Algebra

Relations & Functions

Medium

core

A and B are two sets such that $n(A) = 5$ and $n(B) = 7$ . The number of one-one functions from A to B is

2150

2520

120

✅ Correct Option: 3

Given $n(A) = 5$ and $n(B) = 7$ .

A one-one function assigns each element in set A to a different element in set B. No two elements from A can map to the same element in B.

For the 1st element of A: 7 choices from B

For the 2nd element of A: 6 remaining choices

For the 3rd element of A: 5 remaining choices

For the 4th element of A: 4 remaining choices

For the 5th element of A: 3 remaining choices

Total number of one-one functions:

$7 \times 6 \times 5 \times 4 \times 3$

$= 42 \times 5$

$= 210 \times 4$

$= 840 \times 3$

$= 2520$

This can also be calculated using the permutation formula:

$^nP_r = \dfrac{n!}{(n-r)!}$

Where $n = 7$ and $r = 5$ :

$^7P_5 = \dfrac{7!}{(7-5)!}$

$= \dfrac{7!}{2!}$

$= 2520$

Therefore, the number of one-one functions from A to B is $2520$ .

2025: 26 May Shift 2

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined as $f(x) = [x]$ , where [x] denotes the greatest integer less than or equal to x. Then which of the following statements are correct?

(A) f is one-one but not onto

(B) f is not onto

(D) f is one-one and onto

Choose the correct answer from the options given below:

2025: 13 May Shift 1

Let $f: \mathbb{R}$ -> $\mathbb{R}$ be a function defined as $f(x) = x^4$ . Which one of the following is true?

2026: 25 May Shift 1

For the relations $R_1, R_2, R_3, R_4$ defined on the set $A = \{1,2,3\}$ ,

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. $R_1 = \{(1,2),(2,1),(3,3)\}$	I. Transitive only
B. $R_2 = \{(1,1),(2,2),(3,3)\}$	II. Neither reflexive nor symmetric nor transitive
C. $R_3 = \{(1,2),(2,3),(1,3)\}$	III. Symmetric but neither reflexive nor transitive
D. $R_4 = \{(3,3),(3,1),(1,2)\}$	IV. Equivalence

Choose the correct answer from the options given below:

2023: 22 May Shift 3

Match List - I with List - II.

	List - I		List - II
(A)	$f(x) = \frac{1}{x}, f : \mathbf{R} - \{0\} \to \mathbf{R} - \{0\}$	(I)	neither injective nor surjective
(B)	$f(x) = x^2, f : \mathbf{N} \to \mathbf{N}$	(II)	surjective but not injective
(C)	$f(x) = x^2, f : \mathbf{R} \to \mathbf{R}$	(III)	injective but not surjective
(D)	$f : \{1, 2, 3\} \to \{1, 2\}$ defined as $f : \{(1, 1), (2, 2), (3, 1)\}$	(IV)	injective and surjective

Choose the correct answer from the options given below :

2025: 30 May Shift 1

The relation R in the set $\{1, 2, 3\}$ given by $R = \{(1, 1), (2, 2), (3, 3), (1, 2), (1, 3), (2, 3)\}$ is:

2025: 19 May Shift 1

A function $f: \mathbb{R} \rightarrow \{x \in \mathbb{R}: -1 < x < 1\}$ is defined as $f(x) = \frac{x}{1+|x|}$ , then $f$ is:

A and B are two sets such that n(A)=5n(A) = 5n(A)=5 and n(B)=7n(B) = 7n(B)=7. The number of one-one functions from A to B is

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

A and B are two sets such that $n(A) = 5$ and $n(B) = 7$ . The number of one-one functions from A to B is