Class 11 Maths MCQ – Relations and Functions

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For students diving into Class 11 Maths, mastering these foundational topics can open doors to more advanced areas of study. We’ve curated a set of 20 multiple-choice questions (MCQs) covering Relations and Functions. Let’s dive in and test your knowledge!

1. Which of the following is a relation from set A = {1, 2} to set B = {3, 4}?

a) {(1, 3), (2, 4)}
b) {(1, 1), (2, 2)}
c) {(3, 1), (4, 2)}
d) {(1, 2), (2, 3)}

Answer:

a) {(1, 3), (2, 4)}

Explanation:

A relation consists of ordered pairs where the first element is from set A and the second element is from set B.

2. How many relations can be defined from a set containing 'n' elements to itself?

a) 2^n
b) n^2
c) n!
d) 2^(n^2)

Answer:

d) 2^(n^2)

Explanation:

A relation is a subset of the Cartesian product of a set with itself, so there are 2^(n^2) possible relations.

3. Which of the following is not a function?

a) f(x) = x^2
b) f(x) = √x
c) f(x) = 1/x
d) f(x, y) = x + y

Answer:

d) f(x, y) = x + y

Explanation:

A function has only one output for each input, and in this case, there are two inputs.

4. The domain of the function f(x) = √(x – 3) is:

a) x ≥ 3
b) x > 3
c) x ≤ 3
d) x < 3

Answer:

a) x ≥ 3

Explanation:

The value under the square root must be non-negative for real values.

5. If f and g are two functions defined by f(x) = 2x + 3 and g(x) = x – 5, then (f◦g)(x) is:

a) 2x – 7
b) 2x – 10
c) 2x – 2
d) 2x + 13

Answer:

d) 2x + 13

Explanation:

(f◦g)(x) = f(g(x)) = f(x – 5) = 2(x – 5) + 3.

6. A function which is both one-to-one and onto is called:

a) Bijective
b) Injective
c) Surjective
d) Null function

Answer:

a) Bijective

Explanation:

A function that is both injective (one-to-one) and surjective (onto) is called bijective.

7. The range of the function f(x) = x^3 is:

a) All real numbers
b) All non-negative real numbers
c) All non-positive real numbers
d) x ≠ 0

Answer:

a) All real numbers

Explanation:

The cube of any real number can be any real number.

8. The horizontal line test is used to determine:

a) If a graph represents a function
b) If a function is one-to-one
c) If a function is onto
d) The domain of a function

Answer:

b) If a function is one-to-one

Explanation:

If any horizontal line intersects the graph of a function at most once, the function is one-to-one.

9. Which of the following is the identity function?

a) f(x) = x^2
b) f(x) = x + 1
c) f(x) = 1/x
d) f(x) = x

Answer:

d) f(x) = x

Explanation:

The identity function returns the input value as the output.

10. The relation R on the set A of all books in a library such that 'aRb' if a and b are written by the same author, is:

a) Reflexive
b) Symmetric
c) Transitive
d) Equivalence

Answer:

d) Equivalence

Explanation:

Since every book is written by the same author as itself, the relation is reflexive. If book a and book b are written by the same author, then book b and book a are also written by the same author, making it symmetric. If book a is written by the same author as book b and book b is written by the same author as book c, then book a is written by the same author as book c, making it transitive. Hence, it is an equivalence relation.

11. If the composition of two functions f and g (f◦g) is the identity function, then g is the:

a) Inverse of f
b) Mirror of f
c) Negative of f
d) Square of f

Answer:

a) Inverse of f

Explanation:

The composition of a function and its inverse will give the identity function.

12. The number of relations from a set A containing 3 elements to a set B containing 2 elements is:

a) 6
b) 8
c) 16
d) 32

Answer:

c) 16

Explanation:

The number of relations from set A to set B is 2^(number of elements in A × number of elements in B) = 2^(3×2) = 16.

13. Which of the following relations is not reflexive on the set of natural numbers?

a) R = {(a, a): a is a natural number}
b) R = {(a, b): a divides b}
c) R = {(a, b): a + b is even}
d) R = {(a, b): a > b}

Answer:

d) R = {(a, b): a > b}

Explanation:

For the relation to be reflexive, every element must be related to itself. In the relation "a > b", no natural number is greater than itself.

14. The function defined by f(x) = 2x + 1 is:

a) One-to-one
b) Onto
c) Both one-to-one and onto
d) Neither one-to-one nor onto

Answer:

c) Both one-to-one and onto

Explanation:

For every distinct x, f(x) produces a distinct value, making it one-to-one. And for every real number y, there exists an x such that f(x) = y, making it onto.

15. If the domain of a function is all real numbers, and its codomain is also all real numbers, and it is given that the function is onto, then:

a) Its range is all real numbers
b) Its range is all non-negative real numbers
c) Its range is all non-positive real numbers
d) None of the above

Answer:

a) Its range is all real numbers

Explanation:

Since the function is onto and its codomain is all real numbers, the range must also be all real numbers.

16. A relation that is reflexive, symmetric, and transitive is called:

a) Equivalence relation
b) Partial order relation
c) Total order relation
d) None of the above

Answer:

a) Equivalence relation

Explanation:

A relation that satisfies all three properties (reflexive, symmetric, and transitive) is termed an equivalence relation.

17. The vertical line test is used to determine:

a) If a graph represents a function
b) If a function is one-to-one
c) If a function is onto
d) The range of a function

Answer:

a) If a graph represents a function

Explanation:

If any vertical line intersects the graph of a relation more than once, then the relation is not a function.

18. Which of the following functions has the greatest domain?

a) f(x) = x^2
b) f(x) = √x
c) f(x) = 1/x
d) f(x) = log(x)

Answer:

a) f(x) = x^2

Explanation:

The function f(x) = x^2 is defined for all real numbers.

19. A relation R on a set A is said to be symmetric if:

a) aRb implies bRa
b) aRa for all a in A
c) aRb and bRc implies aRc
d) None of the above

Answer:

a) aRb implies bRa

Explanation:

Symmetry in relations implies that if a is related to b, then b is also related to a.

20. Which of the following is not a function from set A = {1, 2, 3} to set B = {4, 5, 6}?

a) {(1, 4), (2, 5), (3, 6)}
b) {(1, 4), (2, 4), (3, 5)}
c) {(1, 5), (2, 5)}
d) {(1, 6), (2, 6), (3, 6)}

Answer:

c) {(1, 5), (2, 5)}

Explanation:

For a relation to be a function, every element in set A must be related to exactly one element in set B. In this case, 3 is not related to any element in set B.

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