JEE Advanced2014MathematicsBinomial TheoremActual

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

Options

A1051
B1106
C1113
D1120

Correct answer

C. 1113

Step-by-step solution

2 x 1 + 3 x 2 + 4 x 3 = 11 Possibilities are 0 , 1 , 2 ; 1 , 3 , 0 ; 2 , 1 , 1 ; 4 , 1 , 0 ∴ Required coefficients = 4 C 0 × 7 C 1 × 12 C 2 + 4 C 1 × 7 C 3 × 12 C 0 + 4 C 2 × 7 C 1 × 12 C 1 + ( 4 C 4 × 7 C 1 × 1 ) = 1 × 7 × 66 + 4 × 35 × 1 + 6 × 7 × 12 + 1 × 7 = 462 + 140 + 504 + 7 = 1113

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