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# Every body in a room shakes hands with everybody else.The total number of hand shakes is 66.The total number of persons in the room is

$\begin{array}{1 1}(A)\;11\\(B)\;12\\(C)\;13\\(D)\;14\end{array}$

If there are n people in the room ,then there are $n(n-1)12$ handshakes
$\large\frac{n(n-1)}{2}=$$66$
$n^2-n=132$
$n^2-n-132=0$
$n^2-12n+11n-132=0$
$n(n-12)+11(n-12)=0$
$(n+11)(n-12)=0$
$n=12,-11$
Hence total no of persons =12
Hence (B) is the correct answer.