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Question

The coefficient of x7 in the expression (1+x)10+x(1+x)9+x2(1+x)8+········+x10is


A

420

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B

330

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C

210

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D

120

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Solution

The correct option is B

330


Step:1 Find out the relation between each terms

a1=(1+x)10,a2=x(1+x)9,a3==x2(1+x)8,....

Therefore, all the terms of this series are in geometric progression with a=(1+x)10,r=x1+x,n=11

Step:2 Calculating the sum of this G.P series

Sn=a[1-rn]1-r=(1+x)101-(x1+x)111-x1+x=(1+x)11-x11

Step:3 Calculate the coefficient of x7.

Therefore, the coefficient of x7

=C711=11!7!×4!=11×10×9×84×3×2=330

Therefore, Option(B) is the correct answer.


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