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Binomial Theorem question

2023 · 1 Feb · Shift 2 · Q42

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JEE Main
Mathematics
Binomial Theorem
2023 · 1 Feb · Shift 2 · Q42

Binomial Theorem question

2023 · 1 Feb · Shift 2 · Q42

JEE MainMathematicsBinomial TheoremNumerical+4 / −1

Let the sixth term in the binomial expansion of

{\left( {\sqrt {{2^{{{\log }_2}\left( {10 - {3^x}} \right)}}} + \sqrt[5]{{2^{(x - 2){{\log }_2}3}}} } \right)^m}

in the increasing powers of

2^{(x-2) \log _{2} 3}

, be 21 . If the binomial coefficients of the second, third and fourth terms in the expansion are respectively the first, third and fifth terms of an A.P., then the sum of the squares of all possible values of

x

is

\underline{\hspace{2cm}}

.

Numerical answer

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