Q1. 
$F(x)$ is a fourth order polynomial with integer coefficients and with no common factor. The roots of $F(x)$ are –2, –1, 1, 2. If p is a prime number greater than 97, then the largest integer that divides $F(p)$ for all values of $p$ is 
A.  72 

B.  120 

C.  240 

D.  360 
Q2. 
Fortuner, the latest SUV by Toyota Motors, consumes diesel at the rate of $\dfrac{1}{400} \times \left[ \dfrac{1000}{x} + x \right]$ litres per km, when driven at the speed of $x$ km per hour. If the cost of diesel is Rs 35 per litre and the driver is paid at the rate of Rs 125 per hour then find the approximate optimal speed (in km per hour) of Fortuner that will minimize the total cost of the round trip of 800 kms? 
A.  49 km per hour 

B.  55 km per hour 

C.  50 km per hour 

D.  53 km per hour 
Q3. 
In a cricket match, Team $A$ scored 232 runs without losing a wicket. The score consisted of byes, wides and runs scored by two opening batsmen: Ram and Shyam. The runs scored by the two batsmen are 26 times wides. There are 8 more byes than wides. If the ratio of the runs scored by Ram and Shyam is $6:7$, then the runs scored by Ram is: 
A.  88 

B.  96 

C.  102 

D.  112 
Q4. 
Three business entities $X$ Ltd, $Y$ Ltd. and $Z$ Ltd, with 4, 3 and 5 employees respectively, merged into $XYZ$ Ltd in order to jointly raise the capital for setting up a new modern production plant in Jaipur. After two years, on the question of management decisions on the new venture at Jaipur, the employees started adopting differing viewpoints and began to quarrel among themselves. Given the fact that there is no quarrel among the employees of the erstwhile (i.e. former) $X$ Ltd, $Y$ Ltd and $Z$ Ltd, what could be the maximum number of quarrels that can take place within $XYZ$ Ltd? 
A.  31 

B.  53 

C.  47 

D.  41 
Q5. 
$PQRSTU$ is a regular hexagon drawn on the ground. Prashant stands at $P$ and he starts jumping from vertex to vertex beginning from $P$. From any vertex of the hexagon except $S$, which is opposite to $A$, he may jump to any adjacent vertices. When he reaches $S$, he stops. Let Sn be the number of distinct paths of exactly $n$ jumps ending at $S$. What is the value of $S^2k$, where $k$ is an integer? 
A.  $0$ 

B.  $4$ 

C.  $2k$ 

D.  Depends on the value of $k$ 