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Question: The coefficient of \(x^{- 7}\) in the expansion of \(\left( ax - \frac{1}{bx^{2}} \right)^{11}\) wil...

The coefficient of x−7x^{- 7} in the expansion of (ax−1bx2)11\left( ax - \frac{1}{bx^{2}} \right)^{11} will be

A

462a6b5\frac{462a^{6}}{b^{5}}

B

462a5b6\frac{462a^{5}}{b^{6}}

C

−462a5b6\frac{- 462a^{5}}{b^{6}}

D

−462a6b5- \frac{462a^{6}}{b^{5}}

Answer

462a5b6\frac{462a^{5}}{b^{6}}

Explanation

Solution

For coefficient of x−7x^{- 7},

(11−r)(1)+(−2).r=−7⇒11−r−2r=−7⇒r=6(11 - r)(1) + ( - 2).r = - 7 \Rightarrow 11 - r - 2r = - 7 \Rightarrow r = 6; T7=11⥂C6(a)5(−1b)6=462a5b6T_{7} =^{11} ⥂ C_{6}(a)^{5}\left( - \frac{1}{b} \right)^{6} = \frac{462a^{5}}{b^{6}}