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Q.

If n is even and $r^{t h}$ term has the greatest coefficient in the expansion of ${(1 + x)}^{n}$ then

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a

$r = \frac{n}{2} + 1$

b

$r = \frac{n}{2} - 1$

c

$r = \frac{n}{2}$

d

$r = \frac{n}{2} - 2$

answer is B.

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Detailed Solution

Since n is even

Greatest binomial coefficient is $^{n} C_{\frac{n}{2}}$

$T_{r} = T_{r - 1 + 1}$

$\begin{array}{l} here r - 1 = \frac{n}{2} \\ r = \frac{n}{2} + 1 \end{array}$

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