Let nCr denote the binomial coefficient... | Binomial Theorem | JEE Main 2021

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JEE MAIN 2021

18-03-21 S2

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Let ${ }^n C_r$ denote the binomial coefficient of $\underline{X^r}$ in the expansion of $(1+\mathrm{x})^{\mathrm{n}}$. If $\sum_{k=0}^{10}\left(2^2+3 k\right)^n C_k=\alpha \cdot 3^{10}+\beta \cdot 2^{10}, \alpha, \beta \in R$, then $\alpha+\beta$ is equal to $\_\_\_\_$ .

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