## JEE Advanced 2016 Paper 1 Mathematics Question 51

Let $m$ be the smallest positive integer such that the coefficient of $x^2$ in the expansion of $(1+x)^2 + (1+x)^3 + \dots + (1+x)^{49} + (1+mx)^{50}$ is $(3n+1)\ \ {}^{51}C_{3}$ for some positive integer $n$. Then the value of $n$ is

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