JEE Advanced 2026 · Paper 2 · Mathematics Q11

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MathematicsNumerical+4Question 11 of 54

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 $\alpha$ is the mean of the random variable $X$ , then the value of $77\alpha$ is ________.

Your answer

Answer and worked solution

Official answer: 99

Choose $k$ Mathematics and $6-k$ Physics books; $X=|2k-6|$ . Out of $\binom{11}6=462$ choices:

$k$	ways	$X$
1	$6\cdot1=6$	4
2	$15\cdot5=75$	2
3	$20\cdot10=200$	0
4	$15\cdot10=150$	2
5	$6\cdot5=30$	4
6	$1\cdot1=1$	6

$\sum X\cdot\text{ways}=24+150+0+300+120+6=600$ , so $\alpha=\frac{600}{462}$ and
$77\alpha=\frac{600\cdot77}{462}=100.$

Topics:Random variables and distributions Combinations

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JEE Advanced 2026 · Paper 2, Mathematics question 11