Relations and functions class 12 maths cbse Previous year question

Relations and Functions

(2025)
Q.1 For real x, let f(x) = x3 + 5x + 1. Then :
(1 Mark) (CBSE 2025 - 65/4/1)
A. f is one-one but not onto on R
B. f is one-one and onto on R
C. f is neither one-one nor onto on R
D. f is onto on R but not one-one
Q.2




(1 Mark) (CBSE 2025 - 65/4/1)
A. a bijection
B. neither surjective nor injective
C. surjective only
D. injective only
Q.3 Assertion (A) : Let f(x) = ex and g(x) = logx.
Then (f + g) x = ex + log x (f + g)x = ex + logx where domain of (f + g) is R.
Reason (R) : Dom(f + g) = Dom(f) ∩ Dom(g).
(1 Mark) (CBSE 2025 - 65/6/1)

,A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct
explanation of the Assertion (A).
B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the
correct explanation of the Assertion (A).
C. Assertion (A) is false, but Reason (R) is true.
D. Assertion (A) is true, but Reason (R) is false.
Q.4 Domain of f(x) = cos−1x + sin x is :
(1 Mark) (CBSE 2025 - 65/7/1)
A. ϕ
B. (−1,1)
C. R
D. [−1,1]
Q.5 Assertion (A) : Let A = {x ∈ R: −1 ≤ x ≤ 1}. If f : A → A be defined as f(x) =
x2, then f is not an onto function.

Reason (R) : If y = −1 ∈ A, then x = ±
(1 Mark) (CBSE 2025 - 65/5/1)
A. Assertion (A) is false, but Reason (R) is true.
B. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct
explanation of the Assertion (A).
C. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the
correct explanation of the Assertion (A).
D. Assertion (A) is true, but Reason (R) is false.
Q.6 Assertion (A) : Let Z be the set of integers. A function f : Z → Z defined as
f(x) = 3x − 5, ∀ Z is a bijective.
Reason (R) : A function is a bijective if it is both surjective and injective.
(1 Mark) (CBSE 2025 - 65/1/1)

,A. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the
correct explanation of the Assertion (A).
B. Both Assertion (A) and Reason (R) are true and the Reason (R) is the
correct explanation of the Assertion (A).
C. Assertion (A) is true, but Reason (R) is false.
D. Assertion (A) is false, but Reason (R) is true.
Q.7



(2 Mark) (CBSE 2025 - 65/4/1)
Q.8 Find the domain of f(x) = sin−1(−x2).
(2 Mark) (CBSE 2025 - 65/6/1)

Q.9 Let f : A → B be defined by f(x) = where A = R − {3} and B = R − {1}.
Discuss the bijectivity of the function.
(2 Mark) (CBSE 2025 - 65/7/1)
Q.10 Find the domain of the function f(x) = cos−1(x2 − 4).
(2 Mark) (CBSE 2025 - 65/5/1)
Q.11




(3 Mark) (CBSE 2025 - 65/4/1)
Q.12 Let A = {1, 2, 3} and B = {4, 5, 6}. A relation R from A to B is defined as R =
{(x, y) : x + y = 6, x ∈ A, y ∈ B}.
(3 Mark) (CBSE 2025 - 65/4/1)

, (i) Write all elements of R.
(ii) Is R a function ? Justify.
(iii) Determine domain and range of R.
Q.13 A student wants to pair up natural numbers in such a way that they satisfy
the equation 2x + y = 41, x, y ∈ N. Find the domain and range of the relation.
Check if the relation thus formed is reflexive, symmetric and transitive. Hence,
state whether it is an equivalence relation or not.
(3 Mark) (CBSE 2025 - 65/6/1)
Q.14




(3 Mark) (CBSE 2025 - 65/6/1)
Q.15 Let R be a relation defined over N, where N is set of natural numbers,
defined as " mRn if and only if mm is a multiple of n, m, n ∈ N." Find
whether R is reflexive, symmetric and transitive or not.
(3 Mark) (CBSE 2025 - 65/2/1)
Q.16 Show that the function f : R → R defined by f(x) = 4x3 − 5, ∀ x ∈ R is one-
one and onto.
(3 Mark) (CBSE 2025 - 65/7/1)
Q.17 Let R be a relation defined on a set N of natural numbers such that R = {(x,
y) : xy is a square of a natural number, x, y ∈ N}. Determine if the relation RR is
an equivalence relation.
(3 Mark) (CBSE 2025 - 65/7/1)