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Question

The value of nr=2(2)r∣ ∣n2Crn2Cr1n2Cr2311210∣ ∣,(n>2) is

A
2n1+(1)n
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B
2n3+(1)n
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C
2n+1+(1)n1
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D
2n+3+(1)n
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Solution

The correct option is A 2n1+(1)n
Applying, C1C1+2C2+C3
we get,
S=nr=2(2)r∣ ∣nCrn2Cr1n2Cr2011010∣ ∣=nr=2(2)rnCr=nr=0(2)rnCr(nC02nC1)=(12)n(12n) ((1x)n=nr=0(x)rnCr)=2n1+(1)n

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