The coefficient of x 18 in the product 1 + x 1 - x 10 1 + x + x 2 9   is

The coefficient of x18 in the product 1+x1-x101+x+x29  is
  1. 84
  2. -84
  3. -126
  4. 126

Solution

1+x1-x101+x+x29
=1+x1-x1-x91+x+x29
=1-x21-x1+x+x29
=1-x21-x39
So, Coefficient of x18 in 1+x1-x101+x+x29
= Coefficient of x18 in 1-x21-x39
= Coefficient of x18 in 1-x2C0 9+C1 9-x3+C2-x32+… 9
=C6 9-16=C3 9=9.8.71.2.3=84

Asked in: JEE Main 2019 (12 Apr Shift 1)

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