Algebra

Relations & Functions

Medium

core

Let $A = \{ 1,2,3 \}$ , then Match List-I with List-II

LIST-I LIST-II
A. $R_1 = \{(1,1), (2,2), (3,3), (1,2)\}$ I. Symmetric but neither reflexive nor transitive
B. $R_2 = \{(1,1), (3,3), (1,3), (3,1)\}$ II. Reflexive and transitive but not symmetric
C. $R_3 = \{(1,1), (2,2), (3,3), (1,2), (2,1), (2,3), (3,2)\}$ III. Symmetric and transitive but not reflexive
D. $R_4 = \{(2,2), (3,3), (1,2), (2,1)\}$ IV. Reflexive and symmetric but not transitive

Choose the correct answer from the options given below:

LIST-I	LIST-II
A. $R_1 = \{(1,1), (2,2), (3,3), (1,2)\}$	I. Symmetric but neither reflexive nor transitive
B. $R_2 = \{(1,1), (3,3), (1,3), (3,1)\}$	II. Reflexive and transitive but not symmetric
C. $R_3 = \{(1,1), (2,2), (3,3), (1,2), (2,1), (2,3), (3,2)\}$	III. Symmetric and transitive but not reflexive
D. $R_4 = \{(2,2), (3,3), (1,2), (2,1)\}$	IV. Reflexive and symmetric but not transitive

A-II, B-III, C-IV, D-I

A-II, B-IV, C-III, D-I

A-I, B-III, C-IV, D-II

A-I, B-IV, C-III, D-II

✅ Correct Option: 1

$R_1$ contains all $(a,a)$ and is transitive, but $(2,1)$ is missing, so it is reflexive and transitive only (II).

$R_2$ lacks $(2,2)$ but is symmetric and transitive (III).

$R_3$ is reflexive and symmetric, yet $(1,2),(2,3)$ present without $(1,3)$ , so not transitive (IV).

$R_4$ lacks $(1,1)$ and is not transitive, but is symmetric (I).

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:

2026: 29 May Shift 2

Match the LIST-I with LIST-II (Consider N and R as set of natural numbers and set of real numbers respectively)

Choose the correct answer from the options given below:

2026: 29 May Shift 2

For the function $f(x) = |x-1| + |x-2| + |x-3|$

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

2023: 23 May Shift 3

The number of all onto functions from the set {1, 2, .......n} to itself is

2026: 15 May Shift 1

If $A$ be the set of all real numbers and R be the relation on A defined by $R = \{(a,b): a^2+b^2=1, \forall a,b \in A\}$ , then R is

2022: 16 July Shift 2

If $f:\mathbb{R} \to [-5, \infty)$ is defined as $f(x) = x^2 - 5$ , then the function f is

A. one-one

B. many-one

C. onto

D. into

Which of the above statements are true?

Choose the correct answer from the options given below:

Solution