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CalculusFunctionsNumerical Value Two DecimalVery Hard

Q10.\textbf{Q.10} Let

\mathbb{N}

denote the set of all positive integers. Consider the sets

A=\{1,2,3,4,5\}

and

B=\{1,2,3,4,5,6,7\}

. Let

S

be the set of all functions

f:A\rightarrow B

such that

f(2)\ne2

and

f(4)\ne4

. Consider the set

T=\{f\in S : \text{there exists a function } g:B\rightarrow\mathbb{N} \text{ such that } g(f(x))=2^{x} \text{ for all } x\in A\}.

Then the number of elements in the set

T

Subjective / proof problem — work it out in the Scratchpad, then reveal the solution.

citeJEE Advanced · 2026 · Paper 2

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