JEE Advanced · 2026 · 17 May 2026 · Paper 2 · Probability XII

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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 ____.

Answer: 100

Solution

Let

a

= number of Maths books,

b

= number of Physics books. Then

a + b = 6

and

X = ∣ a - b ∣

. Possible values:

X = 6

(a=6,b=0):

P (X = 6) = \frac{1}{^{11} C _{6}}

X = 4

(a=5,b=1 or a=1,b=5):

P (X = 4) = \frac{36}{^{11} C _{6}}

X = 2

(a=4,b=2 or a=2,b=4):

P (X = 2) = \frac{225}{^{11} C _{6}}

X = 0

(a=3,b=3):

P (X = 0) = \frac{200}{^{11} C _{6}}

. Mean

α = \sum X \cdot P (X) = \frac{6 + 144 + 450}{^{11} C _{6}} = \frac{600}{462} = \frac{100}{77}

. Thus

77 α = 100

JEE Advanced · 2026 · 17 May 2026 · Paper 2 · Numerical answer

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JEE Advanced · 2026 · 17 May 2026 · Paper 2 · Probability XII

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