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If $a > 0$ and coefficient of $x^{2}, x^{3}, x^{4}$ in the expansion of ${(1 + \frac{x}{a})}^{6}$ are in $A . P .,$ then a equals

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(4+7)3

(4+3)3

2−3

2+3

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Correct option is A

Coefficient of xr in the expansion of (1+x/a)6=6Cr(1/a)r According to given condition 6C2(1/a)2,6C3(1/a)3,6C4(1/a)4are in A.P.∴ 2 6C31a3=6C21a2+6C41a4⇒ 2(20)a=15a2+1⇒ 3a2−8a+3=0⇒ a=(4+7)3 as a>0.

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If a>0 and coefficient of x2, x3, x4 in the expansion of 1+xa6 are in A.P., then a equals

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If $a > 0$ and coefficient of $x^{2}, x^{3}, x^{4}$ in the expansion of ${(1 + \frac{x}{a})}^{6}$ are in $A . P .,$ then a equals