TS ICET 2015 Question Paper with Solutions for online practice

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Question : 136 of 200

Marks: +1, -0

If the fourth term in the binomial expansion of

(2^x⋅x^2+1/x^2)

is 160,then x =

8
-8
1
-1

Solution:

Given :

(2^x⋅x^2+1/x^2)^6

t_{4}=^{6}c_{3}(2^{x}⋅x^{2})^{3}⋅({1}/{x^{2}})^{3}=160

⇒{6!}/{3!×3!}(2^{3x}⋅x^{6})×{1}/{x^{6}}=160

⇒{6×5×4}/{3×2}(2^{3x}⋅x^{6})({1}/{x^{6}})=160

⇒2^{2x}=8=2^{3}

⇒3x=3⇒x=1

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