question_answer

If the coefficient of\[{{x}^{7}}\]in\[{{\left[ a{{x}^{2}}+\left( \frac{1}{bx} \right) \right]}^{11}}\]equals  the  coefficient  of\[{{x}^{-7}}\]in\[{{\left[ ax-\left( \frac{1}{b{{x}^{2}}} \right) \right]}^{11}},\]then a and b satisfy the relation     AIEEE  Solved  Paper-2005

A) \[ab=1\]                              

B) \[\frac{a}{b}=1\]             

C)                        \[a+b=1\]           

D)        \[a-d=1\]

Correct Answer: A

Solution :

Theth term in the expansion of is Letbe contained inth term in the expansion of For coefficient ofwe put             Coefficient ofin the expansion of Similarly, coefficient ofin the expansion of According to the question,