Gradutate Record Exam

1. If x^2 + 5x^2 - 4 = 0, then sum of all possible values of x is
A. –5
B. –1
C. 0
D. 1
E. 5

2. If x + y = 5 & 2x + 2y = 8, then
Col A: The smallest possible distance between the lines
Col B: 1

3. Given a series 3 + 3^2 + 3^3 +….+3^k. What is the value of 'k' at which the summation will be divisible by 6?
A. 15
B. 18
C. 21
D. 28
E. 53
(Options were something like that)

4. If x^2 + 3x - r = 0, r is a positive integer and if x1, x2 are possible solutions to the equation, then
Col A: x1*x2
Col B: –r

5. If 3x + 5y = 12, then which of the following statements are true
1. x-intercept is positive
2. Slope is negative
3. At any point on the line, at least one coordinate is positive.
A. Statement 1
B. Statement 1 & 2
C. Statement 2
& so on.....

6. Two frequency distribution graphs are given, both are following same pattern, asked for the range, mean and standard deviation that are same for both.

7. If (x-5)(2x+1) - (x-5)(x+7) = 0, then the smallest possible value for x is....?

8. If 'p' is a point located at equal distance from (3, 0) and (3, 5) then
Col A: x-coordinate
Col B: 3

9. If n > 20, n shares are brought at a value of t (each share cost). In June, if a person sold n-20 shares at t+2 value each and rest of the shares for t+3, then
Col A: Total value of the shares sold – Initial value
Col B: 40+n

10. In 1976, the value of '$' is 30% more than in 1972. In 1980, the value is 82% than that in 1972, then
Col A: Percentage increase in '$' value from 1976 to 1980
Col B: 52%

11. Col A: 3x^1 * 3x^-1
Col B: 5x^1*5x^-1

12. If x^4 + 5x^2 - 2 = 0, then which of the following options given cannot satisfies the condition?
(Some numbers were given as options)

13.

If the radius of the circle above is 8, then find the area of the shaded region?

14. There are 40 students in the class and the marks obtained by them are like 50, 60, 70, 80 & 90.
Col A: Median of the 40 students
Col B: Mean of the 40 students.