1.

If `(""^(n+2)C_(6))/(""^(n-2)P_(2))=11`, then n satifes the equationA. `n^(2)+n-110=0`B. `n^(2)+5n-84=0`C. `n^(2)+3n-108=0`D. `n^(2)+2n=0`

Answer» We have,
`(""^(n+2)C_(6))/(""^(n-2)P_(2))=11`
`implies((n+2)!)/((n-4)!6!)xx((n-4))/((n-2)!)=11`
`implies(n+2)(n+1)(n)(n-1)=11xx6!`
`implies(n+2)(n+1)(n)(n-1)=11xx10xx9xx8`
`impliesn+2=11impliesn=9`
This value of n satisfies the equation `n^(2)+3n-108=0`.


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