Gradutate Record Exam

1. Given two concentric circles, such that a tangent to the smaller circle cuts the larger one at two points 'R' and 'S'. If the radius of smaller circle is 2 and larger circle is 5, then what is the length of segment 'RS'?


2. If x < 0, then
Col A: 2x^3+3x^2+5
Col B: 3x^2+5


3. Given the two sides of a triangle as 6 and 5 that are opposite to 'x' and 'y' angles. If the length of the third side is given as 8, then
Col A: x+y
Col B: 90


4. If the remainder when 10^32 is divided by 11 is 'R', then
Col A: R+2
Col B: 3


5. Given A's speed is 50 km/h and B's speed is 55 km/h. If 'A' covers distance in 5 hours, then how much time 'B' takes to cover the same distance?


6. In a shop, if the discount provided is 40% on one jacket and 20% on one shirt, then
Col A: What is the percentage reduction in discount on two jackets and one shirt
Col B: 35%


7. If R = Set of prime numbers from 1 to 50,
S = Set of multiples of 15 from 10 to 50,
T = Set of odd numbers from 1 to 50, then
how numbers will be common in all the three sets?


8. Given numbers 1, 2, 3, 4 & 5. What is the probabilty of choosing two odd numbers at random from the given numbers such that the sum of the two numbers must be an even number?


9. Given a series -9, 10, -11, 12, -13. . . . . . . . . . .80, then
Col A: The sum of first 27 numbers
Col B: -22