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Question

If in the expansion of 1+x21, the coefficients of xr and xr+1 are equal, then r is equal to


A

9

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B

10

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C

11

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D

12

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Solution

The correct option is B

10


Explanation for the correct option:

Find the value of r:

In the expansion of 1+xn, the coefficient of xr is given as Crn.

So as in the expansion of 1+x21, the coefficients of xr and xr+1 are equal so Cr21=Cr+121.

It is known that if Crn=Ckn then r+k=n or r=k.

For Cr21=Cr+121 as r≠r+1, so

r+r+1=21⇒2r=20⇒r=10

So the value of r is 10.

Hence, the correct option is B.


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