If in the expansion of $(1 + x)^{n},$ the coefficient of pth and qth terms are equal and the relation between p and q is p-q =n . Find the value of $p^{2} + q^{2}$ . where $p \neq q .$

Find the term independent of x in the expansion of ${(2 x - \frac{1}{x})}^{10} .$

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In the expansion of (1+x)n, the coefficients of pth and (p+1)th terms are respectively p and q, then p+q=

The correct option is D n+1Given, pth and (p+1)th terms are p and qncp−1=p,ncp=q⇒qp=ncpncp−1=n−p+1p⇒p+q=n+1

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 $p + q =$

The correct option is D $n + 1$
Given, $p^{t h}$ and $(p + 1)^{t h}$ terms are $p$ and $q$
$n_{c_{p} - 1} = p, n_{c_{p}} = q$
$\Rightarrow \frac{q}{p} = \frac{n_{c_{p}}}{n_{c_{p} - 1}} = \frac{n - p + 1}{p}$
$\Rightarrow p + q = n + 1$