Let A =\ 1,2,3, ldots .7\ and let P (1) denote the power set of A . If the number of functions f : A rightarrow P(A) such that a in f(a), forall a in A is m n , m and n in N and m is least, then m + n is equal to

Mathematics · Permutations and Combinations

JEE Main 2024 — 30 January, Shift 1 — Question 24

Let $\mathrm{A}=\{1,2,3, \ldots .7\}$ and let $\mathrm{P}(1)$ denote the power set of $A$ . If the number of functions $\mathrm{f}: A \rightarrow P(A)$ such that $a \in f(a), \forall a \in A$ is $m^{n}, m$ and $\mathrm{n} \in \mathrm{N}$ and m is least, then $\mathrm{m}+\mathrm{n}$ is equal to

Answer: 44

Numerical answer — enter this value.

Step-by-step solution

f : A $\rightarrow \mathrm{P}(\mathrm{A})$ $a \in f(a)$

That means ' $a$ ' will connect with subset which contain element ' $a$ '.

Total options for 1 will be $2^{6}$ . (Because $2^{6}$ subsets contains 1 )

Similarly, for every other element

Hence, total is $2^{6} \times 2^{6} \times 2^{6} \times 2^{6} \times 2^{6} \times 2^{6} \times 2^{6}=2^{42}$

Ans. $2+42=44$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 30 January, Shift 1
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Applications of Permuations and Combination