JEE PYQ: Binomial Theorem Question 13
Question 13 - 2021 (24 Feb Shift 2)
For integers $n$ and $r$, let $\binom{n}{r} = \begin{cases} {}^nC_r, & \text{if } n \geq r \geq 0 \ 0, & \text{otherwise} \end{cases}$. The maximum value of $k$ for which the sum $\sum_{i=0}^{k} \binom{10}{i} \binom{15}{k-i} + \sum_{i=0}^{k+1} \binom{12}{i} \binom{13}{k+1-i}$ exists, is equal to
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Answer: 12
Solution
Note: NTA dropped this question. Using Vandermonde’s identity, maximum $k = 12$.
BETA
