JEE Mains JEE Advance BITSAT
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All years 2026 2025 2024 2022 2021

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 \( f : A \to B \) such that \( f(2) \neq 2 \) and \( f(4) \neq 4 \). Consider the set \( T = \{ f \in S : \text{ there exists a function } g : B \to \mathbb{N} \text{ such that } g(f(x)) = 2^x \text{ for all } x \in A \} \).
Then the number of elements in the set \( T \) is ________.

Let \( S = \{ 1, 2, 3, \ldots, 10 \} \). Consider the set \( X = \{ R : R \) is an equivalence relation on the set \( S \) such that \( R \) has exactly \( 42 \) elements\( \} \). Then the number of elements in \( X \) is ____________.

The number of ways to distribute \( 10 \) identical red pens and \( 14 \) identical blue pens among four persons such that each person gets \( 6 \) pens, is __________.

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JEE Advanced 2026 Paper - 1

Let \( S = \{ 1, 2, 3, \ldots, 10 \} \). Consider the set \( X = \{ R : R \) is an equivalence relation on the set \( S \) such that \( R \) has exactly \( 42 \) elements\( \} \). Then the number of elements in \( X \) is ____________.