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For integers n and r let n r nCr ifn ge r ge 0 0 otherwise: null (Mathematics) | DivineJEE

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Mathematics

Exam

Mathematics

For integers n and r, let

\binom{n}{r} = \begin{cases} ^nC_r, & \text{if } n \ge r \ge 0 \\ 0, & \text{otherwise} \end{cases} \\ \text{The maximum value of } k \text{ 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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