A) 9
B) 12
C) 10
D) 14
Correct Answer: B
Solution :
Let the total number of persons in the room \[=n.\] \[\therefore \] Total number of handshakes \[={{\,}^{n}}{{C}_{2}}.\] But number of handshakes = 66. \[\therefore \] \[\frac{n!}{2!\,(n-2)!}=66\] \[\Rightarrow \] \[\frac{n(n-1)}{2}=66\] \[\Rightarrow \] \[{{n}^{2}}-n-132=0\] \[\Rightarrow \] \[{{n}^{2}}-12n+11\,n-132=0\] \[\Rightarrow \] \[n(n-12)+11\,(n-12)=0\] \[\Rightarrow \] \[(n-12)\,(n+11)=0\] \[\Rightarrow \] \[n=12\] \[(\because \,n\ne -11)\]
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