1. If x + y = k is normal to y2 = 12x, then k is
(A) 6 (B) 9
(C) 12 (D) 18
Ans. (B)
2. Let R be a relation on a set A such that R = R-1. Then R is
(A) Transitive (B) Reflexive
(C) Symmetric (D) None of these
Ans. (C)
3. The period of the function y = +
(A) (B) π
(C) 2π (D) 5π
Ans. (A)
4. If 3, then the maximum value of is
(A) 0 (B) 2
(C) 4 (D) 6
Ans. (D)
5. The number of solution of log4 (x-1) = log2 (x-2) is
(A) 2 (B) 5
(C) 9 (D) 12
Ans. (A)
6. The maximum number of points of intersection of 8 circles is
(A) 42 (B) 56
(C) 64 (D) 72
Ans. (B)
7. 23n – 7n -1 is divided by
(A) 49 (B) 58
(C) 72 (D) 108
Ans. (A)
8. The number of terms in the expansion of (1+3x + 3x2 + x3)6 is
(A) 7 (B) 14
(C) 19 (D) 28
Ans. (C)
9. The sum of all two digit odd numbers is
(A) 2225 (B) 2475
(C) 2755 (D) 3132
Ans. (B)
10. If three lines 3x – y = 2, 5x + ay = 3 and 2x + y = 3 are concurrent, then a is equal to
(A) -2 (B) 0
(C) 1 (D) 3
Ans. (A)
11. The three lines represented by y3 – 4x2y = 0 form which triangle?
(A) Right angle triangle (B) Equilateral triangle
(C) Isosceles triangle (D) None of these
Ans. (D)
12. Number of common tangents to the circles
x2 + y2 = 4 and x2 + y2 – 6x – 8y = 24 is
(A) 1 (B) 2
(C) 3 (D) 5
Ans. (A)
13. If r, s, t are positive numbers and p, q are positive integers such that LCM of p,q is r2 t4 s2, then the number of ordered pairs (p, q) is
(A) 224 (B) 232
(C) 244 (D) 252
Ans. (A)
14. The centre of the ellipse 4x2 + 9y2 + 16x – 18y -11 = 0, is
(A) (1, 1) (B) (1, 2)
(C) (2, 1) (D) (-2, 1)
Ans. (D)
15. The eccentricity of the rectangular hyperbola is
(A) (B)
(C) (D) None of these
Ans. (A)
16. If the mode of a data is 18 and the mean is 24, then median is
(A) 18 (B) 20
(C) 22 (D) 24
Ans. (C)
17. The minimum value of 3 tan2 + 12 cot2 is
(A) 12 (B) 18
(C) 36 (D) 48
Ans. (A)
18. If the lengths of the sides of a triangle are 3, 5, 7 then the largest angle of the triangle is
(A) (B) π
(C) (D)
Ans. (D)
19. From a tower 128 m high, the angle of depression of a car is 260. The distance of the car from the tower is
(A) 224 m (B) 242 m
(C) 258 m (D) None of these
Ans. (D)
20. If sin-1 x = , then cos-1 x is
(A) (B)
(C) (D) None of these
Ans. (C)
