Gradutate Record Exam

1. Given a = (m+p)^2 & b = (m-p)^2. If 3^a/3^b = 3^4, then
Col A: mp
Col B: 1

2. Six amounts are given say 358$, 600$, 478$, 786$, 900$ & 983$. These amounts represent the profit made by 6 people. Out of these 6 values, there is error in 2 of them, one has been increased by 120$ and one has been decreased by 120$ by mistake.
Col A: Standard Deviation of the data given
Col B: Standard Deviation of the actual values (without error)

3. Given sides of a triangle, where all angles are less than 90. If one arm is 3 & other is 4, then find the range of third side?

4. If 'N' is a two-digit number with 'x' in tens place and 'y' in units place, then when this number is multiplied by 5 what will be the result?
A. 5xy
B. 5x+5y
C. 50x+50y
D. 50x+ 5y

5. Two frequency distribution tables are given.
Table I:

Table II:

Out of mean, median & mode which quantity is common for both tables?
A. Mean only
B. Median only
C. Mode only
D. Median & Mode
E. Mean & mode

6. Given two points A(3, 1) & B(-1, 5) and a perpendicular is drawn from point ‘p’ to this line AB
Col A: Slope of the perpendicular line
Col B: 1

7. If x^2 – 36 = 0 & x(x+6)(x+8) = 0, then
Col A: x
Col B: 0

8. If a wheel 'A' has half the diameter of wheel B, then
Col A: Number of revolutions made by wheel A to cover 5000 miles
Col B: Number of revolutions made by wheel B to cover 2500 miles

9. Last year, few girls and boys participated in drama. This year the number of girls and boys increased by x(x>0). If the number of boys is greater than number of girls, then
Col A: Percentage increase in boys from last year to this year
Col B: Percentage increase in girls from last year to this year

10. A circle has centre (0, 2) and a point P (2,-1) lies on its circumference. What is the radius of the circle?
(Question is similar to this)

11. If 'k' is a positive integer, 2^k - 1 cannot have which of the following as the unit's digit?
A. 1
B. 2
C. 3
D. 9
& so on….

12. Five numbers were given in fractional form, asked to find the least amongst them?

13.

‘X’ represents the value by which the height decreases and ‘Y’ represents the value by which the base increases.
Col A: X
Col B: Y

14. A series is given -8, -3, 5, 8, 3, -5...
Col A: The number that would first repeat 3rd time is
Col B: 3
(Something similar to this)

15. If ‘n’ and ‘m’ are positive odd integers, then
Col A: n(m-1) when divided by 2
Col B: 1

16. If x^2 – 49 = 0, then
Col A: x-7
Col B: x+7

17. A compass length, breadth & height were given (in inches) and weight of the compass was given as 17 kg and was asked to find density in kg per cubic feet?
(Density = wt/volume and 1 feet = 12 inches was given)

18. Given a point (2, -1) as the center of the circle and (0, -2) is a point on the circle, find the diameter of the circle?

19. In certain event probability of selecting female is 3/5.
Col A: Ratio of female to male
Col B: 3/2