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Q.

The coefficient of x4 in 1+x+x2+x311 is

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a

990

b

780

c

1040

d

520

answer is A.

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Detailed Solution

1+x+x2+x311=(1+x)111+x211=C0   11+C1   11x+C2   11x2+C3   11x3+…+C11   11x11C0   11+C1   11x2+C2   11x4+…+C11   11x22∴Coefficient of x4=C0   11C2   11+C2   11C1   11+C4   11C0   11                                     =55+605+330                                     =990
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The coefficient of x4 in 1+x+x2+x311 is