$r$ and $n$ are positive integer $r > 1, n > 2$ and coefficient of $(r + 2)^{t h}$ term and 3r $^{t h}$ term in the expansion of $(1 + x)^{2 n}$ are equal then value of $n$ is :

3 r

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3 r + 1

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2 r

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2 r + 1

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Solution

The correct option is B $3 r + 1$
$(r + 2)^{th} term =^{2 n} C_{r + 1}$
$(3 r)^{th} term =^{2 n} C_{3 r - 1}$
$∴^{2 n} C_{r + 1} =^{2 n} C_{3 r - 1}$
$So either r + 1 = 3 r - 1 \Rightarrow r = 1$
$or r + 1 + 3 r - 1 = 2 n$
$but r > 1$
$∴ n = 2 r$

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