Q1. 
The largest number amongst the following that will perfectly divide $101^{100} – 1$ is: 
A.  $100$ 

B.  $10,000$ 

C.  $100^{100}$ 

D.  $100,000$ 
Common Information
$P =1234567891011.............9989991000$
Q2. 
Common Information Question: 1/2 Find the remainder when first 1000 digits of the number $P$ are divided by 16? 
A.  7 

B.  9 

C.  11 

D.  13 
Q3. 
Common Information Question: 2/2 Find the remainder when $P$ is divided by 9? 
A.  8 

B.  7 

C.  1 

D.  6 
Q4. 
Let $n$ be the number of different 5 digit numbers, divisible by 4 with the digits 1, 2, 3, 4, 5 and 6, no digit being repeated in the numbers. What is the value of $n$? 
A.  144 

B.  168 

C.  192 

D.  None of these 
Q5. 
Three gold coins of weight 780gm, 840gm and 960gm are cut into small pieces, all of which have the equal weight. Each piece must be heavy as possible. If one such piece is shared by two persons, then how many persons are needed to give all the pieces of gold coins? 
A.  86 

B.  70 

C.  43 

D.  35 