NIMCET 2023 Mathematics Question 14 with Solution

Question 14

Mathematics Binomial Theorem Hard

The coefficient of \(x^{50}\) in the expression of \({(1 + x)^{1000} + 2x(1 + x)^{999} + 3x^2(1 + x)^{998} + ...... + 1001x^{1000}}\)

(A) \({}^{1005}{{C}}_{50}\)

(B) \({}^{1005}{{C}}_{48}\)

(C) \({}^{1002}{{C}}_{50}\)

(D) \({}^{1002}{{C}}_{51}\)

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Correct Solution: Option C

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