Let α>0, be the smallest number such that the expansion of (x^(2/3)+2/(x³))³⁰ has a term β x^(-α), β N. Then α is equal to _ _ _ _ _ _.

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

JEE Main 2023 · 31 Jan, Morning shift · Q28

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

Let

\alpha>0

, be the smallest number such that the expansion of

\left(x^{\frac{2}{3}}+\frac{2}{x^{3}}\right)^{30}

has a term

\beta x^{-\alpha}, \beta \in \mathbb{N}

. Then

\alpha

is equal to ___________.

Your answerType your answer. Integers and decimals are accepted.