Q11. 
Company $BELIANCE$ hosted a party for $8$ members of Company $AXIAL$. In the party no member of $AXIAL$ had interacted with more than three members of $BELIANCE$. Out of all the members of $BELIANCE$, three members – each interacted with four members of $AXIAL$ and the remaining members – each interacted with two members of $AXIAL$. The greatest possible number of members of company $BELIANCE$ in the party is: 
A.  $9$ 

B.  $10$ 

C.  $11$ 

D.  $12$ 
Q12. 
Each of the $11$ letters $A, H, I, M, O, T, U, V, W, X$ and $Z$ appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many three letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter? 
A.  $12,000$ 

B.  $12,870$ 

C.  $13,000$ 

D.  $\text{None of these}$ 
Q13. 
A sevendigit number comprises of only 2's and 3's. How many of these are multiples of 12? 
A.  $1$ 

B.  $11$ 

C.  $21$ 

D.  $47$ 
Q14. 
When four fair dice are rolled simultaneously, in how many outcomes will at least one of the dice show 3? 
A.  155 

B.  620 

C.  671 

D.  625 
Q15. 
Some boys are standing on a circle at distinct points. Each possible pair of persons, who are not adjacent, sing a 3 minute song, one pair after another. The total time taken by all the pairs to sing is 1 hour. Find the number of boys? 
A.  $6$ 

B.  $7$ 

C.  $8$ 

D.  $9$ 