Q31. 
After every gettogether every person present shakes the hand of every other person. If there were $105$ handshakes in all, how many persons were present in the party? 
A.  14 

B.  13 

C.  15 

D.  16 
Q32. 
How many diagonals can be drawn in a pentagon? 
A.  5 

B.  7 

C.  8 

D.  10 
Q34. 
Find the total number of distinct vehicle numbers that can be formed using two letters followed by two numbers. Letters need to be distinct. 
A.  $60,000$ 

B.  $65,000$ 

C.  $70,000$ 

D.  $75,000$ 
Q35. 
In a railway compartment, there are $2$ rows of seats facing each other with accommodation for $5$ in each, $4$ wish to sit facing forward and $3$ facing towards the rear while $3$ others are indifferent. In how many ways can the $10$ passengers be seated? 
A.  $172,000$ 

B.  $12,600$ 

C.  $45,920$ 

D.  $43,200$ 