Mathematics · Permutations and Combinations

JEE Main 2026 — 21 January, Morning Shift — Question 9

The number of strictly increasing functions f from the set $\{1,2,3,4,5,6\}$ to the set $(1,2,3, \ldots, 9)$ such that $\mathrm{f}(\mathrm{i}) \neq \mathrm{i}$ for $1 \leq \mathrm{i} \leq 6$ , is equal to :

Option A:
$21$
Option B:
$27$
Option C:
$22$
Option D:
$28$
Correct

Answer: D

Step-by-step solution

$f(i) \neq i, f(x)$ is strictly increasing function $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ ,

where $\mathrm{A}\{1,2,3 \ldots \ldots .6\}$ , B $\{1,2,3, \ldots \ldots 9\}$ ,

then number of function $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ is equal to $\mathrm{f}(\mathrm{i}) \neq \mathrm{i}$

Case - i $\mathrm{f}(1)=2 \Rightarrow{ }^{7} \mathrm{C}_{5}=21$

Case- ii $\mathrm{f}(1)=3 \Rightarrow{ }^{6} \mathrm{C}_{5}=6$

Case- iii $\mathrm{f}(1)=4 \Rightarrow{ }^{5} \mathrm{C}_{5}=1$

No of function A to $\mathrm{B}=21+6+1=28$

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 21 January, Morning Shift
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Problems based on both permutations and combinations

Let S=\(m, n): m, n in\1,2,3, ldots ldots, 50\\ . If the number of elements ( m, n ) in S such that 6^ m+9^ n is a multiple of 5 is p and…

Answer: D

Step-by-step solution

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