JEE Main 2015 · 10 Apr · Shift 1 · Mathematics Q86

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MathematicsSingle correct+4 / -1Question 86 of 90

Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X), with replacement, then the probability that A and B have equal number of elements, is :

\dfrac{^{20}C_{10}}{2^{10}}

\dfrac{(2^{10}-1)}{2^{20}}

\dfrac{(2^{10}-1)}{2^{10}}

\dfrac{^{20}C_{10}}{2^{20}}

Answer and worked solution

Official answer: D

$P=\dfrac{\sum_k\binom{10}k^2}{(2^{10})^2}=\dfrac{\binom{20}{10}}{2^{20}}$ .

Topics:Classical probability Properties of binomial coefficients

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JEE Main 2015 · 10 Apr · Shift 1, Mathematics question 86