The coefficient of x 50 in the binomial expansion of (1 + x) 1000 + x(1 + x) 999 + x 2 (1…

Mathematics · JEE Main · NTA ExamsBinomial Theorem And Its Simple Applications

The coefficient of x50 in the binomial expansion of
(1 + x)1000 + x(1 + x)999 + x2(1 + x)998 + ..... + x1000 is:
  1. \(\frac{(1000)!}{(49)!(951)!}\)
  2. \(\frac{(1001)!}{(51)!(950)!}\)
  3. \(\frac{(1001)!}{(50)!(951)!}\)

Answer

(D) (1001)! (50)!(951)!

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