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Question 1 of 67
1. Question
If the function f be defined by then f^{1}(x) is
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Question 2 of 67
2. Question
The position vector of a point A is divides AB internally in the ratio 2 : 3, then the position vector of B is
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Question 3 of 67
3. Question
is equal to
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Question 4 of 67
4. Question
The range of is
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Question 5 of 67
5. Question
If f(x) = sin^{2}x and the composite function gof(x) = sin x, then the function g(x) is equal to
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Question 6 of 67
6. Question
The coordinates of the vertex A of the triangle ABC are (2, 5). If the ccentroid of the triangle is at (−2, 1), then the coordinates of the midpoint of the side BC are
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Question 7 of 67
7. Question
If then the value of f^{−1}(x) is
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Question 8 of 67
8. Question
Orthocentre of the triangle formed by the lines x + y = 1, x = 0 and y = 0 is
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Question 9 of 67
9. Question
Distance between the parallel lines y = 2x + 7 and y = 2x + 5 is
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Question 10 of 67
10. Question
If then the value of is
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Question 11 of 67
11. Question
The domain of definition of the function f(x) = log_{3+x}(x^{2} – 1) is
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Question 12 of 67
12. Question
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Question 13 of 67
13. Question
The ordinate of the circle passing through (0, 0) and (1, 0) and touching the circle x^{2} + y^{2} = 9
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Question 14 of 67
14. Question
The centre of the circle is at (2, −3) and its circumference is 10π, then the equation if the circle is
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Question 15 of 67
15. Question
If then the value of f(2) is
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Question 16 of 67
16. Question
The period of the function sin^{4}x + cos^{4}x is
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Question 17 of 67
17. Question
Given f(0) = 0 and for x ≠ 0
Then the function f(x) is
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Question 18 of 67
18. Question
The angle between the vectors is
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Question 19 of 67
19. Question
Let A = {1, 2, 3} be a given set and a relation R on A be defined as follows.
R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (2, 1), (3, 12)}
Then the relation R on A is
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Question 20 of 67
20. Question
If the vectors are perpendicular to each other than λ = ?
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Question 21 of 67
21. Question
Three vertices of a parallelogram ABCD are A(3, −1, 2), B(1, 2, −4) and C(−1, 1, 2).
The coordinates of D are
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Question 22 of 67
22. Question
The angle between the lines and is
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Question 23 of 67
23. Question
If A and B are events such that P(A) = 0.4, P(B) = 0.8 and P(B/A) = 0.6, then P(A/B) = ?
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Question 24 of 67
24. Question
A couple has 2 children. What is the probability that both are girls, if its known that one of them is a girl.
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Question 25 of 67
25. Question
Two numbers are selected at random from integers a through 9. If the sum is even, what is the probability that both numbers are odd.
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Question 26 of 67
26. Question
If A and B are square matrices of the same order, then (A + B) (A – B) = ?
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Question 27 of 67
27. Question
The value of λ for which the matrix product is an identity matrix.
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Question 28 of 67
28. Question
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Question 29 of 67
29. Question
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Question 30 of 67
30. Question
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Question 31 of 67
31. Question
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Question 32 of 67
32. Question
The general solution of the Differential Equation is
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Question 33 of 67
33. Question
∫e^{x}(cot x + log sin x) dx = ?
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Question 34 of 67
34. Question
If e^{x+y} = xy then,
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Question 35 of 67
35. Question
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Question 36 of 67
36. Question
The equation of parabola whose focus is at (2, 2)) and the equation of the directrix is x + y = 0 is
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Question 37 of 67
37. Question
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Question 38 of 67
38. Question
The principal value of is
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Question 39 of 67
39. Question
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Question 40 of 67
40. Question
If S be the focus of the parabola y^{2} = 2x and PSP’ be a focal chord, then is equal to
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Question 41 of 67
41. Question
The value of is equal to
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Question 42 of 67
42. Question
The equation of directrix of the parabola y^{2} + 4y + 4x + 2 = 0 is
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Question 43 of 67
43. Question
If t_{1} and t_{2} are parameters of the end points of a focal chord of a parabola y^{2} = 4ax then
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Question 44 of 67
44. Question
If when x ≠ 0
= 2 when x = 0
is continuous at x = 0, then the value of m is equal to
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Question 45 of 67
45. Question
If and then is equal to
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Question 46 of 67
46. Question
For all real x, the minimum value of is
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Question 47 of 67
47. Question
If ω is an imaginary cube root of unity then (1 + ω + ω^{2})^{7} equals
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Question 48 of 67
48. Question
The number of different factors of 2160 is
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Question 49 of 67
49. Question
(1 + x^{n}) = C_{0} + C_{1}x + C_{2}x^{2} + C_{3}x^{3} + …… + C_{n}x^{n} then C_{0} – 2C_{1} + 3C_{2} – 4C_{3} + …. +(−1)^{n}^{−1}C_{n} =
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Question 50 of 67
50. Question
The sum of the series is
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Question 51 of 67
51. Question
Imaginary part of is
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Question 52 of 67
52. Question
The value of log_{8}[log_{15} 16 × log_{2} 15] is
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Question 53 of 67
53. Question
If i^{2} = −1, then the value of is
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Question 54 of 67
54. Question
If ^{43}C_{r – 6} = ^{43}C_{3r + 1}, then the value of r is
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Question 55 of 67
55. Question
The sum of the integers from 1 to 100 that are divisible by 2 or 5 is
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Question 56 of 67
56. Question
The number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between two boys is
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Question 57 of 67
57. Question
If α and β are the roots of the equation x^{2} + αx + β = 0 then
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Question 58 of 67
58. Question
If the sum of first n terms of an A.P. series is n^{2} + 2n, then the term of the series having value 201 is
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Question 59 of 67
59. Question
The number of diagonals of a polygon of n sides is
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Question 60 of 67
60. Question
If log_{p} x = a and log_{x} q = b, then the value of log_{p} x is
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Question 61 of 67
61. Question
If then the value of x is
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Question 62 of 67
62. Question
The value of cos[tan^{−1} (tan 2)] is
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Question 63 of 67
63. Question
If then
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Question 64 of 67
64. Question
In any triangle ABC, if a, b, c are in A.P. then are in
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Question 65 of 67
65. Question
If A + B + C = π, then the value of is
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Question 66 of 67
66. Question
The minimum value of 4tan^{2}θ + 9cot^{2}θ =
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Question 67 of 67
67. Question
The set of values of x for which tan 3x – tan 2x = 1 + tan 3x . tan 2x is
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