Let the coefficients of x⁻¹ and x⁻³ in the expansion of (2x^(1/5) - 1/(x^(1/5)))¹⁵,x > 0, be m and n respectively. If r is a positive integer such that m n² = ¹⁵C r. 2^(r), then the value of r is equal to _ _ _ _ _.

Binomial Theorem and Its Simple Applications: JEE Main 2022 Mathematics question

JEE Main 2022 · 29 Jun, Evening shift · Q27

JEE Main 202229 Jun, Evening shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

Let the coefficients of x^

-

1 and x^

-

3 in the expansion of

{\left( {2{x^{{1 \over 5}}} - {1 \over {{x^{{1 \over 5}}}}}} \right)^{15}},x > 0

, be m and n respectively. If r is a positive integer such that

m{n^2} = {}^{15}{C_r}\,.\,{2^r}

, then the value of r is equal to __________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2022 Binomial Theorem and Its Simple Applications Question with Answer (29 Jun Evening shift, Q27) | JEE Arc