Q.

Coefficient of x11 in the expansion of 1+x241+x371+x412 is

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a

1051

b

1106

c

1113

d

1120

answer is C.

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Detailed Solution

2x1+3x2+4x3=11Possibilities 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
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