Gradutate Record Exam

1. If g(x) = 3^(x-1), then what is the value of [g(x+1)-g(x)]/2?

2. There are two similar cylinders. One cylinder ‘A’ has water filled to half of its height and is standing on its base. Other cylinder ‘B’ is lying down with water filled to two third of its height (i.e. its diameter).
Col A: Volume of the Cylinder A
Col B: Volume of the Cylinder B

3. Find the probability of getting an even number, when chosen between 1 to 10 numbers inclusive is?

4. If -1 < x < 0, then which of the following is greatest?
A. x
B.2x
C. x^3
D. 1/x
E. 1/(x^2)

5. If there is a series in which the first number A1 is 4 and An+1 = (An - 3)^2, then what is the 25th number ?
(Here 1, n, n+1 are suffixes)

6. If the average of 6, x and y is 0, then what is the average of x and y?

7. If 5 + 2x > 1, then
Col A: x
Col B: -1.999

8. If n is a positive integer, then

Col A: Remainder when n^2 - n is divided by 2

Col B: 0

9. If a hexagon is inscribed in a circle and all the sides are equal and angles are equal of the hexagon, then what is the perimeter of the hexagon in terms of the circle's diameter 'd'?

10. A certain game has multiple rounds, in each round a participant receives either 2 points or 4 points, the average points received by one particular participant for all the rounds is 2.2
Col A : 9 times the number of rounds in which the participant got 4 points
Col B: the number of rounds in which the participant got 2 points

11. Two lists were given:
A: 12, 10, 30, 35 & 40
B: 30, 50, 20, 10 & 60

Col A: Standard Deviation of A
Col B: Standard Deviation of B

12.

Given a polygon(an equilateral triangle above a square) as above with 5 sides, if the perimeter of this polygon is 30, then find the area of the polygon?

13. Given one triangle whose arms are 3 and 5. If its angles are less than 90, then find the range of other arm?

14. Find the greatest of all?
A. 2/7
B. 71/280
C. 21/72
& so on....

15. Col A: Standard deviation of 50, 60, 70, 80 & 90
Col B: Standard deviation of 50, 55, 70, 85 & 90.

16. Given a rectangle whose length ‘l’ and breath ‘b’ is made, such that its length is increased by 15% and its breadth is been decreased by 15 %.
Col A: Area of original rectangle
Col B: Area of rectangle after change in dimensions

17. Given an equation of the form [x+3] < =5 ( [ ] implies mod) and there were number lines given
A. Number line saying x lies between -2 to 8
B. Number line saying x lies between -2 to 2
C. Number line saying x lies between -8 to 2
D. Number line saying x lies between -8 to 8
& so on....

18. Given X1, X2, X3 can do a job together in 4 hrs. If X1, X2 can do the same job in 6hrs, then how long would it take for X3 to do the job alone?

19. If in a team of 100, 70 liked cricket, 80 liked football and 5 liked neither, then how many people did like cricket but not football?