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Q.The coefficient of x53x^{53} in the expansion of (1+x)100+(1+x)2+⋯+(1+x)100(1 + x)^{100} + (1 + x)^2 + \cdots + (1 + x)^{100} is

a
100×1012\dfrac{100 \times 101}{2}
b
(10053)\binom{100}{53}
c
(10154)\binom{101}{54}
d
(15453)\binom{154}{53}

Correct Answer: Option C

The correct solution involves applying the fundamental concept to derive the final value step by step...

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