If p and q be positive, then coefficients of {x^p} and {x^q} in expansion of {(1 + x)^{p + q}} will

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7.Binomial Theorem

easy

If $p$ and $q$ be positive, then the coefficients of ${x^p}$ and ${x^q}$ in the expansion of ${(1 + x)^{p + q}}$will be

A

Equal

B

Equal in magnitude but opposite in sign

C

Reciprocal to each other

D

None of these

(AIEEE-2002)

Solution

(a) Coefficient of ${x^p}$ is $^{(p + q)}{C_p}$ and coefficient of ${x^q}$ is $^{(p + q)}{C_q}$.

But $^{(p + q)}{C_p} $ $= {\,^{(p + q)}}{C_q}$ $({\,^n}{C_r} = {\,^n}{C_{n – r}}) $

Standard 11

Mathematics

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