Let A =\ 1,2,3,4,5,6\ . The number of one-one functions f : A rightarrow A such that f (1) geq 3, f (3) leq 4 and f(2)+f(3)=5 , is \ \ \ \

Mathematics · Permutations and Combinations

JEE Main 2026 — 5 April, Morning Shift — Question 44

Let $\mathrm{A}=\{1,2,3,4,5,6\}$ . The number of one-one functions $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{A}$ such that $\mathrm{f}(1) \geq 3, \mathrm{f}(3) \leq 4$ and $f(2)+f(3)=5$ , is $\_\_\_\_$

Answer: 72

Numerical answer — enter this value.

Step-by-step solution

$\mathrm{f}(2)+\mathrm{f}(3)=5$ C-I : $f(2)=4, f(3)=1$ so, $f(1)=3,5,6 \rightarrow 3$ choices $\mathrm{f}(4) \rightarrow 3$ choices $\mathrm{f}(5) \rightarrow 2$ choices $\mathrm{f}(6) \rightarrow 1$ choices so total function for C-I : $3 \times 3 \times 2 \times 1=18$

Similarly C-II : $\mathrm{f}(2)=1, \mathrm{f}(3)=4 \rightarrow 18$ function

C-III : $\mathrm{f}(2)=3, \mathrm{f}(3)=2 \rightarrow 18$ function

C-IV : $\mathrm{f}(2)=2, \mathrm{f}(3)=2 \rightarrow 18$ function

Answer total $72$ function

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 5 April, Morning Shift
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Combinations