If ((3⁶)/(4⁴))k is the term, independent of x, in the binomial expansion of (x/4 - 12/(x²))¹², then k is equal to _ _ _ _ _ _.

Binomial Theorem and Its Simple Applications: JEE Main 2021 Mathematics question

JEE Main 2021 · 31 Aug, Morning shift · Q24

JEE Main 202131 Aug, Morning shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

\left( {{{{3^6}} \over {{4^4}}}} \right)k

is the term, independent of x, in the binomial expansion of

{\left( {{x \over 4} - {{12} \over {{x^2}}}} \right)^{12}}

, then k is equal to ___________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2021 · 31 Aug, Morning shift · Q24

JEE Main 202131 Aug, Morning shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

\left( {{{{3^6}} \over {{4^4}}}} \right)k

is the term, independent of x, in the binomial expansion of

{\left( {{x \over 4} - {{12} \over {{x^2}}}} \right)^{12}}

, then k is equal to ___________.

Your answerType your answer. Integers and decimals are accepted.