If m,n,r are positive integers such that r<m,n, then ^mC_r+ ^mC_ r-1 , ^nC_1+ ^mC_ r-2 , ^nC_2+ + ^mC_1 , ^nC_ r-1 + ^nC_r equals

JEE Main Mathematics question

If are positive integers such that , then {}^mC_r+{}^mC_{r-1}\,{}^nC_1+{}^mC_{r-2}\,{}^nC_2+\cdots+{}^mC_1\,{}^nC_{r-1}+{}^nC_r equals

Answer: (B)

The sum is , where the first term () is and the last () is . By

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Question ID VK-021215