# XAT 2016 Preparation series

*Considered as one of the toughest entrance exams for MBA students , we are running a series under XAT 2016 preparation. With the** *new pattern changes* **that have taken place this year, it would be beneficial for you to go through these past year XAT actual questions.We have segregated questions and solutions section wise so that you get a fair idea of the difficulty level of the papers over the previous years, as well as the differential marking scheme for each question. The articles will contain 360+ actual XAT questions.** **You can browse through the posts *here.

1. There are two circles C1, and C2 of radii 3 and 8 units respectively. The common internal tangent, T, touches the circles at points P_{1} and P_{2} respectively. The line joining the centers of the circles intersects T at The distance of X from the center of the smaller circle is 5 units. What is the length of the line segment P_{1}P_{2}?

A. ≤13

B. >13 and ≤14

C. >14 and ≤15

D. >15 and ≤16

E. >16

2. Consider the formula, S = (a * v) / (t + r + v) , where all the parameters are positive integers. If v is increased and a, t and r are kept constant, then S:

A. increases

B. decreases

C. increases and then decreases

D. decreases and then increases

E. cannot be determined

3. Prof Suman takes a number of quizzes for a course. All the quizzes are out of 100. A student can get an A grade in the course if the average of her scores is more than or equal to 90. Grade B is awarded to a student if the average of her scores is between 87 and 89 (both included). If the average is below 87, the student gets a C grade. Ramesh is preparing for the last quiz and he realizes that he must score a minimum of 97 to get an A grade. After the quiz, he realizes that he will score 70, and he will just manage a B. How many quizzes did Prof. Suman take?

A. 6

B. 7

C. 8

D. 9

E. None of the above

4. A polynomial “ax^{3} + bx^{2} + cx + d” intersects x-axis at 1 and -1, and y-axis at 2. The value of b is:

A. -2

B. 0

C. 1

D. 2

E. Cannot be determined

5. The probability that a randomly chosen positive divisor of 10^{29} is an integer multiple of 10^{23} is: a^{2}/b^{2}, then ‘b – a’ would be:

A. 8

B. 15

C. 21

D. 23

E. 45

6. Circle C, has a radius of 3 units. The line segment PQ is the only diameter of the circle which is parallel to the X axis. P and Q are points on curves given by the equations y+a^{x} and y=2a^{x} respectively, where a < 1. The value of a is:

A. 1/6√2

B. 1/6√3

C. 1/3√6

D. 1/√6

E. None of these

7.Consider a rectangle ABCD of area 90 units. The points P and Q trisect AB, and R bisects CD. The diagonal AC intersects the line segments PR and QR at M and N respectively. What is the area of the quadrilateral PQMN?

A. > 9.5 and ≤ 10

B. > 10 and ≤ 10.5

C. > 10.5 and ≤ 11

D. > 11 and ≤ 11.5

E. > 11.5

8.Two numbers, 297_{B} and 792_{B}, belong to base B number system. If the first number is a factor of the second number then the value of B is:

A.11x

B.12

C.15

D.17

E.19

9.A teacher noticed a strange distribution of marks in the exam. There were only three distinct scores: 6, 8 and 20. The mode of the distribution was 8.The sum of the scores of all the students was 504. The number of students in the in most populated category was equal to the sum of the number of students with lowest score and twice the number of students with the highest score. The total number of students in the class was:

A.50

B.51

C.53

D.56

E.57

10. Read the following instruction carefully and answer the question that follows:

Expression can also be written as x/13!

What would be the remainder if x is divided by 11?

A.2

B.4

C.7

D.9

E.None of the above

Answers-

1.A

2.A

3.D

4.A

5.D

6.A

7.D

8.E

9.E

10.D