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Question

The coefficient of x4 in (1+x+x2+x3)11 is

A
990
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B
780
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C
1040
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D
520
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Solution

The correct option is A 990
Coefficient of x4 in (1+x+x2+x3)11 is
= coefficient of x4 in (1+x)11.(1+x2)11
= (coefficient of 1 in (1+x11)).(coefficient of x4in (1+x2)11)+(coefficient of x2in(1+x)11).(coefficient of x2 in (1+x2)11)+(coefficient of x4 in (1+x)11).(coefficient of 1 in (1+x2)11)
=(1.(1112))+((112).(111))+((1112).1)
11.102!+11.11.102!+11.10.9.84!=55+605+330
=990

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