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if D(k) = |{:( 1,,n,,n),(2k,,n^(2)+n+1 ,...

if `D_(k) = |{:( 1,,n,,n),(2k,,n^(2)+n+1 ,,n^(2)+n),(2k-1,,n^(2),,n^(2)+n+1):}|" and " Sigma_(k=1)^(n) D_(k)=56` then n equals

A

4

B

6

C

8

D

7

Text Solution

Verified by Experts

The correct Answer is:
D
`overset(n)underset(k=1)(Sigma) D_(k) =56`
`rArr |{:(overset(n)underset(k=1)(Sigma)1,,n,,n),(overset(n)underset(k=1)(Sigma)2k,,n^(2)+n+1,,n^(2)+n),(overset(n)underset(k=1)(Sigma)(2k-1),,n^(2),,n^(2)+n+1):}|=56`
`" or " |{:(n,,n,,n),(n(n+1),,n^(2)+n+1,,n^(2)+n),(n^(2),,n^(2),,n^(2)+n+1):}|`
Applying `C_(3) to C_(3) -C_(1) " and " C_(2) to C_(2)-C_(1)` we get
`|{:(n,,0,,0),(n(n+1),,1,,0),(n^(2),,0,,n+1):}|=56`
`" or " n(n+1) =56 " or " n=7`
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