If the coefficient of x⁷ in (ax - 1 b x²)¹³ and the coefficient of x⁻⁵ in (ax + 1 b x²)¹³ are equal, then a⁴b⁴ is equal to:

Binomial Theorem and Its Simple Applications: JEE Main 2023 Mathematics question

JEE Main 2023 · 10 Apr, Morning shift · Q2944

JEE Main 202310 Apr, Morning shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

If the coefficient of

{x^7}

{\left( {ax - {1 \over {b{x^2}}}} \right)^{13}}

and the coefficient of

{x^{ - 5}}

{\left( {ax + {1 \over {b{x^2}}}} \right)^{13}}

are equal, then

{a^4}{b^4}

is equal to :