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Q.

The coefficient of x5 in the expansion of  (1+x2)5(1+x)4 is

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a

40

b

50

c

-50

d

60

answer is D.

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Detailed Solution

We have, (1+x2)5(1+x)4 =(1+5C1x2+5C2x4+…)(1+4C1x+4C2x2+4C3x3+4C4x4) =(1+5x2+10x4+…)(1+4x+6x2+4x3+x4)The term giving x5 in the above product is(5x2)(4x3)+(10x4)(4x)=(20+40)x5=60x5Hence, the coefficient is 60.
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