The function f: R arrow R, f(x) =, x, (R is the set of real numbers) is Option 1: injective but not surjective Option 2: surjective but not injective Option 3: both injective and surjective Option 4: neither injective nor surjective

Answer: neither injective nor surjective. Solution: Solution Coming Soon

Algebra

Relations & Functions

Easy

core

The function $f: \mathbb{R} \rightarrow \mathbb{R}, f(x) = |x|$ ( $\mathbb{R}$ is the set of real numbers) is

injective but not surjective

surjective but not injective

both injective and surjective

neither injective nor surjective

✅ Correct Option: 4

Solution Coming Soon

2025: 15 May Shift 1

Let A= {1, 2, 3}, then the possible equivalence relations on A are:

(A) {(1, 1), (2, 2) , (3, 3)}

(B) {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}

(D) {(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)}

Choose the correct answer from the options given below:

2025: 3 June Shift 1

The range of function $f(x) = 4x^2 + 12x + 7, x \in \mathbb{R}$ is

2026: 19 May Shift 2

Let X be a non-empty set and let P be the collection of all subsets of X. Let R be a relation in P, defined by $R = \{(A, B): A \text{ is subset of } B\}$ . Then, R is

A. Reflexive relation

B. Symmetric relation

C. Not a transitive relation

D. Transitive relation

Choose the correct answer from the options given below:

2025: 13 May Shift 1

Let $A = \{a, b, c\}$ . Then number of relations containing $(a,b)$ and $(b, c)$ which are reflexive and transitive but not symmetric is

2025: 13 May Shift 2

Match List-I with List-II

Let $f: A \rightarrow B$ be a function given by $f(x) = x^2$

List-I	List-II
Domain and Co-domain	Kind
(A) $A = \mathbb{R}$ and $B = \mathbb{R}$	(I) $f$ is both one-one and onto
(B) $A = \mathbb{R}$ and $B = [0, \infty]$	(II) $f$ is one-one but not onto
(C) $A = B = [0, \infty]$	(III) $f$ is not one-one but onto
(D) $A = [0, \infty]$ and $B = \mathbb{R}$	(IV) $f$ is neither one-one nor onto

Choose the correct answer from the options given below:

2023: 30 May Shift 3

Relation R on Real Numbers is defined as $R = \{(a, b) : a \leq b\}$ . The relation is :

The function f:R→R,f(x)=∣x∣f: \mathbb{R} \rightarrow \mathbb{R}, f(x) = |x|f:R→R,f(x)=∣x∣ (R\mathbb{R}R is the set of real numbers) is

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The function $f: \mathbb{R} \rightarrow \mathbb{R}, f(x) = |x|$ ( $\mathbb{R}$ is the set of real numbers) is