JEE Main 2022 · 26 Jul · Shift 1 · Mathematics Q25

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MathematicsInteger+4 / -1Question 25 of 90

If the coefficients of $x$ and $x^2$ in the expansion of $(1+x)^p(1-x)^q$ , $p,q\le15$ , are $-3$ and $-5$ respectively, then the coefficient of $x^3$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 23

Coefficients. $p-q=-3$ and $\binom p2+\binom q2-pq=-5$ give $p=8$ , $q=11$ .

$x^3$ . $\binom83-\binom82\binom{11}1+\binom81\binom{11}2-\binom{11}3=56-308+440-165=23$ .

Answer: 23

Topics:Binomial expansion

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JEE Main 2022 · 26 Jul · Shift 1, Mathematics question 25