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

Students can Download Chapter 12 Linear Programming 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 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.

Plus One Economics Chapter Wise Questions and Answers Chapter 3 Organisation of Data

Students can Download Chapter 3 Organisation 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 3 Organisation of Data

Plus One Economics Organisation of Data One Mark Questions and Answers

Question 1.
Under inclusive method ………….
(a) Upper-class limit is excluded
(b) Lower class limit is excluded
(c) Lower class limit is included
(d) None of the above
Answer:
(c) Lower class limit is included

Question 2.
Which of the following alternatives is true?
The class midpoint is equal to:
(a) The average bf the upper-class limit and the lower class limit.
(b) The product of the upper-class limit and the lower class limit.
(c) The ratio of the upper-class limit and the lower class limit.
(d) None of the above.
Answer:
(a) The average bf the upper-class limit and the lower class limit.

Question 3.
Which of the following alternatives is true?
The frequency distribution of two variables is known as ………
(a) Univariate Distribution
(b) Bivariate Distribution
(c) Multivariate Distribution
(d) None of the above
Answer:
(b) Bivariate Distribution

Question 4.
Which of the following alternatives is true?
Statistical calculations in classified data are based on …………
(a) the actual values of observations
(b) the upper-class limits
(c) the lower class limits
(d) the class midpoints
Answer:
(d) the class midpoints

Plus One Economics Chapter Wise Questions and Answers Chapter 3 Organisation of Data

Question 5.
Which of the following alternatives is true?
Under Exclusive method.
(a) the upper-class limit of a class is excluded in the class interval
(b) the upper-class limit of a class is included in the class interval
(c) the lower class limit of a class is excluded in the class interval
(d) the lower class limit of a class is included in the class interval
Answer:
(a) the upper-class limit of a class is excluded in the class interval

Question 6.
Which of the following alternatives is true?
Range is the ………….
(a) difference between the largest and the smallest observations
(b) difference between the smallest and the largest observations
(c) average of the largest and the smallest observations
(d) ratio of the largest to the smallest observation.
Answer:
(a) difference between the largest and the smallest observations

Plus One Economics Organisation of Data Two Mark Questions and Answers

Question 1.
What is classification?
Answer:
Classification of data is a technique with the help of which data is arranged into different groups or classes according to some common characteristics so as to facilitate the tabulation, analysis, and interpretation.

Question 2.
Distinguish between raw data and classified data.
Answer:
Raw data is the collected information in the form of numerical facts. It is the data collected as it is without any processing. The raw data is summurised and made comprehensible is known as classified data.

Question 3.
Distinguish between frequency table and frequency array.
Answer:
Frequency table is the classification of the data for a continuous variable. Frequency array is the classification of the data for a discrete variable.

Question 4.
Distinguish between univariate frequency distribution and bivariate frequency distribution.
Answer:
The frequency distribution of a single variable is called univariate distribution. The frequency distribution of two variables is known as bivariate frequency distribution.

Plus One Economics Chapter Wise Questions and Answers Chapter 3 Organisation of Data

Question 5.
In a city 45 families were surveyed for the number of domestic appliences they used. Prepare a frequency array based on their replies as recorded below.
1, 3, 2, 2, 2, 2, 1, 2, 2, 3, 3, 3, 3, 2, 4, 2, 7, 2, 0, 3, 1, 3, 3, 2, 3, 2, 2, 6, 1, 6, 2, 1, 5, 1, 5, 3, 4, 2, 4, 3, 4, 3
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 3 Organisation of Data img1

Question 6.
Classification of data is a function similar to that of sorting letters in a post office. Do you agree? Explain.
Answer:
Yes, I do agree with the statement that the classification of data is a function similar to that of sorting letters in a post office.

The process of arranging data in groups or classes according to similarities is technically called classification. The classification is somewhat similar to that of sorting letters in a post office. Letters collected in a post office are sorted into different lots on geographical basis.

They are then put in separate bags. Thus by classification, we are trying to make different groups with similar characteristics. Units having a common characteristic place in one class and the whole data are thus divided into a number of classes.

Question 7.
List examples of variables and attributes in your daily life.
Answer:
1. Variables

  • Height
  • Weight
  • Marks obtained in final examination
  • Cricket score

2. Attributes

  • Caste religion
  • Sex
  • Marital status
  • Educational qualification

Plus One Economics Chapter Wise Questions and Answers Chapter 3 Organisation of Data

Question 8.
There are some problems in preparing frequency distribution on the basis of class interval’. Do you agree? Justify.
Answer:
Yes, I agree.
The following problems arise in preparing frequency distribution on the basis of class interval.

  1. Number of class intervals to be formed
  2. Size of class intervals
  3. Class limits.

Plus One Economics Organisation of Data Three Mark Questions and Answers

Question 1.
Answer the following

  1. To arrange things in appropriate order and to put them into homogenous groups means ………..
  2. a variable is continuous when it can be taken within the range ……….
  3. Population refers to ……………

Answer:

  1. classification
  2. any value
  3. both frequency and cumulative frequency

Question 2.
Name the three types of series.
Answer:

  1. Individual series
  2. Discrete series
  3. Continuous series

Plus One Economics Organisation of Data Four Mark Questions and Answers

Question 1.
Can there be any advantage in classifying things?
Answer:
The advantage of classification are the following.

  • It helps in the comparison of data.
  • It helps to understand relationship among variables.
  • It makes statistical analysis easier.
  • It highlights significant features of data at a glance.

Question 2.
State the meaning and example for the following.

  1. Chronological Classification.
  2. Spatial Classification
  3. Qualitative Classification
  4. Quantitative Classification.

Answer:
1. Chronological Classification:
In Chronological classification, data are classified either in ascending or in descending order with reference to time such as years, quarters, months, weeks, etc.
Example: population of India from 1951 to 2011

2. Spatial Classification:
In Spatial Classification the data are classified with reference to geographical locations such as countries, states, cities, districts, etc.
Example: yield of wheat in different states of India.

3. Qualitative Classification:
Attributes can be classified on the basis of either the presence or the absence of a qualitative characteristic. Such a classification of data on attributes is called a Qualitative Classification.
Example: grouping of people on the basis of gender

4. Quantitative Classification:
When the collected data of such characteristics are grouped into classes, the classification is a Quantitative Classification.
Example: marks obtained by students.

Plus One Economics Chapter Wise Questions and Answers Chapter 3 Organisation of Data

Question 3.
What is variable? Distinguish between a discrete and a continuous variable.
Answer:
A simple definition of variable does not tell you how it varies. Different variables vary differently and depending on the way they vary, they are broadly classified into two types:

  1. Continuous and
  2. Discrete.

A continuous variable can take any numerical value. It may take integral values (1, 2, 3, 4,…) or fractional values(1/2, 2/3, 3/4).

Unlike a continuous variable, a discrete variable can take only certain values. Its value changes only by finite “jumps”. It “jumps” from one value to another but does not take any intermediate value between them.

Question 4.
Differentiate between exclusive method and inclusive method.
Answer:
1. exclusive method, the upper-class limit is excluded but the lower class limit of a class is included in the interval.

2. On the other hand, under the inclusive method, the upper-class limit is included in the class interval.

Plus One Economics Organisation of Data Five Mark Questions and Answers

Question 1.
Differentiate between quantitative classification and qualitative classification.
Answer:
Classification done according to quantitative varieties like marks and wages etc. is termed as quantitative classification. On the other hand, classification according to attributes like honesty and beauty is known as qualitative classification.

Question 2.
Prepare a frequency distribution by inclusive and exclusive method for the following data.
28 27 6 16 15 2 14 5 19 25 19 20 28
32 37 13 15 11 32 4 6 9 3 36 12 8
4 1 8 3 18 12 7 17 15 22 29 21 23
2 9 4 10 5 20 20 33 27 21 27 18 9
31 18 9 7 1 26 24 20
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 3 Organisation of Data img2

Plus One Economics Organisation of Data Eight Mark Questions and Answers

Question 1.
Define and illustrate the inclusive and exclusive method used in classification of data.
Answer:
1. Inclusive Method:
In comparison to the exclusive method, the Inclusive Method does not exclude the upper-class limit in a class interval. It includes the upper class in a class. Thus both class limits are parts of the class interval.
An example for inclusive method of frequency distribution is given below.
Plus One Economics Chapter Wise Questions and Answers Chapter 3 Organisation of Data img3

2. Exclusive Method:
The classes, by this method, are formed in such a way that the upper-class limit of one class equals the lower class limit of the next class. In this way, the continuity of the data is maintained. That is why this method of classification is most suitable in case of data of a continuous variable. Under the method, the upper-class limit is excluded but the lower class limit of a class is included in the interval.
An example for exclusive method of frequency distribution is given below.
Plus One Economics Chapter Wise Questions and Answers Chapter 3 Organisation of Data img4

Plus One Economics Chapter Wise Questions and Answers Chapter 1 Statistics for Economics Introduction

Students can Download Chapter 1 Statistics for Economics Introduction 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 1 Statistics for Economics Introduction

Plus One Economics Statistics for Economics Introduction One Mark Questions and Answers

Question 1.
The word statistics is used as ……………
(a) Singular
(b) Plural
(c) Both (a) and (b)
(d) None of (a) and (b)
Answer:
(c) Both (a) and (b)

Question 2.
Statistics deals with …………..
(a) Qualitative data
(b) Quantitative data
(c) Both (a) and (b)
(d) None of (a) and (b)
Answer:
(b) Quantitative data

Question 3.
The statistical method to analyze the data maybe ……….
(a) Explanatory
(b) Non-explanatory
(c) Both (a) and (b)
(d) None of (a) and (b)
Answer:
(a) Explanatory

Plus One Economics Chapter Wise Questions and Answers Chapter 1 Statistics for Economics Introduction

Question 4.
Who is known as the father of statistics?
Answer:
Grottfried Achenwale is known as the father of statistics.

Plus One Economics Statistics for Economics Introduction Two Mark Questions and Answers

Question 1.
Distinguish the singular and plural senses of statistics.
Answer:

  • singular sense statistics is the science of collecting, classifying and using statistics or a statistical fact.
  • In plural sense, it means numerical facts systematically collected or it is data.

Question 2.
Classify the following data into qualitative and quantitative.
Height, weight, marks scored in an exam, truth, honesty, beauty, credibility, income.
Answer:

  • Quantitative data: Income, height, weight, marks scored in an exam.
  • Qualitative data: Truth, honesty, beauty, credibility.

Question 3.
Mention a few examples each for quantitative and qualitative data.
Answer:
1. Quantitative data

  • height
  • weight
  • marks
  • price
  • income

Qualitative data

  • colour
  • intelligence
  • attitude
  • honesty
  • beauty

Plus One Economics Chapter Wise Questions and Answers Chapter 1 Statistics for Economics Introduction

Question 4.
Write some examples for distrust of statistics.
Answer:
Distrust of statistics means lack of confidence in statistical statements and statistical methods. Examples of such distrust are:

  • People keep blind faith in statistics. So they are not careful while accepting statistical figures.
  • People manipulate statistical data to present a wrong idea of their interest.

Plus One Economics Statistics for Economics Introduction Three Mark Questions and Answers

Question 1.
Give the limitations of statistics.
Answer:
The limitations of statistics are given below.

  • Statistical laws are true only on average.
  • Statistics can be misused.
  • Statistics deals only with quantitative data.
  • Statistical results lack mathematical accuracy.
  • Statistical facts are collected for a predetermined purpose.

Question 2.
Identify the data from the following statement.

  1. Indian economy grew at an average rate of 7% after the reforms.
  2. RBI increased the bank rate to 6.5.
  3. The percentage of people below poverty line in India is 26.

Answer:

  1. Average growth rate – 7%
  2. Bank rate – 6.5
  3. Percentage of people below poverty line – 26%

Question 3.
Mark the following statements as true or false

  1. statistics can only deal with quantitative data
  2. statistics solves economic problems
  3. statistics is of no use to economics without data.

Answer:

  1. True
  2. True
  3. True

Plus One Economics Chapter Wise Questions and Answers Chapter 1 Statistics for Economics Introduction

Question 4.
Explain how statistics is helpful in the formulation of economic planning.
Answer:
Statistics is the most important tool in economic planning. Economic planning is the best use of national resources, both in planning, without statistics is a leap in the dark. Every phase in planning, drawing a plan, execution, and review is based on statistics. The success of plan depends upon sufficient and accurate statistical data available at all the stages.

Question 5.
Make a list of economic activities found in your daily life.
Answer:
Some of the economic activities found in our daily life are:

  • Teachers teaching in the school.
  • People working in a factory.
  • Doctor treating a patient.
  • Milkman working in a dairy farm.

Question 6.
‘Statistics plays a vital role in policymaking’. Illustrate with examples.
Answer:
The government and the policymakers use statistical data to formulate suitable policies of economic development. No analysis of a problem would be possible without the availability of data on various factors underlying an economic problem. For example, if the government wants to make policy to solve the problem of unemployment and poverty, reliable data are required for it.

The number of persons who are waiting for a job, unemployed, the number of illiterate people, those living below the poverty line, etc are required. If the government wants to help the people affected by the tsunami earthquakes, the bind flu dangers then the data should be collected and put together about disaster’s cost systematically and correctly.

Modern economists include learning the basic skills involved in making useful studies for measuring poverty, how incomes are distributed, how earning opportunities are related to education, how environmental disasters affect our lives and so on.

Question 7.
Write the important functions of statistics.
Answer:
The important functions of statistics are the following:
1. It enables an economist to present economic facts in a precise and definite form that helps in proper comprehension of what is stated.

2. Statistics also helps in condensing the mass of data into a few numerical measures (such as mean, variance, etc., about which you will learn later). These numerical measures help summarize data.

3. Statistics is used in finding relationships between different economic factors. Statistics find economic relationships using data and verifies them.

4. Statistical tools are used in the prediction of future trends. The economist might be interested in predicting the changes in one economic factor due to the changes in another factor.

5. Statistical methods help formulate appropriate economic policies that solve economic problems.

Plus One Economics Chapter Wise Questions and Answers Chapter 1 Statistics for Economics Introduction

Question 8.
The knowledge of statistics is helpful in several ways. List out the beneficiaries of statistics with examples for each.
Answer:
1. The applications of statistics are so numerous and ever interesting. It can be applied to any field of study whether it be trade, sociology, medicine, etc. Its application in economics, business, research, etc are discussed below.

2. In economics variables like income, consumption, input, saving, etc. are systematically and scientifically analyzed and studied with the tools of statistics. Therefore, it is highly useful in economics.

3. With the help of statistical methods abundant quantitative information can be obtained which can help immensely in formulating suitable policies. Statistics are so important to the state that government in most countries is the biggest collector and user of statistical data.

4. There is hardly any research work today that one can complete without statistical data and statistical methods. The statistical tools are highly needed for research.

5. Thus in this respect, the knowledge of statistics is helpful to society in different ways.

Plus One Economics Statistics for Economics Introduction Four Mark Questions and Answers

Question 1.
List out examples for quantitative data and qualitative data.
Answer:
A. Some examples of quantitative data in daily life are:

  1. family income
  2. family expenditure
  3. monthly saving of a family
  4. expenditure on education
  5. expenditure on medical treatment
  6. marks scored in examination

B. Some examples of qualitative data in daily life are:

  1. nationality
  2. sex
  3. religion
  4. caste
  5. colour
  6. educational qualification

Plus One Economics Chapter Wise Questions and Answers Chapter 1 Statistics for Economics Introduction

Question 2.
Distinguish between quantitative and qualitative data.
Answer:
1. Quantitative data are those data which can be measured in numerical terms.
Eg: height, weight, etc.

2. On the other hand, qualitative data are those facts that cannot be numerically measured.
Eg: intelligence, beauty, etc.

Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra

Students can Download Chapter 10 Vector Algebra 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 10 Vector Algebra

Plus Two Maths Vector Algebra Three Mark Questions and Answers

Question 1.
Find \(\bar{a}+\bar{b}, \bar{a}-\bar{b}\) and \(\bar{b}+\bar{c}\) using the vectors.
\(\bar{a}\) = 3i + 4j + k, \(\bar{b}\) = 2i – 7 j – 3k and \(\bar{c}\) = 2i + 3j – 9k.
Answer:
\(\bar{a}+\bar{b}\) = 3i + 4j + k + 2i – 7j – 3k = 5i – 3j – 2k
\(\bar{a}-\bar{b}\) = 3i + 4j + k – (2i – 7j -3k) = i + 11j + 4k
\(\bar{b}+\bar{c}\) = 2i – 7j -3k + 2i +3j – 9k
= 4i – 4j – 12k.

Question 2.

  1. Find the vector passing through the point A( 1, 2, -3) and B(-1, -2, 1).
  2. Find the direction cosines along AB.

Answer:
1. \(\overline{A B}\) = \(\overline{O B}\) – \(\overline{O A}\) = -i – 2j + k – (i + 2j – 3k) = -2i – 4j + 4k.

2. Unit Vector
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 1
Direction cosines are \(\frac{-2}{6}\), \(\frac{-4}{6}\), \(\frac{4}{6}\).

Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra

Question 3.
Show that the points A, B and C with position vectors \(\bar{a}\) = 3i – 4j – 4k, \(\bar{b}\) = 2i – j + k and \(\bar{c}\) = i – 3j – 5k respectively from the vertices of a right angled triangle.
Answer:
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 2
41 = 35 + 6 ⇒ BC2 = AB2 + CA2
Hence right angled triangle.

Question 4.
Prove that \([\bar{a}+\bar{b} \bar{b}+\bar{c} \bar{c}+\bar{a}]=2[\bar{a} \bar{b} \bar{c}]\).
Answer:
LHS
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 3
Note: If \(\bar{a}\), \(\bar{b}\), \(\bar{c}\) are coplanar then so is \([\bar{a}+\bar{b} \bar{b}+\bar{c} \bar{c}+\bar{a}]\).

Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra

Question 5.
Consider the vector \(\bar{p}\) = 2i – j + k. Find two vectors \(\bar{q}\) and \(\bar{r}\) such that \(\bar{p}\), \(\bar{q}\) and \(\bar{r}\) are mutually perpendicular.
Answer:
Find a vector \(\bar{q}\) such that \(\bar{p} \cdot \bar{q}\) = 0, for this use any \(\bar{q}\) whose two components are randomly selected. Let \(\bar{q}\) = 2i + 2j + xk
\(\bar{p} \cdot \bar{q}\) = (2i – j + k) . (2i + 2 j + xk) = 0
⇒ 4 – 2 + x = 0 ⇒ x = -2
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 4
= 6j + 6k.

Question 6.
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 5
Answer:
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 6
= i(-12 + 7) – j(-9 – 2) + k(-21 – 8)
= -5i + 11j – 29k
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 7
= i(63 + 9) – j(-18 + 6) + k(6 – 14)
= 72i + 12 j – 8k.

Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra

Question 7.
If \(\bar{a}\) = 3i + j + 2k,
(i) Find the magnitude of \(\bar{a}\). (1)
(ii) If the projection of \(\bar{a}\) on another vector \(\bar{b}\) is \(\sqrt{14}\), which among the following could be \(\bar{b}\) ? (1)
(a) i + j + k
(b) 6i + 2j + 4k
(c) 3i – j + 2k
(d) 2i + 3j + k
(iii) If \(\bar{a}\) makes an angle 60° with a vector \(\bar{c}\), find the projection of \(\bar{a}\) on \(\bar{c}\) (1)
Answer:
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 8

(ii) Since projection of \(\bar{a}\) on another vector \(\bar{b}\) and magnitude of \(\bar{a}\) is \(\sqrt{14}\), then \(\bar{a}\) and \(\bar{b}\) are parallel, (b) 6i + 2j + 4k.

(iii) Projection of \(\bar{a}\) on \(\bar{c}\)
= |\(\bar{a}\)|cos60° = \(\sqrt{14}\) × \(\frac{1}{2}\) = \(\frac{\sqrt{14}}{2}\).

Question 8.
(i) The projection of the vector 2i + 3j + 2k on the vector i + j + k is (1)
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 9
(ii) Find the area of a parallelogram whose adjacent sides are the vectors 2i + j + k and 6i – j (2)
Answer:
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 10

(ii) Let \(\bar{a}\) = 2i + j + k, \(\bar{b}\) = i – j
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 11
= i(0 + 1) – j(0 – 1) + k(-2 – 1 ) = i + j -3k
Area =
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 12

Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra

Question 9.
(i) The angle between the vectors i + j and j + k is (1)
(a) 60°
(b) 30°
(c) 45°
(d) 90°
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 13
Answer:
(i) (a) 60°

Plus Two Maths Vector Algebra 3 Mark Questions and Answers 14

Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra

Question 10.
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 15
Answer:
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 16

(ii) Given, \(\bar{a}\) + \(\bar{b}\) + \(\bar{a}\) = \(\bar{0}\), squaring both sides we get
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 17

Plus Two Maths Vector Algebra Four Mark Questions and Answers

Question 1.
Let A (2, 3), B (1, 4), C (0, -2) and D (x, y) are vertices of a parallelogram ABCD.

  1. Write the position vectors A, B, C and D. (2)
  2. Find the value of x and y. (2)

Answer:
1. Position vector of A = 2i + 3 j
Position vector of B = i + 4j
Position vector of C = 0i – 2j
Position vector of D = xi + yj.

2. Since ABCD is a parallelogram, then
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 18
(1) ⇒ -i + j = -xi – (y + 2 )j
x = 1, -2 – y = 1 ⇒ y = -3
∴ D is (1, -3).

Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra

Question 2.
Find the position vector of a point R which divides the line joining the two points P and Q whose vectors i + 2j – k and -i + j + k in the ratio 2:1

  1. internally and
  2. externally.

Answer:
\(\overline{O P}\) = i + 2j – k, \(\overline{O Q}\) = -i + j + k
Let R be the position vector of the dividing point,
1.
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 19

2.
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 20

Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra

Question 3.
(i) Choose the correct answer from the bracket. If a unit vector \(\widehat{a}\) makes angles \(\frac{\pi}{4}\) with i and \(\frac{\pi}{3}\) with j and acute angle θ with k. then θ is
(a) \(\frac{\pi}{6}\),
(b) \(\frac{\pi}{4}\),
(c) \(\frac{\pi}{3}\),
(d) \(\frac{\pi}{2}\) (1)
(ii) Find a unit vector \(\widehat{a}\) (1)
(iii) Write down a unit vector in XY plane, making an angle 60°of with the positive direction of x – axis. (2)
Answer:
(i) (c), Since I = cos\(\frac{\pi}{4}\) = \(\frac{1}{\sqrt{2}}\), m = cos\(\frac{\pi}{3}\) = 1/2;
n = cos θ
l2 + m2 + n2 = 1
n2 = 1 – (\(\frac{1}{2}\))2 – (\(\frac{1}{\sqrt{2}}\))2 = 1/4
n = \(\frac{1}{2}\), cosθ = 1/2 , θ = \(\frac{\pi}{3}\).

(ii)
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 21
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 22

Question 4.
Let the vectors \(\bar{a}\), \(\bar{b}\), \(\bar{c}\) denoted the sides of a triangle ABC.
(i) Prove that (2)
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 23
(ii) Find the projection of the vector i + 3j + 7k on the vector 7i – j + 8k (2)
Answer:
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 24

(ii) Projection of the vector i + 3j + 7k on the vector 7i – j + 8k
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 25

Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra

Question 5.
(i) If \(\bar{a}\) and \(\bar{b}\) are any two vectors, then axb is (1)
(a) a vector on the same plane where \(\bar{a}\) and \(\bar{b}\) lie.
(b) ab cosθ, if θ is the angle between them.
(c) a vector parallel to both \(\bar{a}\) and \(\bar{b}\).
(d) a vector perpendicular to both \(\bar{a}\) and \(\bar{b}\).
(ii) Let \(\bar{a}\) = 2i + 4j – 5k, \(\bar{b}\) = i + 2j + 3k. Then find a unit vector perpendicular to both \(\bar{a}\) and \(\bar{b}\). (2)
(iii) Find a vector of magnitude 5 in the direction perpendicular to both \(\bar{a}\) and \(\bar{b}\) (1)
Answer:
(i) (d) a vector perpendicular to both \(\bar{a}\) and \(\bar{b}\).

(ii) \(\bar{a}\) = 2i + 4j-5k, \(\bar{b}\) = i + 2j+3k
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 26
= i(12 + 10) – j(6 + 5) + k(4 – 4) = 22i – 11j
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 27
Therefore unit vector perpendicular to both \(\bar{a}\) and \(\bar{b}\) is
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 28

(iii) 5 × unit vector perpendicular to both \(\bar{a}\) and \(\bar{b}\)
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 29

Question 6.
Consider a vector that is inclined at an angle 45° to x-axis and 60° to y-axis

  1. Find the dc’s of the vector. (2)
  2. Find a unit vector in the direction of the above vector. (1)
  3. Find a vector which is of magnitude 10 units in the direction of the above vector. (1)

Answer:
1. Let l, m, n are the direction ratios.
Given that, l = cos 45° = \(\frac{1}{\sqrt{2}}\), m = cos 60° = \(\frac{1}{2}\)
⇒ l2 + m2 + n2 = 1
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 30
∴ the dc’s of the vector are \(\frac{1}{\sqrt{2}}\), \(\frac{1}{2}\), \(\frac{1}{2}\)

2. A unit vector in the direction of the above vector is given by li + mj + nk ⇒ \(\frac{1}{\sqrt{2}}\)i + \(\frac{1}{2}\)j + \(\frac{1}{2}\)k.

3. A vector, which is of magnitude 10 units in the direction of the above vector is given by
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 31

Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra

Question 7.
Consider the point A(2, 1, 1) and B(4, 2, 3)

  1. Find the vector \(\overline{A B}\) (1)
  2. Find the direction cosines of \(\overline{A B}\) (2)
  3. Find the angle made by \(\overline{A B}\) with the positive direction of x-axis. (1)

Answer:
1. \(\overline{A B}\) = 2i + j + 2k

2. |\(\overline{A B}\)| = \(\sqrt{4+1+4}\) = 3
The direction cosines are \(\frac{2}{3}\), \(\frac{1}{3}\), \(\frac{2}{3}\).

3. cos α = \(\frac{2}{3}\) ⇒ α = cos-1(\(\frac{2}{3}\)).

Question 8.
If i + j + k, 2i + 5j, 3i + 2 j – 3k, i – 6j – k respectively are the position vector of points A, B,C and D. Then

  1. Find \(\overline{A B}\) and \(\overline{C D}\). (1)
  2. Find the angle between the vectors \(\overline{A B}\) and \(\overline{C D}\). (2)
  3. Deduce that \(\overline{A B}\) parallel to \(\overline{C D}\). (1)

Answer:
1.
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 32

2.
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 33

3. Since the angle between \(\overline{A B}\) and \(\overline{C D}\) is π they are parallel.

Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra

Question 9.
Let ABCD be a parallelogram with sides as given in the figure.

  1. Find area of the parallelogram. (2)
  2. Find the distance between the sides AB and DC. (2)

Plus Two Maths Vector Algebra 3 Mark Questions and Answers 34
Answer:
1. Given;
\(\overline{A B}\) = i – 3j + k and \(\overline{A D}\) = i + j + k
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 35

2. Let h be the distance between the parallelsides AB and DC. Then ; Area = Base × h _____(2)
Here, Base = |\(\overline{A B}\)|
|i – 3j + k| = \(\sqrt{1+9+1}=\sqrt{11}\)
From (1) and (2)
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 36

Question 10.
Consider \(\bar{a}\) = i + 2j – 3k, \(\bar{b}\) = 3i – j + 2k, \(\bar{c}\) = 11i + 2j

  1. Find \(\bar{a}\) + \(\bar{b}\) and \(\bar{a}\).\(\bar{b}\) (2)
  2. Find the unit vector in the direction of \(\bar{a}\) + \(\bar{b}\). (1)
  3. Show that \(\bar{a}\) + \(\bar{b}\) and \(\bar{a}\) – \(\bar{b}\) are orthogonal. (1)

Answer:
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 37

(ii) Unit vector in the direction of
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 38

(iii) We have,
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 39
Therefore, they are orthogonal.

Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra

Question 11.
Let A (1, -1, 4), B ( 2, 1, 2 ) and C (1, -2, -3 )

  1. Find \(\overline{A B}\). (1)
  2. Find the angle between \(\overline{A B}\) and \(\overline{A C}\).(2)
  3. Find the area of the parallelogram formed by \(\overline{A B}\) and \(\overline{A C}\) as adjacent sides. (1)

Answer:
1. \(\overline{A B}\) = P.v of B – P.v of A
= 2 i + j + 2 k – (i – j + 4k) = i + 2 j – 2k

2. \(\overline{A C}\) = P.v of C – P.v of A
= i – 2 j – 3 k -(i – j + 4k) = – j – 7k
Let A be the angle between \(\overline{A B}\) and \(\overline{A C}\)
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 40

3.
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 41
Area of the parallelogram
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 42

Plus Two Maths Vector Algebra Six Mark Questions and Answers

Question 1.
Using this figure answer the following questions.
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 43

  1. Find \(\overline{O A}\), \(\overline{O B}\), \(\overline{O C}\) (2)
  2. Find \(\overline{O D}\) (2)
  3. Find the coordinate of the vertex D. (2)

Answer:
1. \(\overline{O A}\) = (3 – 1)i + (-1 – 2)j + (7 – 3)k = 2i – 3j + 4k
\(\overline{O B}\) = (2 – 1)i + (4 – 2)j +(2 – 3)k = i + 2j – k
\(\overline{O C}\) = (4 – 1)i + (1 – 2 )j + (5 – 3 )k = 3i – j + 2 k.

2. From the figure,
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 44

3. Let the vertex of D be (x , y , z),
Then, \(\overline{O D}\) = (x – 1)i + (y – 2)j + (z – 3)k.
But we have,
\(\overline{O D}\) = 6i – 2j + 5k = (x – 1)i + (y – 2)j +(z – 3)k
x – 1 = 6 ⇒ x = 7, y – 2 = -2 ⇒ y = 0, z – 3 = 5 ⇒ z = 8.

Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra

Question 2.
OABCDEFG is a cube with edges of length 8 units and axes as shown. L, M, N are midpoints of the edges FG, GD, GB respectively.
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 45

  1. Find p.v’s of F, B,D and G. (1)
  2. Show that the angle between the main diagonals is θ = cos-1\(\left(\frac{1}{3}\right)\). (2)
  3. Find the p.v’s of L, M, N. (1)
  4. Show that \(\overline{L M}+\overline{M N}+\overline{N L}=0\). (1)

Answer:
1. \(\overline{O F}\) = 8 j + 8k, \(\overline{O B}\) = 8i + 8k, \(\overline{O D}\) = 8i + 8k, \(\overline{O G}\) = 8i + 8j + 8k.

2. Consider the main diagonals \(\overline{O G}\) and \(\overline{E B}\)
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 46

3. P.V of L = \(\overline{O L}\) = 4i + 8j + 8k
P.V of M = \(\overline{O M}\) = 8i + 8j + 4k
P.V of N = \(\overline{O N}\) = 8i + 4j + 8k

4.
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 47

Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra

Question 3.
Using the figure answer the following questions
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 48

  1. Evaluate \(\overline{A B}\).\(\overline{A C}\) (2)
  2. Find \(\overline{A D}\) . (2)
  3. Find the coordinates of D.

Answer:
1. \(\overline{A B}\) = p.v of B – p.v of A= -4i + 0j + 3k
\(\overline{A C}\) = p.v of C – p.v of A = 0i – 4 j + 4k
\(\overline{A B}\).\(\overline{A C}\) = -4 × 0 + 0 × -4 + 3 × 4 = 12

2.
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 49

3. Let the coordinate of D be (x, y ,z)
⇒ \(\overline{A D}\) = (x – 3)i + (y – 2)j + (z – 1)k,
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 50

Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra

Question 4.
Consider the Parallelogram ABCD
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 51

  1. Find \(\overline{A B}\) and \(\overline{A D}\) (1)
  2. Find the area of the parallelogram ABCD. (1)
  3. Find \(\overline{A C}\). (2)
  4. Find co-ordinate of C. (2)

Answer:
1. \(\overline{A B}\) = p.v of B – p. v of A
= 3i + 5j + 8k – (i + 2j + k) = 2i + 3j + 7k
\(\overline{A D}\) = p.v of D – p. v of A
= i + 3j + 2k – (i + 2j + k)= 0i + j + k.

2.
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 52

3. By triangle inequality;
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 53

4. Let the co-ordinate of C be (x, y, z)
Then, \(\overline{A C}\) = (x – 1)i + (y – 2)j + (z – 1)k = 2i + 4j + 8k
x – 1 = 2 ⇒ x = 3, y – 2 = 4 ⇒ y = 6,
z – 1 = 8 ⇒ z = 9
Co-ordinate of C is (3, 6, 9).

Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra

Question 5.
Consider the following quadrilateral ABCD in which P, Q, R, S are the midpoints of the sides.
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 54

  1. Find \(\overline{P Q}\) and \(\overline{S R}\) in terms of \(\overline{A C}\) (2)
  2. Show that PQRS is a parallelogram. (2)
  3. If \(\bar{a}\) is any vector, prove that (2)

Plus Two Maths Vector Algebra 3 Mark Questions and Answers 55
Answer:
1. Using triangle law of addition, we get
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 56

2. From the above explanation we have,
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 57
and parallel. Similarly, |\(\overline{S P}\)| = |\(\overline{R Q}\)|
Therefore, PQRS is a parallelogram.

3. Let \(\bar{a}\) = a1 i + a2 j + a3 k
Plus Two Maths Vector Algebra 3 Mark Questions and Answers 58

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 3 Private, Public and Global Enterprises

Students can Download Chapter 3 Private, Public and Global Enterprises 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 3 Private, Public and Global Enterprises

Plus One Bussiness Studies Private, Public and Global Enterprises One Mark Questions and Answers

Question 1.
Environmental protection can be best done by the efforts of the
(a) Business people
(b) Government
(c) Scientists
(d) All the people
Answer:
(d) All the people

Question 2.
Reconstruction of a sick public sector unit is taken up by
(a) MOFA
(b) MoU
(c) BIFR
(d) NRF
Answer:
(c) BIFR

Question 3.
Disinvestment of PSE’s implies
Answer:
Sale of equity shares to private sector

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 3 Private, Public and Global Enterprises

Question 4.
Enterprises owned and managed by private individuals is known as_________
Answer:
Private enterprises.

Question 5.
The enterprises which are wholly owned and controlled by Government are known as
Answer:
Public enterprises

Question 6.
Enterprises which are partly in the private sector and partly in the public sector are known as__________
Answer:
Joint sector enterprises

Question 7.
Which among the following type of organization is not a public sector enterprise?
(a) Indian Railways
(b) IFCI
(c) SBI
(d) MRF Tyres Ltd.
Answer:
(d)MRF Tyres Ltd.

Question 8.
Which among the following type of organization has no separate legal entity?
(a) Public corporation
(b) Government company
(c) Departmental organization
(d) Private company
Answer:
(c) Departmental organization.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 3 Private, Public and Global Enterprises

Question 9.
Indian Railway is an example of__________
Answer:
Departmental undertaking

Question 10.
Which of the following is formed by a special Act of parliament?
(a) Bharat Heavy Electricals Ltd
(b) L.G. Electronics India
(c) The East India Company
(d) The Reserve Bank of India
Answer:
(d) The Reserve Bank of India

Question 11.
LlC is an example of one type of govt, organization. Identify its name and give another example.
Answer:
Public corporation. Another example of public corporation is SBI.

Question 12.
_________are the organisations, which are incorporated
under the special Acts of the Parliament/State Legislative Assemblies.
Answer:
Statutory Corporations

Question 13.
A government company is any company in which the paid up capital held by the government is not less than
(a) 49 percent
(b) 51 percent
(c) 50 percent
(d) 25 percent
Answer:
(b) 51 percent

Question 14.
The company which operates in more than one country.
Answer:
MNC

Question 15.
Coco Cola is an example of_________companies
Answer:
MNC

Question 16.
Outright sale of public enterprises is called _________
Answer:
Didinvestment

Plus One Bussiness Studies Private, Public and Global Enterprises Two Mark Questions and Answers

Question 1.
What is meant by public sector and private sector? (2)
Answer:
The economy may be classified into two sectors viz., private sector and public sector.
1. Private Sector:
The private sector consists of business owned by individuals or a group of individuals. The various forms of organization are sole proprietorship, partnership, joint Hindu family, cooperative and company.

2. Public Sector:
The business units owned, managed and controlled by the central, state or local government are termed as public sector enterprises or public enterprises. These are also known as public sector undertakings.

Question 2.
What is a Multinational Company? (2)
Answer:
Global enterprises are huge industrial organizations which extend their industrial and marketing operations through a network of their branches in several countries. Their branches are also called Majority Owned Foreign Affiliates (MOFA).

They are characterized by their huge size, large number of products, advanced technology, marketing strategies and network of operations all over the world. Eg. Pepsi, Coca Cola, Cadbury, Sony, Susuki etc.

Question 3.
What is Joint venture? (2)
Answer:
When two or more independent firms together establish a new enterprise by pooling their capital, technology and expertise, it is known as a joint venture. The risks and rewards of the business are also shared. The aim of the joint venture is business expansion, development of new products or moving into new markets, particularly in another country. Benefits

1. Increased resources and capacity:
Since two or more firms join together to form a joint venture, there is the availability of increased capital and other resources, able to face market challenges and take advantage of new opportunities.

2. Access to new markets and distribution networks:
A foreign company gains access to the vast Indian market by entering into a joint venture with an Indian Company. They can also take advantage of the established distribution channels.

3. Access to technology:
It provides access to advanced techniques of production which increases efficiency and then helps in a reduction in cost and improvement in the quality of a product.

4. Innovation:
Foreign partners can come up with innovative products because of new ideas and technology.

5. Low cost of production:
Low cost of raw materials, technically qualified workforce, management professionals, excellent manpower etc. helps to reduce the cost of production and it results increased productivity.

Established brand name :
When one party has well established brands and goodwill, the other party gets its benefits.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 3 Private, Public and Global Enterprises

Question 4.
What do you mean by Disinvestment? (2)
Answer:
The outright sale of Government shares in public sector undertaking is called disinvestment. Eg. Maruthi Udyog Ltd, Indian Petro Chemicals Ltd., etc. Government company

Question 5.
What is meant by Public sector? (2)
Answer:
Business units owned, managed and controlled by the central, state or local government are termed as public sector enterprises or public enterprises. These are also known as public sector undertakings.

Plus One Bussiness Studies Private, Public and Global Enterprises three Mark Questions and Answers

Question 1.
What are the various types of organizations in the private sector? (3)
Answer:
The private sector consists of business owned by individuals or a group of individuals. The various forms of organization are sole proprietorship, partnership, joint Hindu family, cooperative and company.

Plus One Bussiness Studies Private, Public and Global Enterprises Four Mark Questions and Answers

Question 1.
Identify the following public sector enterprises. (4)

  1.  Business Organisation established by the government and controlled by the Ministry concerned.
  2.  Organizations incorporated under a special Act of Parliament or state legislatur
  3.  1t is managed by the government and is subject to budgetary, accounting and audit control
  4.  Organisation established by the government and registered under the Companies Act

Answer:

  1.  Departmental undertaking
  2.  Statutory corporation
  3.  Government company

Question 2.
Some organizations are directly attached to a particular ministry of the Central or State Government and are under the direct control of concerned Minister. The business decisions are, thus, influenced by political consideration. (4)

  1. (a) State the type of enterprise coming under this category.
  2. (b) give four examples of such enterprises.

Answer:

  1. Departmental undertaking
  2. (b) Railways, Communications, Post & Harbours, Electricity etc.

 

Question 3.
Match the column ‘A’ with column ‘B’ and ‘C’. (4)

ABC
Departmental UndertakingMinimum 51% of paid up capital held by govt.TISCO
Public corporationSpread Operation All Over The WorldMaruthi Udyog Ltd
Govt CompaniesSpecial Act Of ParliamentPonds
MNCDirect Controll Of MinistryFACT
Joint Sector enterprisesOwned And Managed by private individualsLIC
Private sector enterprisesOwned and  controlled jointly by Govt. and private individualsIndian railway

Answer:

ABC
Departmental UndertakingDirect Controll Of MinistryIndian railway
Public corporationSpecial Act Of ParliamentLIC
Govt CompaniesMinimum 51% of paid up capital held by govt.FACT
MNCSpread Operation All Over The WorldPonds
Joint Sector enterprisesOwned and  controlled jointly by Govt. and private individualsMaruthi Udyog Ltd
Private sector enterprisesOwned And Managed by private individualsTISCO

Plus One Bussiness Studies Private, Public and Global Enterprises Six Mark Questions and Answers

Question 1.
“Public sector enterprises have been chosen as a means for having a socialistic pattern of society”. Do you think so? If yes, state the reasons. (6)
Answer:
1. Development of infrastructure:
It is the responsibility of the Government to provide infrastructural facilities to the core sector which requires huge capital investment, complex and upgraded technology etc.

2. Regional balance:
The government is responsible for developing all regions and states in a balanced way and removing regional disparities.

3. Economies of scale:
Public sector enterprises are large in size and are, able to avail the advantages of large scale operations.

4. Check over concentration of economic power:
The development of public enterprises prevents concentration of economic power and wealth in the hands of private sector.

5. Employment opportunities:
Public sector enterprises helps to generate a large number of employment opportunities.

6. Import substitution:
It is also necessary for the economic progress of the country that industries which can decrease imports and increase exports are only promoted. Public enterprises also ensure promotion of such industries.

Question 2.
Some organisations are directly attached to a particular ministry of the Central or State Government.
State the type of enterprise comming under this category.
Explain its merits and demerits. (6)
Answer:
This is the oldest and most common form of organization. These are established as departments of the ministry and are financed, managed and controlled by either central govt, or state govt.. They are managed by government employees and work under the control of a minister. Eg. Railways, Post & Telegraph, All India Radio, Doordarshan, Defense undertakings etc.

Features:

  1.  The enterprise is financed by annual appropriation from the budget of the Government and all revenue is paid to the treasury.
  2.  The enterprise is subject to accounting and audit control.
  3.  It is subject to the direct control of the ministry.
  4.  Its employees are govt, employees and are recruited and appointed as per govt, rules.
  5.  They are accountable to the concerned ministry.

Merits:

  1. These undertakings facilitate the Parliament to exercise effective control overtheiroperations;..
  2.  These ensure a high degree of public accountability.
  3.  The revenue earned by the enterprise goes directly to the treasury and hence is a source of income for the Government.
  4.  Where national security is concerned, this form is most suitable since it is under the direct control and supervision of the concerned Ministry.

Limitations:

  1.  Departmental undertakings lack flexibility because its policies cannot be changed instantly.
  2.  The employees are not allowed to take independent decisions, without the approval of the ministry concerned. This leads to delay in decision making.
  3.  These enterprises are unable to take advantage of business opportunities.
  4.  There is red tapism in day-to-day operations.
  5.  There is a lot of political interference throughthe ministry. .
  6.  These organisations are usually insensitive to consumer needs and do not provide adequate services to them.

Plus One Bussiness Studies Private, Public and Global Enterprises Eight Mark Questions and Answers

Question 1.
Kerala Pharmaceuticals Ltd. registered under the Companies Act of 1956, was started with a paid-up capital of 15 lakhs. 40% of paid-up capital is in the hands of private individuals and the balance is held by the Govt, of Kerala.
(a) Identify the type of enterprise.
(b) Explain its merits and demerits. (8)
Answer:
A Government Company is established under the Indian Companies Act, 1956. According to the Indian. Companies Act 1956, a government company
means any company in which not less than 51percent of the paid up capital is held by the central government, or by any state government or partly
by central government and partly by one or more state governments.

Features:

  • It is registered under the Companies Act, 1956.
  • It has a separate legal entity. It can sue and be sued, and can acquire property in its own name.
  • The management of the company is regulated by the provisions of the Companies Act.
  • Employees are recruited and appointed as per the rules and regulations contained in Memorandum and Articles of association.
  • These companies are exempted from the accounting and audit rules and procedures.
  • The government company obtains its funds from government shareholdings and other private shareholders.

Merits

  • It has a separate legal entity, apart from the Govt.
  • It enjoys flexibility and autonomy in all management decisions
  • These companies by providing goods and services at reasonable prices are able to control the market.
  • The formation of a Government company is easy as compared to other forms of Government enterprises.
  • It can appoint professional managers on high salaries.

Limitations

  • It evades constitutional responsibility as it is not directly answerable to parliament.
  • They are autonomous only in name. Company is operated by the controlling ministry.
  • The law relating to the companies, in general is meaningless for the government companies, as it requires fulfillment of various formalities.

Question 2.
It is an organisation which is formed by a special Act of Parliament.
(a) Identify the type of organisation.
(b) Explain its merits and demerits. (8)
Answer:
Statutory corporations are public enterprises brought into existence by a Special Act of the Parliament. The Act defines its powers and functions, rules and regulations governing its employees and its relationship with government departments. Eg. LIC, IFCI, RBI, SBI, ONGC, UTI, Air India etc.

Features:

  1.  Statutory corporations are set up under an Act of Parliament and are governed by the provisions of the Act.
  2.  It is wholly owned by the state.
  3.  It has a separate legal entity, i.e it can sue and be sued, enter into contract and acquire property in its own name.
  4.  It is usually independently financed.
  5.  It is not subject to budget, accounting, and audit laws.
  6.  The employees of these enterprises are not government or civil servants.

Merits:

  1. They enjoy independence in their functioning and a high degree of operational flexibility
  2. It enjoys administrative and financial autonomy
  3. Since they are autonomous organizations, they can frame their own policies and procedures
  4. A statutory corporation is a valuable instrument for economic development

Limitations:

  1. A statutory corporation does not enjoy as much operational flexibility
  2. Government and political interference has always been there in major decisions
  3. Where there is dealing with public, rampant corruption exists
  4. Commercial principles are ignored in the operation of public corporations which leads to inefficiency.

Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 3 Private, Public and Global Enterprises

Question 3.
Cyclone Ltd. is a software company established in India, during the year 2002. They extended its operations to UK and USA in May 2005, by establishing corporate offices in these countries.(8)

(a) What type of company is this?
(b) Explain the features of these type of companies?
Answer:
(a)MNC

(b) Global enterprises are huge industrial organisations which extend their industrial and marketing operations through a network of their branches in several countries. Their branches are also called Majority Owned Foreign Affiliates (MOFA). They are characterised by their huge size, large number of products, advanced technology, marketing strategies and network of operations all over the world. Eg. Pepsi, Coca Cola, Cadbury, Sony, Susuki etc.

Features of MNCs:
1. Huge capital resources:
Multinational companies have the ability to raise huge funds from different sources such as equity shares, debentures, bonds, etc. They can also borrow from financial institutions and international banks.

2. Foreign collaboration:
Global enterprises usually enter into agreements relating to the sale of technology, production of goods, use of brand name, etc. with local firms in the host countries.\

3. Advanced technology:
Multinational companies can possess latest and advanced technology so that they can provide quality products.

4. Product innovation:
Multinational companies are able to conduct sophisticated research so that they can develop new products.

5. Marketing strategies:
They use aggressive marketing strategies in order to increase their sales in a short period. Their advertising and sales promotion techniques are normally very effective.

6. International Market:
They operate through a network of subsidiaries, branches and affiliates in host countries. Due to their giant size, they occupy a dominant position in the market.

7. Centralized control:
They have their headquarters in their home country and exercise control over all branches and subsidiaries.

Question 4.
What are the benefits of entering into Joint ventures? (8)
Answer:
When two or more independent firms together establish a new enterprise by pooling their capital, technology and expertise, it is known as a joint venture. The risks and rewards of the business are also shared. The aim of joint venture is business expansion, development of new products or moving into new markets, particularly in another country.

Benefits:
1. Increased resources and capacity:
Since two or more firms join together to form a joint venture, there is availability of increased capital and other resources, able to face market challenges and take advantage of new opportunities.

2. Access to new markets and distribution networks:
A foreign company gain access to the vast Indian market by entering into a joint venture with Indian Company. They can also take advantage of the established distribution channels.

3. Access to technology:
It provides access to advanced techniques of production which increases efficiency and then helps in reduction in cost and improvement in quality of product.

4. Innovation:
Foreign partners can come up with innovative products because of new ideas and technology.

5. Low cost of production:
Low cost of raw materials, technically qualified workforce, management professionals, excellent manpower, etc. helps to reduce cost of production and it results increased productivity.

Established brand name :
When one party has well-established brands and goodwill, the other party gets its benefits.

Plus One Economics Chapter Wise Questions and Answers Chapter 10 Comparative Development Experience of India with its Neighbours

Students can Download Chapter 10 Comparative Development Experience of India with its Neighbours 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 10 Comparative Development Experience of India with its Neighbours

Plus One Economics Comparative Development Experience of India with its Neighbours One Mark Questions and Answers

Question 1.
The system in which people collectively cultivated land in China is known as.
Answer:
Commune System.

Question 2.
Which of the following countries has the highest population growth rate?
(i) India
(ii) China
(iii) Pakistan
Answer:
(iii) Pakistan

Question 3.
In which year, China announced its first five-year plan?
(i) 1950
(ii) 1951
(iii) 1952
(iv) 1953
Answer:
(iv) 1953

Plus One Economics Chapter Wise Questions and Answers Chapter 10 Comparative Development Experience of India with its Neighbours

Question 4.
India introduced economic reforms in _______ .
(i) 1990
(ii) 1991
(iii) 1993
(iv) 1995
Answer:
(ii) 1991

Question 5.
Chinas great leap forward was in the year ______ .
(i) 1953
(ii) 1958
(iii) 1978
(iv) 1991
Answer:
(ii) 1958

Question 6.
Commune system is the feature of
(i) India
(ii) China
(iii) Pakistan
(iv) All the above
Answer:
(ii) China

Question 7.
Reforms in ……………… were introduced in 1978. (China, Pakistan, India)
Answer:
China

Plus One Economics Comparative Development Experience of India with its Neighbours Two Mark Questions and Answers

Question 1.
The table shows the growth of crops domestic product of India China and Pakistan.
Plus One Economics Chapter Wise Questions and Answers Chapter 10 Comparative Development Experience of India with its Neighbours img1
State two reasons why Pakistan’s growth rate declined compared to two other countries.
Answer:
Political instability, over-dependence on remittance and foreign aid along with volatile performance of agricultural sector are the reasons for Pakistan’s decline in economic growth.

Plus One Economics Chapter Wise Questions and Answers Chapter 10 Comparative Development Experience of India with its Neighbours

Question 2.
Write full form of the following.

  1. SAARC
  2. ASEAN

Answer:

  1. SAARC – South Asian Association for Regional Co-operation.
  2. ASEAN – Association of Southeast Asian Nations.

Question 3.
Evaluate the various factors that led to rapid economic development in China.
Answer:
Great leap forward, commune system, privalisation, reforms, foreign direct investment, etc were the factors that led to rapid economic development of China.

Question 4.
Name the SAARC nations.
Answer:

  • India
  • Pakistan
  • Napal
  • Bhutan
  • Bangladesh
  • Maldives
  • Srilank

Question 5.
Mention some examples of regional and economic grouping.
Answer:
Some regional and economic grouping are:

  1. SAARC
  2. European Union
  3. ASEAN
  4. G-8
  5. G-20

Plus One Economics Comparative Development Experience of India with its Neighbours Three Mark Questions and Answers

Question 1.
Give the basic feature of an underdeveloped economy.
Answer:
Over-dependence on agriculture, large population growth and low income, large poverty and unemployment are the basic features of underdeveloped economies.

Plus One Economics Chapter Wise Questions and Answers Chapter 10 Comparative Development Experience of India with its Neighbours

Question 2.
State whether true or false

  1. in India, agriculture is the largest contributor to GDP
  2. in china, industry is the largest contributor to GDP
  3. compared to India and Pakistan, China has the highest rank in HDI.

Answer:

  1. False. In India, services sector is the larges contributor to GDP
  2. True
  3. True

Question 3.
Mention the various indicators of Human Development Index.
Answer:

  1. Per capita income
  2. Adult literacy
  3. Life expectancy

Question 4.
Mention the years when first five-year plan was initiated in India, China, and Pakistan.
Answer:

  • China – 1978
  • Pakistan – 1989
  • India – 1991

Question 5.
Prepare a table showing demographic indicators of India, China and Pakistan.
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 10 Comparative Development Experience of India with its Neighbours img2

Question 6.
Group the following features pertaining to the economies of India, China, and Pakistan under three heads One child norm, low fertility, high degree of urbanization, mixed economy, very high fertility rate, large population, high density of population, growth due to manufacturing sector, growth due to service.
Answer:
1. Economy of India:

  • High density of population
  • Growth due to service sector

2. Economy of Pakistan:

  • Mixed economy
  • Very high fertility rate

3. Economy of China:

  • One child norm
  • Low fertility
  • High degree of urbanization’
  • Large population
  • Growth due to manufacturing sector

Question 7.
Prepare a note on ‘Great Leap Forward’ of China.
Answer:
The Great Leap Forward (GLF) campaign initiated in 1958 aimed at industrializing the country on a massive scale. People were encouraged to set up industries in their backyards. In rural areas, communes were started. Under the Commune system, people collectively cultivated lands.

In1958, there were 26,000 communes covering almost all the farm population. GLF campaign met with many problems. A severe drought caused havoc in China killing about 30 million people. When Russia had conflicts with China, it withdrew its professionals who had earlier been sent to China to help in the industrialization process.

Question 8.
Mention the salient demographic indicators of China, Pakistan and India.
Answer:
The population of Pakistan is very small and is about one-tenth of China and India:
Though China is the largest nation among the three, its density is the lowest. Population growth is highest in Pakistan, followed by India and China. Sex ratio is low and biased against females in all the three countries.

The fertility rate is also low in China and very high in Pakistan. Urbanization is high in both Pakistan and China with India having 28 percent of its population living in urban areas.

Plus One Economics Chapter Wise Questions and Answers Chapter 10 Comparative Development Experience of India with its Neighbours

Question 9.
Give the similarities of the development path India, China and Pakistan.
Answer:
India, China and Pakistan had adopted economic reforms for economic development. Five Year Plans were initiated in these countries as development strategy. Agriculture plays an important role in the economic development in these nations.

Plus One Economics Comparative Development Experience of India with its Neighbours Four Mark Questions and Answers

Question 1.
Match column A with column B

AB
Great Proletarian Cultural Revolution1978
Great Leap Forward (GLF)1991
Economic reforms in India1953
Economic reforms in Pakistan1965
Economic reforms in china1951
China’s first five-year plan1958
India’s first five-year plan1988

Answer:

AB
Great Proletarian Cultural Revolution1965
Great Leap Forward (GLF)1958
Economic reforms in India1991
Economic reforms in Pakistan1988
Economic reforms in china1978
China’s first five-year plan1953
India’s first five-year plan1951

Question 2.
China’s rapid industrial growth can be traced back to its reforms in 1978. Do you agree? Elucidate.
Answer:
Yes, China’s rapid industrial growth can be traced back to its reforms in 1978. this is because reforms in agriculture and establishment of infrastructure in the areas of education and health, land reforms, etc. had been taking place with the introduction of reforms.

In the initial phase, reforms were initiated in agriculture, foreign trade, and investment sectors. In the later phase, reforms were initiated in the industrial sector. Private sector firms and township and village enterprises were allowed to produce goods.

Plus One Economics Chapter Wise Questions and Answers Chapter 10 Comparative Development Experience of India with its Neighbours

The reform process also involves dual pricing:
It was found that establishment of infrastructure in the areas of education and health, land reforms, long existence of decentralized planning and existence of small enterprises had helped positively in improving the social and income indicators in the post-reform period. In short, it can be concluded that China’s rapid industrial growth can be traced back to its reforms in 1978.

Plus One Economics Comparative Development Experience of India with its Neighbours Five Mark Questions and Answers

Question 1.
Compare and contrast India, China and Pakistan’s sectoral contribution towards GDP in 2003. Draw inferences.
Plus One Economics Chapter Wise Questions and Answers Chapter 10 Comparative Development Experience of India with its Neighbours img3
Answer:
The table given above shows the sectoral contribution of India, China, and Pakistan towards GDP. It can be seen from the table that in both India and Pakistan, the contribution of agriculture to GDP is the same, at 23 percent, but the proportion of workforce that works in this sector is more in India. In Pakistan, about 49 percent of people work in agriculture whereas in India it is 60 percent.

The sectoral share of output and employment also shows that in all the three economies, the industry and service sectors have less proportion of workforce but contribute more in terms of output. In China, manufacturing contributes the highest to GDP at 53 percent whereas in India and Pakistan; it is the service sector that contributes the highest. In both these countries, service sector accounts for more than 50 percent of GDP.

In the normal course of development, countries first shift their employment and output from agriculture to manufacturing and then to services. This is what is happening in China as can be seen from Table. In both India and Pakistan, the service sector is emerging as a major player of development. It contributes more to GDP and, at the same time, emerges as a prospective employer.

Plus One Economics Chapter Wise Questions and Answers Chapter 10 Comparative Development Experience of India with its Neighbours

Question 2.
Compare the development of China, India, and Pakistan with respect to some salient human development indicators.
Answer:
The following table shows some of the salient features of China, India, and Pakistan with respect to human development indicators.
Plus One Economics Chapter Wise Questions and Answers Chapter 10 Comparative Development Experience of India with its Neighbours img4
It can be found that the HDI index and value are much better in China compared to India and Pakistan. That is China is ahead of India and Pakistan on many human development indicators. Similarly, the life expectancy rate is higher in China compared to India and Pakistan.

In India and Pakistan, the life expectancy rate is almost similar that is 63 years. Adult literacy rate is very high in China and the infant mortality rate is comparatively lower. Thus China has made a better development in respect of HDI compared to India and Pakistan.

Plus One Economics Chapter Wise Questions and Answers Chapter 9 Environment Sustainable Development

Students can Download Chapter 9 Environment Sustainable Development 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 Environment Sustainable Development

Plus One Economics Environment Sustainable Development One Mark Questions and Answers

Question 1.
What is the name of UNCED seminal report?
Answer:
Our Common Future.

Question 2.
Protecting future generations is emphasised by which of the following?
(i) Brundtland commission
(ii) Our common future
(iii) UNCED
(iv) Herman Daly
Answer:
(i) Bmndtland commission

Question 3.
Kyoto protocol was signed in ______ .
(i) 1990
(ii) 1992
(iii) 1997
(iv) 1999
Answer:
(iii) 1997

Plus One Economics Chapter Wise Questions and Answers Chapter 9 Environment Sustainable Development

Question 4.
In which state, Chipko Movement took place?
(i) Karnataka
(ii) Punjab
(iii) Himachal Pradesh
(iv) U.P.
Answer:
(iii) Himachal Pradesh

Question 5.
Identify the strategy for sustainable development.
(i) Wind energy
(ii) Solar energy
(iii) Gobar gas
(iv) All the above
Answer:
(iv) All the above

Plus One Economics Environment Sustainable Development Two Mark Questions and Answers

Question 1.
How does the UNCED define sustainable development?
Answer:
The UNCED defines sustainable development as the development that meets the need of the present generation without compromising the ability of the future generation to meet their own needs.

Question 2.
Explain the supply-demand reversal of environmental resources.
Answer:
In the initial stages of development, the demand for environmental resources was less than that of supply. But now the world is faced with increased demand for environmental resources, but their supply is limited due to overuse and misuse.

Plus One Economics Chapter Wise Questions and Answers Chapter 9 Environment Sustainable Development

Question 3.
Give two instances of

  1. overuse of environmental resources
  2. misuse of environmental resources

Answer:
1. Overuse of environmental resources:

  • land
  • forests

2. Misuse of environmental resources:

  • electricity,
  • water

Question 4.
Classify the following into renewable and non-renewable resources.
[Coal, Forest resources, Fish, Petrol]
Answer:
1. Renewable

  • Forest resources
  • Fish

2. Non-renewable

  • Coal
  • Petrol

Question 5.
A few terms are given below. Make pairs of them.
[Growth, Development, Unidimensional, Multi dimensional]
Answer:

  • Unidimensional – Growth
  • Multidimensional – Development

Question 6.
Outline the steps involved in attaining sustainable development in India.
Answer:
The steps involved in attaining sustainable development in India are:
1. decreasing the absolute poverty of the poor by providing employment opportunities

2. providing livelihood in such a manner that can minimize resource depletion, environmental degradation, cultural disruption, and social instability.

Question 7.
Two major environmental issues facing the world today are ………. and ……………
Answer:
Ozone depletion and global warming.

Question 8.
What is sustainable development?
Answer:
Sustainable development is a development that meets the needs of the present generation without compromising the ability of the future generation to meet their own needs.

Plus One Economics Chapter Wise Questions and Answers Chapter 9 Environment Sustainable Development

Question 9.
Make a list of items that can be recycled.
Answer:
The following are the things that can be recycled

  1. Plastic
  2. Papers
  3. Polythene
  4. Glass, and
  5. Certain categories of waste of industries

Question 10.
What happens when the rate of resource extraction exceeds that of their regeneration?
Answer:
If the rate of resource extraction exceeds that of their regeneration, the environment fails to sustain life by providing genetic and biodiversity. This will result in an economic crisis. The rising population in developing countries and the affluent consumption of resources have placed a huge stress on environments.

Question 11.
Give a short narration of ‘Chipko movement’.
Answer:
‘Chipko Movement’ was started in Karnataka to save trees. The word ‘Chipko’ means ‘to hug’. On 8th September 1983, 160 men, women and children hugged the trees in Salkani forest in Sirsi and forced the woodcutters to leave the ultimate aim of this movement is to save trees.

Plus One Economics Environment Sustainable Development Three Mark Questions and Answers

Question 1.
What are the opportunity costs of negative environmental impacts?
Answer:

  1. As the reserves are exhausted huge amount of money should be spent on research to explore new resources.
  2. Health cost of degraded environmental quality.
  3. Increased financial commitment for the government due to global warming and ozone depletion.

Question 2.
What do you mean by ‘Green net national income’? How is it calculated?
Answer:
Green net national income is the difference between net national income and depreciation of natural capital. It can be calculated using the following formula.
Green net national income = Net national income – depletion of natural resources – environmental degradation.

Question 3.
Match the columns
Plus One Economics Chapter Wise Questions and Answers Chapter 9 Environment Sustainable Development img1
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 9 Environment Sustainable Development img2

Plus One Economics Environment Sustainable Development Four Mark Questions and Answers

Question 1.
Keeping in view your locality, suggest any four strategies of sustainable development.
Answer:
The following strategies can be adopted for the sustainable development of our locality.

  • Use of solar power through photovoltaic cells
  • The practice of bio composting
  • Generating wind power
  • Using bio pest control

Plus One Economics Chapter Wise Questions and Answers Chapter 9 Environment Sustainable Development

Question 2.
Differentiate between natural capital and man made capital?
Answer:
1. Natural capital refers to the sum total of the natural resources and environment available to a country as a free gift of nature.

2. On the other hand, man-made capital refers to the stock of all such things which are produced by man for use as means of production.

Question 3.
Fill in the blanks

  1. Coal is a …………… energy
  2. Burning of fossil fuel leads to …………
  3. Bio composts are used in …………… farming
  4. CFCs cause ……………… depletion

Answer:

  1. non-renewable
  2. global warming
  3. organic
  4. ozone

Question 4.
List out the functions of the environment.
Answer:
The environment performs four vital functions which
are listed out below:
1. It supplies resources:
resources here include both renewable and nonrenewable resources. Renewable resources are those which can be used without the possibility of the resource becoming depleted or exhausted.

That is, a continuous supply of the resource remains available. Examples of renewable resources are the trees in the forests and the fishes in the ocean. Nonrenewable resources, on the other hand, are those which get exhausted with extraction and use, for example, fossil fuel.

2. It assimilates waste

3. It sustains life by providing genetic and biodiversity and

4. It also provides aesthetic services like scenery etc.

Question 5.
Identify the factors contributing to land degradation in India?
Answer:
The following are the factors responsible for land degradation in India.

  1. loss of vegetation occurring due to deforestation.
  2. shifting cultivation.
  3. forest fires.
  4. unsustainable fuelwood extraction.
  5. overgrazing.
  6. non-adoption of soil conservation measures.

Question 6.
“The environmental crisis is a recent phenomenon”. Do you agree?
Answer:
Yes, environment crisis is a recent phenomenon. In early days, when civilisation just began, before the phenomenal increase in population and growth of industrialisation, the demand for environmental resources was within the carrying capacity of the environment and so the pollution was also within the absorptive capacity, of the environment.

Therefore, environmental problems did not arise. But with the advent of industrialisation and outbreak of population, environmental problems arisen and the resources for both production and consumption proved to be beyond the rate of regeneration of the resources and the absorptive capacity of the environment.

Plus One Economics Environment Sustainable Development Five Mark Questions and Answers

Question 1.
Account for the current environmental crisis.
Answer:
Environment performs four functions, namely, supplies resources, assimilates wastes, sustains life and provides aesthetic services. But the rising population of the developing countries, the affluent consumption and production standards of the developing countries and industrial revolution have brought the situation of environmental crisis i.e., it all had put great pressure on the first two functions of the environment.

Many resources have become extinct and the wastes generated are beyond the absorptive capacity of environment. The crisis has worsened by the drying up of rivers. Besides, the intensive and extensive extraction of both renewable and non-renewable resources has exhausted some of these vital resources and thus we are compelled to spend huge resources on technology and research to explore new resources.

The situation becomes more worsened with the current issues of global warming and ozone depletion. They also put great strain on government’s finite financial resources.

Plus One Economics Chapter Wise Questions and Answers Chapter 9 Environment Sustainable Development

Question 2.
In 2007 Nobel Prize for Peace was awarded to an individual Algore and an institution IPCC, both engaged in creating awareness about the consequences of global warming. Suggest some measures to keep global warming under control.
Answer:
Global warming refers to the increase in the atmosphere temperature. The temperature increases due to the emission of greenhouse gases. Greenhouse gases are emerged from the burning of biomass and from the consumption of petrol, coal, etc, can absorb temperature.
This can be reduced by :

  1. Reducing pollution and waste.
  2. Using more solar, wind and tidal energy.
  3. New technology and eco-friendly means of production.
  4. Afforestation
  5. Effective rules and its implementation.

Plus One Economics Environment Sustainable Development Eight Mark Questions and Answers

Question 1.
Prepare a Seminar Report on “Strategies for Sustainable Development”
[Hint: A Seminar Report should have a title, Introduction, Content, and conclusion].
Answer:
“Strategies for Sustainable Development”.
Introduction:
The plus one commerce batch of (Name of school) conducted a seminar on the topic “Strategies for Sustainable Development” on 12/09/ 2017 at 11.0 a.m with the ample guidance of our economics teacher. Our class was divided into five groups to cover the entire area of the topic. Each group focused on two points each. They focused on the area given to them and the group leader presented the seminar paper after required preparation.

Content:
Sustainable development is, in this sense, a development that meets the basic needs of all, particularly the poor majority, for employment, food, energy, water, housing, and ensures growth of agriculture, manufacturing, power, and services to meet these needs.

1. Strategies for sustainable development use of non-conventional Sources of Energy:
India, as you know, is hugely dependent on thermal and hydropower plants to meet its power needs. Both of these have adverse environmental impacts. Thermal power plants emit large quantities of carbon dioxide which is a greenhouse gas. It also produces fly ash which, if not used properly, can cause pollution of water bodies, land and other components of the environment.

2. LPG, Gobar Gas in Rural Areas:
Households in rural areas generally use wood, dung cake or other biomass as fuel. This practice has several adverse implications like deforestation, reduction in green cover, wastage of cattle dung and air pollution. To rectify the situation, subsidized LPG is being provided.

In addition, gobar gas plants are being provided through easy loans and subsidy. As far as liquefied petroleum gas (LPG) is concerned, it is a clean fuel it reduces household pollution to a large extent. Also, energy wastage is minimized

3. CNG in Urban Areas:
In Delhi, the use of Compressed Natural Gas (CNG) as fuel in public transport system has significantly lowered air pollution and the air has become cleaner in the last few years.

4. Wind Power:
In areas where speed of wind is usually high, windmills can provide electricity without any adverse impact on the environment. Wind turbines move with the wind and electricity is generated.

Plus One Economics Chapter Wise Questions and Answers Chapter 9 Environment Sustainable Development

5. Solar Power through Photovoltaic Cells:
India is naturally endowed with a large quantity of solar energy in the form of sunlight. With the help of photovoltaic cells, solar energy can be converted into electricity. These cells use special kind of materials to capture solar energy and then convert the energy into electricity.

6. Mini hydel Plants:
In mountainous regions, streams can be found almost everywhere. A large percentage of such streams are perennial. Mini-hydel plants use the energy of such streams to move small turbines.

7. Traditional Knowledge and Practices:
Traditionally, Indian people have been close to their environment. They have been more a component of the environment and not its controller.

If we look back at our agriculture system, health care system, housing, transport, etc., we find that all practices have been environment-friendly. Only recently have we drifted away from the traditional systems and caused large scale damage to the environment and also our rural heritage.

8. Bio-composting:
In our quest to increase agricultural production during the last five decades or so, we almost totally neglected the use of compost and completely switched over to chemical fertilizers.

9. Bio-pest Control:
With the advent of green revolution, the entire country entered into a frenzy to use more and more chemical pesticides for higher yield. Soon, the adverse impacts began to show; food products were contaminated, soil, water bodies, and even groundwater were polluted with pesticides.

Conclusion:
All five groups presented their topics with necessary facts and figures. After the presentation, there was a question-answer session. The active participation of everyone made this session live and interesting. On the whole, the seminar was a big success.

 

Plus One Economics Chapter Wise Questions and Answers Chapter 8 Infrastructure

Students can Download Chapter 8 Infrastructure 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 Infrastructure

Plus One Economics Infrastructure One Mark Questions and Answers

Question 1.
Which among the following is an economic infrastructure?
(i) Eduction
(ii) Transport
(iii) Healthcare
(iv) Housing
Answer:
(ii) Transport

Question 2.
Who was the largest consumer of commercial energy in 1953-54 in India?
(i) Household sector
(ii) Industry sector
(iii) Agriculture sector
(iv) Transport
Answer:
(iv) Transport

Question 3.
What is the Contribution of nuclear energy of total energy consumption in India?
(i) 2%
(ii) 13%
(iii) 20%
(iv) 10%
Answer:
(i) 2%

Plus One Economics Chapter Wise Questions and Answers Chapter 8 Infrastructure

Question 4.
Which of the following nations has lowest Health expenditure as a percentage of GDP?
(i) India
(ii) China
(iii) USA
(iv) Sri Lanka
Answer:
(iv) Sri Lanka

Question 5.
Identify social infrastructure from the following.
(i) Education
(ii) Energy
(iii) Transport
(iv) Communication
Answer:
(i) Education

Question 6.
Find out conventional energy.
(i) Biogas
(ii) Wind energy
(iii) Petroleum
(iv) Solar energy
Answer:
(iii) Petroleum

Question 7.
Infant mortality rate in India in 2012 was ______ .
(i) 40
(ii) 47
(iii) 57
(iv) 60
Answer:
(ii) 47

Plus One Economics Chapter Wise Questions and Answers Chapter 8 Infrastructure

Question 8.
Write the full form of NTPC.
Answer:
NTPC stands for National Thermal Power Corporation.

Plus One Economics Infrastructure Two Mark Questions and Answers

Question 1.
Write any two features of Indian system of medicine.
Answer:

  1. They are very effective
  2. They are safe and inexpensive

Question 2
State whether true or false.

  1. education comes under social infrastructure
  2. solar energy is nonconventional energy
  3. Ayurveda is an Indian system of medicine
  4. major part power generation in India comes from hydro projects.

Answer:

  1. true
  2. true
  3. true
  4. False, major part power generation in India comes from thermal projects

Question 3.
Name some National Health Care Programme.
Answer:

  • National Malaria Eradication Programme
  • National Filaria Control Programme
  • National Family Welfare Programme
  • National Diarrhoeal Diseases Control Programme

Plus One Economics Infrastructure Three Mark Questions and Answers

Question 1.
Name three sources of non-conventional energy.
Answer:

  1. Solar energy
  2. Wind energy
  3. Tidal power

Plus One Economics Chapter Wise Questions and Answers Chapter 8 Infrastructure

Question 2.
Classify the following into commercial energy and non-commercial energy:
Coal, petrol, agricultural waste, dry animal dung, twig of trees, natural gas.
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 6 Rural Development img5

Question 3.
Classify the following sources of energy into conventional sources and non-conventional sources.
(Coal, Electricity, Wind energy, Solar energy, Petroleum, Tidal energy)
Answer:
1. Conventional source files

  • Coal
  • Petroleum
  • Electricity

2. Non-conventional sources

  • Solar energy
  • Tidal energy
  • Wind energy

Question 4.
List various non-commercial sources of energy?
Answer:
Various non-commercial source of energy are :

  • solar energy
  • wind energy
  • tidal energy
  • energy from firewood
  • energy from vegetable waste
  • energy from dried dung

Question 5.
What are the three basic sources of generating power?
Answer:

  1. Hydroelectricity
  2. Thermal electricity
  3. Nuclear electricity

Question 6.
List the six system of Indian medicine.
Answer:
Six system of Indian medicine are :

  1. Ayurveda
  2. Yoga
  3. Siddha
  4. Unani
  5. Homeopathy
  6. Naturopathy

Question 7.
Explain the term ‘infrastructure’.
Answer:
Infrastructure is the support system on which the sufficient working of a modern industrial economy depends. It is the physical framework which is essential for giving services to people such as roads, railways, airports, ports, dam, power stations, telecommunication educational and health facilities, etc. Infrastructure consists of services like banking, communication, transport, irrigation, power, etc. These are very essential for production of goods.

Plus One Economics Chapter Wise Questions and Answers Chapter 8 Infrastructure

Question 8.
Name different types of energy?
Answer:
The different types of energy are:

  • Coal
  • Petroleum
  • Natural gas
  • Bioenergy
  • Solar energy
  • Atomic energy

Question 9.
Categorize the following as elements of economic infrastructure and social infrastructure.
[Canals, Houses, schools and colleges, railways, ships, hospitals, banks, courts, power plants, satellite stations],
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 6 Rural Development img7

Question 10.
Justify that energy crisis can be overcome with the use of renewable sources of energy.
Answer:
There are two sources of energy namely, commercial and noncommercial. Noncommercial sources are firewood, agricultural waste, and dried dung. These are noncommercial as they are found in nature. Commercial sources of energy like grass hay, twigs and small branches of a tree, sundried cow dung cakes are generally renewable.

More than 60 percent of Indian households depend on these traditional sources of energy for meeting regular cooking and heating needs. The energy crisis can be overcome with the use of renewable sources of energy.

Plus One Economics Infrastructure Four Mark Questions and Answers

Question 1.
Write the names of four atomic energy plants in India.
Answer:

  1. Atomic energy power plant at Tarapur
  2. Atomic energy power plant at Narora
  3. Atomic energy power plant in Kalapakkam (Chennai)
  4. Atomic energy power plant at Rana Pratap Sagar Dam (Kota)

Question 2.
Write a note on ISM.
Answer:
Indian Systems of Medicine (ISM):
It includes six systems: Ayurveda, Yoga, Unani, Siddha, Naturopathy, and Homeopathy (AYUSH). At present, there are 3,004 ISM hospitals, 23,028 dispensaries and as many as 6,11,431 registered practitioners in India. But little has been done to set up a framework standardize education or to promote research.tSM has huge potential and can solve a large part of our health care problems because they are effective, safe and inexpensive.

Plus One Economics Chapter Wise Questions and Answers Chapter 8 Infrastructure

Question 3.
Kerala is experiencing huge energy crisis. Suggest some measures for solving the problem.
Answer:
More public investment, better research and development efforts, exploration, technological innovation and use of renewable energy sources can ensure solution of energy crisis in Kerala. Though the private sector has made some progress, it is necessary to tap this sector to come forward and produce power on a large scale.

One also has to appreciate the efforts made in this regard. More efforts and encouragement should be given by the government for the widespread use of wind, solar and tidal energy production in the state. Moreover, greater reliance on renewable energy resources offers enormous economic, social and environmental benefits.

Question 4.
Analyze the state of health infrastructure in India citing facts and figures.
Answer:
India has built up a vast health infrastructure and manpower at different levels since independence. At the village level, a variety of hospitals have been set up by the government. India also has a large number of hospitals run by voluntary agencies and the private sector.

These hospitals are manned by professionals and paramedical professionals trained in medical, pharmacy and nursing colleges. Since independence, there has been a significant expansion in the physical provision of health services.

During 1951-2000, the number of hospitals and dispensaries increased from 9,300 to 43,300 and hospital beds from 1, 2 to 7.2 million during 1951 – 99, nursing personnel increased from 0.18 to 8.7 lakh and allopathic doctors from 0.62 to 5.0 lakh. Expansion of health infrastructure has resulted in the eradication of smallpox, guinea worms and the near eradication of polio and leprosy.

Question 5.
Differentiate between commercial and noncommercial sources of energy.
Answer:
Commercial sources of energy:
Commercial sources of energy include coal, petroleum, and electricity. They could be bought and sold. They are generally exhaustible in nature. More than 60 percent of Indian households depend on the traditional source of energy.

Non-commercial sources of energy include firewood, agricultural waste, and dried dung. They are found in nature or forests. Lesser number of persons use these resources.

Plus One Economics Chapter Wise Questions and Answers Chapter 8 Infrastructure

Question 6.
Point out the connection between consumption of energy and economic growth?
Answer:
The central issue has been whether economic growth stimulates consumption of energy or is energy consumption itself a stimulus for economic growth. But whatever may be the causal relationship between energy consumption and economic growth of a nation, they are both closely related.

Since energy is an essential input of all productive activities, agricultural or industrial, the process of economic development inevitable demands increasing levels of energy consumption. The higher the degree of economic growth, the higher is the consumption of energy and vice versa. Thus energy consumption is an important indicator of economic growth.

Electricity is one of the most critical infrastructures that determines economic development of a country. The growth rate of demand for power is generally higher than GDP growth rate. In order to have an 8 % GDP growth rate per annum, the power supply needs to grow around 12% annually. This shows that the rates of consumption of energy and economic growth are connected.

Plus One Economics Infrastructure Five Mark Questions and Answers

Question 1.
‘Infrastructure facilities boost production’ Do you agree? Substantiate your answers.
Answer:
Infrastructure facilities boost production in the following manner.
1. Infrastructure provides support services in the main areas of industrial and agricultural production, domestic and foreign trade and commerce.

2. Infrastructure facilities include roads, railways, ports, airports, dams, power stations, oil and gas pipelines, telecommunication facilities, educational systems, health systems, monetary systems, etc. It is the support system on which depends the efficient working of a modern industrial economy.

3. Modem agriculture largely depends on infrastructure for speedy and large scale transport of seeds, pesticides, fertilizers, and the produce by making use of modem roadways, railways, and shipping facilities.

4. Infrastructure contributes to the economic development of a country both by increasing the productivity of the factors of production and improving the quality of life of its people.

Question 2.
“Infrastrucure contribute to the economic development of a country like india” Do you agree? Justify.
Answer:
Yes, I agree with the statement that infrastructure contribute to the economic development of a country like India. The reason why infrastructure is an essential precondition for economic development are pointed out below.

1. Infrastructure contributes to economic development of a country both by increasing the productivity of the factors of production and improving the quality of life of its people.

2. Inadequate infrastructure can have multiple adverse effects on health. Improvements in water supply and sanitation have a large impact by reducing morbidity from major waterborne diseases and reducing the severity of disease when it occurs.

3. In addition to the obvious linkage between water and sanitation and health, the quality of transport and communication infrastructure can affect access to health care.

4. Infrastructure is in itself a source of employment for the large labour force of developing economies like India.

Plus One Economics Chapter Wise Questions and Answers Chapter 8 Infrastructure

Question 3.
Suggest the progammes to increase the effectiveness of health care system.
Answer:
The following are the progammes to increase the effectiveness of health care system

  • Public health facilities should be decentralized
  • People should be educated about the nature, causes, and remedies of general diseases
  • People should be made aware about sanitation facilities, cleanliness, immunization, etc.
  • Efforts should be taken to develop health infrastructure
  • Primary health care facilities should be strengthened
  • Private-public participation in health care system should be encouraged

Question 4.
“India’s power sector faces some challenges today”. Do you agree? If yes mention the challenges.
Answer:
agree with the statement that India’s power sector faces some challenges today.
Some of the challenges that India’s power sector faces today are:

1. India’s installed capacity to generate electricity is not sufficient to feed an annual economic growth of 7 percent. In order to meet the growing demand for electricity, between 2000 and 2012, India needs to add 1,00,000 MW of new capacity, whereas, at present, India is able to add only 20,000 MW a year. Even the installed capacity is underutilized because plants are not run properly

2. State Electricity Boards (SEBs), which distribute electricity, incur losses which exceed Rs 500billion. This is due to transmission and distribution losses, wrong pricing of electricity and other inefficiencies. Some scholars also say that distribution of electricity to farmers is the main reason for the losses; electricity is also stolen in different areas which also adds to the woes of SEBs

3. Private sector power generators are yet to play their role in a major way same is the case with foreign investors

4. There is general public unrest due to high power tariffs and prolonged power cuts in different parts of the country
Thermal power plants which are the mainstay of. India’s power sector are facing a shortage of raw material and coal supplies.

Question 5.
There are some drawbacks in our health care system. Do you agree? Substantiate.
Answer:
Yes, I agree with these statements
The Indian constitution assign, the state, the responsibility of raising the level of nutrition and the standard of living of its people and the improvement of public health. However, the National Health Policy lacks specific measures to achieve broad state goals. The government expenditure on health sector is 5% of total GDP. This is very low compared to other countries.

At present, less than 0% of the population utilises public health facilities However only 38% of the Public Health Centres (PHCs) have the required number of doctors and only 30% of the PHCs have sufficient stock of medicines. The people living in Rural areas do not have sufficient medical infrastructure.

There is shortage of beds, doctors and basic diagnostic facilities in rural areas. This has led to regional inequality in health services. Thus, it can be concluded that there are some draw-backs in our health care system.

Plus One Economics Infrastructure Eight Mark Questions and Answers

Question 1.
Prepare a seminar report on “energy and health infrastructure”.
Answer:
“Energy and health infrastructure”
Introduction:
The plus one commerce batch of (Name of school) conducted a seminar on the topic “Energy and health infrastructure” on 12/09/2018 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.

The first group explained the meaning and relevance of infrastructure, the second group explained the energy infrastructure and the third group presented their idea on health infrastructure. They focused on the area given to them and the group leader presented the seminar paper after required preparation.

Plus One Economics Chapter Wise Questions and Answers Chapter 8 Infrastructure

Content:
Infrastructure:
Infrastructure is the support system on which depends the efficient working of a modern industrial economy. Modern agriculture also largely depends on it for speedy and largescale transport of seeds, pesticides, fertilizers, and the products by making use of modern roadways, railways and shipping facilities.

Infrastructure contributes to economic development of a country both by increasing the productivity of the factors of production and improving the quality of life of its people.

1. Energy:
Energy is a critical aspect of the development process of a nation. It is, of course, essential for industries. Now it is used on a large scale in agriculture and related areas like production and transportation of fertilizers, pesticides and farm equipment. It is required in houses for cooking, household lighting, and heating.

There are commercial and non-commercial sources of energy. Commercial sources are coal, petroleum, and electricity as they are bought and sold. They account for over 50 percent of all energy sources consumed in India. Noncommercial sources of energy are firewood, agricultural waste, and dried dung.

These are noncommercial as they are found in nature/forests. Both commercial and noncommercial sources of energy are known as conventional sources of energy. There are three other sources of energy which are commonly termed as nonconventional sources solar energy, wind energy, and tidal power.

The most visible form of energy, which is often identified with progress in modern civilization, is power, commonly called electricity; it is one of the most critical components of infrastructure that determines the economic development of a country. The growth rate of demand for power is generally higher than the GDP growth rate.

Studies point that in order to have8 percent GDP growth per annum, power supply needs to grow around 12per cent annually. Electricity is a secondary form of energy produced from primary energy resources including coal, hydrocarbons, hydro energy, nuclear energy, renewable energy, etc. Primary energy consumption takes into account the direct and indirect consumption of fuels.

2. Health:
Health is not only absence of disease but also the ability to realize one’s potential. It is a yardstick of one’s wellbeing. Health is the holistic process related to the overall growth and development of the nation. Development of health infrastructure ensures a country of healthy manpower for production of goods and services.

In recent times, scholars argue that people are entitled to health care facilities. It is the responsibility of the government to ensure the right to healthy living. Health infrastructure includes hospitals, doctors, nurses and other paramedical professionals, beds, equipment required in hospitals and a well developed pharmaceutical industry.

Conclusion:
All the three groups presented their topics with necessary facts and figures. After the presentation, there was a question-answer session. The active participation of everyone made this session live and interesting. On the whole, the seminar was a big success.

Plus Two Maths Chapter Wise Questions and Answers Chapter 9 Differential Equations

Students can Download Chapter 9 Differential Equations 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 9 Differential Equations

Plus Two Maths Differential Equations Three Mark Questions and Answers

Question 1.
y = e2x(a + bx), a and b are arbitrary constants.
Answer:
y = e2x(a + bx) ____(1)
Differentiating with respect to x,
\(\frac{d y}{d x}\) = e2xb + (a + bx)2e2x
\(\frac{d y}{d x}\) = 2y + be2x ⇒ \(\frac{d y}{d x}\) – 2y = be2x ____(2)
Differentiating (2) with respect to x,
Plus Two Maths Differential Equations 3 Mark Questions and Answers 1

Plus Two Maths Chapter Wise Questions and Answers Chapter 9 Differential Equations

Question 2.
y = ex(acosx + 6sinx), a and b are arbitrary constants.
Answer:
y = ex(acosx + 6sinx) ___(1)
Differentiating with respect to x,
\(\frac{d y}{d x}\) = ex(-asinx + bcosx) + ex(acosx + bsinx) \(\frac{d y}{d x}\) = ex(-asin x + b cos x) + y
\(\frac{d y}{d x}\) – y = ex(-a sin x + b cos x) ____(2)
Differentiating (2) with respec to x,
Plus Two Maths Differential Equations 3 Mark Questions and Answers 2

Question 3.
y = c1ex + c2 e-x , c1 and c1 are arbitrary constants.
Answer:
y = c1ex + c2 e-x ___(1)
Differentiating with respect to x,
\(\frac{d y}{d x}\) = c1ex + c2 e-x __(2)
Differentiating (2) with respect to x,
Plus Two Maths Differential Equations 3 Mark Questions and Answers 3

Plus Two Maths Chapter Wise Questions and Answers Chapter 9 Differential Equations

Question 4.
(x – a)2 + 2y2 = a2, a is a arbitrary constants.
Answer:
(x – a)2 + 2y2 = a2 ___(1)
Differentiating with respect to x,
Plus Two Maths Differential Equations 3 Mark Questions and Answers 4

Question 5.
Find the equation of a curve passing through the point (0, -2) given that at any point (x, y) on the curve, the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.
Answer:
y\(\frac{d y}{d x}\) = x ⇒ ydy = xdx
Integrating on both sides,
∫ydy = ∫xdx + c
⇒ \(\frac{y^{2}}{2}=\frac{x^{2}}{2}\) + c ____(1)
Since it passes through (0, -2),
Plus Two Maths Differential Equations 3 Mark Questions and Answers 5

Plus Two Maths Chapter Wise Questions and Answers Chapter 9 Differential Equations

Question 6.
Form the DE representing the family of parabolas having a vertex at origin and axis along positive direction of x-axis.
Answer:
Let (a, 0) be focus of the given family of parabolas.
y2 = 4ax ____(1)
Differentiating with respect to x,
Plus Two Maths Differential Equations 3 Mark Questions and Answers 6
Plus Two Maths Differential Equations 3 Mark Questions and Answers 7

Question 7.
For the DE xy \(\frac{d y}{d x}\) = (x + 2)(y + 2), find the solution curve passing through the point(1,- 1).
Answer:
xy \(\frac{d y}{d x}\) = (x + 2)(y + 2)
⇒ \(\frac{y}{y+2} d x=\frac{x+2}{x} d x\)
Integrating on both sides,
Plus Two Maths Differential Equations 3 Mark Questions and Answers 8
⇒ y – 2 log|y + 2| = x + 2log|x| + c ____(1)
Since it passes through (1, -1),
⇒ -1 – 2log|-1 + 2| = 1 + 2log|l| + c
⇒ -2 = c
(1) ⇒ y – 2log|y + 2| = x + 2log|x| – 2.

Plus Two Maths Chapter Wise Questions and Answers Chapter 9 Differential Equations

Question 8.
Solve the initial value problem: \(\frac{d y}{d x}\) = y tan 2x; y(0) = 2.
Answer:
\(\frac{d y}{d x}\) = y tan 2x
⇒ \(\frac{d y}{y}\) tan 2xdx,
This is a variable type
∴∫\(\frac{d y}{y}\) = ∫tan 2xdx ⇒ log y = \(\frac{1}{2}\) log|sec 2x| + c
Given y(0) = 2 ⇒ log 2 = \(\frac{1}{2}\) log|sec 0| + c ⇒ c = log 2
log y = \(\frac{1}{2}\) log|sec 2x| + log 2 ⇒
Plus Two Maths Differential Equations 3 Mark Questions and Answers 9

Plus Two Maths Differential Equations Four Mark Questions and Answers

Question 1.
(i) Consider the differential equation given below. (1)
\(\frac{d^{4} y}{d x^{4}}-\sin \left(\frac{d^{3} y}{d x^{3}}\right)=0\). Write the order and degree of the DE (if defined)
(ii) Find the Differential equation satisfying the family of curves y2 = a(b2 – x2), a and b are arbitrary constants. (3)
Answer:
(i) 4; degree is not defined

(ii) y2 = a(b2 – x2) ____(1)
Differentiating with respect to x,
2y \(\frac{d y}{d x}\) = -a2x ⇒ y\(\frac{d y}{d x}\) = -ax ____(2)
Differentiating (2) with respect to x,
Plus Two Maths Differential Equations 3 Mark Questions and Answers 10
Which is the differential equation.

Plus Two Maths Chapter Wise Questions and Answers Chapter 9 Differential Equations

Question 2.

  1. Find the Differential equation satisfying the family of curves y = ae3x + be-2x, a and b are arbitrary constants. (3)
  2. Hence write the degree and order of the DE. (1)

Answer:
1. y = ae3x + be-2x ____(1)
Differentiating with respect to x,
\(\frac{d y}{d x}\) = ae3x × 3 + be-2x × -2 ____(2)
Differentiating (2) with respect to x,
⇒ \(\frac{d^{2} y}{d x^{2}}\) = 9ae3x + 4be-2x ____(3)
Now, (3) + 2 × (2) ⇒ \(\frac{d^{2} y}{d x^{2}}+2 \frac{d y}{d x}=15 a e^{3 x}\)
Plus Two Maths Differential Equations 3 Mark Questions and Answers 11
Using (4), (5) in (1), we have,
Plus Two Maths Differential Equations 3 Mark Questions and Answers 12

2. Order: 2; degree: 1.

Question 3.
Consider the equation of all circles which pass through the origin and whose centres are on the x-axis.

  1. Define the general equation of the circle.(1)
  2. Find the DE corresponding to the above equation. (3)

Answer:
1. The general equation of the circle, passing through the origin and whose centers lies on x-axis can be taken as (x – h)2 + y2 = h2 where h being an arbitrary constant.

2. Simplifying (x – h)2 + y2 = h2 we get,
x2 – 2hx + h2 + y2 = h2 ⇒ x2 – 2hx + h2 = 0 _____(1)
Differentiating we get,
2x + 2y \(\frac{d y}{d x}\) – 2h = 0 ⇒ h = x + y \(\frac{d y}{d x}\)
Substituting in (1) we can eliminate h
Plus Two Maths Differential Equations 3 Mark Questions and Answers 13

Plus Two Maths Chapter Wise Questions and Answers Chapter 9 Differential Equations

Question 4.
Find a particular solution satisfying the given condition. (x3 + x2 + x +1)\(\frac{d y}{d x}\) = 2x2 + x, y = 1, when x = 0.
Answer:
Plus Two Maths Differential Equations 3 Mark Questions and Answers 14
Integrating on both sides,
∫dy = ∫\(\frac{2 x^{2}+x}{\left(x^{2}+1\right)(x+1)} d x\)
Splitting into partial fractions we have, (see Unit:7)
Plus Two Maths Differential Equations 3 Mark Questions and Answers 15
Plus Two Maths Differential Equations 3 Mark Questions and Answers 16

Plus Two Maths Chapter Wise Questions and Answers Chapter 9 Differential Equations

Question 5.

  1. Write the degree of the DE y’ = 2xy. [0, 1, 2, 3] (1)
  2. Express y’ = 2xy in the form Mdx = Ndy. Where M is a function of x and N is the function of y. (2)
  3. Solve y’ = 2xy, y(0) = 1 (1)

Answer:

1. Degree = 1

2. We have, \(\frac{d y}{d x}\) = 2xy ⇒ \(\frac{d y}{y}\) = 2xdx, which is of the form Mdx = Ndy.

3. Solution is ∫\(\frac{d y}{y}\) = 2∫xdx ⇒ log|y| = x2 + c
Given y(0) = 1 ⇒ log|1| = 0 + c ⇒ c = 0
⇒ log|y| = x2 ⇒ y = ex2.

Question 6.
Solve the following DE \(\frac{d y}{d x}=\frac{y^{2}-x^{2}}{2 x y}\).
Answer:
\(\frac{d y}{d x}=\frac{y^{2}-x^{2}}{2 x y}\), this is a Homogeneous DE.
Therefore, put y = vx and \(\frac{d y}{d x}\) = v + x\(\frac{d v}{d x}\) to convert it into variable separable form.
The DE becomes,
Plus Two Maths Differential Equations 3 Mark Questions and Answers 17
Plus Two Maths Differential Equations 3 Mark Questions and Answers 18
Therefore integrating we get,
Plus Two Maths Differential Equations 3 Mark Questions and Answers 19
Plus Two Maths Differential Equations 3 Mark Questions and Answers 20

Plus Two Maths Chapter Wise Questions and Answers Chapter 9 Differential Equations

Question 7.
Solve the linear differential equation \(x \frac{d y}{d x}-y=(x-1) e^{x}\).
Answer:
Given, x\(\frac{d y}{d x}\) – y = (x – 1)ex, dividing both sides by x ,we get
Plus Two Maths Differential Equations 3 Mark Questions and Answers 21
Solution is
y × IF = ∫Q(IF)dx + c
Plus Two Maths Differential Equations 3 Mark Questions and Answers 22

Question 8.
(i) Choose the correct answer from the bracket. The solution of the differential equation xdy + ydx = 0 represents (1)
(a) a rectangular hyperbola
(b) a parabola whose centre is origin
(c) a straight line whose centre is origin
(d) a circle whose centre is origin.
(ii) From the DE of the family of circles touching the x-axis at origin. (3)
Answer:
(i) (c) a straight line whose centre is origin.

(ii) Let (0, a) be the centre of the circle. Therefore the equation of the circle is
x2 + (y – a)2 = a2
⇒ x2 + y2 = 2ay
⇒ \(\frac{x^{2}+y^{2}}{y}\) = 2a ____(1)
Plus Two Maths Differential Equations 3 Mark Questions and Answers 23
Differentiating with respect to x,
Plus Two Maths Differential Equations 3 Mark Questions and Answers 24

Plus Two Maths Chapter Wise Questions and Answers Chapter 9 Differential Equations

Question 9.
Solve the DE x2\(\frac{d y}{d x}\) = x2 – 2y2 + xy.
Answer:
x2\(\frac{d y}{d x}\) = x2 – 2y2 + xy
Plus Two Maths Differential Equations 3 Mark Questions and Answers 25
this is a Homogeneous DE.
Put y = vx and \(\frac{d y}{d x}=v+x \frac{d v}{d x}\)
Plus Two Maths Differential Equations 3 Mark Questions and Answers 26
Integrating on both sides,
Plus Two Maths Differential Equations 3 Mark Questions and Answers 27

Question 10.
Choose the correct answer from the bracket

  1. The DE \(\frac{d y}{d x}+\frac{y}{x}\) = ex, x > 0 is of order …..[0,1,2,3] (1)
  2. The integrating factor \(\frac{d y}{d x}+\frac{y}{x}\) = ex, is……..[x, ex, -x, e-x] (1)
  3. Solve \(\frac{d y}{d x}+\frac{y}{x}\) = ex (2)

Answer:
1. Order = 1

2. \(\frac{d y}{d x}+\frac{y}{x}\) = ex is of the form \(\frac{d y}{d x}\) + Py = Q,
where P = \(\frac{1}{x}\), Q = ex
IF = e∫Pdx = e∫\(\frac{1}{x}\)dx = elogx = x

3. Solution is y.IF = ∫ex. IFdx
⇒ yx = ∫x.exdx ⇒ yx = x.ex – ∫exdx
⇒ yx = x.ex – ex + c ⇒ yx = ex(x – 1) + c.

Plus Two Maths Chapter Wise Questions and Answers Chapter 9 Differential Equations

Question 11.
Solve the DE \(\frac{d y}{d x}=\frac{x+y}{x-y}\).
Answer:
\(\frac{d y}{d x}=\frac{x+y}{x-y}\), this is a Homogeneous DE.
Put y = vx and \(\frac{d y}{d x}\) = v + x\(\frac{d v}{d x}\)
Plus Two Maths Differential Equations 3 Mark Questions and Answers 28
Integrating on both sides,
Plus Two Maths Differential Equations 3 Mark Questions and Answers 29

Plus Two Maths Differential Equations Six Mark Questions and Answers

Question 1.
Consider the DE \(\frac{d y}{d x}=\frac{y^{3}+3 x^{2} y}{x^{3}+3 x y^{2}}\)

  1. Identify the DE ? Give reason. (1)
  2. Explain the method of solving the DE. (1)
  3. Solve the DE. (4)

Answer:
1. Given DE is a Homogeneous DE. Since y3 + 3x2y and x3 + 3xy2 are Homogeneous functions of same degree (deg = 3).

2. By giving a substitution y = v x and \(\frac{d y}{d x}\) = v + x\(\frac{d y}{d x}\)
we can convert the DE into variable separable.

3. Now we have, \(\frac{d y}{d x}=\frac{y^{3}+3 x^{2} y}{x^{3}+3 x y^{2}}\)
Plus Two Maths Differential Equations 3 Mark Questions and Answers 30
∴ Integrating we get,
\(\int \frac{1+3 v^{2}}{2 v\left(1-v^{2}\right)} d v=\int \frac{d x}{x}\)
Plus Two Maths Differential Equations 3 Mark Questions and Answers 31
\(\frac{1}{2}\) log v – log(1 – v2) = log x + log c
Plus Two Maths Differential Equations 3 Mark Questions and Answers 32

Plus Two Maths Chapter Wise Questions and Answers Chapter 9 Differential Equations

Question 2.
Consider the D.E \(\frac{d y}{d x}+\frac{y}{x}=x^{2}\)

  1. Find degree and order of DE . (1)
  2. Solve the D.E. (4)
  3. Find the particular solution when x = 1, y = 1. (1)

Answer:
1. Degree: 1, Order: 1.

2. The given D.E is first order linear DE of the form
\(\frac{d y}{d x}\) + Py = Q. Comparing we get, P = \(\frac{1}{x}\), Q = x2
∴ ∫Pdx = ∫\(\frac{1}{x}\)dx = logx
Integrating factor (I.F) = e∫Pdx = elogx = x
y.x = ∫x2.xdx + c = ∫x3 dx + c
⇒ y.x = \(\frac{x^{4}}{4}\) + c ___(1)

3. Given, y = 1 when x = 1, then (1)
⇒ 1 × 1 = \(\frac{1}{4}\) + c ⇒ c = \(\frac{3}{4}\)
Therefore particular solution is
y.x = \(\frac{x^{4}}{4}\) + \(\frac{3}{4}\) ⇒ 4xy = x3 + 3.

Plus Two Maths Chapter Wise Questions and Answers Chapter 9 Differential Equations

Question 3.
Consider the equation.\(\frac{d y}{d x}\) + y = sin x

  1. What is the order and degree of this equation? (1)
  2. Find the integrating factor. (2)
  3. Solve this equation. (3)

Answer:
1. Order = 1, Degree = 1

2. Given, \(\frac{d y}{d x}\) + y = sin x is of the form
\(\frac{d y}{d x}\) + Py = Q ⇒ P = 1, Q = sinx
Integrating factor = e∫Pdx = e∫1dx = ex

3. Therefore solution is
y.IF = ∫Q.IFdx + c ⇒ yex = ∫ex sinxdx + c ____(1)
∫sinx.exdx = ex sinx – ∫cosx.exdx
= ex sin x – cosx.ex – ∫sinx.ex dx
⇒ 2∫ex sin xdx = ex(sin x – cos x)
⇒ ∫ex sinxdx = \(\frac{e^{x}}{2}\)(sinx – cosx)
(1) ⇒ yex = \(\frac{e^{x}}{2}\)(sinx – cosx) + c.

Plus Two Maths Chapter Wise Questions and Answers Chapter 9 Differential Equations

Question 4.
Considerthe D.E (x2 – 1)\(\frac{d y}{d x}\) + 2(x + 2)y = 2(x + 1)

  1. Find \(\frac{d y}{d x}\), degree and order of the above differential equation. (1)
  2. Find the integrating factor of the above differential equation. (2)
  3. Solve the differential equation. (3)

Answer:
1. Given, (x2 – 1)\(\frac{d y}{d x}\) + 2(x + 2)y = 2(x + 1)
Plus Two Maths Differential Equations 3 Mark Questions and Answers 33
Here, Degree = 1, Order = 1.

2. The given DE is of the form \(\frac{d y}{d x}\) + Py = Q
Where,
Plus Two Maths Differential Equations 3 Mark Questions and Answers 34
Splitting it into partial fractions we get,
Plus Two Maths Differential Equations 3 Mark Questions and Answers 35
Put x = 1, ⇒ 6 = 2B ⇒ B = 3,
put x = -1, ⇒ 2 = -2A ⇒ A = -1
Plus Two Maths Differential Equations 3 Mark Questions and Answers 36

3. Solution is y × IF = ∫Q × IFdx + c
Plus Two Maths Differential Equations 3 Mark Questions and Answers 37

Plus Two Maths Chapter Wise Questions and Answers Chapter 9 Differential Equations

Question 5.
(i) The degree of the differential Equation \(\frac{d^{2} y}{d x^{2}}+\cos \left(\frac{d y}{d x}\right)=0\) is
(a) 2
(b) 1
(c) 0
(d) Not defined
(ii) Solve \(\frac{d y}{d x}\) + 2y tanx = sinx; y = 0, x = \(\frac{\pi}{3}\) (5)
Answer:
(i) (d) Not defined.

(ii) \(\frac{d y}{d x}\) + 2y tanx = sinx
Then, P = 2tanx, Q = sinx
IF = e∫Pdx = e∫2tanxdx = e2log sec x = sec2 x Solution is; y × IF = ∫Q(IF)dx + c
⇒ ysec2 x = ∫sinx sec2 xdx + c
⇒ ysec2 x = ∫tanx secx dx + c
⇒ ysec2x = secx + c
Here; y = 0, x = \(\frac{\pi}{3}\)
⇒ 0 × sec2 \(\frac{\pi}{3}\) = sec\(\frac{\pi}{3}\) + c ⇒ c = -2
⇒ ysec2 x = secx – 2.

Question 6.
(i) The order of the differential equation \(x^{4} \frac{d^{2} y}{d x^{2}}=1+\left(\frac{d y}{d x}\right)^{3}\) is
(a) 1
(b) 3
(c) 4
(d) 2
(ii) Find the particular solution of the (1 + x2) \(\frac{d y}{d x}\) + 2 xy = \(\frac{1}{1+x^{2}}\); y = 0, when x = 1 (5)
Answer:
(i) (d) 2

(ii) (1 + x2) \(\frac{d y}{d x}\) + 2 xy = \(\frac{1}{1+x^{2}}\); y = 0, when x = 1
Plus Two Maths Differential Equations 3 Mark Questions and Answers 38
⇒ 0(1 + 12) = tan-11 + c ⇒ c = \(-\frac{\pi}{4}\)
⇒ y(1 + x2) = an-1x – \(\frac{\pi}{4}\).

Plus One Economics Chapter Wise Questions and Answers Chapter 7 Employment-Growth, Informalisation and Related Issues

Students can Download Chapter 7 Employment-Growth, Informalisation and Related Issues 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 Employment-Growth, Informalisation and Related Issues

Plus One Economics Employment-Growth, Informalisation and Related Issues One Mark Questions and Answers

Question 1.
Some instances of people engaging in economic activity in given below. Identify worker from there.
Answer:
(a) A man who temporarily abstains from work due to illness.
(b) A woman is paid by her employer.
(c) A self-employed farmer.
(d) All the above
Answer:
(d) All the above

Question 2.
Which among the activity?
(a) Trade
(b) Transportation
(c) Construction
(d) Mining
Answer:
(d) Mining

Question 3.
Which organisation is responsible for estimating unemployment in India?
(a) ILO
(b) NSSO
(c) NitiAayog
(d) None of these
Answer:
(b) NSSO

Plus One Economics Chapter Wise Questions and Answers Chapter 7 Employment-Growth, Informalisation and Related Issues

Question 4.
Identify the activity not included in secondary sector.
(a) Quarrying
(b) Manufacturing
(c) Construction
(d) Water supply
Answer:
(a) Quarrying

Question 5.
Choose the correct answer Workforce refers to that part of:
(a) labour force which is employed
(b) population which is employed
(c) population which is forced to work
(d) labour force which is employed
Answer:
(a) labour force which is employed

Question 6.
Name the sector in the main source of employment for the majority of workers in India.
(a) Primary Sector
(b) Secondary Sector
(c) Service Sector
(d) Tertiary sector
Answer:
(a) Primary Sector

Question 7.
Who developed the concept of unemployment in India?
Answer:
National Sample Survey Organisation (NSSO) has developed the concepts of unemployment suitable to Indian conditions.

Question 8.
The newly emerging jobs are found mostly in the …………. sector (Service/agriculture/manufacturing).
Answer:
Service.

Plus One Economics Chapter Wise Questions and Answers Chapter 7 Employment-Growth, Informalisation and Related Issues

Question 9.
Name the main sector providing maximum employment in India?
(a) Agriculture
(b) Industry
(c) Service
(d) None of these
Answer:
(a) Agriculture sector/primary sector.

Plus One Economics Employment-Growth, Informalisation and Related Issues Two Mark Questions and Answers

Question 1.
Meena is a housewife. Besides taking care of household duties, she works in a cloth shop which is owned and operated by her husband. Can she be considered as a worker? Why?
Answer:
Meena’s activities in the cloth shop owned by her husband are not considered as the activity of a worker since she is not paid for her service. If she works in the shop owned by some other person and is paid for her services then she will be considered as a worker.

Question 2.
List any five activities that contribute to national income in India.
Answer:
The activities that contribute to national income in India are:

  • farming
  • trading
  • mining
  • treatment of a doctor in hospital
  • manufacturing
  • forestry

Plus One Economics Chapter Wise Questions and Answers Chapter 7 Employment-Growth, Informalisation and Related Issues

Question 3.
Distinguish between usual status and weekly status?
Answer:
Usual status refers to a situation where a person usually spends majority of his time in work. In India, 183 days of work is a standard cutoff per usual status. On the other hand, if the person is found to be a part of the workforce during the stipulated week, he will be considered as employed by weekly status.

Question 4.
Given below some economic activities. Classify them as primary, secondary and tertiary sector activities. Agriculture, Mining and Quarrying, Manufacturing, Electricity Gas and Water Supply Construction, Trade, Transport and Storage, Services.
Answer:
1. Primary sector

  • Agriculture
  • Mining and Quarrying

2. Secondary sector

  • Manufacturing
  • Electricity, Gas and Water Supply
  • Construction

3. Tertiary sector

  • Trade
  • Transport and Storage
  • Services

Question 5.
What is a worker-population ratio?
Answer:
Worker population ratio is the percentage of total population engaged in work. When the total number of workers is divided by population and multiplied by 100, we get the worker – population ratio.
Worker population ratio = \(\frac{\text { Total number of workers }}{\text { Population }} \times 100\)

Question 6.
Write a short note on RLEGP.
Answer:
RLEGP stands for Rural Landless Employment Guarantee Programme. It was introduced in August 1983. This programme guarantees employment to at least one members of every landless family up to 100daysin a year.

Plus One Economics Employment-Growth, Informalisation and Related Issues Three Mark Questions and Answers

Question 1.
Match the following

AB
Primary sectorschool teacher
Secondary sectorFarmer
Tertiary sectorWelder in a factory

Answer:

AB
Primary sectorFarmer
Secondary sectorWelder in a factory
Tertiary sectorSchoolteacher

Plus One Economics Chapter Wise Questions and Answers Chapter 7 Employment-Growth, Informalisation and Related Issues

Question 2.
Raj is going to school. When he is not in school, you will find him working in his farm. Can you consider him as a worker? Why?
Answer:
Raj, when he is busy in his farm contributes to production but he is not paid for his work. He helps his parents in agricultural jobs. As he is not paid, he is not a paid worker.

Question 3.
Kerala economy is experiencing huge unemployment problems. Similarly, the number of workers from outside Kerala are visiting our states and engaging in different activities. What do you infer from this? Justify your answer.
Answer:
In Kerala there exists problem of unemployment, especially educated unemployment. The educated people are usually unwilling to engage in manual works and therefore prefer white color jobs. They often go outside the state and even abroad to find a suitable job in accordance with their education level. At the same time, the usual works in the state are done by people coming from outside the state.

Plus One Economics Employment-Growth, Informalisation and Related Issues Four Mark Questions and Answers

Question 1.
Name some of the recent employment generation programmes launched by the Govt, of India.
Answer:
Following are some of the recent employment generation programmes launched by the Govt, of India.

  • Rural Landless employment Guarantee programme (RLEGP)
  • National Rural Employment Guarantee programme (NREGP)
  • Bharat Nirman Programme
  • Janani Suraksh%JTojana

Question 2.
Distinguish between open unemployment and technical unemployment?
Answer:
When the country’s labour force does not get opportunities for gainful employment, it is termed as open unemployment. On the other hand technical unemployment refers to persons who have been thrown out of work by the introduction of superior technology.

Plus One Economics Chapter Wise Questions and Answers Chapter 7 Employment-Growth, Informalisation and Related Issues

Question 3.
Classify the following into organized sector and unorganized sector.
Street vender, school teacher, business executive, agricultural labourer, mechanic, railway ticket examiner, college professor, software engineer, head load worker, cart puller, washerman.
Answer:
1. Organized sector:

  • Schoolteacher
  • Business executive
  • Mechanic
  • Railway ticket examiner
  • College professor
  • Software engineer

2. Unorganized sector:

  • Street vender
  • Agricultural labourer
  • Head load worker
  • Cart puller
  • Washerman

Question 4.
Analyze the recent trends in sectoral distribution of workforce in India.
Answer:
Primary sector is the main source of employment for majority of workers in India. Secondary sector provides employment to only 16% of workforce. About 24% of workers are in service sector. More than three – fourth of the workforce in the rural India depends on agriculture and mining. About 10% of the rural workers are working in manufacturing industries, construction and other sectors.

Service sector provides employment to only about 13% of rural workers. About 60% of urban workers are in the service sector. The secondary gives employment to about 30% of the urban workforce. Women workers concentration is very high in primary sector. Men get opportunities in both secondary and services sectors.

Question 5.
Prepare a note on NREGP.
Answer:
The government of India passed an Act in Parliament known as the National Rural Employment Guarantee Act 2005. As a result of this act, the employment generation programme known as National Rural Employment Guarantee Programme (NREGP) came into existence. By 2008, it has been extended to all the districts of the country.

lt promises 10Odays of guaranteed wage employment to all adult members of rural households who volunteer to do unskilled manual work. The families, which are living below poverty line, will be covered under the scheme. This scheme is one of the many measures that the government implements to generate employment for those who are in need of jobs in rural areas.

Plus One Economics Employment-Growth, Informalisation and Related Issues Five Mark Questions and Answers

Question 1.
The following table shows Worker-Population Ratio in India during 1999-2000.
Plus One Economics Chapter Wise Questions and Answers Chapter 6 Rural Development img4

  1. Analyze the table
  2. Give reasons for the findings

Answer:
1. It shows the different levels of participation of people in economic activities. For every 100 persons, about 40 (by rounding off 39.5) are workers in India. In urban areas, the proportion is about 34 whereas in rural India, the ratio is about 42.

2. People in rural areas have limited resources to earn a higher income and participate more in the employment market. Many do not go to schools, colleges and other training institutions. Even if some go, they discontinue in the middle to join the workforce; whereas, in urban areas, a considerable section is able to study in various educational institutions.

Urban people have a variety of employment opportunities. They look for the appropriate job to suit their qualifications and skills. In rural areas, people cannot stay at home as their economic condition may not allow them to do so.

Plus One Economics Chapter Wise Questions and Answers Chapter 7 Employment-Growth, Informalisation and Related Issues

Question 2.
Suggest the measures to be adopted to solve the problem of unemployment in India?
Answer:
Measures to solve the unemployment in India are suggested as follows.

  1. Investment in heavy and basic industries and consumer goods industries should be increased. They should provide more employment with the supply consumer goods.
  2. Cottage and small scale industries should be developed because they provide more employment by adopting labour intensive technique.
  3. Educational System should be changed. Emphasis should be given to vocational education.
  4. Means of transport and communication should be developed.
  5. Rapidly rising population should be checked by adopting family planning and welfare schemes,
  6. Rural work programme should be developed.
  7. Youth enterpreneurs should be financed for self-employment.
  8. Infrastructure of the economy should be increased.

Question 3.
How far formal sector is differentiated from informal sector? Point out some of the benefits of working in the formal sector. Analyze the informalization found among the Indian workforce.
Answer:
All the public sector establishments and those private sector establishments which employ 10 hired workers or more are called formal sector establishments and those who work in such establishments are formal sector workers. All other enterprises and workers working in those enterprises form the informal sector.

Thus, informal sector includes millions of farmers, agricultural labourers, owners of small enterprises and people working in those enterprises as also the self-employed who do not have any hired workers.

There are several benefits enjoyed by the workers in the formal sector. Some of them are :

  • Those who are working in the formal sector enjoy social security benefits.
  • They earn more than those in the informal sector.
  • Developmental planning envisaged that as the economy grows, more and more workers would become formal sector workers and the proportion of workers engaged in the informal sector would dwindle.

We learn that there are about 400 million workers in the country. There are about 28 million workers in the formal sector. That is only about seven per cent (28/400 × 100). Thus, the rest 93 per cent are in the informal sector. Out of 28 million formal sector workers, only 4.8 million, that is, only 17 percent (4.8/28 × 100) are women.

In the informal sector, male workers account for69 per cent of the workforce Since the late 1970s, many developing countries, including India, started paying attention to enterprises and workers in the informal sector as employment in the formal sector is not growing.

Workers and enterprises in the informal sector do not get regular income; they do not have any protection or regulation from the government. Workers are dismissed without any compensation. Technology used in the informal sector enterprises is outdated; they also do not maintain any accounts. Workers of this sector live in slums and are squatters.

Plus One Economics Chapter Wise Questions and Answers Chapter 7 Employment-Growth, Informalisation and Related Issues

Question 4.
Discuss causes responsible for unemployment in India.
Answer:
The causes responsible for unemployment in India may be discussed below.
1. Slow economic growth:
The nature of Indian economy is underdeveloped and the rate of economic growth is slow. This causes lower employment opportunities to the rising population.

2. Rapid Growth of Population:
Constant increase in population has been a great problem of India. It is one of the main causes of unemployment. Despite the completion of nine Five Year Plans, the number of unemployed has actually increased inspite of decreasing.

3. Agriculture:
A Seasonal Occupation: Agriculture is so underdeveloped in India that it largely offers seasonal employment. Most of the farmers remain idle for three to four months in a year. The volume of disguised unemployment is estimated to be nearly 15 percent of the total working population in agriculture.

4. Lack of Irrigation Facilities:
Despite the completion of Nine Five Year Plans, irrigation facilities could be provided only to 34 percent of agriculture area. For want of irrigation only one crop is grown in a year on the large part of agricultural land. Consequently, the farmers remain unemployed for quite sometime during the year.

5. Joint Family Systme:
It encourages disguised unemployment. Joint family system is more prevalent in rural areas; hence a high degree of disguised unemployment exists there.

6. Decline of Cottage and Small Industries:
The industrial development policy adopted by the Britishers adversely affected the artisans working in small and cottage industries. The goods previously produced by these industries are now being produced by large scale industries.

These artisans were, therefore, thrown out of employment. After Independence, Government of India has been taken several measures to revive and develop small scale and cottage industries, but still, these continue to be in distress.

7. Low Savings and Investment:
There is shortage of capital in India, and even the scarce capital has not been wisely invested. Bulk of the capital has been invested in large scale industries with high capital-output ratio needing more capital per unit of output.

8. Mobility of Labour:
Mobility of labour in India is very low. Owing to their attachment to the family, people generally do not move out to far off areas even when jobs are available there. Factors like diversity of language, religion and customs also contribute to low mobility. Lesser the mobility, greater the unemployment.

Plus One Economics Chapter Wise Questions and Answers Chapter 6 Rural Development

Students can Download Chapter 6 Rural Development 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 Rural Development

Plus One Economics Rural Development One Mark Questions and Answers

Question 1.
Rural developments include:
(i) education and skill developments
(ii) land reforms
(iii) measures for alleviation of poverty
(iv) all of the above
Answer:
(iv) all of the above

Question 2.
Shift of workforce from agriculture to other allied activities like livestock, poultry, fisheries, etc, is known as.
Answer:
Diversification.

Question 3.
Golden revolution is associated with?
(i) Horticulture
(ii) Livestock
(iii) Fisheries
(iv) Pulses
Answer:
(i) Horticulture

Plus One Economics Chapter Wise Questions and Answers Chapter 6 Rural Development

Question 4.
How many banks were nationalised in 1969?
(i) 6
(ii) 9
(iii) 14
(iv) 20
Answer:
(iii) 14

Question 5.
White revolution is related to
(i) Bamboo
(ii) Cash crop
(iii) Milk
(iv) Foodgrain
Answer:
(iii) Milk

Question 6.
Blue revolution is related to
(i) Milk
(ii) Fish
(iii) Egg
(iv) None of these
Answer:
(ii) Fish

Question 7.
Which among the following is an advantage of organic fanning
(i) It is labour intensive
(ii) It is environment-friendly
(iii) It uses locally produced organic inputs
(iv) All the above
Answer:
(iv) All the above

Question 8.
Complete the following statement.
The credit provisions of SHGs are generally referred to as ………………..
Answer:
Microcredit programs.

Plus One Economics Chapter Wise Questions and Answers Chapter 6 Rural Development

Question 9.
“Regulated Market yards benefit farmers as well as consumers”. Do you agree with this statement?
Answer:
Yes, I agree with this statement that the Regulated Market yields benefit farmers as well as consumers.

Plus One Economics Rural Development Two Mark Questions and Answers

Question 1.
What is TANWA?
Answer:
TANWA stands for Tamil Nadu Women in Agriculture. It is a project initiated in Tamil Naud to train women in latest agricultural techniques. It includes women to actively participate in raising agricultural productivity and family income. They promote small scale household activities like soap manufacturing, doll making etc.

Question 2.
Name few horticultural crops.
Answer:
Names of horticultural crops are:

  • Fruits
  • Vegetables
  • Medicinal plants

Plus One Economics Rural Development Three Mark Questions and Answers

Question 1.
Complete the following.
a. Percentage of population living in the rural area is
(i) 25%
(ii) 50%
(iii) 75%
(iv) 90%
b. NABARD is the open bank providing credit to sector
(i) ombined sector
(ii) industrial sector
(iii) agricultural sector
(iv) tertiary sector
c. The Golden revolution was a period of very high productivity in
(i) food grain production
(ii) horticulture
(iii) organic farming
(iv) pisciculture
Answer:
a. (iii) 75%
b. (iii) agricultural sector
c. (ii) horticulture

Question 2.
Why the co-operative marketing could not gain momentum in India?
Answer:
Co-operative marketing has failed to gain adequate success in India because of inadequate coverage of farmer members and lack of appropriate link between marketing and processing management.

Question 3.
What do you mean by organic farming?
Answer:
Eco-friendly technology of cultivation is known as organic farming, it is the farming without using chemical fertilizers or pesticides. It uses natural mannure.

Plus One Economics Chapter Wise Questions and Answers Chapter 6 Rural Development

Question 4.
Give reasons for the declining share of agriculture in GDP of India.
Answer:
After the initiation of reforms, the growth rate of agriculture sector has declined to 2.3% during the 1990s which was lower than earlier years. The reasons for this decline are inadequate infrastructure, alternate employment opportunities in the industry or service sector, increase in casualisation of employment in agriculture, etc.

Question 5.
Explain the term ‘golden revolution’.
Answer:
The growth of horticulture sector at a spectacular speed is called ‘Gloden Revolution’. The period between 1991 – 2003 is known as the period of golden revolution. During this period, the investment in horticulture became highly productive and the sector emerged as a sustainable livelihood option. Thus India could become leading producer of mangoes, bananas, coconuts etc.

Question 6.
Name a few traditional industries in India.
Answer:
The traditional industries of India are:

  • Pottery
  • Crafts
  • Handloom
  • Textiles
  • Bamboo

Question 7.
Prepare a note on ‘Kudumbashree’ in Kerala.
Answer:
Kudumbasree is a women-oriented community-based poverty reduction programme being implemented in kerala. The objective of this group is to encourage savings. The small savings in women’s group creates more employment and productive atmosphere in women’s groups.

Question 8.
Prepare a note on NABARD?
Answer:
NABARD stands for National Bank for Agriculture and Rural Development. It was established in 1982, July. It has been assigned the role performed by agricultural refinance and development corporation and also the role performed by RBI for rural credit. NABARD provides short term loans for agricultural operation.

Plus One Economics Rural Development Four Mark Questions and Answers

Question 1.
What are the alternative channels available for agricultural marketing? Give examples:
Answer:
Following are the alternative channels available for agricultural marketing.

  1. Co-operative Credit Societies
  2. Reserve Bank of India
  3. Regional Rural Banks
  4. Commercial Banks
  5. NABARD
  6. Self Help Groups (SHGs)

Plus One Economics Chapter Wise Questions and Answers Chapter 6 Rural Development

Question 2.
Critically appraise Rural banking operations in the light of recent farmers suicides in India.
Answer:
Operation of rural banking had a positive effect on rural farm and non-farm output, income, and employment. Farmers were given a variety of loans for meeting production needs. This helped India to achieve food security and to gain a huge buffer stock of grains.

However our banking system in the rural area could not meet all loan needs of the farmers. Some of the farmers still depend on local moneylenders. This system failed to develop a culture of deposit mobilization. Agriculture loan default was very high.

Question 3.
Mention some obstacles that hinder the mechanism of agricultural marketing.
Answer:
The farmers suffer from many problems relating to agricultural marketing. Some obstacles that hinder the mechanism of agricultural marketing are mentioned below.

  • faulty weighing
  • manipulation of accounts
  • forced to sell at lower prices
  • lack of proper storage facilities
  • lack of infrastructure facilities
  • inadequate coverage of farmers by cooperatives
  • inefficient financial management

Question 4.
Match the following.
Plus One Economics Chapter Wise Questions and Answers Chapter 6 Rural Development img1
Answer:
Plus One Economics Chapter Wise Questions and Answers Chapter 6 Rural Development img2

Question 5.
‘Rainbow revolution is meant for overall agricultural development’, comment.
Answer:
The rainbow revolution is meant for overall development of Indian agriculture. Under rainbow revolution, the following revolutions are included.
Plus One Economics Chapter Wise Questions and Answers Chapter 6 Rural Development img3

Plus One Economics Rural Development Five Mark Questions and Answers

Question 1.
State whether true or false.

  1. Organic food has higher nutritional value compared to non-organic food
  2. Ten commercial banks were nationalized in 1969
  3. Golden revolution happened in fisheries
  4. SHG stands for Social Health Groups
  5. Use of chemical fertilizers lead to pollution.

Answer:

  1. True
  2. False. Fourteen commercial banks were nationalized in 1969
  3. False. Golden revolution happened in horticulture
  4. False. SHG stands for Self Help Groups
  5. True

Question 2.
“Organic farming and sustainable development are closely related to each other”. Substantiate.
Answer:
In recent years, awareness of the harmful effect of chemical-based fertilizers and pesticides on our health is on a rise. Conventional agriculture relies heavily on chemical fertilizers and toxic pesticides etc., which enter the food supply, penetrate the water sources, harm the livestock, deplete the soil and devastate natural eco-systems.

Efforts in evolving technologies which are ecofriendly are essential for sustainable development and one such technology which is eco-friendly is organic farming. In short, organic agriculture is a whole system of farming that restores, maintains and enhances the ecological balance.

There is an increasing demand for organically grown food to enhance food safety throughout the world. Thus it can be stated that organic farming and sustainable development are closely related to each other.

Plus One Economics Chapter Wise Questions and Answers Chapter 6 Rural Development

Question 3.
Identify the benefits and limitations of organic farming.
Answer:
A. Benefits of Organic Farming
1. Organic agriculture offers a means to substitute costlier agricultural inputs with locally produced organic inputs that are cheaper and thereby generate good returns on investment.

2. Organic agriculture also generates incomes through international exports as the demand for organically grown crops is on a rise. Studies across countries have shown that organically grown food has more nutritional value than chemical farming thus providing us with healthy foods.

3. Since organic farming requires more labour input than conventional farming, India will find organic farming an attractive proposition

4. the organic produce is pesticide-free and produced in an environmentally sustainable way

5. Organic fanning helps in sustainable development of agriculture and India has a clear advantage in producing organic products for both domestic and international markets.

B. Limitations of organic farming
1. Popularizing organic farming requires awareness and willingness on the part of farmers to adapt to new technology.

2. Inadequate infrastructure and the problem of marketing the products are major concerns which need to be addressed apart from appropriate agriculture policy to promote organic farming.

3. It has been observed that the yields from organic farming are less than modem agricultural farming in the initial years. Therefore, small and marginal farmers may find it difficult to adapt to large scale production.

4. Organic produce may also have more blemishes . and a shorter shelf life than sprayed produce. Moreover choice in production of off-season crops is quite limited inorganic farming.

Question 4.
Narrate the importance of agricultural diversification in promoting rural sector?
Answer:
Agricultural diversification is a system of fanning that encourages production of a variety of plant and animals and their products. Non-farm employment provides greater income stability, economies of size also reduces uncertainty of business. It involves maximum number of persons as it is labour intensive in nature.

The majority of small and marginal farmers cultivate mainly low-value subsistence crops. In the absence of farm and non-farm employment opportunities, they are forced to live below poverty line. So this problem is solved with the help of commercialisation and diversification of small farmers within and outside agriculture and their proper integration with local and global markets.

This is helpful not only in liberating the small and marginal farmers from the poverty trap, but also to meet the country’s growing demands for fruits, vegetables, milk and milk products, meat, fishes, eggs, etc. which generally show rising trends with increasing levels of per capita income in the economy.

Question 5.
“Rural development focuses on actions for the development of the areas that are lagging behind in the overall development of the development of the village economy” point out the areas of rural development.
Answer:
Rural development is quite a comprehensive term but it essentially means a plan of action for the development of areas which are lagging behind in socio-economic development. Some of the areas which are challenging and need fresh initiatives for development in India include

a. Development of human resources including:

  1. Literacy, more specifically, female literacy, education and skill development
  2. Health, addressing both sanitation and public health

b. Land reforms

c. Development of infrastructure development like electricity, irrigation, credit, marketing, transport facilities including construction of village roads and feeder roads to nearby highways, facilities for agriculture research and extension, and information dissemination

d. Introduction of special measures for alleviation of poverty and bringing about significant improvement in the living conditions of the weaker sections of the population emphasizing access to productive employment opportunities.

Plus One Economics Chapter Wise Questions and Answers Chapter 6 Rural Development

Question 6.
Explain some measures taken by the government to improve agricultural marketing.
Answer:
Agricultural marketing encompasses all activities in moving farm products from the producers to the final consumers such as storage, transport, processing, etc. In India, agricultural marketing was regarded as operationally inefficient and exploitative in character. Hence to improve the position of agricultural marketing following things are required :

  1.  Facilities for storing goods.
  2. Adequate and economical transport.
  3. Eliminination of intermediaries.
  4. Basic information of market conditions to get better prices for the produce.

The above mentioned requirements for efficient agricultural marketing can be also classified into the following.

  1. Promotion of cooperative agricultural marketing societies.
  2. Developing regulated markets where marketing practices have been standardized so as to provide encouragement to farmers to come to mandis to dispose off their produce and prevent them from exploitation in the hand of Dallas.
  3. Granding and standardisation of produce to help the farmer to fetch better prices.
  4. Developing warehousing facilities, road transport, etc.
  5. Declaration of support price that offers a minimum price to the farmers for their produce.

Plus Two Maths Chapter Wise Questions and Answers Chapter 8 Application of Integrals

Students can Download Chapter 8 Application of Integrals 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 8 Application of Integrals

Plus Two Maths Application of Integrals Four Mark Questions and Answers

Question 1.
Consider the following figure.
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 1

  1. Find the point of intersection (P) of the given parabola and the line. (2)
  2. Find the area of the shaded region. (2)

Answer:
1. We have, y = x2 and y = x ⇒ x = x2
⇒ x2 – x = 0 ⇒ x(x – 1) = 0 ⇒ x = 0, 1
When x = 0, y =0 and x = 1, y = 1.
Therefore the points of intersections are (0, 0) and(1, 1).

2. Required area
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 2

Question 2.
1. Find the point of intersection ‘p’ of the given parabola and the line. (2)
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 3
2. Find the area of the shaded region. (2)
Answer:
1. Given, y = x2, y = 2x
⇒ 2x = x2 ⇒ x2 – 2x = 0 ⇒ x(x – 2) = 0 ⇒ x = 0, 2
We have, y = 2x
⇒ when x = 0 ⇒ y = 0, when x = 2 ⇒ y = 4
‘P’ has co-ordinate (2, 4)

2. Area = \(\int_{0}^{2} 2 x d x-\int_{0}^{2} x^{2} d x=\left(x^{2}\right)^{2}-\left(\frac{x^{3}}{3}\right)_{0}^{2}=4-\frac{8}{3}=\frac{12-8}{3}=\frac{4}{3}\).

Plus Two Maths Chapter Wise Questions and Answers Chapter 8 Application of Integrals

Question 3.
Consider the following figure.
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 4

  1. Find the point of Intersection P of the circle x2 + y2 = 32 and the line y = x. (1)
  2. Find the area of the shaded region. (3)

Answer:
1. x2 + x2 = 32 ⇒ 2x2 = 32 ⇒ x2 = 16 = 4
Therefore the point of intersection P is (4, 4).

2. We have x2 + y2 = 32 ⇒ y = \(\sqrt{32-x^{2}}\).
The required area =
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 5
= 8 + [8π – 8 – 4π] = 4π.

Question 4.

  1. Shade the area enclosed by x2 = 4y, y = 2, y = 4 and the y-axis in the first quadrant. (2)
  2. Find the area of the region bound by x2 = 4y, y = 2, y = 4 and the y-axis in the first quadrant. (2)

Answer:
1.
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 6

2. Area
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 7

Plus Two Maths Chapter Wise Questions and Answers Chapter 8 Application of Integrals

Question 5.

  1. Draw a rough sketch of the graph of the function y2 = 4x. (2)
  2. Find the area by the curve and the line x= 2. (2)

Answer:
1.
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 8

2. Area
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 9

Plus Two Maths Application of Integrals Six Mark Questions and Answers

Question 1.

  1. Draw the graph of y2 = 4x and y = x. (2)
  2. Find the points of intersection of y2 = 4x and y = x. (2)
  3. Find the area bounded by the graphs.(2)

Answer:
1. y2 = 4x is a parabola and y = x is a straight line passing through the origin.
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 10

2. x2 = 4x ⇒ x2 – 4x = 0 ⇒ x(x – 4) = 0 ⇒ x = 0, 4
When x = 0, y = 0 and when x = 4, y =4. Therefore the points of intersection are (0, 0) and (4, 4).

3. Area bounded by the graphs = Area under the parabola in the first quadrant – Area under the line.
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 11

Plus Two Maths Chapter Wise Questions and Answers Chapter 8 Application of Integrals

Question 2.

  1. Draw the graph of the function y = x2 and x = y2 in a coordinate axes. (2)
  2. Find the point of intersection of the above graphs. (2)
  3. Find the area of the region bounded by the above two curves. (2)

Answer:
1. The two function are parabolas as shown in the figure.
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 12

2. We have, y = x2 and x = y2
x = (x2)2 ⇒ x – x4 = 0 ⇒ x(1 – x3) = 0 ⇒ x = 0, 1
When x= 1, y= 1 and x = 0, y = 0.
Therefore the point is (0, 0) and (1, 1).

3. The required area = \(\int_{0}^{1} \sqrt{x} d x-\int_{0}^{1} x^{2} d x\)
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 13

Question 3.
Using the figure answer the following questions
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 14

  1. Find the area of the shaded region as the sum of the area of two triangles. (2)
  2. Define the function of the given graph. (2)
  3. Verify the area of the shaded region using integration. (2)

Answer:
1. Area = Area of ∆OAD + Area of ∆ ABC
\(\frac{1}{2}\) × 3 × 3 + \(\frac{1}{2}\) × 2 × 2 = \(\frac{9}{2}\) + 2 = \(\frac{13}{2}\).

2. Area = \(\int_{0}^{5}\)f(x) dx = \(\int_{0}^{3}\)(-x + 3) dx + \(\int_{3}^{5}\)(x – 5) dx
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 15
Therefore verified.

Plus Two Maths Chapter Wise Questions and Answers Chapter 8 Application of Integrals

Question 4.
The figure given below contains a straight line L with slope \(\sqrt{8}\) and a circle.
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 16

  1. Find the equation of the line L and circle. (1)
  2. Find the point of intersection P. (2)
  3. Find the area of the shaded region. (3)

Answer:
1. The line L passes through origin and have slope 3, therefore its equation is y = \(\sqrt{8}\) x. The circle passes through origin and have radius 3, therefore its equation is x2 + y2 = 9.

2. We have, y =3x and x2 + y2 = 9
⇒ x2 + (\(\sqrt{8}\)x)2 = 9 ⇒ 9x2 = 9
⇒ x = 1
∴ y = \(\sqrt{8}\) × 1 = \(\sqrt{8}\).
Therefore, coordinate of ‘P’ is (1, \(\sqrt{8}\)).

3. Area of the shaded region
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 17

Plus Two Maths Chapter Wise Questions and Answers Chapter 8 Application of Integrals

Question 5.
Using the given figure answer the following
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 18

  1. Define the equation of the circle and ellipse in the figure. (1)
  2. Find the area of the ellipse using integration. (4)
  3. Find the area of the shaded region. (Use formula to find the area of the circle.) (1)

Answer:
1. From the figure equation of the circle is x2 + y2 = 4 and that of the ellipse is \(\frac{x^{2}}{4}+\frac{y^{2}}{1}=1\).

2. We have, \(\frac{x^{2}}{4}+\frac{y^{2}}{1}=1\)
⇒ y2 = 1 ⇒ y = \(\frac{1}{2} \sqrt{4-x^{2}}\)
Area of the ellipse = 4 \(\int_{0}^{2}\)y dx
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 19

3. Area of the circle of radius 2 = π (2)2 = 4π
∴ Area of the shaded region = Area of the circle – Area of the ellipse
= 4π – 2π = 2π.

Question 6.

  1. Find the area bounded by the curve y = sin x with X – axis, between x = 0 and x = 2π. (2)
  2. Find the area of the region bounded by the curve y = x2 and y = |x| (4)

Answer:
1. Area of y = sin x in each loop is same. Therefore;
2\(\int_{0}^{\pi}\)sin xdx = \(-2(\cos x)_{0}^{\pi}\) = -2 (cos π – cos0)
= -2(-1 – 1) = 4

2.
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 20
Area
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 21

Plus Two Maths Chapter Wise Questions and Answers Chapter 8 Application of Integrals

Question 7.
Using integration, find the area of the region bounded by the triangle whose vertices are(-1, 1), (0, 5) and (3, 2). (6)
Answer:
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 22
Equation of BC is \(\frac{y-5}{1-5}=\frac{x-0}{-1-0}\)
⇒ y – 5 = 4x ⇒ 4x – y + 5 = 0 ⇒ y = 4x + 5
Equation of AB is x + y – 5 = 0 ⇒ y = 5 – x
Equation of AC is x – 4y + 5 = 0 ⇒ y = \(\frac{x}{4}+\frac{5}{2}\)
The required area = Area of the region PABCQP – Area of the region PACQP
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 23

Question 8.
Consider the functions f(x) = sin x and g(x) = cosx in the interval [0, 2π]

  1. Find the x coordinates of the meeting points of the functions. (1)
  2. Draw the rough sketch of the above functions. (2)
  3. Find the area enclosed by these curves in the given interval. (3)

Answer:
1. f(x) = sin x and g(x) = cos x meet at multiples of \(\frac{\pi}{4}\)
x = \(\frac{\pi}{4}\), \(\frac{5 \pi}{4}\).

2.
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 24

3. Area = 2{Area under f(x) = sinx from \(\frac{\pi}{4}\) to π – Area under g(x) = cosx from \(\frac{\pi}{4}\) to \(\frac{\pi}{2}\)}
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 25

Plus Two Maths Chapter Wise Questions and Answers Chapter 8 Application of Integrals

Question 9.

Evaluate \(\int_{0}^{r} \sqrt{r^{2}-x^{2}} d x\), where r is a fixed positive number. Hence prove the area of the circle of radius r is π r2. (2)
Find the area of the circle, x2 + y2 = 16 which is exterior to parabola y2 = 6x. (4)

Answer:
1.
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 26
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 27

2. Given, x2 + y2 = 16 and y2 = 6x ⇒ x2 + 6x = 16 ⇒ x2 + 6x – 16 = 0 ⇒ (x + 8)(x – 2) = 0 ⇒ x = -8, 2.
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 28
Area = Area of the circle – Interior area of the parabola.
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 29

Plus Two Maths Chapter Wise Questions and Answers Chapter 8 Application of Integrals

Question 10.
Using the figure answer the following questions
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 30

  1. Define the equation of the ellipse and circle in the given figure. (1)
  2. Find the area of the ellipse using integration. (4)
  3. Find the area of the shaded region. (Area of the circle can be found using direct formula). (1)

Answer:
1. Equation of the ellipse is \(\frac{x^{2}}{4}+\frac{y^{2}}{1}=1\) and circle is x2 + y2 = 1.

2. We have, \(\frac{x^{2}}{4}+\frac{y^{2}}{1}=1\)
⇒ y2 = 1 ⇒ y = \(\frac{1}{2} \sqrt{4-x^{2}}\)
Area of the ellipse = 4 \(\int_{0}^{2}\)y dx
Plus Two Maths Application of Integrals 4 Mark Questions and Answers 31

3. Area of the circle = πr2 = π × 1 = π
Required area = Area of ellipse – area of the circle = 2π – π = π.