Coefficient of x 11 in the expansion of 1 + x 2 4   1 + x 3 7   1 + x 4 12 is

Coefficient of x11 in the expansion of 1+x24 1+x37 1+x412 is
  1. 1051
  2. 1106
  3. 1113
  4. 1120

Solution

2x1+3x2+4x3=11
Possibilities are 0, 1, 2;1, 3, 0;2, 1, 1;4, 1, 0
∴    Required coefficients
= 4C0× 7C1× 12C2+ 4C1× 7C3× 12C0+ 4C2× 7C1× 12C1+( 4C4× 7C1×1)
=1×7×66+4×35×1+6×7×12+1×7
=462+140+504+7=1113

Asked in: JEE Advanced 2014 (Paper 2)

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