

Answer:
Let X denotes the random variable of number of spades cards in an experiment of 5 trials. Clearly X has a Binomial Distribution with n = 5
Plus Two Maths Probability 4 Mark Questions and Answers 56
1. P(all 5 are spades) = P(X = 5)
Plus Two Maths Probability 4 Mark Questions and Answers 57

2. P(3 are spades) = P(X = 3)
Plus Two Maths Probability 4 Mark Questions and Answers 58

3. P(non-spade) = P(X = 0) =
Plus Two Maths Probability 4 Mark Questions and Answers 59

Question 11.
Find the probability distribution, Mean and Variance of the number of success in two tosses of a die, where a success is defined as

  1. number greater than 4. (3)
  2. 6 appears on at least on die. (3)

Answer:
1. Let X denotes the random variable of getting a 5, 6. Clearly X can take values 0, 1, 2.
When number 1, 2, 3, 4 appears in both die. Number of such cases = 4 × 4 = 16
P(X=0) = P(no success) = \(\frac{16}{36}=\frac{4}{9}\)
When 5, 6 in one die and other with 1, 2, 3, 4 and visa versa.
Number of such cases is 2 × 4 + 4 × 2 = 16.
P(X= 1) = P(1 success and 1 no success) = \(\frac{16}{36}=\frac{4}{9}\)
When number 5, 6 appears in Jjoth die. Number Hof such cases = 2 × 2 = 4.
P(success) = \(\frac{4}{36}=\frac{1}{9}\)
The required Probability Distribution is
Plus Two Maths Probability 4 Mark Questions and Answers 60

2. Let X denotes the random variable of getting at least 6 on one die. Clearly X can take values 0, 1.
No success means 1, 2, 3, 4, 5 appears on both die. Number of such cases is 5 × 5 = 25.
P(X=0) = P(no success) = \(\frac{25}{36}\)
When 6 in one die and other with 1, 2, 3, 4, 5 and visa versa. Number of such cases is 1 × 5 + 5 × 1 = 10
When both the die is 6. Number of such case is 1. Therefore total cases is 1 + 10 = 11
P(X=1) = P(1 success) = P(at least 1 six) = \(\frac{11}{36}\)
The required Probability Distribution is
Plus Two Maths Probability 4 Mark Questions and Answers 61

Plus Two Maths Chapter Wise Questions and Answers Chapter 13 Probability

Question 12.
(i) If A and B are two events such that A ⊂ B and P(A) ≠ 0 then P(A/B) is (1)
Plus Two Maths Probability 4 Mark Questions and Answers 62
(ii) There are two identical bags. Bag I contains 3 red and 4 black balls while Bag II contains 5 red and 4 black balls. One ball is drawn at random from one of the bags.
(a) Find the probability that all the ball drawn are red. (3)
(b) If the balls drawn is red what is the probability that it was drawn from Bag I? (2)
Answer:
(i) Describe the events as follows.
A: ‘getting a red ball’.
E1: ‘choosing Bag I.’
E2: ‘choosing Bag II.’
P(E1) = P(E2) = \(\frac{1}{2}\)
P(A/E1) = P
(drawing a red ball from Bag I) = \(\frac{3}{7}\)
P(A/E2) = P
(drawing a red ball from Bag II) = \(\frac{5}{9}\)
P (All the balls drawn is red)
= P(A) = P(E1)P(A/E1) + P(E2)P(A/E2)
Plus Two Maths Probability 4 Mark Questions and Answers 63
Plus Two Maths Probability 4 Mark Questions and Answers 64

Question 13.
Consider the following probability distribution of a random, variable X.
Plus Two Maths Probability 4 Mark Questions and Answers 65

  1. Find the value of k. (2)
  2. Determine the Mean and Variance of X. (4)

Answer:
(i) We have; Σpi = 1
Plus Two Maths Probability 4 Mark Questions and Answers 66

(ii)
Plus Two Maths Probability 4 Mark Questions and Answers 67

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 8 Sources of Business Finance

Students can Download Chapter 8 Sources of Business Finance Questions and Answers, Plus One Business Studies Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examination

Kerala Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 8 Sources of Business Finance

Plus One Sources of Business Finance One Mark Questions and Answers

Question 1.
Equity shareholders are called
(a) Owners of the company
(b) Partners of the company
(c) Executive of the company
(d) Guardians of the company
Answer:
(a) Owners of the company

Question 2.
Fund required for purchasing current assets is an example of __________
Answer:
Working capital

Question 3.
Under the lease agreement, the lessee get the rights to __________
Answer:
Use the asset for a specified period.

Question 4.
Under the factoring agreement, the factor
Answer:
Collects the client’s debt or account receivables.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 8 Sources of Business Finance

Question 5.
Internal sources of capital are those that are
Answer:
generated within the business.

Question 6.
Preference shares abd equity shares are called ____________ securities.
Answer:
Ownership Securities

Question 7.
Equity shareholders are called
(a) Owners of the company
(b) Partners of the company
(c) Executives of the company
(d) Guardians of the company
Answer:
(a) Owners of the company

Question 8.
Equity share capital is called ________ capital
Answer:
Risk

Question 9.
Which of the following is not a characteristic of equity shares?
(a) Voting rights
(b) Ownership security
(c) Fixed rate of return
(d) Residual owners
Answer:
(c) Fixed rate of return

Question 10.
Which source is called as permanent source of capital?
Answer:
Equity Share Capital

Question 11.
__________ shareholders have the right to control the company.
Answer:
Equity Shareholders

Question 12.
Which source is called as permanent source of capital?
Answer:
Equity Share Capital

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 8 Sources of Business Finance

Question 13.
Sumesh an NRI is interested to invest in companies, but he is not ready to take up more risk. Which type of security he should buy?
Answer:
Preference shares.

Question 14.
_________ shareholders have the right to get dividend at a fixed rate .
Answer:
Preference shareholders

Question 15.
This source of finance is called ‘internal source of financing’ and ‘self financing’. Identify the source of finance and mention its three merits.
Answer:
Ploughing back of profit

Question 16.
Retained earnings are parts of __________ capital.
Answer:
Ownership Capital

Question 17.
Employment of corporate savings use of accumulated saving in the business in the form of reserves is called
Answer:
Ploughing back of profits

Question 18.
___________ are the cheapest source of finance.
Answer:
Retained earnings

Question 19.
___________ are called creditorship securities
Answer:
Debentures

Question 20.
Debentures which are secured by a charge on the assets of the company are called _________
Answer:
Secured debentures

Question 21.
Debentures which can be converted in equity shares are called _________
Answer:
Convertable debentures

Question 22.
Debenture issued without the name of owner is __________ debenture.
Answer:
Unregistered or naked

Question 23.
Which of the following is not a characterstics features of debentures?
(a) Ownership security
(b) Generally secured
(c) Participate in the surplus profit
(d) Guarantee of returms
Answer:
(c) Participate in the surplus profit

Question 24.
An Indian Company can now raise funds not only from India but also through foreign equity participation. How is it possible?
Answer:

  1. GDRs
  2. ADRs
  3. FDI

Question 25.
Expand the term GDR
Answer:
Global Depositors Receipts.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 8 Sources of Business Finance

Question 26.
Expand the term ADR
Answer:
American Depository Receipt

Question 27.
ADRs are issued in
(a) Canada
(b) China
(c) India
(d) USA
Answer:
(d) USA

Question 28.
Identify the type of financial services belonged to each cash explain its features.

  1. Acquired a machinery for monthly rental basis from an outside agency.
  2. Gives the right for collecting their accounts receivable to a specialised agency.
  3. An organization which collects and pools funds from public and invests in securities.

Answer:

  1. Leasing
  2. Factoring
  3. Mutual fund

Question 29.
A company decided to raise its funds by selling its account receivables to an agency. Which type of financial service is maintaining here.
Answer:
Factoring

Question 30.
I render specialized services to companies in the collection of their accounts receivables.
Answer:
Factoring

Question 31.
State the appropriate term to denote the arrangement of acquiring the right to use an asset without actually owning it.
Answer:
Leasing

Plus One Sources of Business Finance Two Mark Questions and Answers

Question 1.
What is business finance? Why do businesses need funds? Explain. (2)
Answer:
Nature of Business Finance:

1. Fixed capital requirements:
In order to start a business funds are needed to purchase fixed assets like land and building, plant and machinery. This is called fixed capital requirement.

2. Working Capital requirements:
A business needs funds for its day to day operation. This is known as working Capital requirements. Working capital is required for purchase of raw materials, to pay salaries, wages, rent and taxes.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 8 Sources of Business Finance

Question 2.
These are shares which carry preferential rights over the equity shares. Being a commerce student, identify this type of share. And state its 2 preferential rights. (2)
Answer:
Preference shares.
Their preferential rights are:

  1. The right to get a fixed rate of divided
  2. The right to claim repayment of capital in the event of winding up of the company.

Question 3.
Match the following

  1. Equity share – Fixed percentage of interest
  2. Debenture – International source of finance
  3. Preference share – Real owner
  4. American depository – No voting right receipt

Answer:

  1. Equity share – Real owner
  2. Debenture – Fixed percentage of interest
  3. Preference share – No voting right
  4. American depository receipt – International source of finance

Question 4.
An Indian company can expand not only through the fund in India but also from foreign equity participation. How is it possible? (2)
Answer:
FDI. It refers to direct subscription to the equity capital of an Indian company by a multinational corporation. It includes Establishment of a new enterprise in a foreign.

Plus One Sources of Business Finance Three Mark Questions and Answers

Question 1.
An Indian company can now raise funds not only from India, but also through foreign equity participation. How is it possible? Explain
Answer:
GDR: Global Depository Receipts are issued by an Indian company to an intermediary abroad called an Overseas Depository Bank. They are issued and traded in European capital market.

ADR: American Depository receipts are issued and traded in U.S.A.

Question 2.
List sources of raising long-term and short-term finance. (3)
Answer:
Long Term Sources:
The amount of funds required by a business for more than five years is called long-term finance. Generally this type
of finance is required for the purchase of fixed assets like land and building, plant and machinery furniture, etc. It include sources such as shares and debentures, long-term borrowings and loans from financial institutions.

Short Term Sources:
Short-term funds are those which are required for a period not exceeding one year. These sources include Trade credit, loans from commercial banks and commercial papers etc. Short-term finance is used for financing of current assets such as accounts receivable and inventories.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 8 Sources of Business Finance

Question 3.
Name any three special financial institutions and state their objectives. (3)
Answer:
Financial Institutions:
The state and central government have established many financial institutions to provide finance to companies. These institutions aim at promoting the industrial development of a country, these are also called ‘development Bank’. These are IFCI, ICICI, IDBI and LIC, UTI.

This source of financing is considered suitable when large funds for longer duration are required for expansion, reorganisation and modernisation of an enterprise.
Merits:

  1. Financial Institution provide long term finance which is not provided by Commercial Bank
  2. These institutions provide financial, managerial and technical advice and consultancy to business firms.
  3. It increases the goodwill of the borrowing company in the capital market.
  4. As repayment of loan can be made in easy installments, it does not prove to be much of a burden on the business.
  5. The funds are made available even during periods of depression, when other sources of finance are not available.

Limitations:

  1. The procedure for granting loan is time consuming due to rigid criteria and many formalities.
  2. Financial Institution place restrictions on the powers of the borrowing company.
  3. Financial institutions may have their nominees on the Board of Directors of the borrowing company thereby restricting the autonomy of the company.

Question 4.
While presenting a seminar paper on different sources of business finance, your friend Vineeth, pointed out that “ownership capital is the risk capital of the business”. Can you explain why it is called risk capital? (3)
Answer:
Equity shareholders are the real owners of the company. Equity shareholders will get their dividend only after dividend is paid to preference shareholders. They can claim back their capital only on winding up after discharging all other liabilities of the company. So we can say that ownership capital is the risk capital of the business.

Question 5.
“ADR & GDR serves the same purpose whenever shares are issued abroad by Indian companies”. Then why can’t we call them by the same name? (3)
Answer:
The important differences between ADR and GDR are:

ADRGDR
They are issued and traded in USAThey are issued and traded in European capital market
Both individual and institutional investors can make investmentOnly institutional investors can invest
It can be converted into shares and shares into ADROnce converted into shares, it cannot be converted back.
Legal and accounting costs are highLegal and accounting costs are comparatively less

Plus One Sources of Business Finance Four Mark Questions and Answers

Question 1.
What is the difference between internal and external sources of raising funds?
Answer:

Internal sourcesExternal Sources
Funds are generated from within the organisationFunds are generated from outside the organization
Fulfill limited needs of the businessFulfill long term needs f the business
It is not costlyIt is costly as compared to internal sources of fund
No need to mortgage the assets of the company to obtain fund from internal sourcesNeed to mortgage the assets of the company to obtain fund from internal sources

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 8 Sources of Business Finance

Question 2.
What is the difference between GDR and ADR? (4)
Answer:

ADRGDR
They issued and traded in USAThey issued and traded in European capital market
Both individual and institutional investors can make investmentOnly institutional investors can make investment
It can be converted into shares and shares into ADROnce converted into shares, it cannot be converted back
Legal and accounting costs are highLegal and accounting costs are less

Question 3.
Discuss the financial instruments used in international financing. (4)
Answer:
International Financing:

1. Commercial Banks:
Commercial banks all over the world extend foreign currency loans for business purposes. Standard chartered is a major source of foreign currency loan to the Indian industry.

2. International Agencies and Development Banks:
A number of international agencies and development banks provide long and medium term loans and grants to promote the development of economically backward areas in the world. Eg. International Finance Corporation (IFC), EXIM Bank and Asian Development Bank.

3. International Capital Markets:

a. Global Depository Receipts (GDR’s):
Under GDR, shares of the company are first converted into depository receipts by international banks. These depository receipts are denominated in US dollars. Then these depository receipts are offered for sale globally through foreign stock exchanges. GDR is a negotiable instrument and can be traded freely like any other security.

The holder of GDRs are entitled for dividend just like shareholders. But they do not enjoy the voting rights. Many Indian companies like ICICI, Wipro etc. have raised foreign capital through issue of GDRs.
Feature of GDR:

  • GDR can be listed and traded on a stock exchange of any foreign country other than America.
  • It is negotiable instrument.
  • A holder of GDR can convert it into the shares.
  • Holder gets dividends
  • Holder does not have voting rights.
  • Many Indian companies such as Reliance, Wipro and ICICI have issue GDR.

b. American Depository Receipts (ADR’s):
The depository receipts issued by a company in the USA are known as American Depository Receipts.
Feature of ADR:

  • It can be issued only to American Citizens.
  • It can be listed and traded is American stock exchange.
  • Indian companies such as Infosys, Reliance issued ADR

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 8 Sources of Business Finance

Question 4.
Explain different types of Preference shares. (4)
Answer:
Types of Preference Shares:

a. Cumulative and Non-cumulative Preference Share:
in cumulative preference shares, the unpaid dividends are accumulated and carried forward for payment in future years. On the other hand, in non- cumulative preference share, the dividend is not accumulated if it is not paid out of the current year’s profit.

b. Participating and Non-participating Preference Share:
Participating preference shares have a right to share the profit after making payment to the equity shares. The non-participating preference shares do not enjoy such a right.

c. Convertible and Non-convertible Preference Share:
The preference shares which can be converted into equity shares after a specified period of time are known as convertible preference share. Non-convertible shares cannot be converted into equity shares.

d. Redeemable and Irredeemable Preference Share:
Redeemable preference shares are those where the company undertakes to repay it after a specified period. Where the amount of the preference shares is refunded only at the time of liquidation, are known an irredeemable preference shares.

Merits:

  1. Preference shares provide reasonably steady income in the form of fixed rate of return and safety of investment.
  2. Preference shares are useful for those investors who want fixed rate of return with comparatively low risk

Limitations:

  1. Preference shareholders have no voting right.
  2. The dividend paid is not deductible from profit for income tax.

Plus One Sources of Business Finance Five Mark Questions and Answers

Question 1.
What is a commercial paper? What are its advantages and limitations. (5)
Answer:
Commercial Paper (CP):
It is an unsecured promissory note issued by a firm to raise funds for a short period. The maturity period of commercial paper usually ranges from 90 days to 364 days. Being unsecured, only firms having good credit rating can issue the CP and its regulation comes under the purview of the Reserve Bank of India.
Merits:

  1. A commercial paper does not contain any restrictive conditions.
  2. As it is a freely transferable instrument, it has high liquidity.
  3. A commercial paper provides a continuous source of funds.
  4. They are cheaper than a bank loan.

Limitations:

  1. Only financially sound and highly rated firms can raise money through commercial papers
  2. The size of money that can be raised through commercial paper is limited
  3. Commercial paper is an impersonal method of financing. Extending the maturity of a CP is not possible.
  4. Issue of commercial paper is very closely regulated by the RBI guidelines.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 8 Sources of Business Finance

Question 2.
Mr. Ganesh, a sole trader, acquired a machinery on a monthly rental basis from an outside agency. Identify the type of financial service in which he entered into. Explain it. (5)
Answer:
Lease Financing:
A lease is a contractual agreement whereby the owner of an asset (lessor) grants the right to use the asset to the other party (lessee). The lessor charges a periodic payment for renting of an asset for some specified period called lease rent.
Merits:

  1. It enables the lessee to acquire the asset with a lower investment;
  2. Lease rentals paid by the lessee are deductible for computing taxable profits;
  3. It provides finance without diluting the ownership or control of business
  4. The lease agreement does not affect the debt raising capacity of an enterprise;
  5. Simple documentation makes it easier to finance assets.

Limitations:

  1. A lease arrangement may impose certain restrictions on the use of assets.
  2. The normal business operations may be affected in case the lease is not renewed.
  3. The lessee never becomes the owner of the
    asset.

Question 3.
Both Equity shares and Preference shares are ownership funds of a company. But there is significant difference between these two funds. Can you identify the same. (5)
Answer:

Equity SharesPreference Shares
It is compulsory to issue these shares.It is not compulsory to issue these shares
Rate of dividend varies according to the profits of the companyRate of dividend is fixed
Face value is lowerFace value is higher
No priority in dividend and repayment of capitalPriority in dividend and repayment of capital
It cannot be redeemedIt can be redeemed
Risk is highRisk is low
They have voting rightsThey do not have voting rights
They can participate in the managementThey can not participate in the management

Plus One Sources of Business Finance Eight Mark Questions and Answers

Question 1.
“The issue of debentures provides wide options to the company as well as investors in terms of its features”. Can you substantiate the statement from the point of view of its classification? (8)
Answer:
Debentures:
A debenture is a document issued by a company under its seal to acknowledge its debt. Debenture holders are, therefore, termed as creditors of the company. Debenture holders are paid a fixed rate of interest.
Types of Debentures:

a. Secured and Unsecured Debentures:
Secured (Mortgaged) debentures are debentures which are secured by a charge on the assets of the company. Unsecured (Simple or naked) debentures do not carry any charge or security on the assets of the company.

b. Registered and Bearer Debentures:
In the case registered debentures, the name, address and other details of the debenture holders are entitled in the books of the company. The debentures which are transferable by mere delivery are called bearer (Unsecured) debentures.

c. Convertible and Non-convertible Debentures:
Convertible debentures are those debentures that can be converted into equity shares after the expiry of a specified period. On the other hand, non¬convertible debentures are those which cannot be converted into equity shares.

d. First and Second:
Debentures that are repaid before other debentures are repaid are known as first debentures. The second debentures are those which are paid after the first debentures have been paid back.

Merits:

  1. It. is preferred by investors who want fixed income at lesser risk
  2. Debenture holder do not have voting right
  3. Interest on Debentures is a tax deductable expense
  4. It does not dilute control of equity shareholders on management
  5. Debentures are less costly as compared to cost of preference shares.
  6. They guarantee a fixed rate of interest
  7. It enables the company to take the advantage of trading on equity.
  8. The issue of debentures is suitable when the sales and earnings are relatively stable

Limitations:

  1. It is not suitable for companies with unstable future earnings.
  2. The company has to mortgage its assets to issue debentures.
  3. Debenture holders do not enjoy any voting rights.
  4. In case of redeemable debentures, the company has to make provisions for repayment on the specified date, even during periods of financial difficulty.
  5. With the new issue of debentures, the company’s capability to further borrow funds reduces.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 8 Sources of Business Finance

Question 2.
Distinguish between Shares and Debentures. (8)
Answer:

SharesDebentures
Shareholders are the owners of the companyDebenture holders are the creditors of the company
Shareholders get dividendsDebenture holders get interest
Shareholders have voting rightDebenture holders have no voting right
No security is required to issue sharesGenerally debentures are secured
Shares are not redeemableDebentures are redeemable
Share capital is payable after paying all outside liabilitiesDebenture holders have the priority of repayment over shareholders

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 7 Formation of a Company

Students can Download Chapter 7 Formation of a Company Questions and Answers, Plus One Business Studies Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examination

Kerala Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 7 Formation of a Company

Plus One Formation of a Company One Mark Questions and Answers

Question 1.
Application for approval of name of a company is to be made to
Answer:
Registrar of companies.

Question 2.
A prospectus is issued by
Answer:
Public company

Question 3.
Preliminary contracts are signed
Answer:
Before the incorporation

Question 4.
At which stage in the formation of a company does it interact with SEBI
Answer:
Capital subscription

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 7 Formation of a Company

Question 5.
The first stage in the formation of a company is __________
Answer:
Promotion

Question 6.
“I undertake to form a new company and carry out all the preliminary work in connection with its establishment” Who am I?
Answer:
Promoter

Question 7.
Preliminary Contracts are signed
1. Before the incorporation
2. After incorporation but before capital subscription
3. After incorporation but before of commencement of business
4. After commencement business
Answer:
1. Before the incorporation

Question 8.
Spot the odd one and state the reason
1. Memorandum of Association
2. Articles of Association
3. Certificate of incorporation
4. Certificate of commencement of business
Answer:
5. Certificate of commencement of business

Question 9.
_____________ is the magnacarta of the company.
Answer:
Memorandum of Association

Question 10.
_____________ is the birth certificate of a company.
Answer:
Certificate of incorporation

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 7 Formation of a Company

Question 11.
The procedure for conducting company meetings, voting, quorum, poll and proxy will be mentioned in the
1. Prospectus
2. Memorandum of Association
3. Articles of Association
Answer:
3. Articles of Association

Question 12.
The provision regarding the internal management of a company will appear in its
Answer:
Articles of Association

Question 13.
Public Companies need __________ to commence the business.
Answer:
Certificate of commencement of business

Question 14.
Directors of a public Ltd. Co. decided to give advertisement in all newspapers for subscribing their shares. Identify the document given below
1. table A
2. memorandum of association
3. prospectus
Answer:
3. Prospectus

Question 15.
This clauses is the form of a declaration, it states that the subscribers express the willingness and agreement to form a company. Name the clause of memorandum of association.
Answer:
Association Clause

Question 16.
This clause specifies the name of the state where the registered office of the Co. is situated. Identify the clause.
Answer:
Situation clause

Question 17.
This clause specifies the name of the company.
Answer:
Name clause

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 7 Formation of a Company

Question 18.
Identify the document in which the following information about a company can be found.

  1. Object with which the company is formed.
  2. Rules and regulations of internal management
  3. Investing deposits from the public
  4.  Acknowledgement of debt in a company

Answer:

  1. Memorandum of Association
  2. Articles of Association
  3. Mutual fund
  4. Debenture

Question 19.
TABLE A is a model of _________ given in companies Act.
Answer:
Articles of Association

Question 20.
Identify the documents in which following information about a company is found.

  1. Authorized capital
  2.  Rules and regulation for internal management.
  3.  Date of opening and closing of subscription list.

Answer:

  1. Memorandum of Associaiton
  2. Articles of Association
  3. Prospectus

Question 21.
Identify the relevant clauses in the memorandum of association in which the following information can be included.

  1. The registered office is in Kerala.
  2. Statutory declaration by members
  3. Ram Limited
  4. The scope of activities of company

Answer:

  1. Situation clause
  2. Association clause
  3. Name clause
  4. Object clause

Question 22.
State the odd item in the case of a private limited company.
1. memorandum of association
2. articles of association
3. certificate of incorporation
4. certificate of commencement of business
Answer:
4. Certificate of Commencement of business

Question 23.
Mention the name of the certificates/documents relating to following activities / formalities

  1. The certificate issued by the Registrar of companies certifying that the company has come into existence.
  2. The document, which contains the various rules and regulations that govern the management of the company.
  3. The document that defines the objectives of the company.

Answer:

  1. Certificate of Incorporation
  2. Articles of Association
  3. Memorandum of Association

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 7 Formation of a Company

Question 24.
Name the following documents.

  1. The document issued by the company to the public to invite them to subscribe its share capital.
  2. The document that binds a member with the company, company with members and members with members.
  3. The document that contains rules for internal management of the company.
  4. The document that specifies the aims of the company.
  5. The document issued by the public company which does not want to issue a prospectus.

Answer:

  1. Prospectus
  2. Articles of Association
  3. Articles of Association
  4. Memorandum of Association
  5. Statement in lieu of Prospectus

Plus One Formation of a Company Two Mark Questions and Answers

Question 1.
Name the stages in the formation of a company?
Answer:

  1. Promotion
  2. Incorporation
  3. Capital subscription
  4. Commencement of business (2)

Question 2.
Name the stages in the formation of a company. (2)
Answer:

  1. Promotion
  2. Incorporation
  3. Commencement of business

Question 3.
What do you mean by promotion? (2)
Answer:
The identification of business opportunities, analysis of its prospects and initiating steps to form a joint stock company is called promotion.

Question 4.
For incorporating a private limited company, Deepthi Pvt. Ltd., the directors submit all relevant documents to the registrar of company except Articles of Association. But the registrar insists that, registration will not be granted without filing Articles of Association. But the directors of Deepthi Pvt. Ltd., argue that the provisions of ‘Table A’ can be adopted in the absence of Articles of Association. Whose argument is correct? Justify your answer. (2)
Answer:
The argument of the Company Registrar is right because filing of Articles of association is compulsory for Pvt. Ltd company by shares.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 7 Formation of a Company

Question 5.
Arya Ltd. commences its business immediately on getting the certificate of incorporation. The registrar of companies serves a notice to them for remitting a fine of ₹500 for everyday of its operation. Is it legally enforceable? Give your suggestion. (2)
Answer:
Yes. Public Ltd. Company can commence business only after getting the certificate of commencement of business.

Question 6.
It is proposed to conduct a seminar on the topic ‘important documents in the formation of joint stock company’ in your class. You are selected as the leader of one of the groups and are directed to submit a seminar paper for the same. Suggest valuable points that should be included in the paper. (2)
Answer:

  1. Memorandum of Association
  2. Articles of Association
  3. Prospectus

Question 7.
What do you mean by Minimum Subscription? (2)
Answer:
Minimum subscription is the minimum amount of shares that must be subscribed by the public. This amount is stated in the prospectus. A company can allot shares only after receiving minimum subscription.

Question 8.
I lay down the charter or the constitution of the company. I define the object and powers of the company.

  1. Identify who am I?
  2. Also name my companion who provides rules and regulations for the internal management of the company. (Both are two documents). (2)

Answer:

  1. Memorandum of Association
  2. Articles of Association

Plus One Formation of a Company Three Mark Questions and Answers

Question 1.
Is it necessary for a public company to get its shares listed on a stock exchange? What happens if a public company fails to get the permission from stock exchange? (3)
Answer:
Yes. A public company must list its shares with at least any one of the stock exchange for the allotment of shares. Therefore, the promoters must apply in a stock exchange for permission to deal in its shares or debentures. If permission is not granted before the expiry of ten weeks from the date of Closure of subscription list, the allotment shall become void and the application money must be returned to the applicants within eight days.

Question 2.
State the difference between certificate of incorporation and certificate of commencement of business. (3)
Answer:
Certificate of Incorporation gives legal status to the company. It is also known as birth certificate of the company. But certificate of commencement of business allows to start the operation.

These two certificates are required by the public limited company, but in case of private limited company only certificate of Incorporation is required to start the operation.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 7 Formation of a Company

Question 3.
Nisha, Shani and Sheena are promoters of a public company. But they do not want to raise capital by approaching the public. They decide to raise capital by issuing shares to a few persons. Is it possible? If yes, what document is used for raising capital? (3)
Answer:
Yes. They can raise capital by issuing shares to a few persons. For this they can issue Statement in lieu of prospectus.

Plus One Formation of a Company Four Mark Questions and Answers

Question 1.
Identify the documents required for commencing business for the following companies. (4)

  1. Athira Pvt. Ltd.
  2. Aditya Ltd.

Answer:
1. Athira Pvt. Ltd – A private company must file the following documents for commencing business

  • Certificate of incorporation
  • Statutory declaration duly verified by one of the directors.

2. Aditya Ltd., a public company, must file the following documents for commencing business.

  • Certificate of incorporation
  • Certificate of commencement of business
  • Prospectus
  • Statutory declaration duly verified by one of the directors.

Question 2.
The details of a proposed private company having limited liability is given below. You are required to identify as to which clauses in the Memorandum of Association have to be rightly inserted. (4)
Proposed names:
Mahatma Gandhi Khadi – Company
Premier Mills (P) Ltd.
Kerala Government Khadi Company
Sobha Co-operative Company
Maximum capital which can be collected is 20 lakhs rupees
Nature of shares
Equity shares at Rs. 10/- share

Address:
Pushpa Nivas Kodunganoor (P.O)
Thiruvananthapuram 13
Kerala State
India.

Nature of business:
To produce Khadi clothes through machine To stitch Khadi ready wears Name of the persons who are wishing to form the company
P. Sudarsanan
K. Muraleedharan Nair
S. Renjith
Answer:

  1. Name clause
  2. Capital clause
  3. Situation clause
  4. Object clause
  5. Association clause

Plus One Formation of a Company Five Mark Questions and Answers

Question 1.
“Promoter would be personally liable for the preliminary contracts, if they are not ratified by the company after incorporation. Analyse the statement. (5)
Answer:
Promotion:
Promotion is the first stage in the formation of a company. The identification of business opportunities, analysis of its prospects and initiating steps to form a joint stock company is called promotion. The person who undertakes to form a company is called promoter.

Functions of a Promoter:

1. Identification of business opportunity:
The first and foremost activity of a promoter is to identify a business opportunity.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 7 Formation of a Company

2. Feasibility studies:
After identifying a business opportunity, the promoters undertake some feasibility studies to determine the viability and profitability of the proposed activity.

  • Technical feasibility – To determine whether the raw materials or technology is easily available
  • Financial feasibility – To determine the total estimated cost of the project
  • Economic feasibility – To determine the I profitability of the proposed project

3. Name approval:
After selecting the name of company the promoters submit an application to the Registrar of companies for its approval. The selected name is not the same or identical to an existing company.

4. Fixing up signatories to the Memorandum of Association:
Promoters have to decide about the members who will be signing the Memorandum of Association of the proposed company.

5. Appointment of professional:
Promoters appoint merchant bankers, auditors etc. to assist them in the preparation of necessary documents.

6. Preparation of necessary documents:
The promoters prepare certain legal documents which are to be submitted to the Registrar of companies. They are

  • Memorandum of Association
  • Articles of Association,
  • Consent of proposed Directors
  • Agreement, if any, with proposed managing or whole time director
  • Statutory declaration

Position of Promoters:
The promoter is neither an agent nor a trustee of the company. The promoter stands in the fiduciary relationship with the company. He should not make any secret profits out of the dealings. Any, such gains are to be disclosed. The promoter must act honestly, in good faith and in the best interest of the company.

The promoter is personally liable for all the preliminary contracts with the other parties before incorporation. The promoter is also liable for any omission of facts or false statements in the prospectus.

Question 2.
Memorandum of Association is the charter or magna carta of the company. Elucidate the statement. (5)
Answer:
Memorandum of Association:
It is the charter or magnacarta of the company. It defines the objects of the company and provides the framework beyond which the company cannot operate. It lays down the relationship of the company with outside world.

Memorandum of Association must be printed, divided into paragraphs, numbered consecutively. The Memorandum of Association must be signed by at least seven persons in case of a public company and by two persons in case of a private company.

Contents of Memorandum of Association
Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 7 Formation of a Company 1
1. The name clause:
Under this clause the name of the company is mentioned. A company can select any name subject to the following restrictions.

  • The proposed name should not be identical with the name of another company
  • A name which can mislead the public
  • In case of a public company the name should end with the word ‘Limited’ and in case of a private company the name should end with the word ‘Private Limited’
  • The name must not directly or indirectly imply any participation of the Central or State Govt.
  • The name must not suggest any connection or patronage of a national hero
  • It should not include the word cooperative.

2. Registered office clause:
This clause contains the name of the state, in which the registered office of the company is proposed to be situated. It must be informed to the Registrar within thirty days of the incorporation of the company.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 7 Formation of a Company

3. Objects clause:
This is the most important clause of the memorandum. It defines the purpose for which the company is formed. A company is not legally entitled to undertake an activity, which is beyond the objects stated in this clause.

4. Liability clause:
It states that the liability of members is limited to the face value of shares held by them or the amount guaranteed to be paid on winding up.

5. Capital clause:
This clause specifies the maximum capital which the company will be authorised to raise through, the issue of shares.

6. Association clause:
In this clause, the signatories to the Memorandum of Association state their intention to be associated with the company and also give their consent to purchase qualification shares.

Question 3.
Explain the contents of prospectus. (5)
Answer:
Prospectus:
Prospectus is a document issued by the public companies inviting the public to subscribe for shares or debentures of the company. It contains all information regarding the company’s affairs and its future prospects. A prospectus must be dated and signed by all the directors. A copy of the prospectus must be filed with Registrar before it is issued to public.

Contents of prospectus

  1. Name and address of the registered office of the company.
  2. Main objects of the company.
  3. Classes of shares and debentures.
  4. Name, address and occupation of the signatories to the memorandum.
  5. Details of the borrowing powers of the company.
  6. Name, address and occupation of the directors and managing director.
  7. Name and address of the promoters.
  8. Minimum subscription.
  9. Time of opening and closing of subscription.
  10.  The amount payable on application and allotment of each class of shares.
  11.  Name of underwriters.
  12.  Details of preliminary expenses.
    Companies which do not want to issue a prospectus may submit a statement in lieu of prospectus to the Registrar of Companies. It is a copy of the prospectus but is not issued to the public.

Question 4.
The details of a proposed limited company are given below. You are required to identify them as to which clause of the memorandum of association they have to be inserted. (5)

  1. Proposed name: Jnana Construction Company Ltd
  2. Maximum Capital: ₹10,00,000
  3. Registered office: Kollam
  4. Nature of liability: Limited
  5. Nature of Business: Construction company
  6. Names of promoters: Jnana, Akshara, Pooja, Ajay

Answer:

  1. Name clause
  2. Capital clause
  3. Situation / Domicile clause
  4. Liability clause
  5. Object clause
  6. Association clause

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 7 Formation of a Company

Question 5
A public company can commence business only after getting the certificate of commencement of business. Abhijith, a plus two student wants to know the conditions to be fulfilled to obtain the certificate of commencement of business.
Answer:
Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 7 Formation of a Company 2
Commencement of Business:
A public company can commence business only after getting certificate of commencement of business from the Registrar. The company must file the following documents to obtain the certificate of commencement of business.

  1. Declaration that the minimum subscription has been received in cash to allot shares.
  2. A declaration that all directors have taken up and paid for their qualification shares
  3. A statutory declaration stating that necessary legal formalities have been complied with has to be filed.

The Registrar shall examine these documents. If these are found satisfactory, a ‘Certificate of Commencement of Business’ will be issued. This certificate is conclusive evidence that the company is entitled to do business. With the grant of this certificate the formation of a public company is complete and the company can legally start doing business.
Documents used in the formation of a company

Plus One Formation of a Company Six Mark Questions and Answers

Question 1.
I govern the internal affairs of the company. Explain who am ‘I’? List out my contents.
OR
For the purpose of registering a new company, the promoter requires a document containing the rules and regulations governing its internal affairs. (6)

  1. What is that document? Explain.
  2. State the contents of this statement.

Answer:
Articles of Association:
The Articles of Association is the second important document of a company. The Articles define the rights, duties and powers of the officers and the Board of directors. It contains the rules regarding internal management of the company. It shows the relationship between the company and its members.

Contents of Articles of Association:

  1. The share capital of the company and its division.
  2. Rights of each class of shareholders.
  3. Details of contracts made with different parties.
  4. Procedure for making allotment of shares.
  5. Procedure for issuing share certificate.
  6. Procedure for transfer and transmission of shares.
  7. Procedure for forfeiture and reissue of shares.
  8. Procedure for conducting meetings, voting, proxy and poll
  9. Procedure for appointing, removal and remuneration of directors.
  10. Procedure for declaration of and payment of dividend.
  11. Keeping books of account and audit of the company.
  12. Procedure regarding alteration of share capital.
  13. Procedure regarding winding up of the company.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 7 Formation of a Company

Table A:
A public limited company may adopt Table A which is a model set of articles given in the Companies Act. Table A is a document containing rules and regulations for the internal management of a company. If a company adopts Table A, there is no need to prepare separate Articles of Association.

Question 2.
Vishnu, a promoter of a public company, approaches you to get information relating to raising of capital from public. As a commerce student mention the document required for inviting the public to purchase or subscribe to its shares and debentures. Explain. (6)
Answer:
Prospectus:
Prospectus is a document issued by the public companies inviting the public to subscribe for shares or debentures of the company. It contains all information regarding the company’s affairs and its future prospects. A prospectus must be dated and signed by all the directors. A copy of the prospectus must be filed with Registrar before it is issued to public.

Contents of prospectus:

  1. Name and address of the registered office of the company.
  2. Main objects of the company.
  3. Classes of shares and debentures.
  4. Name, address and occupation of the signatories to the memorandum.
  5. Details of the borrowing powers of the company.
  6. Name, address and occupation of the directors and managing director.
  7. Name and address of the promoters.
  8. Minimum subscription.
  9. Time of opening and closing of subscription.
  10. The amount payable on application and allotment of each class of shares.
  11. Name of underwriters.
  12. Details of preliminary expenses.

Companies which do not want to issue a prospectus may submit a statement in lieu of prospectus to the Registrar of Companies. It is a copy of the prospectus but is not issued to the public.

Question 3.
It is often said that Memorandum of Association and Articles of Association are the first and second important documents of a company. As a commerce student can you differentiate between these two documents? (6)
Answer:

Memorandum of AssociationArticles of Association
It defines the object for which the company is formedThey are rules of internal management of the company. They indicate how the objectives of the company are to be achieved
It is the main document of the companyIt is a subsidiary document of the Memorandum of Association
It defines the relationship of the company with outsidersIt defines the relationship of the company with members
Acts beyond the Memorandum of Association are invalid and cannot be ratified.Acts beyond the Articles of Association can be ratified by the members. But they do not violate memorandum
Filing of Memorandum is compulsoryFiling of Articles is not compulsory for public company
Alteration of Memorandum is very difficultIt can be altered by passing a special resolution

Plus One Formation of a Company Eight Mark Questions and Answers

Question 1.
Explain the steps in the incorporation of a company. (8)
Answer:
Incorporation:
A company comes into existence only when it is registered with the Registrar of Companies. For this purpose the promoter has to take the following steps:
Steps for Incorporation

1. Application for incorporation:
Promoters make an application for the incorporation of the company to the Registrar of companies.

2. Filing of documents:
The following documents must be filed with the Registrar of Companies for incorporation.

  • The Memorandum of Association duly stamped, signed and witnessed
  • Articles of Association duly stamped, signed and witnessed
  • Written consent of the proposed directors
  • Agreement, if any, with proposed managing or whole time director
  • A copy of the Registrar’s letter approving the name of the company.
  • Statutory declaration
  • A notice about the exact address of the registered office.
  • Documentary evidence of payment of registration fees.

The Registrar verifies the entire document submitted. If he is satisfied then he enters the name of the company in his Register. After the registration, the Registrar issues a Certificate called Certificate of Incorporation. This is called the birth certificate of the company. With effect from November 1, 2000, the Registrar of Companies allots a CIN (Corporate Identity Number) to the Company.

Effect of the Certificate of Incorporation:
Certificate of Incorporation is the conclusive evidence of the legal existence of the company. A private company can commence its business after receiving Certificate of Incorporation. The certificate of incorporation is the birth certificate of the company.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 7 Formation of a Company

Question 2.
Explain the contents of Memorandum of Association.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 7 Formation of a Company 1
Answer:
Memorandum of Association: It is the charter or magnacarta of the company. It defines the objects of the company and provides the framework beyond which the company cannot operate. It lays down the relationship of the company with outside world.

Memorandum of Association must be printed, divided into paragraphs, numbered consecutively. The Memorandum of Association must be signed by at least seven persons in case of a public company and by two persons in case of a private company.

Contents of Memorandum of Association:

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 7 Formation of a Company 1
1. The name clause:
Under this clause the name of the company is mentioned. A company can select any name subject to the following restrictions.

  • The proposed name should not be identical with the name of another company
  • A name which can mislead the public
  • In case of a public company the name should end with the word ‘Limited’ and in case of a private company the name should end with the word ‘Private Limited’
  • The name must not directly or indirectly imply any participation of the Central or State Govt.
  • The name must not suggest any connection or patronage of a national hero
  • It should not include the word co operative.

2. Registered office clause:
This clause contains the name of the state, in which the registered office of the company is proposed to be situated. It must be informed to the Registrar within thirty days of the incorporation of the company.

3. Objects clause:
This is the most important clause of the memorandum. It defines the purpose for which the company is formed. A company is not legally entitled to undertake an activity, which is beyond the objects stated in this clause.

4. Liability clause:
It states that the liability of members is limited to the face value of shares held by them or the amount guaranteed to be paid on winding up.

5. Capital clause:
This clause specifies the maximum capital which the company will be authorised to raise through, the issue of shares.

6. Association clause:
In this clause, the signatories to the Memorandum of Association state their intention to be associated with the company and also give their consent to purchase qualification shares.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 7 Formation of a Company

Question 3.
Mr. Hemand, a Gulf returnee, intends to start a business in the form of private limited company. But he lias no clear idea about the business opportunities in Kerala and the formalities to be followed in the formation of company. (8)

  1. As a commerce student can you suggest a specialised person who would undertake all activities for the formation of a company?
  2. Explain the functions of those specialised persons.

Answer:

Promotion:
Promotion is the first stage in the formation of a company. The identification of business opportunities, analysis of its prospects and initiating steps to form a joint stock company is called promotion. The person who undertakes to form a company is called promoter.

Functions of a Promoter:

1. Identification of business opportunity:
The first and foremost activity of a promoter is to identify a business opportunity.

2. Feasibility studies:
After identifying a business opportunity, the promoters undertake some feasibility studies to determine the viability and profitability of the proposed activity.

  • Technical feasibility – To determine whether the raw materials or technology is easily available
  • Financial feasibility – To determine the total estimated cost of the project
  • Economic feasibility – To determine the I profitability of the proposed project

3. Name approval:
After selecting the name of company the promoters submit an application to the Registrar of companies for its approval. The selected name is not the same or identical to an existing company.

4. Fixing up signatories to the Memorandum of Association:
Promoters have to decide about the members who will be signing the Memorandum of Association of the proposed company.

5. Appointment of professional:
Promoters appoint merchant bankers, auditors, etc. to assist them in the preparation of necessary documents.

6. Preparation of necessary documents:
The promoters prepare certain legal documents which are to be submitted to the Registrar of companies. They are

  • Memorandum of Association
  • Articles of Association,
  • Consent of proposed Directors
  • Agreement, if any, with proposed managing or whole time director
  • Statutory declaration

Position of Promoters:
The promoter is neither an agent nor a trustee of the company. The promoter stands in the fiduciary relationship with the company. He should not make any secret profits out of the dealings. Any, such gains are to be disclosed. The promoter must act honestly, in good faith and in the best interest of the company.

The promoter is personally liable for all the preliminary contracts with the other parties before incorporation. The promoter is also liable for any omission of facts or false statements in the prospectus.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 6 Social Responsibilities of Business and Business Ethics

Students can Download Chapter 6 Social Responsibilities of Business and Business Ethics Questions and Answers, Plus One Business Studies Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examination

Kerala Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 6 Social Responsibilities of Business and Business Ethics

Plus One Social Responsibilities of Business and Business Ethics One Mark Questions and Answers

Question 1.
Identify which of the following is not a social responsibility of business _________
1. Offering goods and services at reasonable price.
2. Keeping environment pollution free
3. Giving reasonable pay to workers
4. Help in nation building activities
Answer:
3. Giving reasonable pay to workers

Question 2.
State Bank of India gives scholarship to bright students each year. This is a part of their __________
1. Sales promotion
2. Social responsibility
3. Charity work
4. Business ethics
Answer:
2. Social responsibility

Question 3.
Application of general ethics and principles in business practice is ____________
Answer:
Business ethics

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 6 Social Responsibilities of Business and Business Ethics

Question 4.
It is the belief in what is right, proper and just. Identify it.
Answer:
Business ethics

Question 5.
______________ is the code of conduct followed and performed by businessmen.
Answer:
Business ethics

Question 6.
Which among the following is not a case for an ethical activity.
1. child labour
2. equal pay for equal work
3. dumbing of waste in river
4. high usage of preservatives in products.
Answer:
2. Equal pay for equal work

Plus One Social Responsibilities of Business and Business Ethics Two Mark Questions and Answers

Question 1.
Roy and Rejitha joined in a factory as peons on the same day. Both of them are doing 8 hrs work a day. Roy is paid ₹100 while Rejitha ₹80 per day. Do you think the owner of the factory is fair to Rejitha? If not, give your opinion. (2)
Answer:
No. The owner of the factory is not fair to Rejitha. It is the social and moral responsibility of the business to offer equal pay for equal work without considering any caste, sex, etc.

Question 2.
Explain the need for pollution control. (2)
Answer:
Need for Pollution Control:

1. Reduction of health hazard:
Pollution control measures can check diseases like cancer, heart attack & lung complications and support a healthy life on earth.

2. Reduced Risk of Liability:
It is a sound business policy to install pollution control devices in its premises to reduce the risk of liability of paying compensation to the affected people.

3. Cost Saving:
An effective pollution control programme is needed to save costs of operating business.

4. Improved Public Image:
A firm that adopts pollution control measures enjoys a good reputation as a socially responsible enterprise.

5. Other social benefits:
Pollution control results in many other benefits like clearer visibility, cleaner buildings, better quality of life, and the availability of natural products in a purer form.

Plus One Social Responsibilities of Business and Business Ethics Three Mark Questions and Answers

Question 1.
George is working in a manufacturing industry. The manager compels him to do 10hrs work continuously without giving any additional benefits. Do you agree with the manager? Give your suggestions. (3)
Answer:
No. We cannot agree with the decision of the manager. It is against the social responsibility of the business. George has to work only 8 hours a day. Compelling to do 10 (without any additional benefits) hours is a violation of human right. Managers cannot ask a worker to do work continuously without giving remuneration. It is also a violation of human rights.

Plus One Social Responsibilities of Business and Business Ethics Four Mark Questions and Answers

Question 1.
Match column A with columns B and C
Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 6 Social Responsibilities of Business and Business Ethics 1
Answer:

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 6 Social Responsibilities of Business and Business Ethics 2

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 6 Social Responsibilities of Business and Business Ethics

Question 2.
Jaleel, owner of a fish stall, usually sells damaged and decayed fish by pouring chemicals, ice, along with sea sand for creating an impression in the minds of consumers that it is newly caught. Is it justifiable from the point of view of business ethics? How will it affect the reputation of the business? (4)
Answer:
Business ethics refer to the socially determined moral principles which should govern business activities.
A few examples of business ethics are

  • charging fair prices from customers
  • providing quality products
  • using fair weights for measurement of commodities
  • giving fair treatment to workers & earning only reasonable profits.

Ethical business behaviour improves public image, earns people’s confidence and trust, and leads to greater success. Selling damaged and decayed fish is unethical.

It will affect the reputation of the business and finally it leads to business loss. He must not goods of low quality for personal gain. No business can make progress without adopting ethical values.

Plus One Social Responsibilities of Business and Business Ethics Five Mark Questions and Answers

Question 1.
Anchu, a stationery dealer distributed good quality products at low price by suffering huge losses, in order to eliminate the competition from Chinju, another stationery dealer, in the same locality. When Chinju stopped her business, Anchu started to supply low quality products at high price. (5)

  1. Can you justify Anchu’s action from point of view of the society?
  2. Give a few undesirable practices which a business follow in a real life situation.

Answer:
1. No. We cannot justify Anchu’s action. It is against business ethics. Business ethics refers to moral values which should be followed in business activities.

2. Examples of unethical practices are

  • Providing low quality products at high prices.
  • Making misleading advertisements.
  • Creating artificial scarcity to increase demand.
  • Keeping false accounts to avoid paying taxes.
  • Acceptance of bribe for personal benefits.
  • Manufacture and sale of adulterated goods.
  • Polluting the environment.
  • Exploiting workers.

Plus One Social Responsibilities of Business and Business Ethics Six Mark Questions and Answers

Question 1.
What steps can an enterprise take to protect the environment from the dangers of pollution? (6)
Answer:
Role of Business in Environmental Protection:

1. A definite commitment by top management to create a work culture for environmental protection

2. Ensuring that commitment of environmental protection is shared throughout the enterprise by all divisions and employees.

3. Developing clear cut policies and programmes for purchasing good quality raw materials, introducing superior technology, using scientific techniques of disposal of waste and developing employee skills for pollution control

4. Complying with the laws and regulations enacted by the Government for prevention of pollution.

5. Participation in government programs relating to management of hazardous substances, cleaning up of polluted rivers, plantation of trees, and checking deforestation.

6. Periodical assessment of pollution control programmes in terms of costs and benefits with a view to improve them.

7. Arranging educational workshops and training materials to share technical information with everyone involved in pollution control.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 6 Social Responsibilities of Business and Business Ethics

Question 2.
Explain the elements of business ethics. (6)
Answer:
Business Ethics:
Ethics is concerned with what is right and what is wrong in human behavior. Business ethics refer to the socially determined moral principles which should govern business activities.

Business ethics is the code of conduct followed and performed by every business. Ethical business behavior improves public image earn’s public confidence and leads to greater success.
Examples of Business Ethics:

  1. Charging fair prices from customers
  2. Using fair weights for measurement of commodities
  3. Giving fair treatment to workers
  4. Earning reasonable profits.
  5. Avoiding adulteration, hoarding etc.
  6. Using environmentally friendly products

Elements of Business Ethics:

1. Top management commitment:
The Chief Executive Officer and higher level managers must give continuous leadership for developing and upholding the moral values of the organisation.

2. Publication of a Code:
‘Code’ refers to a formal written document of the principles, values and standards that guide a firm’s actions. It may cover the areas of fundamental honesty and adherence to laws, product safety and quality, health and safety in the workplace, etc.

3. Establishment of Compliance Mechanism:
A suitable mechanism should be developed to comply with the ethical standards of the enterprise.

4. Employees Involvement:
To make ethical business a reality, employees at all levels must be involved.

5. Measuring Results:
Ethical results must be verified and audited that how far work is being carried according to ethical standards.

Plus One Social Responsibilities of Business and Business Ethics Eight Mark Questions and Answers

Question 1.
Build up arguments for and against social responsibilities. (8)
Answer:
Arguments in favour of Social Responsibility:

1. Justification for Existence and Growth:
The prosperity and growth of business is possible only through continuous service to society.

2. Long term Interest of the firm:
A firm can improve its image and builds goodwill in the long run when its highest goal is to serve the society.

3. Avoidance of government regulations:
Business can avoid the problem of government regulations by voluntarily assuming social responsibilities.

4. Maintenance of society:
Law alone can’t help out people with all the difficulties they face. A socially responsible business can contribute something for social peace and harmony.

5. Availability of resources with business:
Business has valuable financial and human resources which can be effectively used for solving problems of the society.

6. Better environment for doing business:
Social responsibility creates better environment for business operations as it improves quality of life and standard of living of the people.

7. Contribution to social problems:
Some of the social problems have been created by business firms themselves such as pollution, unsafe workplaces, discrimination, etc. Therefore, it is the moral obligation of business to solve such social problems.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 6 Social Responsibilities of Business and Business Ethics

Arguments Against Social Responsibility:

1. Violation of profit maximization objective:
According to this argument, business exists only for the maximum profit to its shareholders and do not have responsibility to the society as a whole.

2. Burden on consumers:
Involvement of business in social responsibilities involve a lot of expenditure which will ultimately be borne by the customers.

3. Lack of Social Skills:
The business firms and managers are not expert to tackle the social problems like poverty, overpopulation etc.

4. Lack of public support:
Business cannot fulfill social responsibility because of lack of public confidence & cooperation.

Question 2.
Mr. Biju, a readymade garment manufacturer, is of the view that “different interest groups always claim some sort of protection from the business as such. These interest groups, no doubt consist of persons connected with business in one way or other, such as shareholders, employees, society and so on”. Do you agree with this statement? Explain. (8) 

OR

“Business is a social institution having responsibilities towards different interest group.” Do you agree. Explain the responsibility towards each group.
Answer:
Social Responsibility towards different interest groups

1. Responsibility towards share holders or owners:

  1. Provide a fair and regular return on the investment of shareholders.
  2. Provide regular and accurate information on the financial position of the firm.
  3. To ensure the safety of their investment.

2. Responsibility Towards the workers:

  1. Providing fair wages
  2. Providing good working conditions and welfare amenities.
  3. Respect democratic rights of workers to form
    unions.

3. Responsibility toward consumers:

  1. Supply right quality and quantity of goods and services at reasonable prices.
  2. Avoiding unfair trade practices like adulteration, poor quality, misleading advertisement etc.
  3. Inform them about new products, its features, uses and other matters relating to the products.
  4. To handle the customers grievance promptly.

4. Responsibility Towards Government:

  1. Respect the laws of the country
  2. Pay taxes regularly and honestly.
  3. act according to the well accepted values of the society.

5. Responsibility towards community:

  1. Make employment opportunities
  2. Protect the environment from pollution.
  3. To uplift the weaker sections of society

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 6 Social Responsibilities of Business and Business Ethics

Question 3.
Prosperity and higher living standards are the hallmarks of industrial development for any nation. But during this course, it equally causes damages to the environment. (8)

  1. Explain the different types of pollution.
  2. Substantiate the above statement with regard to various types of pollution.

Answer:
Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 6 Social Responsibilities of Business and Business Ethics 3

Business & Environmental Protection Causes of Pollution: Many industrial organisations have been responsible for causing air, water, land and noise pollution.

1. Air Pollution:
Air pollution is mainly due to Carbon monoxide emitted by automobiles and smoke and other chemicals from manufacturing plants. It has created a hole in the ozone layer leading to global warming.

2. Water pollution:
Water becomes polluted primarily from chemical and waste dumping. It has led to the death of several animals and posed a serious problem to human life.

3. Land Pollution:
Dumping of toxic wastes reduces the quality of land and making it unfit for agriculture or plantation.

4. Noise Pollution:
Noise caused by the running of factories and vehicles create a serious health hazard such as loss of hearing, malfunctioning of the heart and mental disorders.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 6 Social Responsibilities of Business and Business Ethics

Question 4.
Explain the role of business in environmental protection. (8)
Answer:
Role of Business in Environmental Protection:

  1. A definite commitment by top management to create a work culture for environmental protection
  2. Ensuring that commitment of environmental protection is shared throughout the enterprise by all divisions and employees.
  3. Developing clear cut policies and programmes for purchasing good quality raw materials, introducing superior technology, using scientific techniques of disposal of waste and developing employee skills for pollution control
  4. Complying with the laws and regulations enacted by the Government for prevention of pollution.
  5. Participation in government programs relating to management of hazardous substances, cleaning up of polluted rivers, plantation of trees, and checking deforestation.
  6. Periodical assessment of pollution control programmes in terms of costs and benefits with a view to improve them.
  7. Arranging educational workshops and training materials to share technical information with everyone involved in pollution control.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 5 Emerging Modes of Business

Students can Download Chapter 5 Emerging Modes of Business Questions and Answers, Plus One Business Studies Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examinations

Kerala Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 5 Emerging Modes of Business

Plus One Emerging Modes of Business One Mark Questions and Answers

Question 1.
Carrying business activity through internet is popularly known as _______
Answer:
E-commerce

Question 2.
____________ refers to illegal entry into the web site of an enterprise and thereby damaging data input there.
Answer:
Hacking

Question 3.
____________ are programmes designed to corrupt data in a system.
Answer:
Viruses

Question 4.
Mr. Arun, a retailer pays tax online. Identify this E-Commerce Transaction
Answer:
C2G

Question 5.
Which of the following helps to purchase goods and services without making spot payments and zero balance in the account?

  1. ATM card
  2. credit card
  3. debit card
  4. Kisan card

Answer:
2. credit card

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 5 Emerging Modes of Business

Question 6.
The advancement of technology helps people for shopping goods for cash without holding cash or making any deposits with banks. How is it possible explain the identified term?
Answer:
Credit card

Plus One Emerging Modes of Business Two Mark Questions and Answers

Question 1.
What do you mean by cryptography? (2)
Answer:
It refers to the art of protecting information by transforming it into an unreadable format called ‘cyphertext’. Only those who processes a secret key can decrypt the message into plaintext.

Question 2.
What are the ethical concerns involved in outsourcing? (2)
Answer:
In the name of cost cutting, unlawful activities such as child labour, wage discrimination, etc. may be encouraged in other countries.

Plus One Emerging Modes of Business Three Mark Questions and Answers

Question 1.
Anish, an NRI businessman, sends money to his wife, Nisha. She in turn deposits all this money in her bank account. She is very thankful to the technology and can withdraw money whenever she is in need of money even after banking hours. What type of technology she might be using? Explain. (3)
Answer:
ATM. From the ATM, customers can withdraw cash from the account by using ATM card. ATM card is a plastic card bearing a number for each customer. The card is to be entered into the machine and enter the PIN. This opens the account and we can deposit cash into it or withdraw from it at any time.

Question 2.
The advancement of technology facilitates shopping -goods for cash without holding cash or making any deposit with banks. How is it possible? (3)
Answer:
It is possible through credit card. A credit card is an instrument issued by a bank in the name of the customer providing for credit up to a specified amount. The sellers get cash from the bank and the buyers have to pay for the purchase within the credit period.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 5 Emerging Modes of Business

Question 3.
Majority of people in India, even internet users, hesitate shopping through internet. Can you cite a few reasons for their hesitation for buying online? (3)
Answer:
The important reasons forthe hesitation of shopping through internet are:

  1. Time to deliver goods is too long.
  2. Disclosure of credit card details is not safe.
  3. Choices are not very interesting.

Plus One Emerging Modes of Business Four Mark Questions and Answers

Question 1.
Elaborate the steps involved in online trading. (4)
Answer:
Online Transactions:
Online transaction means receiving information about goods, placing an order, receiving delivery and making payment through medium of internet.

Buying / Selling Process:
Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 5 Emerging Modes of Business 1

Steps involved in online purchase:
1. Register with the online vendor by filling-up a registration form.

2. Place the order for the items put by customer in his virtual shopping cart, an online record of what has been picked up while browsing the Online store.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 5 Emerging Modes of Business

3. Payment for the purchases through online shopping may be done in a number of ways: i.e Cash on delivery, cheque, net banking transfer, debit/credit card.

Question 2.
Name the resources required for E-commerce. (4)
Answer:
Resources Required for Successful e-Business Implementation:

  1. Computer system
  2. Internet connection and technically qualified workforce
  3. A well developed web page
  4. Effective telecommunication system
  5. A good system for making payment using credit instruments.

Question 3.
Explain any 4 types of outsourcing services. (4)
Answer:

  1. Financial services.
  2. Advertising services
  3. Courier services
  4. Customer support services

Plus One Emerging Modes of Business Five Mark Questions and Answers

Question 1.
List two examples each for B2B, B2C, B2G and B2E transactions (5)
Answer:
B2B:

  • Transactions between businessmen
  • Collaboration
  • Placing order with suppliers
  • Forming joint ventures
  • Transfer of goods between branches
  • Transfer of goods between suppliers

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 5 Emerging Modes of Business

B2C:

  • Business offering services to customers
  • Consumer placing order online
  • Electronic payment
  • Consumers seeking clarification on price, terms etc. (any two)

B2G:

  • Payment of taxes
  • Application for licence
  • Seeking government clearance

B2E:

  • Employees salary payments
  • Operation of welfare schemes
  • Information to employees on business process
  • Seeking employees suggestions online

Question 2.
Sankar and Co is a leading can manufacturing company. They are not concentrating on their advertisement due to lack of time. In orderto boost up the sales they made a contract with an advertising agency to make an advertisement which can be released through the media. Analyze this situation. Do you favour this activity of the company? Can you identify the concept and brings out its merit? (5)
Answer:
Business Process Outsourcing (BPO)

Plus One Emerging Modes of Business Six Mark Questions and Answers

Question 1.
State any three differences between e-business and traditional business.
Answer:

Traditional businesse-business
Its formation is difficultIts formation is easy
Investment is very highInvestment is low
Physical presence is requiredPhysical presence is not required
Location is importantLocation is not important
Operating cost is highOperating cost is low
Contact with suppliers and customers is through intermediariesDirect contact with the suppliers and customers
Business process cycle is longBusiness process cycle is shorter
Inter personal touch is highPersonal touch is less
Limited market coverageAccess to the global market
Communication is in hierarchical orderCommunication is in non hierarchical order
Transaction risk is lessTransaction risk is high

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 5 Emerging Modes of Business 3
Outsourcing or Business Process Outsourcing (BPO):
Outsourcing is a management strategy by which an organisation contracts out its major non-core functions to specialized service providers with a view to benefit from their expertise, efficiency and cost effectiveness, and allow managers to concentrate on their core activities.

Merits of outsourcing:

  1. It provides an opportunity to the organisation to concentrate on areas in which it has core competency or strength.
  2. It helps better utilisation of its resources as the management can focus its attention on selected activities and attain higher efficiency.
  3. It helps the organisation to get an expert and specialised service at competitive prices. It helps in improved service and reduction in costs.
  4. It facilitates inter-organisational knowledge sharing and collaborative learning.
  5. It enables expansion of business as resources saved from outsourcing can be used for expanding the production capacity and diversified products.

Limitations of outsourcing:

  1. It reduces confidentiality as outsourcing involves sharing a lot of information with others.
  2. It may be opposed by labour unions who feel threatened by possible reduction in their employment.
  3. In the name of cost cutting, unlawful activities such as child labour, wage discrimination maybe encouraged in other countries.
  4. The organisation hiring others may face the problem of loss of managerial control because it is more difficult to manage outside service providers than managing one’s own employees.
  5. It causes unemployment in the home country.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 5 Emerging Modes of Business

Question 2.
Evaluate the need for outsourcing and discuss its limitations. (6)
Answer:
Outsourcing or Business Process Outsourcing (BPO):
Outsourcing is a management strategy by which an organisation contracts out its major non-core functions to specialized service providers with a view to benefit from their expertise, efficiency and cost effectiveness, and allow managers to concentrate on their core activities.

Merits of outsourcing:

  1. It provides an opportunity to the organisation to concentrate on areas in which it has core competency or strength.
  2. It helps better utilisation of its resources as the management can focus its attention on selected activities and attain higher efficiency.
  3. It helps the organisation to get an expert and specialised service at competitive prices. It helps in improved service and reduction in costs.
  4. It facilitates inter-organisational knowledge sharing and collaborative learning.
  5. It enables expansion of business as resources saved from outsourcing can be used for expanding the production capacity and diversified products.

Limitations of outsourcing:

  1. It reduces confidentiality as outsourcing involves sharing a lot of information with others.
  2. It may be opposed by labour unions who feel threatened by possible reduction in their employment.
  3. In the name of cost cutting, unlawful activities such as child labour, wage discrimination maybe encouraged in other countries.
  4. The organisation hiring others may face the problem of loss of managerial control because it is more difficult to manage outside service providers than managing one’s own employees.
  5. It causes unemployment in the home country.

Question 3.
What is online transactions? Explain its steps. (6)
Answer:
On line Transactions:
On line transaction means receiving information about goods, placing an order, receiving delivery and making payment through medium of internet.

Buying / Selling Process:
Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 5 Emerging Modes of Business 1
Steps involved in online purchase:

  1. Register with the online vendor by filling-up a registration form.
  2. Place the order for the items put by customer in his virtual shopping cart, an on-line record of what has been picked up while browsing the On-line store.
  3. Payment for the purchases through online shopping may be done in a number of ways: i.e Cash on delivery, cheque, net banking transfer, debit/credit card.

Plus Two Maths Chapter Wise Questions and Answers Chapter 12 Linear Programming

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Kerala Plus Two Maths Chapter Wise Questions and Answers Chapter 12 Linear Programming

Plus Two Maths Linear Programming Four Mark Questions and Answers

Question 1.
Solve the following LPP Graphically;
Maximise; Z = 60x + 15y
Subject to constraints;
x + y ≤ 50, 3x + y ≤ 90, x ≥ 0, y ≥ 0.
Answer:
1. In the figure the shaded region OABC is the fesible region. Here the region is bounded. The corner points are O(0, 0), A(30, 0), B(20, 30), C(0, 50).
Plus Two Maths Linear Programming 4 Mark Questions and Answers 1
Given; Z = 60x + 15y

Corner pointsValue of Z
OZ = 0
AZ = 60(30) + 15(0) = 1800
BZ = 60(20) + 15(30) = 1650
CZ = 60(0) + 15(50) = 750

Since maximum value of Z occurs at A, the soluion is Z = 1800, (30, 0).

Plus Two Maths Chapter Wise Questions and Answers Chapter 12 Linear Programming

Question 2.
Solve the following LPP Graphically;
Minimise; Z = -3x + 4y
Subject to constraints;
x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0
Answer:
In the figure the shaded region OABC is the fesible region. Here the region is bounded. The corner points are O(0, 0), A(4, 0) B(2, 3), C(0, 4).
Plus Two Maths Linear Programming 4 Mark Questions and Answers 2
Given; Z = -3x + 4y

Corner pointsValue of Z
OZ = 0
AZ = -3(4) + 4(0) = -12
BZ = -3(2) + 4(3) = 6
CZ = -3(0) + 4(4) = 16

Since minimum value of Z occurs at A, the soluion is Z = -12, (4, 0).

Plus Two Maths Chapter Wise Questions and Answers Chapter 12 Linear Programming

Question 3.
Solve the following LPP Graphically;
Maximise; Z = 3x + 5y
Subject to constraints;
x + 3y ≥ 3, x + y ≥ 2, x ≥ 0, y ≥ 0
Answer:
In the figure the shaded region ABC is the fesible region. Here the region is unbouded.
Plus Two Maths Linear Programming 4 Mark Questions and Answers 3
The corner points are A(3, 0), B\(\left(\frac{3}{2}, \frac{1}{2}\right)\), C(0, 2)
Given; Z = 3x + 5y

Corner pointsValue of Z
AZ = 3(3) + 5(0) = 9
BZ = 3\(\left(\frac{3}{2}\right)\) + 5\(\left(\frac{1}{2}\right)\) = 7
CZ = 3(0) + 5(2) = 10

Form the table, minumum value of Z is 7 at B\(\left(\frac{3}{2}, \frac{1}{2}\right)\). The feasible region is unbounded, so consider the inequality 3x + 5y < 7. Clearly the feasible region has no common points with 3x + 5y < 7, Thus minimum value of Z occurs at B, the soluion is Z = 7.

Plus Two Maths Linear Programming Six Mark Questions and Answers

Question 1.
One kind of a cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1kg of fat assuming that there is no shortage of the other ingredients, used in making the cake.
Answer:
Let the number of cakes made of type I are x and that of type II are y. Then the total number of cakes will be Z = x + y
Flour constraint 200x + 100y ≤ 5000
Fat constraint 25x + 50y ≤ 1000
Therefore;
Maximise; Z = x + y
2x + y ≤ 50; x + 2y ≤ 40; x ≥ 0, y ≥ 0
Plus Two Maths Linear Programming 6 Mark Questions and Answers 4
In the figure the shaded region OABC is the feasible region. Here the region is bounded. The corner points are O(0, 0), A(25, 0), B(20, 10), C(0, 20)
Given; Z = x + y

Corner pointsValue of Z
OZ = 0
AZ = 25 + 0 = 25
BZ = 20 + 10 = 30
CZ = 0 + 20 = 20

Since maximum value of Z occurs at B, the soluion is Z = 30, (20, 10).

Plus Two Maths Chapter Wise Questions and Answers Chapter 12 Linear Programming

Question 2.
A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine and 3hours of craftman’s time in its making, while a cricket bat takes 3 hours of machine time and 1 hour of craftman’s time. In a day, the factory has availability of not more than 42 hours of machine time and 24 hours of craftman’s time.

  1. What no. of rackets and bats must be produced if the factory is to work at full capacity?
  2. If the profit on a racket and a bat is 10 find maximum profit.

Answer:
Let the number of rackets made = x and that of bats = y.
Maximise; Z = x + y
Machine constraints 1.5x + 3y ≤ 42
Craftsman’s constraint 3x + y ≤ 24
Therefore; Maximise; Z = x + y
x + 2y ≤ 14, 3x + y ≤ 24, x ≥ 0, y ≥ 0
In the figure the shaded region OABC is the fesible region. Here the region is bounded. The corner points are O(0, 0), A(8, 0), B(4, 10), C(0, 14).
Plus Two Maths Linear Programming 6 Mark Questions and Answers 5
Given; Z = x + y

Corner pointsValue of Z
OZ = 0
AZ = 8 + 0 = 8
BZ = 4 + 12 = 16
CZ = 0 + 14 = 14

Since maximum value of Z occurs at B, the soluion is Z = 16, (4, 12).

Plus Two Maths Chapter Wise Questions and Answers Chapter 12 Linear Programming

Question 3.
Two godowns A and B have grains capacity of 100 quintals and 50 quintals respectively. They supply to 3 ration shops D, E, and F whose requirement are 60, 50 and 40 quintals respectively. The cost of transportation per quintal from the godowns to the shops is given in the following table; Transportation cost per quintal(in Rs.)
Plus Two Maths Linear Programming 6 Mark Questions and Answers 6
Hence should the supplies be transported in order that the transportation cost is minimum? What is the minimum cost?
Answer:
Plus Two Maths Linear Programming 6 Mark Questions and Answers 7
Express the problem diagrammatically as shown above. The total transportation cost is given by
Z = 6x + 3y + 2.5{100 – (x + y)} + 4(60 – x) + 2(50 – y) + 3(-60 + (x + y))
⇒ Z = 2.5x + 1.5y + 410
100 – (x + y) ≥ 0 ⇒ x + y ≤ 100
60 – x ≥ 0 ⇒ x ≤ 60
50 – y ≥ 0 ⇒ y ≤ 50 – 60 + x + y ≥ 0 ⇒ x + y ≥ 60
Then the given LPP is
Minimise; Z = 2.5x + 1.5y + 410
x + y ≤ 100, x + y ≥ 60
0 ≤ x ≤ 60, 0 ≤ y ≤ 50
Plus Two Maths Linear Programming 6 Mark Questions and Answers 8
In the figure the shaded region ABCD is the feasible region. Here the region is bounded. The corner points are
A(60, 0), B(60, 40), C(50, 50), D(10, 50).
Given; Z = 2.5x + 1.5y + 410

Corner pointsValue of Z
AZ = 2.5(60) + 1.5(0) + 410= 560
BZ = 2.5(60) + 1.5(40) + 410 = 620
CZ = 2.5(50) + 1.5(50) + 410 = 610
DZ = 2.5(10) + 1.5(50) + 410 = 510

Since minimum value of Z occurs at D, the soluion is Z = 510.

Plus Two Maths Chapter Wise Questions and Answers Chapter 12 Linear Programming

Question 4.
(i) Choose the correct answer from the bracket. If an LPP is consistent, then its feasible region is always
(a) Bounded
(b) Unbounded
(c) Convex region
(d) Concave region
(ii) Maximize Z = 2x + 3y subject to the constraints x + y ≤ 4, x ≥ 0, y ≥ 0.
Answer:
(i) (c) Convex region.

(ii)
Plus Two Maths Linear Programming 6 Mark Questions and Answers 9
Corner points of the feasible region are as follows

Corner pointsZ = 2x + 3y
0(0, 0)0
A(0, 4)12 → Maximum
B(4, 0)8

∴ the maximum value of Z is 12 attained at (0, 4).

Plus Two Maths Chapter Wise Questions and Answers Chapter 12 Linear Programming

Question 5.
The graph of a linear programming problem is given below. The shaded region is the feasible region. The objective function is Z = px + qy
Plus Two Maths Linear Programming 6 Mark Questions and Answers 10

  1. What are the co-ordinates of the comers of the feasible region.
  2. Write the constraints
  3. If the Max. Z occurs at A and B, what is the relation between p and q?
  4. If q = 1, write the objective function
  5. Find the Max Z

Answer:
1. Corner points are O(0, 0), A(5, 0), B(3, 4), C(0, 5).

2. Constraints are 2x + y ≤ 10, x + 3y ≤ 15, x ≥ 0, y ≥ 0.

3. At (3, 4), Z = 3p + 4q
At (5, 0), Z = 5p
⇒ 3p + 4q = 5p ⇒ p = 2q.

4. If q = 1, p=2
Then the objective function is,
Maximize Z = 2x + y.

5. At (3, 4) Z = 2 × 3 + 4 = 10 is the maximum value.

Plus Two Maths Chapter Wise Questions and Answers Chapter 12 Linear Programming

Question 6.
A diet is to contain at least 80 units of vitamin A and 100 units of minerals. Two foods F1 and F2 are available. Food F1 costs Rs 4 per unit food and F2 costs Rs 6 per unit. One unit of food F1 contains 3 units of vitamin A and 4 units of minerals. One unit of food F2 contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem. Find the minimum costs for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.
Answer:
Let x units of food F1 and y units of food F2 be in the diet
Total cost Z = 4x + 6y
Then the LPP is
Minimize Z = 4x + 6
Subject to the constraints
3x + 6y ≥ 80
4x + 3y ≥ 100
x, y ≥ 0
Plus Two Maths Linear Programming 6 Mark Questions and Answers 11
The feasible region is unbounded
Plus Two Maths Linear Programming 6 Mark Questions and Answers 12
As the feasible region is unbounded, 104 may or may not be the minimum value of Z. For this we draw a graph of the inequality 4x + 6y < 104 or 2x + 3y < 52 and check whether the resulting half plane has points in common with the feasible region or not.

It can be seen that the feasible region has no common points with 2x + 3y < 52 Therefore minimum cost of the mixture will be 104.

Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry

Students can Download Chapter 11 Three Dimensional Geometry Questions and Answers, Plus Two Maths Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry

Plus Two Maths Three Dimensional Geometry Three Mark Questions and Answers

Question 1.
Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry 1

  1. Write the Cartesian equation. (1)
  2. Find the angle between the line. (2)

Answer:
1.
Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry 2

2. cosθ
Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry 3

Question 2.
Find the vector equation of the plane passing through the intersection of the planes \(\bar{r}\).(i + j + k) = 6 and \(\bar{r}\).(2i + 3 j + 4k) = -5 at the point (1,1,1).
Answer:
The Cartesian equation of the planes are x + y + z = 6 and 2x + 3y + 4z = – 5. Therefore the equation of the plane passing through the intersection of these planes is
x + y + z – 6 + k(2x + 3y + 4z + 5) = 0
Since it pass through (1, 1, 1) we get,
1 + 1 + 1 – 6 + k(2 + 3 + 4 + 5) = 0 ⇒ -3 + k14 ⇒ k = \(\frac{3}{14}\)
∴ the equation is
x + y + z + -6 + \(\frac{3}{14}\) (2x + 3 y + 4z + 5) = 0
14x + 14y + 14z – 84 + 6x + 9y + 12z + 15 = 0
20x + 23y + 26z = 69
Vector equation is \(\bar{r}\). (20i + 23j + 26k) = 69.

Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry

Question 3.
Find the equation of the plane passing through the intersection of the planes x + y + 4z + 5 = 0 and 2x – y + 3z + 6 = 0 and contains the point (1, 0, 0).
Answer:
The equation of the planes passing through the intersection of the planes
x + y + 4z + 5 = 0 and 2x – y + 3z + 6 = 0 is
x + y + 4z + 5 + k(2x – y + 3z + 6) = 0 ____(1)
Since (1) pass through (1, 0, 0)
⇒ 1 + 0 + 0 + 5 + k(2 – 0 + 0 + 6) = 0
⇒ 6 + 8k = 0 ⇒ k = –\(\frac{3}{4}\); Then (1)
⇒ x + y + z + 5 + \(\frac{3}{4}\)(2x – y + 3z + 6) = 0
⇒ 4x + 4y + 16z + 20 – 6x + 3y – 9z – 18 = 0
⇒ 2x – 7y – 7z = 2.

Plus Two Maths Three Dimensional Geometry Four Mark Questions and Answers

Question 1.
Consider the point (-1, -2, -3).

  1. In which octant, the above point lies.(1)
  2. Find the direction cosines of the line joining (-1, -2, -3) and (3, 4, 5). (1)
  3. If P is any point such that OP = \(\sqrt{50}\) and direction cosines of OP are \(\frac{3}{\sqrt{50}}\), \(\frac{4}{\sqrt{50}}\) and \(\frac{5}{\sqrt{50}}\), then find the co-ordinate of P. (2)

Answer:
1. The point lies in the octant X’OY’Z’.

2. Direction ratios of the line joining (-1, -2, -3) and (3, 4, 5) are (3 + 1), (4 + 2), (5 + 3) ⇒ 4, 6, 8 ⇒ 2, 3, 4.
Therefore direction cosines are
Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry 4

3. Given, OP = \(\sqrt{50}\)
Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry 5
Therefore the point is (3, 4, 5).

Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry

Question 2.
Consider a cube of side ‘a’ unit has one vertex at the origin O.
Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry 6

  1. Write down the co-ordinate of 0, 0′, A and A’ (1)
  2. Find the direction ratios of OO’ and AA’. (2)
  3. Show that the angle between the main diagonals of the above cube is cos-1\(\left(\frac{1}{3}\right)\) (1)

Answer:
1. O(0, 0, 0), O'(a, a, a), A(a, 0, 0) and A'(0, a, a).

2. Direction ratios along OO’ is a – 0, a – 0, a – 0
⇒ a, a ,a ⇒ 1, 1, 1

3. cosθ
Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry 7

Question 3.
Consider two points A and B and a line L as shown in the figure.
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 8

  1. Find \(\overline{A B}\) (1)
  2. Find the Cartesian equation of the line L.  (1)
  3. Find the foot of the perpendicular drawn from ( 2, 3, 4 ) to the line L. (2)

Answer:
1. \(\overline{A B}\) = (3 – 1)i + (- 3 – 3)j + (3 – 0)k = 2i – 6j + 3k.

2. The Cartesian equation of a line passing through the point (4, 0, -1 ) and parallel to the vector \(\overline{A B}\) is
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 9

3. We take, \(\frac{x-4}{2}=\frac{y}{-6}=\frac{z+1}{3}\) = r then any point of the line can be taken as (2r + 4, -6r, 3r – 1). Assume that this point be the foot of the perpendicular drawn from (2, 3, 4 ). The dr’s of the line is 2 : – 6 : 3 and dr’s of the perpendicular line L is
2r + 4 – 2 : -6r – 3 : 3r – 1 – 4 ⇒ 2r + 2: -6r – 3 : 3r – 5
Since perpendicular,
2(2 r + 2) – 6(-6 r -3) + 3(3r – 5) = 0
49r = -7 ⇒ r = \(\frac{-7}{49}\) = –\(\frac{1}{7}\). Therefore the foot of the
perpendicular is
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 10

Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry

Question 4.
Cartesian equation of two lines are
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 11
(i) Write the vector equation of the lines. (2)
(ii) Shortest distance between the lines. (2)
Answer:
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 12
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 13
Question 5.
Consider the points (1, 3, 4) & (-3, 5, 2)

  1. Find the equation of the line through P and Q. (1)
  2. At which point that the above line cuts the plane 2x + y + z + 3 = 0. (3)

Answer:
1. Equation of a line passing through( 1, 3, 4) and (-3, 5, 2) is given by,
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 14
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 15

2. Let \(\frac{x-1}{-2}=\frac{y-3}{1}=\frac{z-4}{-1}\) = λ
Then any point on the line is (-2λ + 1, λ + 3, -λ + 4)
Since the plane 2x + y + z + 3 = 0 cuts the aboveline. We have,
⇒ 2(-λ + 1) + λ + 3 – λ + 4 + 3 = 0
⇒ -2λ + 2 + λ + 3 – λ + 4 + 3 = 0
⇒ -2λ = -12 ⇒ λ = 6
∴ point of intersection is (-2 × 6 + 1, 6 + 3, -6 + 4)
⇒ (-11, 9, -2).

Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry

Question 6.
Let the equation of a plane be \(\bar{r}\). (2i – 3j + 5k) = 7, then

  1. Find the Cartesian equation of the plane. (1)
  2. Find the equation of a plane passing through the point (3, 4, -1) and parallel to the given plane. (2)
  3. Find the distance between the parallel planes. (1)

Answer:
1. Given, \(\bar{r}\).(2i – 3j + 5k) = 7 and if we substitute \(\bar{r}\) = xi + yj + zk Then we get the Cartesian equation as 2x – 3y + 5z – 7 = 0.

2. The equation of a plane parallel to the above plane differ only by a constant, therefore let the equation be 2x – 3y + 5z + k = 0.
⇒ 6 – 12 – 5 + k = 0 ⇒ k = 11
Therefore the equation is 2x – 3y + 5z + 11 = 0

3. The distance between the parallel planes
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 16

Question 7.

  1. State the condition for the line \(\bar{r}\) = \(\bar{a}\) + λ \(\bar{b}\) is parallel to the plane \(\bar{r}\).\(\bar{n}\) = d. (2)
  2. Show that the line \(\bar{r}\) = i + j + λ(2i + j + 4k) is parallel to the plane \(\bar{r}\). (-2i + k) = 5. (1)
  3. Find the distance between the line and The Plane in (ii). (1)

Answer:
1. The line \(\bar{r}\) = \(\bar{a}\) + λ \(\bar{b}\) is parallel to the plane \(\bar{r}\).\(\bar{n}\) = d, if the normal of the plane is perpendicularto the line.
∴ \(\bar{b}\).\(\bar{n}\) = 0.

2. Given,
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 17
The line \(\bar{r}\) = i + j + λ(2i + j + 4k) is parallel to the plane \(\bar{r}\). (-2i + 4k) = 5 ⇒ -2x + 4y = 5.

3. Distance = Distance between – 2x + 4y = 5 and point (1, 1, 0) on the line
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 19

Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry

Question 8.
Choose the correct answer from the bracket,
(i) If a line in the space makes angle α, β and γ with the coordinates axes, then cos2α + cos2β + cos2γ is equal to (1)
(a) 1
(b) 2
(c) 0
(d) 3
(ii) The direction ratios of the line are \(\frac{x-6}{1}=\frac{2-y}{2}=\frac{z-2}{2}\) (1)
(a) 6, -2, -2
(b) 1, 2, 2
(c) 6, 1, -2
(d) 0, 0, 0
(iii) If the vector equation of a line is \(\bar{r}\) = i + j + k + µ(2i – 3j – 4k), then the Cartesian equation of the line
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 20
(iv) If the Cartesian equation of a plane is x + y + z =12, then the vector equation of the line is (1)
(a) \(\bar{r}\).(2i + j + k) = 12
(b) \(\bar{r}\).(i + j + k) = 12
(C) \(\bar{r}\).(i + y + 2k) = 12
(d) \(\bar{r}\).(i + 3j + k) = 12
Answer:
(i) (a) 1

(ii) (b) 1, 2, 2

(iii) (b) \(\frac{x-I}{2}=\frac{y-1}{-3}=\frac{z-1}{-4}\)

(iv) (b) \(\bar{r}\).(i + j + k) = 12.

Question 9.
Consider the lines \(\bar{r}\) = (i + 2j – 2k) + λ(i + 2 j) and \(\bar{r}\) = (i + 2j – 2k) + µ(2j – k)

  1. Find the angle between the lines.
  2. Find a vector perpendicular to both the lines.
  3. Find the equation of the line passing through the point of intersection of lines and perpendicular to both the lines.

Answer:
1. \(\bar{b}_{1}\) = i + 2j; \(\bar{b}_{2}\) = 2j – k
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 21

2. Perpendicular vector = \(\bar{b}_{1}\) × \(\bar{b}_{2}\)
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 22
= i(-2 – 0) -j(-1 – 0) + k(2 – 0)
= -2i + j + k.

3. Equation of line is \(\bar{r}\) = (i + 2j – k) + µ(-2i + j + 2k).

Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry

Question 10.
Consider the line \(\bar{r}\) = (2i – j + k) + λ(i + 2j + 3k)

  1. Find the Cartesian equation of the line.
  2. Find the vector equation of the line passing through A (1, 0, 2) and parallel to the above line.
  3. Write two points on the line obtained in (ii) which are equidistant from A.

Answer:
1. \(\frac{x-2}{1}=\frac{y+1}{2}=\frac{z-1}{3}\).

2. \(\bar{r}\) = (i + 2k) + λ(i + 2j + 3k).

3. Put λ = a and λ = -a for any real value ‘a’.
Let us put λ = 1 and λ = -1
\(\bar{r}\) = (i + 2k) + 1(i + 2j + 3k) = 2i + 2j + 5k
⇒ (2, 2, 5)
\(\bar{r}\) = (i + 2k) – 1(i + 2j + 3k) = 0i – 2j – k
⇒ (0, -2, -1)
The equidistant points are(2, 2, 5) and (0, -2, -1).

Question 11.

  1. Find the equation of the plane through the point(1, 2, 3) and perpendicular to the plane x – y + z = 2 and 2x + y – 3z = 5 (2)
  2. Find the distance between the planes x – 2y + 2z – 8 = 0 and 6y – 3x – 6z = 57 (2)

Answer:
1. Required equation is
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 23
(x – 1)(3 – 1) – (y – 2)(-3 – 2) + (z – 3)(1 + 2) = 0
2(x – 1) + 5(y – 2) + 3(z – 3) = 0
2x + 5y + 3z – 2 – 10 – 9 = 0
2x + 5y + 3z – 21 = 0

2. The planes are
x – 2y + 2z – 8 = 0 and 3x – 6y + 6z + 57 = 0
ie, 3x – 6y + 6z – 24 = 0 and 3x – 6y + 6z + 57 = 0
Distance
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 24

Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry

Question 12.
Consider the Cartesian equation of a line \(\frac{x-3}{2}=\frac{y+1}{3}=\frac{z-5}{-2}\)

  1. Find the vector equation of the line. (1)
  2. Find its intersecting point with the plane 5x + 2y – 6z – 7 = 0 (2)
  3. Find the angle made by the line with the plane 5x + 2y – 6z – 7 = 0 (1)

Answer:
1. The vector equation is \(\bar{r}\) = (3i – j + 5k) + λ(2i + 3 j – 2k).

2. Any point on the line is
\(\frac{x-3}{2}=\frac{y+1}{3}=\frac{z-5}{-2}\) = λ
x = 2λ + 3, y = 3, λ – 1, z = -2λ + 5
Since this lies on the plane ,it satisfies the plane
5(2λ + 3) + 2(3λ – 1) -6(-2λ + 5) – 7 = 0
10λ + 6λ + 12λ + 15 – 2 – 30 – 7 = 0
28λ = 24
λ = 6/7
The point of intersection is \(\left[\frac{33}{7}, \frac{11}{7}, \frac{23}{7}\right]\).

3. Let θ be the angle between the line and the plane. The direction of the line and the plane
\(\bar{b}\) = 2i + 3j + k; \(\bar{m}\) = 5i + 2j – 6k
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 25

Question 13.
From the following figure
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 26

  1. Find \(\overline{A B}\). (1)
  2. Find the vector equation of line L. (1)
  3. Find a point on line L other than C. (2)

Answer:
1. P.v of A = i – j + 4k,
P.v. of B = 2i + j + 2k
\(\overline{A B}\) = p. v. of B – p. v. of A
= 2i + j + 2k -(i – j + 4k) = i + 2j – 2k.

2. The line L passes through (1, -2, -3) and parallel to \(\overline{A B}\)
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 28
∴ Vector equation of line L is \(\bar{r}=\bar{a}+\lambda \bar{m}\)
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 29

3. From (1) of part (ii), we have
xi + yj + zk = (l + λ)i + (-2 + 2λ)j + (-3 – 2λ)k
Put λ = 1
⇒ xi +yj + zk = (1 +1)i + (-2 + 2)j + (-3 – 2 )k
⇒ xi + yj + zk = 2i + 0j – 5k
Therefore a point on line L is (2, 0, -5).

Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry

Question 14.
Find the vector equation of the plane which is at a distance of \(\frac{6}{\sqrt{29}}\) from the origin with perpendicular vector 2i – 3j + 4k. Convert into Cartesian form. Also, find the foot of the perpendicular drawn from the origin to the Plane.
Answer:
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 30
Perpendicular distance from origin = d = \(\frac{6}{\sqrt{29}}\)
The equation of the Plane is \(\bar{r}\).\(\hat{n}\) = d
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 31
Cartesian equation is 2x – 3y + 4z = 6
The direction cosines perpendicular to the Plane is \(\frac{2}{\sqrt{29}},-\frac{3}{\sqrt{29}}, \frac{4}{\sqrt{29}}\).
Perpendicular distance to the Plane is as \(\frac{6}{\sqrt{29}}\)
Hence the foot of the perpendicular is
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 32

Question 15.
Consider the Plane \(\bar{r}\).(-6i -3j – 2k) + 1 = 0, find the direction cosines perpendicular to the Plane and perpendicular distance from the origin.
Answer:
Convert the equation of the plane into normal form
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 33
Direction cosines perpendicular to the Plane is \(\frac{6}{7}, \frac{3}{7}, \frac{2}{7}\)
Perpendicular distance from the origin is \(\frac{1}{7}\).

Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry

Question 16.
Consider three points (6, -1, 1), (5, 1, 2) and (1, – 5, -4) on space.

  1. Find the Cartesian equation of the plane passing through these points. (2)
  2. Find direction ratios normal to the Plane.(1)
  3. Find a unit vector normal to the Plane. (1)

Answer:
1. Equation of a plane passing through the points (6, -1, 1),(5, 1, 2) and (1, -5, 4)
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 34
⇒ (x – 6)(-10 + 4) – (y + 1)(5 + 5) + (z – 1)(4 + 10) = 0
⇒ (x – 6)(-6) – (y + 1)(10) + (z – 1)(14) = 0
⇒ -6x + 36 – 10y – 10 + 14z – 14 = 0
⇒ 6x +10y – 14z -12 = 0.

2. Dr’s normal to the plane are 6 : 10 : -14 ⇒ 3 : 5 : -7.

3. Since the dr’s normal to the plane are 3 : 5 : -7, a unit vector in this direction is
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 35

Question 17.
Consider a straight line through a fixed point with position vector 2i – 2j + 3k and parallel to i – j + 4k.

  1. Write down the vector equation of the straight line. (1)
  2. Show that the straight line is parallel to the plane \(\bar{r}\).(i + 5y + k) = 5 (1)
  3. Find the distance between the line and plane. (2)

Answer:
1. Vector equation of a straight line is \(\bar{r}=\bar{a}+\lambda \bar{b}\) where a is \(\bar{a}\) fixed point and \(\bar{b}\) is a vector parallel to the line. Here \(\bar{a}\) = 2i – 2y + 3 it and \(\bar{b}\) = i – j + 4k. Therefore vector equation of the line \(\bar{r}\) = 2i – 2j + 3k + λ(i – j + 4k).

2. The vector parallel to the line is i – j + 4k and vector normal to the plane is i + 5j + k.
Then, (i – j + 4k). (i + 5j + k) = 1 – 5 + 4 = 0
implies that straight line and plane are parallel.

3. A point on the line is 2i – 2j + 3k. Then the distance of 2i – 2j + 3k to the given plane
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 36

Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry

Question 18.
Consider the vector equation of two planes \(\bar{r}\).(2i + j + k) = 3, \(\bar{r}\).(i – j – k) = 4

  1. Find the vector equation of any plane through the intersection of the above two planes. (2)
  2. Find the vector equation of the plane through the intersection of the above planes and the point (1, 2, -1 ) (2)

Answer:
1. The cartesian equation are 2x + y + z – 3 = 0 and x – y – z – 4 = 0 Required equation of the plane is
(2x + y + z – 3) + λ(x – y – z – 4) = 0
(2+ λ)x + (1 – λ)y + (1 – λ)z + (-3 – 4λ) = 0.

2. The above plane passes through (1, 2, -1)
(2+ λ)1 + (1 – λ)2 + (1 – λ)(-1) + (-3 – 4λ) = 0
3 – 3 + 4λ = 0
λ = 0
Equation of the plane is 2x + y + z – 3 = 0
\(\bar{r}\).(2i + j + k) = 3.

Question 19.
(i) Distance of the point(0, 0, 1) from the plane x + y + z = 3
(a) \(\frac{1}{\sqrt{3}}\) units
(b) \(\frac{2}{\sqrt{3}}\) units
(c) \(\sqrt{3}\) units
(d) \(\frac{\sqrt{3}}{2}\) units
(ii) Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to x – y + z = 0 (3)
Answer:
(i) (b) \(\frac{2}{\sqrt{3}}\) units.

(ii) Equation of the plane passing through the intersection is of the form
x + y + z – 1 + λ(2x + 3y + 4z – 5) = 0 _____(1)
(1 + 2λ)x + (1 + 3λ)j + (1 + 4λ)z – 1 – 5λ = 0
Thr Dr’s of the required plane is
(1 + 2λ), (1 + 3λ), (1 + 4λ)
Thr Dr’s of the Perpendicular plane is 1, -1, 1
⇒ (1 + 2λ)(1) + (1 + 3λ)(-1) + (1 + 4λ)(1) = 0
⇒ 1 + 2λ – 1 – 3λ + 1 + 4λ = 0
⇒ 3λ + 1 = 0 ⇒ λ = \(\frac{-1}{3}\)
(1) ⇒ x + y + z – \(\frac{1}{3}\)(2x + 3y + 4z – 5) = 0
⇒ 3x + 3y + 3z – 2x – 3y – 4z + 5 = 0
⇒ x – z + 2 = 0.

Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry

Question 20.
Consider a plane \(\bar{r}\).(6i – 3j – 2k) + 1 = 0

  1. Find dc’s perpendicular to the plane. (2)
  2. Find a vector of magnitude 14 units perpendicular to given plane. (1)
  3. Find the equation of a line parallel to the above vector and passing through the point (1, 2, 1 ). (1)

Answer:
1. Given, \(\bar{r}\).(6i – 3j – 2k) + 1 = 0 ____(1)
Now, |6i – 3j – 2k| = \(\sqrt{36+9+4}\) = 7
∴ \(\frac{6}{7} i-\frac{3}{7} j-\frac{2}{7} k\) is a unit perpendicular to the plane (1)
⇒ the dc’s perpendicular to the plane (1) are \(\frac{6}{7},-\frac{3}{7},-\frac{2}{7}\).

2. We have, \(\frac{6}{7} i-\frac{3}{7} j-\frac{2}{7} k\) is a unit perpendicular to the Plane (1). Therefore, a vector of magnitude 14 units perpendicular to the Plane (1) is 14(\(\frac{6}{7} i-\frac{3}{7} j-\frac{2}{7} k\))
⇒ 12i – 6j – 4k.

3. Equation of a line parallel to the vector 12i – 6j – 4k and passing through the point (1, 2, 1 )is given by
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 37

Plus Two Maths Three Dimensional Geometry Six Mark Questions and Answers

Question 1.
Consider the pair of lines whose equations are
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 38

  1. Write the direction ratios of the lines. (1)
  2. Find the shortest distance between the above skew lines. (4)
  3. Find the angle between these two lines. (1)

Answer:
1. The direction ratios are 2, 5, – 3 and – 1, 8, 4.

2. The given lines are \(\bar{r}\) = (2i + j – 3k) + λ(2i + 5j – 3k)
i.e. \(\bar{r}\) = \(\overline{a_{1}}+\lambda \overline{b_{1}}\),
where \(\overline{a_{1}}\) = 2i + j – 3k) + λ(2i + 5j – 3k)
and \(\bar{r}\) =(-i + 4j + 5k) + µ(-i + 8j + 4k)
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 39

3. cosθ
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 40

Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry

Question 2.
Consider the pair of lines \(\bar{r}\) = 3i + 4j – 2k + λ(-i + 2j + k) ——L1, \(\bar{r}\) = i – 7j – 2k + µ(i + 3j + 2k) ——L2

  1. Find one point each on lines L1 and L2. (1)
  2. Find the distance between those points. (2)
  3. Find the shortest distance between L1 and L2. (3)

Answer:
1. By putting λ = 0 in line L1 and µ = 0 in L2 we get the required points. L1 ⇒ \(\bar{r}\) = 3i + 4j – 2k
∴ Co-ordinate is (3, 4, -2)
L2 ⇒ \(\bar{r}\) = i – 7j – 2k
∴ Co-ordinate is (1, -7, -2).

2. Distance between (3, 4, -2) and (1, -7, -2)
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 41

3. Let L1 ⇒ \(\bar{r}\) = 3i + 4j – 2k + λ(-i + 2j + k) is of the form \(\bar{r}=\overline{a_{1}}+\lambda \overline{b_{1}}\) where
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 42

Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry

Question 3.
Consider the points A (2, 2, -1), B (3, 4, 2) and C (7, 0, 6).

  1. Are A, B, and C collinear? Explain.
  2. Find the vector and Cartesian equation of the plane passing these three points. (2)
  3. Find the angle between the above plane and the line \(\bar{r}\) = (i + 2j – k) + λ(i – j + k) (2)

Answer:
1. Direction ratios along A and B is 3 -2, 4 -2, 2 + 1 ⇒ 1, 2, 3
Direction ratios along B and C is
7 -3, 0 -4, 6 -2 ⇒ 4, -4, 4
Since the direction ratios are not proportional they are not collinear.

2. Cartesian equation of the Plane is
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 43
⇒ (x – 2)(14 + 6) -(y – 2)(7 – 15) + (z + 1)(-2 -10) = 0
⇒ 20(x – 2) + 8(y – 2) – 12(z + 1) = 0
⇒ 20x – 40 + 8y – 16 – 12z – 12 = 0
⇒ 20x + 8y – 12z = 68
⇒ 5x + 2y – 3z = 17
Vector Equation is \(\bar{r}\).(5i + 2j – 3k) = 17.

3. Angle between the Plane and the Line
\(\bar{r}\) = (i + 2j – k) + λ(i – j + k)
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 44

Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry

Question 4.
Consider three points on space ( 2, 1, 0 ), (3, -2, -2)and(3, 1, 7)

  1. Find the Cartesian equation of the plane passing through the above points. (2)
  2. Convert the above equation into vector form.
  3. Hence, find a unit vector perpendicular to the above plane and also find the perpendicular distance of the plane from the origin. (2)

Answer:
1. Equation of the plane is
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 45
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 46
⇒ (x – 2)(-21) – (y – 1)(7 + 2) + z(0 + 3) = 0
⇒ 21x + 42 – 9y + 9 + 3z = 0 ⇒ -21x – 9y + 3z + 51 = 0
⇒ 7x + 3y – z = 17.

2. Vector form is \(\bar{r}\).(7i + 3j – k) = 17 _____(1)

3. Now, |7i + 3j – k| = \(\sqrt{49+9+1}=\sqrt{59}\)
Dividing equation (1) by \(\sqrt{59}\), we get
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 47
Therefore the above equation is the normal form of the plane. Then \(\frac{7 i+3 j-k}{\sqrt{59}}\) is the unit vector perpendicular to the plane and \(\frac{17}{\sqrt{59}}\) is the perpendicular distance from the origin.

Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry

Question 5.
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 48
\(\overline{O A}\) = i + 2j + 3k
\(\overline{O B}\) = i – 2j + 4k
\(\overline{O C}\) = 2i + 3j + k
are adjacent sides of the parallelopiped.

  1. Find the base area of the parallelopiped. (2)
    (Base determined by \(\overline{O A}\) and \(\overline{O B}\))
  2. Find the volume of the parallelopiped. (2)
  3. Find the height of the parallelopiped. (2)

Answer:
1. \(\overline{O A}\) × \(\overline{O B}\) =
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 49
= 14i – j – 4k
Base area = |l4i – j – 4k|
\(=\sqrt{196+1+16}=\sqrt{213}\)

2. Volume of the parallelopiped is
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 50
= (14i – j – 4k).(2i + 3 j + k)
= 28 – 3 – 4 = 21.

3. Height = \(\frac{\text {volume}}{\text {base area}}=\frac{21}{\sqrt{213}}\).

Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry

Question 6.

  1. Find the equation of the line passing through the point (2, 1, 0) and (3, 2, -1) (3)
  2. Find the shortest distance of the above line from the line \(\bar{r}\) = (i – j + 2k) + λ(2i + j – 3k) (3)

Answer:
1.
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 51

2.
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 52
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 53
= i(-3 + 1) – j(-3 + 2) + k(1 – 2)
= -2i + j – k
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 54

Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry

Question 7.
The equation of two lines are
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 55

  1. Find the dr’s of the given lines. (2)
  2. Find the angle between the given lines. (2)
  3. Find the equation of the line passing through (2, 1, 3) and perpendicular to the given lines. (2)

Answer:
1. The given lines are
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 56
The dr’s of (1) are 2, 2, 3 and dr’s of (2) are -3, 2, 5.

2. The angle between (1) and (2) is given by
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 57

3. Let a, b, c be the dr’s of the line perpendicular to lines (1) and (2).
∴ 2a + 2b + 3c = 0, -3a + 2b + 5c = 0
Solving by the rule of cross-multiplication, we get
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 58
∴ dr’s of the required line are 4, -19, 10 and the line passes through (2, 1, 3).
∴ Equation of the required line is
\(\frac{x-2}{4}=\frac{y-1}{-19}=\frac{z-3}{10}\).

Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three Dimensional Geometry

Question 8.

  1. Find the direction cosines of the vector 2i + 2j – k. (1)
  2. Find the distance of the point (2, 3, 4) from the plane \(\bar{r}\).(3i – 6j + 2 k) = -11. (2)
  3. Find the shortest distance between the lines \(\bar{r}\) = (2i – j – k)+ λ(3i – 5 j + 2k) an \(\bar{r}\) = (i+ 2 j + k)+ µ(i – j + k) (3)

Answer:
1. Direction ratios of the vector 2i + 2j – k is 2, 2, -1
Direction cosines of the vector 2i + 2j – k is
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 59

2. The equation of the plane in the Cartesian form is 3x – 6y + 2z + 11 = 0 . Then distance from the point (2, 3, 4) is
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 60

3. The given lines are \(\bar{r}\) = (2i – j – k) + λ(3i – 5j + 2k)
Plus Two Maths Three Dimensional Geometry 4 Mark Questions and Answers 61

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 4 Business Services

Students can Download Chapter 4 Business Services Questions and Answers, Plus One Business Studies Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examinations

Kerala Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 4 Business Services

Plus One Business Services One Mark Questions and Answers

Question 1.
Name the type of account opened in a bank with an over draft facility
Answer:
Current Account

Question 2.
DTH services are provided by
Answer:
Cellular companies

Question 3.
CWC Stands for
Answer:
Central warehousing corporation

Question 4.
Mr. James running a software development business, incur heavy expenditure for replacement of computers due to updation in technology. To avoid this expenditure he may opt for
(a) Factoring
(b) Venture capital
(c) Leasing
(d) Merchant banking
Answer:
(c) Leasing

Question 5.
Name the type of account opened in the bank with overdraft facility
Answer:
Current account

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 4 Business Services

Question 6.
Classify the following into appropriate categories SBI, Federal Bank, American Express Bank.
Answer:

  • SBI – Public Bank
  • Federal Bank – Private bank
  • American Express bank – Foreign bank

Question 7.
Which among the following helps in issue management of shares,
(a) Mutual fund
(b) Merchant banks
(c) Venture Capital
(d) Factoring
Answer:
(b) Merchant banks

Question 8.
Classify the following bank into Appropriate Categories,

  1. IDBI
  2. HDFC
  3. Axis Bank
  4. Canara Bank
  5. HSFC
  6. CITI Bank

Answer:

  1. IDBI – Private Bank
  2. HDFC – Private Bank
  3. Axis Bank – Public Bank
  4. Canara Bank – Public Bank
  5. HSFC – Private Bank
  6. CITI Bank – Foreign Bank

Question 9.
Which facility allows a current account holder to withdraw more amount than his deposit?
Answer:
Overdraft

Question 10.
Which of the following is not applicable in life insurance contract?
(a) Conditional contact
(b) Unilateral contract
(c) Indemnity contract
(d) None of the above
Answer:
(c) Indemnity contract

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 4 Business Services

Question 11.
When the same subject matter is insured with more than one insurer, it is called
Answer:
Double insurance

Question 12.
________ is a contract of insurance entered into by the insurer with another insurer to reduce the risk.
Answer:
Reinsurance

Question 13.
Rajiv insures his shop for ₹5,00,000 against fire. His shop is completely damaged by a mob attack. Rajiv claims ₹5,00,000/- from the insurance company.

  1. Will the company admit the claim of Rajiv?
  2. Which principle of insurance is applicable here?

Answer:

  1. No.
  2. Causa Proxima

Question 14.
Principle of indemnity does not apply to __________
(a) Life insurance
(b) Health insurance
(c) Fire insurance
(d) Marine insurance
Answer:
(a) Life insurance

Question. 15
I will give security against fraudulent practices of employees who deal with cash or other variables. Can you identify me? Explain its features?
Answer:
Fidelity insurance

Question 16.
Govind insures his shop for ₹6,00,000. in a fire accident. The shop incurred a loss of ₹3,00,000. But he claimed for the assured sum. Will the insurance co admit the claim in full? Identify the principle of insurance which is applicable here.
Answer:
No. Principle of indemnity

Question 17.
Life insurance is a contract of ________
Answer:
Guarantee

Question 18.
_______ principle states, the insurer step into the shoes of insured.
Answer:
Subrogation.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 4 Business Services

Question 19.
Jacob purchased a new car for ₹15,00,000 and insured it with National insurance company and Oriental Insurance Company for ₹15,00,000 each. On an accident, the car was damaged completely and he claimed compensation from both companies.

  1. Can he get compensation from both companies?
  2. Identify relevant principle of insurance.

Answer:

  1. No
  2. Principle of Contribution

Question 20.
According to _________ principle, the insured is not allowed to make any profit out of his loss.
Answer:
Indemnity

Question 21.
Rajan wants to take an insurance policy covering the risk arising from the dishonesty of employees. Which type to policy close he have to take?
Answer:
Fidelity insurance

Question 22.
__________ is a contract whereby the insurer, in consideration of premium, undertakes to compensate the insured for the loss or damage suffered due to fire.
Answer:
Fire insurance

Plus One Business Services Two Mark Questions and Answers

Question 1.
Define service and goods. (2)
Answer:
Services are those identifiable and intangible activities that provide satisfaction of wants. Goods is a physical product which can be delivered to a purchaser and involves the transfer of ownership from the seller to customer.

Question 2.
Explain various telecom services available for enhancing business. (2)
Answer:
The various types of telecom services are:

1. Cellular mobile services:
Mobile communication device including voice and non-voice messages, data services and PCO services utilising any type of network equipment within their service area.

2. Radio paging services:
It means of transmitting information to persons even when they are mobile.

3. Fixed line services:
It includes voice and non-voice messages and data services to establish linkage for long distance traffic.

4. Cable services:
Linkages and switched services within a licensed area of operation to operate media services which are essentially one way entertainment related services.

5. VSAT services (Very small Aperture Terminal):
It is a Satellite-based communication service. It offers government and business agencies a highly flexible and reliable communication solution in both urban and rural areas.

6. DTH services (Direct to Home):
It is a Satellite based media services provided by cellular companies with the help of small dish antenna and a set up box.

Question 3.
Mr. Dino is running a textile shop. He insured the shop for ₹1,00,000 against natural calamities. After this the shop was completely destroyed by fire due to electrics short circuit. He claimed for compensation. But the insurance company refused to admit the claim on the ground that the shop was insured against natural calamities. (2)

  1. Can you justify the decision of insurance company.
  2. Which principle of insurance is applicable here.

Answer:

  1. Yes.
  2. Causa proxima. It states that insurance company will admit the claim only if mishap has resulted directly by an event covered by under insurance.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 4 Business Services

Question 4.
Mr. Sabu is running a provision store. He insured the shop for ₹ 50,000 against fire. One day during course of business the shop caught fire and Mr. Sabu purposefully did not take any efforts to minimize the loss. He claimed for compensation. In this situation. (2)

  1. What will be your decision assuming that you are the officer in charge of admitting the claims for insurance company?
  2. Which principle is applicable here?

Answer:

  1. The claim can not be admitted because the insurer did not take any reasonable steps to minimize the loss.
  2. Principle of mitigation of loss

Question 5.
Why do we say that the principle of indemnity is not applicable to life insurance. Illustrate your answer. (2)
Answer:
The loss due to death of the insured cannot be measured in terms of money. So principle of indemnity is not applicable to Life insurance.

Question 6.
Mr. Sibi purchased a new car and it was completely damaged in an accident. Subsequently, he lodged a claim with the insurance company and the same was admitted. Later, the insurance company recovered the destroyed property. (2)

  1. Why did the company take ownership of the car?
  2. State the relevant principle. Explain.

Answer:

  1. Ownership of the damaged car is vested with the insurance company.
  2. According to the principle of subrogation, once the claim of the insured has been settled, the right of ownership of such property passes to .the insurer.

Question 7.
Mr. Anand your friend has started a new business. He decided to open a bank account with SBI. He has only a vague idea about the type of accounts available to the business people. So he seeks your help to choose the most favourable account for him. Give reason. (2)
Answer:
Mr. Anand can open current account. There is no restriction on the frequency and volume of deposits or withdrawals of money.

Question 8.
Match the following

AB
WarehousingMutual Funds
Unit Trust Of IndiaHindrance Of Time
InsuranceExternal Comunication
TelecomCausa proxima

Answer:

AB
WarehousingHindrance Of Time
Unit Trust Of IndiaMutual Funds
InsuranceCausa proxima
TelecomExternal Comunication

Plus One Business Services Three Mark Questions and Answers

Question 1.
Mr. Janardhanan, a business man, has a current a/c of ₹1,00,000 in the S.B.I. He is in need of another ₹50,000 for the purpose of expansion of his business. By availing which facility, can he have money from the bank? Explain its features. (3)
Answer:
Overdraft: Overdraft is an arrangement where customers are allowed to withdraw up to a level over and above their deposits in the current account. Interest is to be paid only on the actual amount of overdraft availed by him. OD is granted to businessmen against their current account.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 4 Business Services

Question 2.
Write a detailed note on various facilities offered by Indian Postal Department. (3)
Answer:
1. Postal services:
Indian post and telegraph department provides various postal services across India. Various facilities provided by postal department are
(a) Financial facilities:
They provide postal banking facilities to the general public and mobilise their savings through the saving schemes like public provident fund (PPF), Kisan Vikas Patra, National Saving Certificate, Recurring Deposit Scheme and Money Order facility

(b) Mail facilities:
1. Mail services consist of

  • Parcel facilities that is trans-mission of articles from one place to another
  • Registration facility to provide security of the transmitted articles
  •  Insurance facility to provide insurance cover for all risks in the course of transmission by post.

2. Allied Postal Services

  • Greetings Post: Greetings card can be sent through post offices.
  •  Media Post: Corporate can advertise their brands through post cards, envelops etc.
  •  Speed Post: It allows speedy transmission of articles to people in specified cities.
  •  e-bill post: The post offices collect payment of telephone, electricity, and water bills from the consumers.
  •  Courier Services: Letters, documents, parcels etc. can be sent through the courier service.

(2) Telecom Services:
The various types of telecom services are:

1. Cellular mobile services:
Mobile communication device including voice and non-voice messages, data services and PCO services utilising any type of network equipment within their service area.

2. Radio paging services:
It means of transmitting information to persons even when they are mobile.

3. Fixed line services:
It includes voice and non-voice messages and data services to establish linkage for long distance traffic.

4. Cable services:
Linkages and switched services within a licensed area of operation to operate media services which are essentially one way entertainment related services.

5. VSAT services (Very small Aperture Terminal):
It is a Satellite based communication service. It offers government and business agencies a highly flexible and reliable communication solution in both urban and rural areas.

6. DTH services (Direct to Home):
It is a Satellite based media services provided by cellular companies with the help of small dish antenna and a set up box.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 4 Business Services

Question 3.
What is e-banking? What are the advantages of e-banking? (3)
Answer:]
e-banking is a service provided by many banks, that allows a customer to conduct banking transactions, such as managing savings, checking accounts, applying for loans or paying bills over the internet using a personal computer, mobile telephone. Eg. Electronic Fund Transfer (EFT), ATM etc.

Question 4.
Babu insures his shop for ₹3,00,000. In a fire accident the shop burned and incurred a loss of ₹1,50,000. Babu claimed for the assured sum i.e, ₹3,00,000. (3)

  1. Will the insurance company admit the claim in full. Why?
  2. Which principle of insurance is applicable here.

Answer:

  1. No. According to the principle of indemnity, in the event of occurrence of loss, the insured will be indemnified to the extent of actual value of his loss or the sum insured which ever is less,
  2. Principle of Indemnity

Question 5.
Mrs. Anjali has a medical shop and it is insured with two insurers for ₹50,000 each against natural calamities. During the rainy season, the subject matter was partly destroyed by flood. The total amount of loss was estimated at ? 30,000. She claimed compensation from both insurance companies for ₹30,000 each. (3)

  1. Can she get the claim from both the insurers?
  2. Justify your answer with regard to the relevant principle of insurance.

Answer:

  1. No. She cannot get claim from both the insurance.
  2. According to the principle of contribution, the insured is eligible to receive a claim only up to the amount of actual loss suffered by her.

Question 6.
Mr. Joy keep stock of inflammable materials in his shop premises, takes an insurance policy for the shop against fire. But he did not disclose anything about the inflammable materials to the insurance company. Later, the inflammable goods caught fire and the shop was completely destroyed by fire. The insurance company refused to admit the claim of Mr. Joy on the ground that he did not disclose information about the inflammable goods. (3)

  1. Can you justify the decision of the insurance company?
  2. What principle of insurance is applicable here ?

Answer:

  1. Yes.
  2. Principle of utmost good faith. The insured must disclose all material facts about the subject matter to the insurer. Otherwise the insurer can cancel the contract. The insurer must disclose all the terms and conditions in the insurance contract to the insured.

Plus One Business Services Four Mark Questions and Answers

Question 1.
Mr. Surendran is running an electrical shop which is insured against fire for ₹50,000. Due to heavy rainfall his stock was fully damaged and he claimed for compensation. The insurance company refused to admit the claim as goods were not insured against natural calamities. Can you justify the decision of the insurance company? Which principle of insurance is applicable here? (4)
Answer:
Yes. The decision taken by the insurance company is correct. Mr. Surendran has no right to claim compensation from the insurance company. The principle of insurance applicable here is causa proxima. It states that insurance company will admit the claim only if the mishap has resulted directly by an event covered under the insurance. An event covered under the insurance.

Question 2.
Draw a chart showing types of insurance. (4)
Answer:
Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 4 Business Services 1

Question 3.
Explain the functions of Transport. (4)
Answer:
Functions of Transport:

  1. Helps in the movement of goods and materials from one place to another
  2. Helps in the stabilisation of prices.
  3. Helps in the social, economic and cultural development of the country
  4. Helps in national and international trade
  5. Facilitates large scale production
  6. Generates employment opportunities
  7. Increases growth of towns and cities
  8. Connects all part of the world

Plus One Business Services Five Mark Questions and Answers

Question 1.
Explain the functions of warehousing. (5)
Answer:
Functions of Warehousing:

  1. Warehouse helps in supplying the goods to the customers when it is needed.
  2. By maintaining a balance of supply of goods warehousing leads to price stabilization.
  3. By keeping the goods in the warehouse, the trader can relieve himself of the responsibility of keeping of goods.
  4. The warehouse performs the function of dividing the bulk quantity of goods into smaller quantities.
  5. Warehousing helps in the seasonal storage of goods to select businesses.
  6. The functions of grading, branding and packing of goods can be done in warehouses.
  7. The warehousing receipt can be used as a collateral security for obtaining loans.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 4 Business Services

Question 2.
Name the principle of insurance violated in the following cases. (5)

1. ‘A’does not own the building but is trying to get it insured as a party to the insurance policy.

2.  ‘A’ enters into life insurance contract with LIC of India. ‘A’ was ailing with heart decease but he did not reveal this at the time of entering the contract. ‘

3. ‘B’ enters into insurance contract with two companies ‘C’ and ‘D’. The subject matter is a building worth ₹ 5 lakh. The building caught fire and properties worth ₹3 lakhs were damaged. ‘C’ paid the entire claim and asked ‘D’ to share the claim. ‘D’ denies.

4. Goods worth ₹50,000 are damaged and the insurance company pays the claim to ‘Z’ for the loss. ‘Z’ not only took the compensation for loss but also claims the damaged goods.

5. ‘P’ takes an insurance policy for ₹1 lakh with ‘Q’ company. The goods of ‘P’ are damaged due to fire the loss incurred is ₹25,000. ‘Q’ shall restore the actual loss but ‘P’ claims full amount of the policy.

Answer:

  1. Principle of insurable interest
  2. Principle of utmost good faith
  3. Principle of contribution
  4. Principle of subrogation
  5. Principle of Indemnity

Question 3.
Match A with B and C.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 4 Business Services 2

Answer:

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 4 Business Services 3

Plus One Business Services Six Mark Questions and Answers

Question 1.
Distinguish between life insurance and general insurance. (6)
Answer:

Life InsuranceFire insuranceMarine Insurance
The subject matter of insurance is human lifeThe subject matter is any asset.The subject matter is a ship, cargo or freight.
it has the elements of protection and investmentIt has only the element of ProtectionIt has only the element of Protection.
insurable interest exists at the time of contract alone.Insurable interest exists at the time of contract and at the time of loss.Insurable interest exists at the time of contract
Period of coverage is long periodPeriod of coverage is up to one yearMarine insurance policy is for one or period of voyage or mixed.
Life insurance is not a contract of indemnityFie insurance is a contract of indemnity.Marine insurance is a contract of indemnity
Loss Is not measurable.Loss is measurabie.Loss is measurable.
Surrender of policy is possibleSurrender of policy is not possibleSurrender of policy is not possible
One can insure for any amount in life insurance.The amount of the policy cannot be more than the value of the subject matter.The amount of the policy can be the market value of the ship or cargo.
It is contract of assuranceIt is contract of insuranceIt is contract of insurance

Question 2.
I will give security against fraudulent practices of employees who deal with cash or other valuables

  1. Can you identify me?
  2. Explain my features. (6)

Answer:
1. Fidelity insurance.

2. This type of policy is taken by the employer of a fire to cover the risk arising out of fraud or dishonesty of his employees. Banks, Financial institutions and other business firms commonly use such insurance policies.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 4 Business Services

Question 3.
What are services? Explain their distinct characteristics? (6)
Answer:
Nature of Services
1. Intangibility:
Services are intangible, i.e., they cannot be touched. They are experiential in nature, e.g. Treatment by a doctor.

2. Inconsistency:
Since there is no tangible product, services have to be performed according to the demand and expectations of the different customers, e.g. Mobile services/Beauty parlour.

3. Inseparability:
Another important characteristic of services is the simultaneous activity of production and consumption being performed, i.e. They are inseparable, e.g. ATM may replace clerk but presence of customer is a must.

4. Less Inventory:
Services cannot be stored for future use.

5. Involvement:
Participation of the customer in the service delivery is a must.

Plus One Business Services Eight Mark Questions and Answers

Question 1.
Suppose you have visited a commercial bank in your locality. Then what information you have collected from there with regard to. (8)

  1. Deposit schemes
  2. Lending scheme
  3. Other services

Answer:
Functions of Commercial Banks:
a. Acceptance of deposits:
A commercial bank accepts following types of deposits. They are

1. Current deposit:
This type of account is usually opened by business men.lt carries no interest. There are no restrictions on number of deposits or withdrawals.

2. Savings deposit:
Savings accounts are for encouraging savings by individuals. Banks pay rate of interest as decided by RBI on these deposits. Withdrawal from these accounts has some restrictions.

3. Fixed deposit:
Fixed accounts are time deposits with higher rate of interest. They cannot be withdrawn before the maturity period.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 4 Business Services

b. Lending of funds:
The second important function of a commercial bank is to grant loans and advances out of the money received through deposits. These advances can be made in the form of overdrafts, cash credits, discounting trade bills, term loans, consumer credits and other miscellaneous advances.
1. Cash Credit:
Under this arrangement, the bank advances loan up to a specified limit against current assets. The bank opens an account in the name of the borrower and allows him to withdraw the money up to the sanctioned limit. Interest is charged on the amount actually withdraw.

2. Bank Overdraft:
Overdraft is an arrangement where customers are allowed to withdraw up to a level over and above their deposits in the current account. Interest is to be paid only on the actual amount of overdraft availed by him. OD is granted to businessmen against their current account.

3. Discounting of bill of exchange:
Under this, a bank gives money to its customers on the security of a bill of exchange before the expiry of the bill after deducting a small amount of discount.

4. Term Loans:
These loans are provided by the banks to their customers for a fixed period. Interest will be charged to the entire amount of loan.

c. Secondary Functions:
The secondary functions of commercial banks are as under:
1. Agency Functions:

  • Cheque facility: Bank collects customers cheque drawn on other bank. There are two types of cheques mainly
    Bearer cheques, which are encashable immediately at bank counters Crossed cheques which are to be deposited only in the payees account.
  • Payment of insurance premium, telephone charges, collection of dividend etc
  • Purchase and sale of shares and debentures
  • Acting as trustees or executors
  • Providing credit information

2. General utility services:

  • Providing lockers for safe custody of jewellery and others valuables of customers
  • Issuing letter of credit, pay orders, bank draft, credit cards, traveller’s cheques to customers.
  • Underwriting issues of shares and debentures
  • Providing foreign exchange to importers and traveller’s going abroad.

Bank Draft:
It is a financial instrument with the help of which money can be remitted from one place to another. The payee can present the draft on the drawee bank at his place and collect the money. Bank charges some commission for issuing a bank draft.

Pay Order:
It is almost like a bank draft. Banks issue pay order for local purpose and issue bank draft for outstations.

Question 2.
“For the smooth conducting of insurance the insurer and Insured should know the relevant factors underlying the insurance contracts.” In the light of this statement, can you state the principles of Insurance?
Answer:

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 4 Business Services 3

1. Utmost good faith:
The insured must disclose all material facts about the subject matter to the insured. Otherwise the insurer can cancel the contract. The insurer must disclose all the terms and conditions jn the insurance contract to the insured.

2. Insurable interest:
The insured must have an insurable interest in the subject matter of insurance. Insurable interest means the interest shown by the insured in the continued existence of the subject matter or the financial loss he is subjected to on the happening of an event against which it has been insured.

3. Indemnity:
All insurance contracts, except life insurance are contracts of indemnity. According to the principle of indemnity, in the event of occurrence of loss, the insured will be indemnified to the extent of the actual value of his loss or the sum insured which ever is less. The objective behind this principle is nobody should treat insurance contract as the source of profit.

4. Subrogation:
According to this principle, after the insured is compensated for the loss to the property insured by him the right of ownership of such property passes on to the insurer. This is because the insured should not be allowed to make any profit, by selling the damaged property.

5. Causa proxima:
When the loss is the result of two or more causes, the proximate cause for the loss alone will be considered by the insurance company for admitting the claim.

6. Contribution:
In certain cases, the same subject matter is insured with one or more insurer. In case there is a loss, the insured is eligible to receive a claim only up to the amount of actual loss suffered by him.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 4 Business Services

7. Mitigation of loss:
This principle states that it is the duty of the insured to take reasonable steps to minimize the loss or damage to the insured property. If reasonable care is not taken then the claim from the insurance company may be rejected.

Question 3.
Prepare a seminar paper on Types of warehouses. (8)
Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 4 Business Services 5
Answer:
Warehousing:
Warehousing means holding or preserving goods in huge quantities from the time of their purchase or production till their consumption. Warehousing is one of the important auxiliaries to trade. It creates time utility by bridging the time gap between production and consumption of goods.
Functions of Warehousing:

  • Warehouse helps in supplying the goods to the customers when it is needed.
  • By maintaining a balance of supply of goods warehousing leads to price stabilization.
  • By keeping the goods in the warehouse, the trader can relieve himself of the responsibility of keeping of goods.
  • The warehouse performs the function of dividing the bulk quantity of goods into smaller quantities.
  • Warehousing helps in the seasonal storage of goods to select businesses.
  • The functions of grading, branding and packing of goods can be done in warehouses.
  • The warehousing receipt can be used as a collateral security for obtaining loans.

Types of Warehouses:
Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 4 Business Services 5
1. Private warehouses:
Private warehouses are owned by big business concerns or wholesalers for keeping their own products.

2. Public warehouses:
They are owned by some agencies, offer storage facilities to the public after charging certain fees. The working of public warehouses is subject to some govt, regulations. They are also known as Duty paid warehouses.

3. Bonded warehouses:
These warehouses are used to keep the imported goods before the payment of import duties. It offers many advantages to the importer, i.e. The importer can releases the goods in part by paying the proportionate amount of duty. The goods can be branded, blended and packed in the warehouse itself.

4. Government warehouses:
These warehouses are fully owned and managed by the government. For example, Food Corporation of India, State Trading Corporation, and Central Warehousing Corporation.

5. Co-operative warehouses:
Marketing co operative societies and agricultural oo operative societies have set up their own warehouses for members of their cooperative society.

Plus One Economics Chapter Wise Questions and Answers Chapter 2 Collection of Data

Students can Download Chapter 2 Collection of Data Questions and Answers, Plus One Economics Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examinations

Kerala Plus One Economics Chapter Wise Questions and Answers Chapter 2 Collection of Data

Plus One Economics Collection of Data One Mark Questions and Answers

Question 1.
Which among the following is a method of primary data collection?
(i) Direct personal interview
(ii) Telephonic interview
(iii) Mailed questionnaire method
(iv) All the above
Answer:
(iv) All the above

Question 2.
Identify the random sampling method from the following.
(i) Judgment sampling
(ii) Stratified sampling
(iii) Convenience sampling
(iv) Quota sampling
Answer:
(ii) Stratified sampling

Question 3.
Which among the following is a source of secondary data?
(i) CSO
(ii) NSSO
(iii) RGI
(iv) All the above
Answer:
(iv) All the above

Plus One Economics Chapter Wise Questions and Answers Chapter 2 Collection of Data

Question 4.
Identify an advantage of sample method.
(i) Less time consuming
(ii) Less cost is needed
(iii) Gives more reliable information
(iv) All the above
Answer:
(iv) All the above

Question 5.
Name the different types of data.
Answer:
Primary data and secondary data

Plus One Economics Collection of Data Two Mark Questions and Answers

Question 1.
Differentiate between census survey and sample survey.
Answer:
Under census method, we collect information from each and every unit of population relating to the problem under investigation. On the other hand, under-sample method, rather than collecting information about all the units of population, we collect information from a few selected items from population.

Question 2.
Name the two important errors related to sampling?
Answer:

  1. Sampling error.
  2. Non – sampling error.

Question 3.
Give one example of primary data and one example of secondary data.
Answer:
The price of rice collected from a shop is primary data. The price of rice collected from a daily is secondary data.

Question 4.
Do samples provide better results than surveys? Give reasons for your answer.
Answer:
In sample method, we take part of the information. A small number of trained investigators can collect complete data. This information is reliable. In the case of doubt, enquiries can be undertaken for verification. Follow up is made easy in this case. In survey many difficulties are faced when the universe is very large. A large number of investigators are required in surveys. In case of doubts, it is difficult to undertake the enquiry again for verification.

Question 5.
List out the different steps involved in planning the survey.
Answer:

  1. Purpose of the survey
  2. Scope of the survey
  3. Unit of data collection
  4. Sources of data
  5. Technique of data collection
  6. Choice of the frame
  7. Degree of accuracy needed
  8. Miscellaneous considerations

Question 6.
Point out the advantages of sample method over census method?
Answer:
The advantages of sample method over census method are:

  1. Less time consuming
  2. Less cost is needed,
  3. Gives more reliable information
  4. Gives more detailed information.

Plus One Economics Chapter Wise Questions and Answers Chapter 2 Collection of Data

Question 7.
Suppose you want to select 50 households from a total of 5100 households by giving equal opportunity to all the units. Which method you would prefer for this purpose? Substantiate.
Answer:
Simple random sampling is appropriate for this purpose. It refers to that technique in which each and every unit of population has an equal opportunity of being selected in the sample. The selection depends purely on chance. Random samples may be selected by lottery method.

Plus One Economics Collection of Data Three Mark Questions and Answers

Question 1.
What are the advantages of mailed questionnaire method?
Answer:
Advantages of mailed questionnaire method are the following.

  • Least expensive
  • The only method to reach remote areas
  • No influence on respondents
  • Better for sensitive questions

Question 2.
How the non-sampling errors can be controlled?
Answer:
Sampling errors can be controlled by taking the following steps.

  1. Sample should be selected with care.
  2. Scientific methods of data collection should be used.
  3. The investigator should be well trained.
  4. A test check should be done.

Question 3.
List out the errors you would expect in the field survey by census method?
Answer:
Some of the errors expected in the field survey by census method are:

  1. Errors of measurement
  2. Errors due to mishandling of the questionnaire
  3. Recording mistakes
  4. Errors of non-response
  5. Arithmetic errors

Question 4.
Suppose the Wayanad district Panchayat wants to study the literacy of tribal population in the district.

  1. Which method would you suggest for data collection? Why?
  2. Give a popular instance Is this method suitable in all cases? If not, what are the drawbacks.

Answer:
1. I would suggest census method of data collection to the panchayat authorities in this situation. In this method, we get reliable information from all units of the population for which the study is conducted.

2. A popular instance where this method is used is population census conducted ever 10 years.

3. It is not suitable in all cases because there are some drawbacks – the effort, money and time required will be very high.

Question 5.
Give two examples each of sample, population and variable.
Answer:
1. Examples each of samples:

  • A representative group of few individuals taken form a particular locality to study the impact of rise in prices of petroleum products
  • A group of students from the school is selected to study average monthly expenditure

2. Examples each of population:

  • All individuals residing in a particular locality about . whom the information is to be collected
  • All students in a school for whom the information is to be collected.

3. Examples of each of variables:

  • Changing price of petrol
  • Increase or decrease in the production of rice.

Question 6.
List the demerits of telephone interviews.
Answer:
Demerits of telephone interview are:

  • Reactions cannot be watched
  • Limited use
  • Possibility of influencing respondents.

Plus One Economics Chapter Wise Questions and Answers Chapter 2 Collection of Data

Question 7.
Point out the precautions to be taken while using secondary data?
Answer:
While using secondary data it should be ensured that the following precautions are taken

  1. Ability of the collecting organisation
  2. Objective and scope of investigation
  3. Method of collection of secondary data
  4. Time and conditions of collection of data Definition of the unit, and
  5. Accuracy of the data

Question 8.
Point out the advantages of conducting pilot survey.
Answer:
Once the questionnaire is ready, it is advisable to conduct a try out with a small group which is known as Pilot Survey or PreTesting of the questionnaire. The pilot survey helps the investigator in the following ways.

  • The pilot survey helps in providing a preliminary idea about the survey.
  • It helps in pretesting of the questionnaire, so as to know the shortcomings and drawbacks of the questions.
  • Pilot survey also helps in assessing the suitability of questions, clarity of instructions, performance of enumerators and the cost and time involved in the actual survey

Question 9.
Explain the procedure of selecting a random sample of 3 students out of 10 in your class by using random number table.
Answer:
The procedures of selecting a random sample of 3 students out of 10 are as follows

  1. Prepare 10 slips of paper of identical size and shape
  2. Write the names of students on the slips
  3. Place the slips in a box and mix them properly
  4. Draw three slips without looking into the box
  5. The students, whose names appear on the slips drawn, constitute the required random sample.

Question 10.
Mention the important sources of collecting secondary data.
Answer:
The main sources of secondary data can be classified into two. They are:
A. Published sources

  • Government publications
  • Semi government publications
  • International publications
  • Private publications
  • Research publications

B. Unpublished sources

  • Studies made by scholars
  • Studies of various institutions

Question 11.
Prepare a note on NSSO?
Answer:
The National Sample Survey Organisation was established by the Government of India to conduct nationwide surveys on socioeconomic issues. The data collected by NSSO surveys on different socioeconomic subjects are released through reports and its quarterly journal Sarvekshana.

NSSO provides periodic estimates of literacy, school enrolment, utilisaiton of educational services, employment, unemployment, manufacturing and service sector enterprises, morbidity, maternity, child care, utilisation of the public distribution system, etc.

The NSSO also undertakes the fieldwork of annual surveys of industries, conducts crop estimation surveys, collects rural and urban retail prices for complication of consumer price index numbers.

Plus One Economics Chapter Wise Questions and Answers Chapter 2 Collection of Data

Question 12.
“Non-sampling errors are more serious than sampling errors”. Do you agree? Mention the possible nonsampling errors occur in sampling.
Answer:
Yes, I agree with the statement that non-sampling errors are more serious than sampling errors because a sampling error can be minimized by taking a larger sample. It is difficult to minimize non-sampling error, even by taking a large sample. Even a Census can contain nonsampling errors.
Some of the non-sampling errors are:
1. Errors in Data Acquisition:
This type of error arises from recording of incorrect responses. Suppose, the teacher asks the students to measure the length of the teacher’s table in the classroom. The measurement by the students may differ. The differences may occur due to differences in measuring tape, carelessness of the students, etc.

2. Non-Response Errors:
Non-response occurs if an interviewers unable to contact a person listed in the sample or a person from the sample refuses to respond. In this case, the sample observation may not be representative.

3. Sampling Bias:
Sampling bias occurs when the sampling plan is such that some members of the target population could riot possibly be included in the sample.

Plus One Economics Collection of Data Four Mark Questions and Answers

Question 1.
Prepare a chart showing different methods of sampling.
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 2 Collection of Data img1

Question 2.
Give the advantages of direct personal interview.
Answer:
Advantages of direct personal interview.

  • Highest response rate
  • Allows use of all types of questions
  • Allow clarification of ambiguous questions
  • Better for using open ended questions

Question 3.
“Certain principles should be kept in mind while drafting a questionnaire” explain.
Answer:
The principles that are to be kept in mind while drafting a questionnaire are given below.

1. The questionnaire should not be too long. The number of questions should be as minimum as possible. Long questionnaires discourage people from completing them.

2. The series of questions should move from general to specific. The questionnaire should start from general questions and proceed to more specific ones.

3. The questions should be precise and clear.

4. The questions should not be ambiguous, to enable the respondents to answer quickly, correctly and clearly.

5. The question should not use double negatives. The questions starting with “Wouldn’t you” or “Don’t you” should be avoided, as they may lead to biased responses.

6. The question should not be a leading question, which gives a clue about how the respondent should answer.

7. The question should not indicate alternatives to the answer.

Plus One Economics Collection of Data Five Mark Questions and Answers

Question 1.
State true or false

  1. there are many sources of data
  2. telephone survey is the most suitable method of collecting data when their population is literate and spread over a large area
  3. data collecting by investigator is called secondary data
  4. non-sampling errors can be minimized by taking large samples
  5. there is a certain bias involved in the non-random selection of samples.

Answer:

  1. true
  2. true
  3. false
  4. false
  5. true

Plus One Economics Collection of Data Eight Mark Questions and Answers

Question 1.
Prepare a seminar report on the topic “methods of collecting primary data”
Answer:
“Methods of collecting primary data”
Introduction:
The plus one commerce batch of (Name of school) conducted a seminar on the topic “methods of collecting primary data” on 05/08/2017 at 11.0 a.m with the ample guidance of our economics teacher. Our class was divided into three groups to cover the entire area of the topic. Each group presented one objective each. They focused on the area given to them and the group leader presented the seminar paper after required preparation.

Content:
There are three basic ways of collecting data:

  1. Personal Interviews,
  2. Mailing (questionnaire) Surveys, and
  3. Telephone Interviews

1. Personal Interviews:
This method is used when the researcher has access to all the members. The researcher (or investigator) conducts face to face interviews with the respondents. Personal interviews are preferred due to various reasons. Personal contact is made between the respondent and the interviewer.

The interviewer has the opportunity of explaining the study and answering any query of the respondents. The interviewer can request the respondent to expand on answers that are particularly important. Misinterpretation and misunderstanding can be avoided.

Watching the reactions of the respondents can provide supplementary information. Personal interview has some demerits too. It is expensive, as it requires trained interviewers. It takes longer time to complete the survey.

Plus One Economics Chapter Wise Questions and Answers Chapter 2 Collection of Data

2. Mailing Questionnaire:
When the data in a survey are collected by mail, the questionnaire is sent to each individual by mail with a request to complete and return it by a given date. The advantages of this method are that it is less expensive. It allows the researcher to have access to people in remote areas too, who might be difficult to reach in person or by telephone.

It does not allow influencing of the respondents by the interviewer. It also permits the respondents to take sufficient time to give thoughtful answers to the questions. The disadvantages of mail survey are that there is less opportunity to provide assistance in clarifying instructions, so there is a possibility of misinterpretation of questions. Mailing is also likely to produce low response rates due to certain factors.

3. Telephone Interviews:
In a telephone interview, the investigator asks questions over the telephone. The advantages of telephone interviews are that they are cheaper than personal interviews and can be conducted in a shorter time. They allow the researcher to assist the respondent by clarifying the questions.

Telephone interview is better in the cases where the respondents are reluctant to answer certain questions in personal interviews. The disadvantage of this method is accessible to people, as many people may not own telephones. Telephone Interviews also obstruct visual reactions of the respondents.

Conclusion:
All the three groups presented their topics with necessary facts and figures. After the presentation, there was the question-answer session. The active participation of everyone made this session live and interesting. On the whole, the seminar was a big success.