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MathematicsInteger+4Question 43 of 60

JEE Advanced 2015 · Paper 2, Mathematics question 43

The coefficient of x9x^9 in the expansion of (1+x)(1+x2)(1+x3)⋯(1+x100)(1+x)(1+x^2)(1+x^3)\cdots(1+x^{100}) is

Answer and worked solution

Official answer: 8

The coefficient counts ways to write 9 as a sum of distinct positive integers:

  • 9
  • 8+1, 7+2, 6+3, 5+4
  • 6+2+1, 5+3+1, 4+3+2

That is 8 ways.

Answer: 8

Topics:Distribution and arrangements
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