If the constant term in the binomial expansion of ((x^(5/2))/2-4/(x^(l)))⁹ is -84 and the coefficient of x^(-3 l) is 2^(α) β, where β<0 is an odd number, then |α l-β| is equal to _ _ _ _.

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

JEE Main 2023 · 31 Jan, Evening shift · Q30

JEE Main 202331 Jan, Evening shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

If the constant term in the binomial expansion of

\left(\frac{x^{\frac{5}{2}}}{2}-\frac{4}{x^{l}}\right)^{9}

-84

and the coefficient of

x^{-3 l}

2^{\alpha} \beta

, where

\beta<0

is an odd number, then

|\alpha l-\beta|

is equal to ________.

Your answerType your answer. Integers and decimals are accepted.