In This Post we are  providing Chapter-2 RELATIONS AND FUNCTIONS NCERT MOST IMPORTANT QUESTIONS for Class 11 MATHS which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MOST IMPORTANT QUESTIONS ON RELATIONS AND FUNCTIONS

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1. If P = {1,3}, Q = {2,3,5}, find the number of relations from A to B

Ans. 

= 64

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2. If A = {1,2,3,5} and B = {4,6,9}, R = {(x, y) : |x – y| is odd, x ∈ A, y ∈ B} Write R in roster form

Ans. Function

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3.

Let f and g be two real valued functions, defined by, f(x) = x2, g(x) = 3x +2.

Ans. Not a function

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4. Find the domain of the relation, R = { (x, y) : x, y ϵ Z, xy = 4} Find the range of the following relations : (Question-23, 24)

Ans. {–4, –2, –1,1,2,4}

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5.If and form the sets and are these two Cartesian products equal?

Ans. Given and by definition of cartesion product, we set

and 

By definition of equality of ordered pains the pair is not equal to the pair therefore 

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6.If and are finite sets such that and find the number of relations from to 

Ans. Linen 

the number of subsets of 

then the number of subsets of 

Since every subset of is a relation from A to B therefore the number of relations from A to B = 2^mk

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7.Let be a function from z to z defined by for same integers a and b determine a and b.

Ans. Given 

Since 

Subtracting (i) from(ii) we set a=2

Substituting a=2 is (ii) we get 2+b=1

b = -1

Hence a = 2, b = -1

8.Express as the set of ordered pairs

Ans. Since and 

Put 

For anther values of we do not get 

Hence the required set of ordered peutes is 

9.Function is defined by find 

Ans. 

10.Let and be the relation, is one less than from to then find domain and Range of 

Ans. Given and is the relation ‘is one less than’ from to therefore 

Domain of and range of 

11.Let be a relation from to define by.

Is the following true implies 

Ans. No; let As so but so 

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12.Let be the set of natural numbers and the relation be define in by =what is the domain, co domain and range of? Is this relation a function?

Ans. Given 

Domain of co domain of and Range of is the set of even natural numbers.

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13. Let A = {1,2,3,4}, B = {1,4,9,16,25} and R be a relation defined from A to B as, R = {(x, y) : x ϵ A, y ϵ B and y = x²}

(a) Depict this relation using arrow diagram.

(b) Find domain of R.

(c) Find range of R.

(d) Write co-domain of R.

Ans.

(b) {1,2,3,4}

(c) {1,4,9,16}

(d) {1,4,9,16,25}

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14. Let R = { (x, y) : x, y ϵ N and y = 2x} be a relation on N. Find :

(i) Domain

(ii) Codomain

(iii) Range

Is this relation a function from N to N

Ans. (i) N

(ii) N

(iii) Set of even natural numbers

yes, R is a function from N to N.

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15. Find the domain and range of, f(x) = |2x – 3| – 3

Ans. Domain is R

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