If the co-efficient of x⁹ in (α x³ + 1/(β x))¹¹ and the co-efficient of x⁻⁹ in (α x - 1/(β x³))¹¹ are equal, then (αβ)² is equal to _ _ _ _ _ _.

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

JEE Main 2023 · 29 Jan, Morning shift · Q27

JEE Main 202329 Jan, Morning shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

If the co-efficient of

x^9

{\left( {\alpha {x^3} + {1 \over {\beta x}}} \right)^{11}}

and the co-efficient of

x^{-9}

{\left( {\alpha x - {1 \over {\beta {x^3}}}} \right)^{11}}

are equal, then

(\alpha\beta)^2

is equal to ___________.

Your answerType your answer. Integers and decimals are accepted.