Q1. 
A father with $8$ children takes $3$ children at a time to the zoological garden, as often as he can without taking the same $3$ children together more than once. Then: 
A.  number of times he will go to zoological garden is $56$. 

B.  number of times each child will go to the zoological garden is $21$. 

C.  number of times a particular child will not go to the zoological garden is $35$. 

D.  All of the above. 
Q2. 
If the letters of the word $CHASM$ are rearranged to form $5$ letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word $CHASM$? 
A.  24 

B.  31 

C.  32 

D.  30 
Q3. 
In how many ways can $5$ different toys be packed in $3$ identical boxes such that no box is empty, if any of the boxes may hold all of the toys? 
A.  20 

B.  30 

C.  25 

D.  600 

E.  480 
Q4. 
What is the value of $1×1! + 2×2! + 3×3! + ............ n×n!$; where $n!$ means $n$ factorial or $n(n1)(n2)...1$ 
A.  $n(n1)(n1)!$ 

B.  ${(n+1)!}/{n(n1)}$ 

C.  $(n+1)!  n!$ 

D.  $(n + 1)!  1!$ 
Q5. 
When six fair coins are tossed simultaneously, in how many of the outcomes will at most three of the coins turn up as heads? 
A.  $2^5$ 

B.  $41$ 

C.  $22$ 

D.  $42$ 

E.  $31$ 