If the coefficient of x⁷ in [ a x² + (1/bx) ]¹¹ equals the coefficient of x⁻⁷ in [ ax - (1 b x²) ]¹¹, then a and b satisfy the relation

Binomial Theorem and Its Simple Applications: JEE Main 2005 Mathematics question

JEE Main 2005 · Annual, Paper 1 · Q2906

JEE Main 2005Annual, Paper 1MathematicsHardBinomial Theorem and Its Simple Applications131× since 2002

If the coefficient of

{x^7}

{\left[ {a{x^2} + \left( {{1 \over {bx}}} \right)} \right]^{11}}

equals the coefficient of

{x^{ - 7}}

{\left[ {ax - \left( {{1 \over {b{x^2}}}} \right)} \right]^{11}}

, then

a

and

b

satisfy the relation