Gradutate Record Exam

1.

Given a figure similar to the above, as EFGH inscribed in ABCD, 'E' on AB, 'H' on AD; 'F' is on BC and is the midpoint of BC & a line segment connecting H and C. The point where 'F' intersects HC is G. Here E and H are not mid-pts of respective sides as “F”. If angle DHC=45 and side AE=4, then find the area of rectangle EFGH?

2. Find the number of integers that are not divisible by 7 between 67 and 177?

3. If x > 0, then
Col A: (2x)^0+(2x)^1/(2x)^2+(2x)
Col B: 1/x

4. Which of the following is less than 30% of 1
A. 3/17
B. 1/3
C. 22/25
D. 0.6
& so on…

5. The given question had a figure of equilateral triangle with a circle inscribed in it and the length of one side is given as ‘6’.
Col A: Area of circular region
Col B: 9 pi

6. Given numbers from 1 to 10. Two numbers are to be selected from these 10 numbers and they can be same also. What is the probability that at least one of them is even?
A. 1/2
B. 3/4
C. 1/4
& so on....

7. If -1 < x < 0, then which of the following will have greater value?
A. x
B. x^3
C. x^3-1
D. x-1

8. If a number is divisible by 5, the remainder is 3 and when the same number is divided by 7 the remainder is 4. What is the least possible number?