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Question

If the coefficients of x9,x10,x11 in the expansion of (1+x)n are in arithmetic progression then n2−41n is:

A
398
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B
298
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C
398
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D
198
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Solution

The correct option is A 398
Coefficients of x9,x10,x11 in (1+x)n are in A.P.
nC9,nC10,nC11 are in A.P.
We know that,
2nC10=nC9+nC11
nC9nC10+nC11nC10=2

10n9+n1011=2

110+n219n+9011n99=2

n241n=398 is the answer.

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