1. A survey shows that 63% of Indians like milk and 76% like butter. If x% of the Indians like both milk and butter, then find the value of x.

(a) x lies b/w [38,64]
(b) x lies b/w [39,63]
(c) x lies b/w [37,63]
(d) None of these

2. If, A={a,b,c}, then what is the number of proper subsets of A?

(a) 5
(b) 6
(c) 7
(d) 8

3. In a certain town 25% of families own a cell phone, 15% of families own a scooter and 65% of families own neither a cell phone nor a scooter. If 1500 families own both a cell phone and a scooter, then the total number of families in the town is-

a. 10,000
b. 20,000
c. 30,000
d. 40,000

4. If a is positive and if A and G are the arithmetic mean and the geometric mean of the roots of x^2 – 2ax + a^2 =0 respectively, then

a. A = G
b. A = 2G
c. 2A = G
d. A2 = G

5. Suppose that two persons A and B solve the equation x2 +ax + b = 0. While solving commits a mistake in commits a mistake in the coefficient of x was taken as 15 in place of –9 and finds the roots as –7 and –2. Then the equation is-
a. x^2 + 9x + 14 = 0
b. x^2 – 9x + 14 = 0
c. x^2 + 9x – 14 = 0
d. x^2 – 9x – 14 = 0
6. If x2 +2x + n > 10 for all real numbers x, then which of the following conditions is true?
a. n < 11
b. n = 10
c. n = 11
d. n > 11
7. If the sum of the 12th and 22nd terms of an A.P is 100, then the sum of the first 33 terms of the A.P. is-

a. 1700
b. 1650
c. 3300
d. 3400

8. The number of ways in which 5 ladies and 7 gentlemen can be seated at a round table so that no two ladies sit together, is

a. 3.5X(720)^2
b. 7(360)^2
c. 7(720)^2
d. 720

9. All the words that can be formed using alphabets A, H, L, U, and R are written as in a dictionary (no alphabet is repeated). Then the rank of the word RAHUL is

a. 70
b. 71
c. 72
d. 74

10. A matrix that is symmetric and skew-symmetric is

a. Orthogonal matrix b. Idempotent matrix

c. Null matrix d. None of these

11. Given that the drawn ball from U2 is white, the probability that the head appeared on the coin is

a. 17/23
b. 11/23
c. 15/23
d. 12/23
12. A fair coin is tossed a fixed number of times. If the probability of getting exactly 3 heads equals the probability of getting exactly 5 heads, then the probability of getting exactly one head is-

a. 1/64
b. 1/32
c. 1/16
d. 1/8

13. If sinx = sin 15° + sin 45°, where 0° < x < 90°, then x is equal to

a. 45°
b. 54°
c. 60°
d. 75°

14. If O is at the origin, OA is along the negative x-axis and (–40, 9) is a point on OB, then the value of sin AOB is

a. 5/16
b. 9/40
c. 9/41
d. 19/41

15. The equation of a line through the point (1, 2) whose distance from the point (3, 1) has the greatest value, is

a. y = 2x
b. y = x + 1
c. x + 2y = 5
d. y = 3x – 1

16. If a line with y-intercept 2, is perpendicular to the line 3x – 2y = 6, then its x-intercept is –

a. 1
b. 2
c. –4
d. 3

17. If the lines ax + ky + 10 = 0, bx + (k + l)y + 10 = 0 and cx + (k + 2)y + 10 = 0 are concurrent, then-

a. a,b, c are in G.P.
b. a, b, c are in H.P.
c. a, b, c are in A.P.
d. (a + b)2 = c 58.

18. A line passes through the point of intersection of the lines 100x + 50y –1= 0 and 75x + 25y + 3 = 0 and makes equal intercepts on the axes. Its equation is

a. 25x + 25y – 1= 0
b. 5x – 5y + 3 = 0
c. 25x + 25y – 4 = 0
d. 25x – 25y + 6 = 0

19. The circumcentre of the triangle with vertices (0, 30), (4, 0), and (30, 0) is

a. (10, 10)
b. (10, 12)
c. (12, 12)
d. (17, 17)

20. The lines (a+2b)x +(a–3b)y = a – b for different values of a and b pass through the fixed point whose coordinates are .
a. (2/5,2/5)
b. (3/5,3/5)
c. (1/5,1/5)
d. (2/5,3/5)