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Question

If r=∣ ∣ ∣1nn2rn2+n+1n2+n2r1n2n2+n+1∣ ∣ ∣ and nr=1r=56, then n is equal to

A
4
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B
6
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C
7
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D
9
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Solution

The correct option is D 7
Putting r=1,2,3,...,n and using the formula
1=n
and r=n(n+1)2
(2r1)=1+3+5+....=n2
Therefore, nr=1r=∣ ∣ ∣nnnn(n+1)n2+n+1n2+nn2n2n2+n+1∣ ∣ ∣=56
Applying C1C1C3,C2C2C3, we get
∣ ∣ ∣00n01n2+nn1n1n2+n+1∣ ∣ ∣=56
n(n+1)=56
n2+n56=0
(n+8)(n7)=0
n=7,(n8).

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