Plus One

Kerala State Board New Syllabus Plus One Maths Chapter Wise Previous Questions and Answers Chapter 16 Probability.

Kerala Plus One Maths Chapter Wise Previous Questions Chapter 16 Probability

Plus One Maths Probability 3 Marks Important Questions

Question 1.
(i) If \(\frac{2}{11} \) is the probability of an event A, then what is the probability of the event ‘not A’? (MARCH-2011)
(ii) If P(A) = \(\frac{3}{5} \) and P(B) = \(\frac{1}{5} \) , then find P(A∪B), if A and B are mutually exclusive events.
(iii) A coin is tossed twice. What is the probability that atleast one tail occurs?
Answer:

Question 2.
A bag contains 9 balls of which 4 are red, 3 are blue and 2 are yellow. The balls are similar in shape and size. A ball is drawn at random from the bag. Calculate the probability that the ball drawn will be (MARCH-2013)
(i) Red.
(ii) Not yellow.
(iii) Either red or yellow.
Answer:
(i) P (Red) = \(\frac{4}{9} \)
(ii) P(No yellow) \(\frac{7}{9} \)
(iii) P(Either red or yellow) = \(\frac{4+2}{9}=\frac{6}{9}=\frac{2}{3}\)

Question 3.
A and B are two events in a random experiment such that \(P(A)=\frac{1}{3} ; P(B)=\frac{1}{5} ; P(A \cup B)=\frac{7}{15}\) (IMP-2014)
(i) Find P(A∩B)
(ii) Find P(A’)
Answer:

Question 4.
(i) The probability of a sure event is ……… (IMP-2014)
(ii) Two dice are thrown together. What is the probability that the sum of the numbers on the two faces is 8?
Answer:
(i) 1
(ii) A = {(2,6),(3,5),(4,4),(5,3),(6,2)}
\(P(A)=\frac{5}{36}\)

Question 5.
If A and B are two events such that P(A) = 0.42, P(B) = 0.48 andP(yinS) = 0.16 then, find: (IMP-2014)
(i) P(not A)
(ii) P(not B)
(iii) P(A∪B)
Answer:
(i) P(not A) = P(A’) = 1-P(A) = 1-0.42=0.58
(ii) P(not B) = P(B’) -1 -P(B) = 1 -0.48=0.52
(iii) P(A∪B) = P(A) + P(B)-P(A∩B)
= 0.42 + 0.48-0.16 = 0.74

Plus One Maths Probability 4 Marks Important Questions

Question 1.
Two students A and B appeared in an examination. The probability that A passes the examination is 0.25 and that B passes is 0.45. Also the probability that both will pass is 0.1. Find the probability that: (MARCH-2010)
i) Both will not pass.
ii) Only one of them will pass.
Answer:

Question 2.
If M and N are events such that: (IMP-2010)

Find
i) P(M or N)
ii) P(not M and not N)
(Imp (Science) – 2010)
Answer:

Question 3.
A and B are two events associated with (MARCH-2013)
i) a random experiment such that P(A) = 0.3, P(B) = 0.4 and P(A∪B) = 0.5
a) Find P(A∩B)
b) Find P(A’∪B’)
ii) A coin is tossed twice. What is the probability that at least one tail occurs?
Answer:

Question 4.
If A and B are two events in a random (IMP-2013)
experiment, then P(A) + P(B)-P(A∩B) = ……….
ii) Given P(A) = 0.5, P(B) = 0.6 and P(A∩B)=03. Find P(A∪B) and P(A’)
iii) Two dice are thrown simultaneously.
Find the probability of getting a doublet.
Answer:

Question 5.
The probability that Ramu pass the examination in both Mathematics and Physics is 0.5, the probability of passing neither Mathematics nor Physics is 0.1, the probability of passing Mathematics is 0.75 (MARCH-2014)
i) What is the probability of passing Mathematics or Physics?
ii) What is probability of passing Physics?
Answer:

Question 6.
If A and B are two events such that (MARCH-2014)

then find;
4 2 8
i) P(A’)
ii) P(A∪B)
iii) P(A∩B)
Answer:

Question 7.
The number of outcomes in the sample space of the random experiment of throwing two dice is… (MARCH-2015)
a) 6³
b)6
c) 6²
d)12
ii) Two students, Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is 0.05
Answer:
i) 6²

Question 8.
i) If A and B are mutually exclusive and exhaustive events then
P(A) + P(B) = ……….. (IMP-2015)
a) 0
b) 1
c) 1/2
d) 2
ii) Two students A and B appeared in an examination. The probability that A will qualify the examination is 0.25 and B will qualify is 0.45 and both will qualify the examination is 0.1. Find the probability that: (IMP-2015)
a) Both A and B will not qualify the examination.
b) One of them will qualify the examination.
Answer:
i) b) 1

Question 9.
i) In a random experiment, 6 coins are tossed simultaneously. Write the number of sample points in the sample space. (MARCH-2016)
(a) 2² 
(b) 2⁴
(c) 2⁶
(d) 2⁵
ii) Given that P(A) = 0.5, P(B) = 0.6,
P(A∩B) = 0.3
Find P(A’),P(A∪B),P(A’∩B’) and P(A’∪B’)
Answer:

Question 10.
i) If P(A’) = 0.8 .write the value of P(A). (SAY-2017)
ii) In a class of 60 students; 30 selected for NCC, 32 selected for NSS and 24 selected for both NCC and NSS. If one of these students is selected at random, find the probability that:
a) the students selected for NCC or NSS.
b) the students has selected neither NCC nor NSS.
Answer:

Plus One Maths Probability 6 Marks Important Questions

Question 1.
Two dice are thrown. Let A be an event to get an even number on first die and B be an event to get sum of the numbers obtained on two dice is 8. (IMP-2011)
i) Write the sample space.
ii) Write the outcomes favorable to the event A, the event B.
iii) Find P(A or B).
Answer:

Question 2.
A box contains 6 red, 5 blue and 4 green balls. 3 balls are drawn from the box. Find the probability that (IMP-2011)
i) All are blue.
ii) All balls are either red or blue.
iii) Atleast one green ball.
Answer:

Question 3.
i) A coin is drawn repeatedly until a tail comes up. What is the sample space (IMP-2012)
a) no head
b) exactly one head.
c) atleast one head.
d) atleast two heads.
Answer:

Question 4.
If E and F are two events such that (IMP-2012)

find
i) P(E);P(F)
ii) P(E or F)
iii) P(not E and not F)
Answer:

Question 5.
John and Mary appeared in an examination. The probability that John will qualify the examination is 0.05 and that Mary will qualify the examination is 0.10. The probability that both will qualify is 0.02. Find the probability that (MARCH – 2012)
i) John or Mary qualifies the examination.
ii) Both John and Mary will not qualify the examination.
iii) Atleast one of them will not qualify the examination.
Answer:

Question 6.
In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find: (MARCH – 2012)
i) The probability that the student opted for NCC or NSS.
ii) The probability that the student has opted for exactly one of NCC or NSS.
Answer:
i) Let the events be defined as A – NCC and B – NSS

Question 7.
i) A coin is tossed repeatedly until a head comes up. Write the sample space,
ii) If A and B are two events in a random experiment, then (MARCH – 2014)
P(A∪B) = P(A) + P{B) – …………
iii)

Find P(not A and not B).
iv) A bag contains 9 discs of which 4 are red, 3 are blue and 2 are yellow. A disc is drawn at random from the bag. Calculate the probability that it will be
a) Red.
b) Not yellow.

Answer:

Question 8.
Match the following: (MARCH-2017)
i)

ii) Two dice are thrown at random. Find the probability of
a) Getting a doublet.
b) Getting sum of the numbers on the
dice 8.
Answer:

Kerala State Board New Syllabus Plus One Maths Chapter Wise Previous Questions and Answers Chapter 14 Mathematical Reasoning.

Kerala Plus One Maths Chapter Wise Previous Questions Chapter 14 Mathematical Reasoning

Plus One Maths Mathematical Reasoning 3 Marks Important Questions

Question 1.
i) Write the converse of the statement. (IMP-2010)
p: If a divides b then b is a multiple of a.
ii) Consider the compound statement,
p: 2 + 2 is equal to 4 or 6
1) Write the component statements.
2) Is the compound statement true? Why?
Answer:
i) Converse statement is “If a is a multiple of b then a divides b.”
ii) 1) q: 2+2 is equal to 4
r. 2+2 is equal to 6.
2) q is true and r is false, so p is true.

Question 2.
Verify by method of contradiction p. √2 is irrational. (IMP-2012)
Answer:
Assume that √2 is rational. Then can be written in the form √2 = \(\frac { p }{ q }\) , where p and q are integers without common factors.
Squaring; 2 = \(\frac { p² }{ q² }\)
=> 2q² = p²
=> 2 divides p² => 2 divides p
Therefore, p = 2k for some integer k.
=> p² = 4k²
=> 2q² = 4k²
=> q² = 2k²
=> 2 divides q² => 2 divides q
Hence p and g have common factor 2, which
contradicts our assumption. Therefore, √2 is irrational.

Question 3.
i) Write the negation of the following . statement, ‘Every natural number is an integer’. (MARCH-2013)
ii) Write the contrapositive and converse of the following statement, ‘If x is a prime number, then x is odd ’.
Answer:
Negation of the statement is ‘Every natural ’ number is not an integer’,
ii) The contrapositive statement, ‘If x is not odd, then x is not a prime number.’
The converse of the statement, ‘If x is odd, then x is a prime number’.

Question 4.
i) Write the component statement of the  following statement: “All rational
numbers are real and all real numbers are complex. (IMP-2014)
ii) Write the contrapositive and converse
of the following statement: ‘If a number is divisible by 9, then it is divisible by 3.’
(Imp (Commerce) – 2014)
Answer:
i) p: All rational numbers are real,
q: All real numbers are complex,
ii) Contrapositive:
If a number is not divisible by 3, it is not divisible by 9.
Converse:
If a number is divisible by 3 then it is divisible by 9.

Question 5.
i) Write the negation of the statement: the sum of 3 and 4 is 9. (IMP-2014)
ii) Write the component statements of ‘Chandigarh is the capital of Haryana and Uttar Pradesh.’
iii) Write the converse of the statement: ‘If a number n is even, then n² is even.’
Answer:
i) Negation: ‘The sum of 3 and 4 is not equal to 9.’
ii) p: Chandigarh is the capital of Haryana.
q: Chandigarh is the capital of Uttar Pradesh.
iii) Converse: If a number n² is even then n is even.

Plus One Maths Mathematical Reasoning 4 Marks Important Questions

Question 1.
i) Write the negation of the statement.“Both the diagonals of a rectangle have the same length.” (MARCH-2013)
ii) Prove the statement, “Product of two odd integers is odd,” by proving its contrapositive.
Answer:
i) “Both the diagonals of a rectangle do not have the same length.”
ii) Let us name the statements as below p: ab is odd. q: a, b is odd.
We have to check p => q is true or not, that is by checking its contrapositive statement
~ q =>~ p
~ q: ab is even.
Let a and b be two even numbers. Then, a = 2n and b = 2m, where m and n are any integer.
a x b = 2n(2m) = 4 nm
Then product of a and b is even. That is ~ p is true. Hence by the contrapositive principle we say that “Product of two odd integers is odd,”

Question 2.
Consider the compound statement “ √5 is a rational number or irrational number”. (IMP-2011)
i) Write the component statements of
above and check whether these component statements are true or false.
ii) Check whether the compound statement is true or false.
(Imp (Commerce) – 2011)
Answer:
i) The component statements are
p: √5 is a rational number
q: √5 irrational number.
Here p is false and q is true,
ii) In this compound statement “or” is exclusive, p is false and q is true and therefore compound statement is true.

Question 3.
i) Write the converse of the statement: “If a number n is even, then n² is even” (MARCH-2011)
ii) Verify by method of contradiction: “ √2 is irrational”.
Answer:
i) “If n² is even, then n is even”
ii) Assume that √2 is rational. Then √2 can
be written in the form √2=\(\frac { p }{ q }\), where p and q are integers without common factors.
Squaring; 2 = \(\frac { p² }{ q² }\)
=> 2q²= p²
=> 2 divides p² => 2 divides p
Therefore, p = 2k tot some integer k.
=> p² = 4k²
=> 2q² = 4k²
=> q² = 2k²
=> 2 divides
q² => 2 divides q
Hence p and g have common factor 2, which contradicts our assumption.
Therefore, √2 is irrational.

Question 4.
Which of the following sentences are statements? Give reason for your answer. (IMP-2012)
a) The cube of a natural number is an odd number.
b) The product of (- 4) and (- 5) is 20.
Write the negation of the following statements and check whether the resulting statements are true.
a) √2 is rational.
b) Every natural number is greater than zero.
Answer:
a) This sentence is a statement. Since for a particular natural number it is true
and for other it is false. (1)³ = 1 and 2³ = 8
b) This sentence is a statement. Since the product is always 20 and true.
a) √2 is not rational. The negation statement is true.
b) Every natural number is not greater than zero. The negation statement is false.

Question 5.
Consider the statement, “If x is an integer and x² is even, then x is also even.” (MARCH-2012)
i) Write the converse of the statement.
ii) Prove the statement by the contra-positive method.
Answer:
i) Converse of the statement is “If x is an even number, then x is an integer and x² is even.”
ii) The contrapositive of a statement p => q is the statement ~ q => ~ p .
The contrapositive statement is “If x is an odd integer, then x² is odd.”
Let x is an odd number.
Then x= 2n+1
x² =(2n+1)² =4n² +4n+1
= 4(n² +n)+1
Which is odd.
ie; if q is not true then p is not true.

Question 6.
i) Write the negation of the following statement: “All triangles are not equilateral triangles”. (MARCH-2013)
ii) Verify by the method of contradiction. p:√7 is irrational.
Answer:
i) All triangles are equilateral triangles
ii) Assume that is rational. Then √7 can be written in the form√7 =\(\frac { p }{ q }\), where p and q are integers without common factors.
Squaring; 7 = \(\frac { p² }{ q² }\)
=> 7q² = p²
=> 7 divides p² => 7 divides p
Therefore, p = 7k tot some integer k.
=>p² = 49k²
7q² = 49k²
=>q² = 7k²
=>7 divides q² =>7 dividesq
Hence p and q have common factor 7, which contradicts our assumption.
Therefore, √7 is irrational.

Question 7.
i) Write the contrapositive of the statement. “If x is a prime number, then x is odd.” (IMP-2013)
ii) Verify by the method of contradiction p : √5 is irrational.
Answer:
i) Contrapositive statement is “If x is not odd, then x is not prime number.”
ii) Assume that √5 is rational. Then √5 can be written in the form √5 = \(\frac { p }{ q }\), where p and q are integers without common factors.
=> 5q² = p²
=> 5 divides p²=> 5 divides p
Therefore, p = 5k for some integer k.
=>p² = 25k²
=> 5q² = 25k²
=> q² = 5k²
=> 5 divide q² => 5 divides q
Hence p and g have common factor 5, which contradicts our assumption.
Therefore, √5 is irrational.

Question 8.
i) Write the negation of the following statement : “ √5 is not a complex number.” (MARCH-2014)
ii) Verify using the method of contradiction:
“p: √2 is irrational number.”
Answer:
i) Negation statement:” √5 is a complex number.”
ii) Assume that √2 is rational. Then √2 can
be written in the form √2=\(\frac { p }{ q }\), where p and q are integers without common factors.
Squaring; 2 = \(\frac { p² }{ q² }\)
=> 2q²= p²
=> 2 divides p² => 2 divides p
Therefore, p = 2k tot some integer k.
=> p² = 4k²
=> 2q² = 4k²
=> q² = 2k²
=> 2 divides
q² => 2 divides q
Hence p and g have common factor 2, which contradicts our assumption.
Therefore, √2 is irrational.

Question 9.
i) Write the negation of the statement: “√7 is rational.”  (MARCH-2015)
ii) Prove that“√7 is rational.” by the method of contradiction.
(March – 2015)
Answer:
i) Negation is : “ √7 is not rational.”
ii) Assume that is rational. Then √7 can be written in the form√7 =\(\frac { p }{ q }\), where p and q are integers without common factors.
Squaring; 7 = \(\frac { p² }{ q² }\)
=> 7q² = p²
=> 7 divides p² => 7 divides p
Therefore, p = 7k tot some integer k.
=>p² = 49k²
7q² = 49k²
=>q² = 7k²
=>7 divides q² =>7 dividesq
Hence p and q have common factor 7, which contradicts our assumption.
Therefore, √7 is irrational.

Question 10.
i) Which of the following is the contrapositive of the statement (IMP-2015)
a) q => p
b) ~ p =>~ q
c) ~ q =>~ p
d) p =>~ q
ii) Prove by contrapositive method. “If x is an integer and x² is even then x is also even.”
(Imp-2015)
Answer:
i) c) ~ q =>~ p
ii) The contrapositive of a statement p => q is the statement ~ q => ~ p .
The contrapositive statement is “If x is an odd integer, then x² is odd.”
Let x is an odd number.
Then x= 2n+1
x² =(2n+1)² =4n² +4n+1
= 4(n² +n)+1
Which is odd.
ie; if q is not true then p is not true.

Question 11.
i) Write the negation of the statement: “Every natural number is greater than zero.” (MARCH-2016)
ii) Verify by the method of contradiction: “P: √13 is irrational.”
Answer:
i) Negation of the statement: “It is false that every natural number is greater than zero.”
ii) Assume that √13 is rational. Then √13 can be written in the form √13 = \(\frac { p }{ q }\) ,
where p and q are integers without common factors.
Squaring; 13 = \(\frac { p² }{ q² }\)
=>13q² = p²
=>13 divides p² => 13 divides p
Therefore, p = 13k for some integer k.
=> p² = 169k²
=> 13q² = 169k²
q²= 13k²
=>13 divides q²
=> 13 divides q
Hence p and q have common factor 13, which contradicts our assumption.
Therefore, √13 is irrational.

Question 12.
i) Write the negation of the statement
“ √2 is not a complex number.”
ii) Prove by the method of contradiction,
P: √11 is irrational.”
Answer:
i) “√2 is a complex number.”
ii) Assume that √11 is rational. Then √11 can be written in the form√11 = \(\frac { p }{ q }\),
where p and q are integers without common factors.
Squaring; 11 = \(\frac { p² }{ q² }\)
=> 11q² =p²
=> 11 divides p² => 11 divides p
Therefore, p =11k for some integer k.
=>p² =121 k²
=>11q² = 121k²
=> q² = 11k²
=> 11 divides q² => 11 divides q
Hence p and q have common factor 11, which contradicts our assumption. Therefore,
√11 is irrational.

Question 13.
i) Write the contrapositive of the statement “If a number is divisible by 9, then it is divisible by 3.”
ii) Prove by the method of contradiction.
“P: √5 is irrational.”
Answer:
i) “If a number is not divisible by 9, then it is not divisible by 3.”
ii) Assume that √5 is rational. Then √5 can be written in the form √5 = \(\frac { p }{ q }\), where p and q are integers without common factors.
=> 5q² = p²
=> 5 divides p²
=> 5 divides p
Therefore, p = 5k for some integer k.
=>p² = 25k²
=> 5q² = 25k²
=> q² = 5k²
=> 5 divide q² => 5 divides q
Hence p and g have common factor 5, which contradicts our assumption.
Therefore, √5 is irrational.

Kerala State Board New Syllabus Plus One Maths Chapter Wise Previous Questions and Answers Chapter 13 Limits and Derivatives.

Kerala Plus One Maths Chapter Wise Previous Questions Chapter 13 Limits and Derivatives

Plus One Maths Limits and Derivatives 3 Marks Important Questions

Question 1.
Find the derivative of y = tan x from first principles. (MARCH-2010)
Answer:

Question 2.
Choose the most appropriate answer from those given in the bracket (IMP-2010)

Answer:

Question 3.

(IMP-2010)
Answer:

Question 4.
Using the first principle of derivatives, find the derivatives of \(\frac { 1 }{ x }\) (MARCH-2011)
Answer:

Question 5.
Using the quotient rule find the derivative mof f(x) = cot x (MARCH-2011)
Answer:

Question 6.
Find the derivatives of the following: (MARCH-2011)

Answer:

Question 7.
Prove that (MARCH-2012)

Answer:

Question 8.
Find the derivative of y = cotx from first principles. (MARCH-2012)
Answer:

Question 9.
i) The value of \(\lim _{x \rightarrow 0} \frac{\sin x}{x}\) (MARCH-2013)
ii) Evaluate \(\lim _{x \rightarrow 0} \frac{\sin 4 x}{3 x}\)
Answer:
i) 1
ii)

Question 10.
i) The value of \(\lim _{x \rightarrow a} \frac{x^{n}-a^{n}}{x-a}\) (MARCH-2013)
ii) Evaluate \lim _{x \rightarrow 1} \frac{x^{15}-1}{x^{10}-1}
Answer:

Question 11.
Find the derivative of f(x) = sin x from the first principle. (MARCH-2013)
Answer:

Question 12.
Find the derivative of \(\frac{x+\cos x}{\tan x}\) (MARCH-2014)
Answer:

Question 13.
Find the derivatives of f(x) = sinx using the first principle. (MARCH-2014)
Answer:

Question 14.
Find the derivative of \(\frac{x^{5}-\cos x}{\sin x}\) using the quotient rule. (MARCH-2014)
Answer:

Question 15.
Using the first principle, find the derivative of cosx . (IMP-2011)
Answer:

Question 16.
Find the derivative of \(\frac{\cos x}{2 x+3}\) (IMP-2012)
Answer:

Plus One Maths Limits and Derivatives 4 Marks Important Questions

Question 1.
Evaluate (MARCH-2010)

Answer:

Question 2.
(MARCH-2011)
Answer:

Question 3.
Compute the derivative of sec x with respect to x from first principle. (IMP-2010)
Answer:

Question 4.
Find \(\lim _{x \rightarrow 2} \frac{x^{4}-4 x^{2}}{x^{2}-4}\) (IMP-2011)
ii) If y = sin 2x .Prove that \(\frac{d y}{d x}=\) = 2cos2x
Answer:

Question 5.

(IMP-2011)
Answer:

Question 6.
Find the derivative of y = cosec x from first principle. (IMP-2012)
Answer:

Question 7.
Find the derivative of y = cosec x from first principle. (IMP-2012)
Answer:

Question 8.
Find the derivative of \(\frac{x+1}{x-1}\) from first principle (IMP-2013)
Answer:

Question 9.
i) The value of \(\lim _{x \rightarrow 0} \frac{\sin 5 x}{5 x}\) (MARCH-2014)
ii) Evaluate \(\lim _{x \rightarrow 0} \frac{\sin a x}{\sin b x}, a, b \neq 0\)
Answer:
i) 1
ii)

Plus One Maths Limits and Derivatives 6 Marks Important Questions

Question 1.
Find the derivative of \(\frac{1}{x}\) from first principle. (IMP-2010)
Find the derivative of
(ax + b)ⁿ (ax + c)^m
Answer:

Question 2.
i) Find \(\lim _{x \rightarrow-2} \frac{x^{2}+5 x+6}{x^{2}+3 x+2}\) (IMP-2011)
ii) Find f ‘(x) given f(x) = \(\frac{x^{2}+5 x+6}{x^{2}+3 x+2}\)
Answer:

Question 3.
i) Evaluate \(\lim _{x \rightarrow 3}\left(\frac{x^{3}-27}{x^{2}-9}\right)\) (MARCH-2012)
ii) Evaluate \(\lim _{x \rightarrow 0} \frac{\tan x-\sin x}{\sin ^{3} x}\)
Answer:

Question 4.
i) Evaluate \(\lim _{x \rightarrow 0} \frac{\sin 5 x}{\sin 3 x}\) (MARCH-2013)
ii) Find the derivate of y = cosx from the first principle.
Answer:
i)

ii)

Question 5.
i) Find the derivative of \(\frac{\sin x}{x+\cos x}\) (MARCH-2014)
ii) Match the following:

Answer:

Question 6.
i) \(\frac{d}{d x}(\tan x)\) = ……… (IMP-2014)
ii) Find the derivative of 3 tan x + 5 sec x
iii) Find the derivative of /(x) = (x² + 1)sinx
Answer:

Question 7.
i) Match the following (MARCH-2015)

ii) Find the derivative of tanx using first principle.
Answer:

Question 8.
i) Match the following: (MARCH-2015)

ii)

Answer:

Question 9.

iii) Using first principles, find the derivative of cos x. (IMP-2015)
Answer:

iii)

Question 10.
i) Derivative of x² – 2 at x = 10 is (IMP-2016)
a) 10
b) 20
c) -10
d) -20

Answer:

Question 11.
i) \(\frac{d}{d x}\left(\frac{x^{n}}{n}\right)\) = ………… (MARCH-2016)
ii) Differentiate \(y=\frac{\sin x}{x+1}\) with respect to x
iii) Use first principles, find the derivative of cosx.
Answer:

iii)

Question 12.
i) \(\frac{d}{d x}(-\sin x)\) = ………….. (MARCH-2016)
ii) Find\(\frac{d y}{d x}\) if \(y=\frac{a}{x^{4}}-\frac{b}{x^{2}}+\cos x\) where a, b are constants.
iii) Using first principles, find the derivative of sinx.
Answer:

iii)

Question 14.

iii) Using the first principle, find the derivative of cosx (MAY-2017)
Answer:

iii)

Question 15.

(MARCH-2017)
Answer:
i) cos x
ii)

iii)

Question 16.
i) \(\lim _{x \rightarrow 0} \frac{e^{\sin x}-1}{x}=\) …….(MARCH-2017)
a) 0
b) 1
c) 2
d) 3
ii) Find
\(\lim _{x \rightarrow 0} \frac{\sqrt{1+x}-1}{x}\)
iii) Find the derivative of f(x) = sin x by using first principal.
Answer:
i) b) 1
ii)

iii)

Kerala State Board New Syllabus Plus One Maths Chapter Wise Previous Questions and Answers Chapter 12 Introduction to Three Dimensional Geometry.

Kerala Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry

Plus One Maths Three Dimensional Geometry 3 Marks Important Questions

Question 1.
Consider the triangle with vertices (0,7,- 10), (1,6,- 6) and (4,9,- 6) (MARCH-2010)
i) Find the sides AB, BC and CA.
ii) Prove that the triangle is right triangle.
iii) Find the centroid of the triangle.
Answer:

Question 2.
i) Find the co-ordinates of the points which trisect the line segment joining the points P(4,0,1) and Q(2,4,0). (IMP-2010)
ii) Find the locus Of the set of points P such that the distance from A(2,3,4) is equal to twice the distance from B(-2,1,2).
Answer:
i)

Let R and S be two points which trisect the line join of PQ. Therefore PR = RS = SQ

Question 3.
i) Write the coordinate of the centroid of the triangle whose vertices are
(x₁, y₁, z₁) ; (x₁, y₁, z₁)and(x₁, y₁, z₁) (IMP-2011)
ii) If the centroid of the triangle ABC is (1,1,1) and A and B are (3,-5,7), (1,1,2) then find the coordinate of C.
Answer:

Question 4.
Given three points A(- 4,6,10), B(2,4,6) and C(14,0,- 2) (IMP-2012)
i) Find AB.
ii) Prove that the points A, B and C are collinear.
Answer:
i)

ii)

Question 5.
Name the octants in which the points A(1,6,- 6) and B(- 1,- 6,- 6). Find the distance between A and B. (IMP-2012)
Answer:
ASP A(1,6,- 6) and B(-1 ,-6,-6) in the octants XOYZ’ and X’OY’Z’ respectively.

Question 6.
i) If P is a point in YZ-plane, then its x coordinate is ………….. (IMP-2013)
ii) Find the ratio in which the YZ-plane divides the line segment formed by joining the points (-2,4,7) and (3,-5,8).
Answer:
i) Zero
ii) Let the ratio be kA. Since the point lies on the YZ plane, its x-coordinate. will be zero. Hence

Therefore the ratio is 2:3.

Question 7.
i) Find the distance between the points (2- 1,3) and (- 2,1,3) (MARCH-2013)
ii) Find the coordinate of the point which divides the line segment joining the points (- 2,3,5) and (1,- 4,6) internally in the ratio of 2:3.
Answer:

Question 8.
i) Name the octant in which the points (3,- 2,1) and (- 5,- 6,1) lie. (MARCH-2014)
ii) Find the distance between the points P(1,- 3,4) and Q(- 4,1,2).
(March(Commerce) – 2014)
Answer:
i) (3,-2,1) lie on octant XOYZ and (-5,-6,1) lie on octant X’OY’Z.
ii)

Question 9.
Find the centroid of the triangle with vertices (3,- 5,7), (- 1,7,- 6) and (1,1,2). (IMP-2010)
Answer:

= (1,1,1)

Question 10.
Show that the points (-2,3,5), (1,2,3) and (7,0,-1) are collinear. (IMP-2014)
Answer:

Question 11.
Find the coordinate of the points which divides the line segment joining the points (- 2,3,5) and (1,- 4,6) in the ration 2 : 3 internally. (IMP-2014)
Answer:
coordinate of the point is:

Question 12.
i) State whether the following is TRUE or FALSE. (MAY-2017)
“The point (4,-2,-5) lies in the eight octant.”
ii) Find the equation of the set of points such that its distances from the points A (3,4,- 5) and B (- 2,1,4) are equal.
Answer:
i) True
ii) PA = PB

Question 13.
i) The distance between the point (1,-2,3) and (4,1,2) is …………. (MARCH-2017)
(a) √2
(b) √19
(c) √11
(d) √15
ii) the centroid of the triangle ABC is at the point (1,2,3). If the coordinates of A and B are (3,- 5,7) and (- 1,7,- 6) respectively. Find the coordinates of the point C.
Answer:
i) (b) √19
ii)

Plus One Maths Three Dimensional Geometry 4 Marks Important Questions

Question 1.
Consider the points A(- 2,3,5), B(1,2,3) and C(7,0,- 1) (MARCH-2011)
i) Using the distance formula, show that the points A, B and C are collinear.
ii) Find the ratio in which B divides the line segment AC.
Answer:

Question 2.
i) The x – coordinate of the point in the YZ plane is ………….. (MARCH-2013)
ii) Find the ratio in which the YZ plane divides the line segment joining the points (- 2,4,7) and (3,- 5,8).
Answer:
i) zero
ii) Let the ratio be k:1. Since the point lies on the YZ plane, its Xrcoordinate will be zero. Hence

Question 3.
i) Find the distance between the points (2,3,5) and (4,3,1). (MARCH-2014)
ii) Find the ratio in which the line segment joining the points A(4,8,10) and B (6,10,-8) is divided by the XY plane. (March (Science) – 2014)
Answer:

Question 4.
A point in the XZ plane is (MARCH-2015)
a) (1,1,1)
b) (2,0,3)
c) (2,3,0)
d) (-1,2,3)
ii) Show that the points A(1,2,3), B(- 1,- 2,- 1), C(2,3,2) and D(4,7,6) are the vertices of a parallelogram.
Answer:


Here; AB = CD and BC = DA, therefore ABCD is a parallelogram

Question 5.
i) Which of the following lies in the sixth octant? (MARCH-2016)
a) (- 3,- 2,- 2)
b) (- 3,1,- 2)
c) (3,- 1,2)
d) (3,- 1,-2)
ii) Find the ratio in which the YZ plane divides the line joining the points (- 2, 4, 7) and (3,- 5,8)
Answer:
i) b) (- 3,1,- 2)
ii) Let the ratio be k:1. Since the point lies on the YZ plane, its Xrcoordinate will be zero. Hence

Question 6.
i) Which one of the following points lies in the sixth octant? (IMP-2015)
a) (-4,2,-5)
b) (-4,-2,-5)
c) (4,-2,-5)
d) (4,2,5)
ii) Find the ratio in which the YZ plane divides the line segment formed by joining the points (-2,4,7) and (3,-5,8).
Answer:
i) a) (-4,2,-5)
ii) Let the line joining the points A(-2,4,7) and B(3,-5, 8) is divided by the yz-plane in the ratio k: 1.
Then the coordinate

Plus One Maths Three Dimensional Geometry 6 Marks Important Questions

Question 1.
i) If \(\left(\frac{5}{3}, \frac{22}{3}, \frac{-22}{3}\right)\) is the centriod of is the centroid of ∆PQR with vertices P(a,7,-10), Q(1,2b,-6) and R(4,9,3c), Find the value of a, b, c. (MARCH-2012)
ii) Prove that ∆PQR is isosceles.
Answer: