CUET Mathematics Algebra > Relations & Functions PYQs

neither reflexive nor symmetric nor transitive

reflexive but not symmetric

symmetric but not transitive

transitive but neither reflexive nor symmetric

onto only

both one-one and onto

one-one only

neither one-one nor onto

$[-2, \infty)$

$[0, \infty)$

$\mathbb{R}$

$(-2, \infty)$

$x^2 + y^2$

$x^2 - y^2$

$2 + x^2 + y^2$

$2 + x^2 - y^2$

It is reflexive and symmetric but not transitive

It is reflexive, symmetric and transitive

It is reflexive and transitive but not symmetric

It is neither reflexive nor symmetric nor transitive

$[0, \pi]$

$[-\sqrt{5}, -\sqrt{3}] \cup [\sqrt{3}, \sqrt{5}]$

$[-\sqrt{5}, -\sqrt{3}] \cap [-\sqrt{5}, \sqrt{3}]$

$[-1, 1]$

Reflexive and transitive

Neither Reflexive nor symmetric

Reflexive but not symmetric

Not Reflexive but symmetric

one-one but not onto

onto but not one-one

neither one-one nor onto

both one-one and onto

(A) and (D) only

(A), (B) and (D) only

(B) and (C) only

(A) and (C) only

injective but not surjective

surjective but not injective

both injective and surjective

neither injective nor surjective

$f$ is one-one but not onto

$f$ is onto but not one-one

$f$ is both one-one and onto

$f$ is neither one-one nor onto

symmetric

not reflexive

not transitive

both reflexive and transitive

Reflexive and symmetric but not transitive

An equivalence relation

Symmetric and transitive but not reflexive

Reflexive and transitive but not symmetric

one-one only

onto only

both one-one and onto

neither one-one nor onto

one-one but not onto

onto but not one-one

Both one-one and onto

Neither one-one nor onto

$[-1, 1]$

$[0, 1]$

$[1, 2]$

$[0, 2]$

(B) and (C) only

(A), (B) and (C) only

(B), (C) and (D) only

(C) and (D) only

1

2

3

5

-3

$-\frac{7}{2}$

1

0

$f$ is one-one but not onto.

$f$ is onto but not one-one

$f$ is both one-one and onto

$f$ is neither one-one nor onto

Reflexive and symmetric but not transitive

Neither reflexive nor transitive but symmetric

Neither symmetric nor transitive but reflexive

Neither reflexive nor symmetric nor transitive

$y = |x + 1|$

$y = |x + 1| + 1$

$y = |x - 1| + 1$

$y = |x + 1| - 1$

35

2150

2520

120

1

2

3

4

$\frac{3\pi}{5}$

$\frac{-\pi}{10}$

$\frac{\pi}{10}$

$\frac{-3\pi}{10}$

neither injective nor surjective

injective only

surjective only

bijective

R is reflexive but neither symmetric nor transitive

R is symmetric but neither reflexive nor transitive

R is an equivalence relation

R is reflexive and transitive but not symmetric

Reflexive, Symmetric but not Transitive

Reflexive, Transitive but not Symmetric

Symmetric, Transitive, but not Reflexive

an equivalence relation

injective but not surjective

surjective but not injective

bijective

neither injective nor surjective

neither one-one nor onto

one-one only

onto only

both one-one and onto

Reflexive relation

Transitive but not symmetric

Reflexive and transitive but not symmetric

Neither reflexive nor symmetric nor transitive

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

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

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

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

R∪S is also an equivalence relation.

(R∪S)⁻¹ is also an equivalence relation.

(R∩S)⁻¹ is also an equivalence relation.

R∩S is not an equivalence relation.

(A), (B) and (D) only

(A), (B) and (C) only

(A), (C) and (D) only

(B), (C) and (D) only

[1,2]

[-1,1]

(1,2)

(-1,1)

$2^n - 1$

$2^n - 2$

$^nP_2$

$n!$

Reflexive

Symmetric

Transitive

Reflexive and transitive

$f(x) = x^3$

$f(x) = 2x + 1$

$f(x) = x^2 + 1$

$f(x) = x + 2$

(A), (B) and (D) only

(B), (C) and (D) only

(C) and (D) only

(A), (B) and (C) only

Reflexive and Symmetric but NOT Transitive.

Symmetric and Transitive but NOT Reflexive.

Reflexive and Transitive but NOT Symmetric.

Equivalence Relation.

one-one and onto

one-one but not onto

onto but not one-one

neither one-one nor onto

f is both one-one and onto

f is onto but not one-one

f is one-one but not onto

f is neither one-one nor onto

1

2

3

4

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

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

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

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

(A) only

(B) and (C) only

(B) and (D) only

(B), (C) and (D) only

$f$ is one-one and onto

$f$ is one-one but not onto.

$f$ is onto but not one-one.

$f$ is neither one-one nor onto.

1

2

3

4

(B) only

(A), (B) and (D) only

(A) and (C) only

(A), (C) and (D) only

Symmetric

An Equivalence relation

Transitive

Reflexive