Let X= ( ^ 10 C_1 )^2+2 ( ^ 10 C_2 )^2+3 ( ^ 10 C_3 )^2+ +10 ( ^ 10 C_ 10 )^2, where ^ 10 C_r, r 1,2, ,10 denote binomial coefficients. Then, the value of 1 1430 X is _____.

JEE Advanced 2018 Mathematics question

Let

X=({}^{10}+2({}^{10}+3({}^{10}+·s+10({}^{10},

where , denote binomial coefficients. Then, the value of is .

Answer: 646

, so \sum_{r=1}^{10}9C_{r-1}C_{10-r}$=10 {}^{

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Question ID VK-026803