If the coefficient of 4th term in the expansion of x+α2xn is 20, then the respective values of α and nare

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$If the coefficient of 4^{th} term in the$ $expansion of {(x + \frac{α}{2 x})}^{n} is 20, then$ $the respective values of α and n$ are

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2,6

3,6

5,8

2,7

answer is D.

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Detailed Solution

$T_{4} = {}^{n}C_{3} x^{n - 3} {(\frac{α}{2 x})}^{3} \Rightarrow {}^{n}C_{3} x^{n - 6} {(\frac{α}{2})}^{3} = 20$

$If n = 6, then {}^{6}C_{3} {(\frac{α}{2})}^{3} = 20 \Rightarrow α = 2$

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