JEE Advanced 2026 — Paper 2 — MATH-III solution

JEE Advanced2026Paper 2MATH-III

A bookshelf contains 6 distinct books of Mathematics and 5 distinct books of Physics. From these 11 books, 6 books are chosen at random. Let $X$ be the absolute value of the difference between the number of Mathematics books chosen and the number of Physics books chosen. If $α$ is the mean of the random variable $X$ , then the value of $77 α$ is _________.

Your answer

Solution

Let $a$ be the number of Mathematics books chosen and $b$ the number of Physics books chosen, with $a + b = 6$ , $0 \leq a \leq 6$ , $0 \leq b \leq 5$ . The denominator throughout is $(6 11) = 462$ .

Enumerate $(a, b)$ and $X = ∣ a - b ∣$ :

$(a, b)$	$X$	Ways
$(6, 0)$	$6$	$(6 6) (0 5) = 1$
$(5, 1)$ and $(1, 5)$	$4$	$(5 6) (1 5) + (1 6) (5 5) = 30 + 6 = 36$
$(4, 2)$ and $(2, 4)$	$2$	$(4 6) (2 5) + (2 6) (4 5) = 150 + 75 = 225$
$(3, 3)$	$0$	$(3 6) (3 5) = 200$

$α = E [X] = \frac{6 \cdot 1 + 4 \cdot 36 + 2 \cdot 225 + 0 \cdot 200}{462} = \frac{6 + 144 + 450}{462} = \frac{600}{462} = \frac{100}{77}$ .

$∴ 77 α = 100$ .

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