If the coefficients of x and x² in the expansion of (1+x)^(p)(1-x)^(q), p, q ≤ 15, are -3 and -5 respectively, then the coefficient of x³ is equal to _ _ _ _ _ _ _.

Binomial Theorem and Its Simple Applications: JEE Main 2022 Mathematics question

JEE Main 2022 · 26 Jul, Morning shift · Q26

JEE Main 202226 Jul, Morning shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

If the coefficients of

x

and

x^{2}

in the expansion of

(1+x)^{\mathrm{p}}(1-x)^{\mathrm{q}}, \mathrm{p}, \mathrm{q} \leq 15

, are

-3

and

-5

respectively, then the coefficient of

x^{3}

is equal to _____________.

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