Let ⁿ C r denote the binomial coefficient of x^(r) in the expansion of (1 + x)ⁿ. If Σ k = 0 ¹⁰ (2² + 3k) ¹⁰C k = α.3¹⁰ + β.2¹⁰,α,β R, then α + β is equal to _ _ _ _ _ _.

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

JEE Main 2021 · 18 Mar, Evening shift · Q27

JEE Main 202118 Mar, Evening shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

Let

{}^n{C_r}

denote the binomial coefficient of x^r in the expansion of (1 + x)^n. If

\sum\limits_{k = 0}^{10} {({2^2} + 3k)} {}^{10}{C_k} = \alpha {.3^{10}} + \beta {.2^{10}},\alpha ,\beta \in R

, then

\alpha

\beta

is equal to ___________.

Your answerType your answer. Integers and decimals are accepted.