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  • If the coefficient of  in <img alt="\left[a x^2+\left(\frac{1}{b x}\right)\right]^{11}" src="https://e

If the coefficient of x^{7} in \left[a x^2+\left(\frac{1}{b x}\right)\right]^{11} equals the coefficient of x^{-7} in \left[a x-\left(\frac{1}{b x^2}\right)\right]^{11}, then a and b satisfy the relation
 

Option: 1

a + b = 1    
 


Option: 2

a –  b = 1
           


Option: 3

ab = 1


Option: 4

\frac{a}{b}=1


Answers (1)

best_answer

\begin{aligned} & \text { Coefficient of } x^7 \text { in }\left[a x^2+\left(\frac{1}{b x}\right)\right]^{11}={ }^{11} C_5 \frac{a^6}{b^5} \\ & \text { Coefficient of } x^{-7} \text { in }\left[a x-\left(\frac{1}{b x^2}\right)\right]^{11}={ }^{11} C_6 \frac{a^5}{b^6} \\ & \therefore a b=1 . \end{aligned}

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Rakesh

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