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If a(i), i=1,2,…..,9 are perfect odd squ...

If `a_(i)`, `i=1,2,…..,9` are perfect odd squares, then `|{:(a_(1),a_(2),a_(3)),(a_(4),a_(5),a_(6)),(a_(7),a_(8),a_(9)):}|` is always a multiple of

A

`4`

B

`7`

C

`16`

D

`64`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`(a,c,d)` Let `a_(1)=(2m+1)^(2)`, `a_(2)=(2n+1)^(2)`
`impliesa_(1)-a_(2)=4(m(m+1)-n(n+1))=8k`
so, difference of any two odd square is always a multiple of `8`
Now apply `C_(1)-C_(3)` and `C_(2)-C_(3)`, then `C_(1)` and `C_(2)` both become multiple of `8` so `Delta` always a multiple of `64`.
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