Q1. 
The number of ways of arranging $n$ students in a row such that no two boys sit together and no two girls sit together is $m(m > 100)$. If one more student is added, then number of ways of arranging as above increases by $200\%$, The value of $n$ is: 
A.  $12$ 

B.  $8$ 

C.  $9$ 

D.  $10$ 
Q2. 
How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed? 
A.  499 

B.  500 

C.  375 

D.  376 

E.  501 
Q3. 
How many five digit positive integers that are divisible by 3 can be formed using the digits $0, 1, 2, 3, 4$ and $5$, without any of the digits getting repeating? 
A.  15 

B.  96 

C.  216 

D.  120 

E.  625 
Q4. 
There are 10 seats around a circular table. If 8 men and 2 women have to seated around a circular table, such that no two women have to be separated by at least one man. If $P$ and $Q$ denote the respective number of ways of seating these people around a table when seats are numbered and unnumbered, then $P : Q$ equals, 
A.  $9 : 1$ 

B.  $72 : 1$ 

C.  $10 : 1$ 

D.  $8 : 1$ 
Q5. 
How many factors of $2^5 × 3^6 × 5^2$ are perfect squares? 
A.  $20$ 

B.  $24$ 

C.  $30$ 

D.  $36$ 