In the expansion of $(1 + x)^{n}$ the coefficients of $p^{t h}$ and $(p + 1)^{t h}$ terms are respectively $p$ and $q$ then $p + q =$

n

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n + 1

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n + 2

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n + 3

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Solution

The correct option is B $n + 1$
Binomial Coefficient of $p^{t h}$ term $^{n} C_{p - 1} = p$
Binomial Coefficient of $(p + 1)^{t h}$ term $^{n} C_{p} = q$
Therefore, with respect to the above question.
$\frac{^{n} C_{p - 1}}{^{n} C_{p}} = \frac{p}{q}$
$\frac{n! (n - p)! p!}{n! (n - p + 1)! (p - 1)!} = \frac{p}{q}$
$\frac{p}{n - p + 1} = \frac{p}{q}$
$n - p + 1 = q$
$n = p + q - 1$
$n + 1 = p + q$
Hence answer is $n + 1$

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