JEE PYQ: Binomial Theorem Question 10
Question 10 - 2021 (18 Mar Shift 2)
Let ${}^nC_r$ denote the binomial coefficient of $x^r$ in the expansion of $(1+x)^n$. If $\sum_{k=0}^{10} (2^2 + 3k), {}^{10}C_k = \alpha \cdot 3^{10} + \beta \cdot 2^{10}$, $\alpha, \beta \in R$, then $\alpha + \beta$ is equal to ____.
Show Answer
Answer: 19
Solution
$\sum(4+3k){}^{10}C_k = 4 \cdot 2^{10} + 30 \cdot 2^9 = 19 \cdot 2^{10}$. So $\alpha = 0, \beta = 19$.
BETA
