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B
n2+5n−84=0
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C
n2+3n−108=0
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D
n2+n−110=0
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Solution
The correct option is Cn2+3n−108=0 n+2C6n−2P2=11⇒n+2C6=11.n−2P2⇒(n+2)!6!(n−4)!=11.(n−2)!(n−4)!⇒(n+2)(n+1)(n)(n−1)=11×6!⇒(n+2)(n+1)(n)(n−1)=11×10×9×8⇒n=9→which satisfiesn2+3n−108=0