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JEE Advanced 2026 Mathematics question

MathematicsPermutations and CombinationsJEE Advanced 2026

Let 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 be the set of all functions such that and . Consider the set

T=\{ f S\ :\ there exists a function g:B→Missing argument for \mathbb\mathbb N such that g(f(x))=2x for all x A \}.

Then the number of elements in the set is .

Answer: 1860

Solution

**Step 1 — translate the condition on .** Suppose such a exists. If then , so . Hence must be injective. Conversely, if is injective, define on the image by (well defined precisely because is one-one) and define

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Question ID VK-104762