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Question 1 of 67
1. Question
A natural number is selected from first 20 natural numbers. The probability that is
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Question 2 of 67
2. Question
A and B are two events such that P(A)>0 and P(B) ≠ 1 then is equal to
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Question 3 of 67
3. Question
The range of the function f(x) = ^{7 – x}P_{x – 3} is
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Question 4 of 67
4. Question
Let f(x) = x – 1, then
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Question 5 of 67
5. Question
If X and Y are two sets, then X ∩ (X ∪ Y)^{C} equals
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Question 6 of 67
6. Question
The area of the region bounded by the curves y = x – 2; x = 1, x = 3 and xaxis is
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Question 7 of 67
7. Question
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Question 8 of 67
8. Question
What is the last digit in the expansion of (2457)^{754}?
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Question 9 of 67
9. Question
If 3^{x} + 27(3^{−x}) = 12, then x = ?
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Question 10 of 67
10. Question
If x = 1 + √2, then x^{4} + 4x^{3} + 4x^{2} = ?
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Question 11 of 67
11. Question
The sum of the series is
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Question 12 of 67
12. Question
The sum of any ten positive real numbers multiplied by the sum of their reciprocals is
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Question 13 of 67
13. Question
If S_{n} denotes the sum of integer n terms of an A.P. and S_{2n} = 3 S_{n} then the ratio S_{3n}/S_{n} = ?
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Question 14 of 67
14. Question
The value of cos^{2} α + cos^{2}(α + 120^{0}) + cos^{2}(α – 120^{0}) is
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Question 15 of 67
15. Question
If A = sin^{2} θ + cos^{4} θ, the for all real values at θ
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Question 16 of 67
16. Question
The principal value of is
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Question 17 of 67
17. Question
The smallest positive root of the equation tan x = x lies in
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Question 18 of 67
18. Question
The sum of the series is
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Question 19 of 67
19. Question
Suppose f(x) is differential at x = 1 and then f ʹ(1) =
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Question 20 of 67
20. Question
If and W = 1, then Z lies on
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Question 21 of 67
21. Question
If ω is an imaginary cube root of unity, then (1 + ω – ω^{2})^{7} =
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Question 22 of 67
22. Question
If ^{n+1}C_{3} = 2 ^{n}C_{2}, then the value of n =
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Question 23 of 67
23. Question
If f : R → S, defined by f(x) = sin x – √3 cos x + 1 is onto, then the interval of S is
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Question 24 of 67
24. Question
Area of the greatest rectangle that can be inscribe in an ellipse is
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Question 25 of 67
25. Question
The points (−a, −b), (0, 0), (a, b) and (a^{2}, ab) are
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Question 26 of 67
26. Question
The area enclosed between the curve y = log_{e}(x + e) and the coordinate axes is
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Question 27 of 67
27. Question
If the roots of the equation x^{2} – bx + c = 0 be two consecutive integers, then b^{2} – 4c =
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Question 28 of 67
28. Question
If the angle θ between the line and the plane is that then the value of λ is
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Question 29 of 67
29. Question
A line through the point P(0, 6, 8) intersects the sphere x^{2} + y^{2} + z^{2} = 36 in points A and B, then PA × PB = ?
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Question 30 of 67
30. Question
The third term of a geometric progression is 4. The product of first five terms is
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Question 31 of 67
31. Question
If the first term minus third term of G.P. = 768 and the third term minus seventh term of the same G.P. = 240, then the product of first 21 terms is
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Question 32 of 67
32. Question
If x, y, z are pth, qth and rth term respectively of an A.P. and also of a G.P. then x^{y – z }y^{z – x}z^{x – y} = ?
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Question 33 of 67
33. Question
If 2a + 3b + 6c = 0, then at least one root of the equation ax^{2} + bx + c = 0, lies in the interval of
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Question 34 of 67
34. Question
If x + y = 2y, then y as a function of x is
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Question 35 of 67
35. Question
If then is
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Question 36 of 67
36. Question
If y = aI_{n}x + bx^{2} + x has extreme values at x = −1 and x = 2, then
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Question 37 of 67
37. Question
There are 8 players from which four teams each of two players are formed. What is the probability that two specific players are in one team?
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Question 38 of 67
38. Question
The number of ways of putting 10 different things in 2 boxes, such that there are not less than 2 things in any of the two boxes is
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Question 39 of 67
39. Question
Four dice are rolled. The number of possible outcomes in which altleast two dice show 6 is
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Question 40 of 67
40. Question
The domain of definition of the function y(x) has given by the equation 2^{x} + 2^{y} = 2 is
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Question 41 of 67
41. Question
The number log_{2} 7 is
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Question 42 of 67
42. Question
If two circles (x – 1)^{2} + (y – 3)^{2} = r^{2} and x^{2} + y^{2} – 8x + 2y + 8 = 0 intersect in two distinct points, then
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Question 43 of 67
43. Question
If f(x) = cos (lnx), then has the value
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Question 44 of 67
44. Question
For any integer n, the integer has the value
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Question 45 of 67
45. Question
In triangle PQR, if are the roots of the equation ax^{2} + bx + c = 0, a ≠ 0, then
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Question 46 of 67
46. Question
If then the value of x is
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Question 47 of 67
47. Question
For which value of x, sin[cot^{−1}(x + 1)] = cos(tan^{−1}x) ?
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Question 48 of 67
48. Question
If α and β are roots of x^{2} + px + q = 0 and α^{4} and β^{4} are the roots of r^{2} – rx + s = 0, then the equation x^{2} – 4qx + 2q^{2} – r = 0 ha always
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Question 49 of 67
49. Question
For real value of x, the function will assume all real values provided
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Question 50 of 67
50. Question
The number of real solutions of the equation x^{2} – 3x + 2 = 0 is
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Question 51 of 67
51. Question
Both the roots of the equation (x – b) (x – c) + (x – a) (x – c) + (x – a) (x – b) = 0 are always
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Question 52 of 67
52. Question
The value of is
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Question 53 of 67
53. Question
The value of the definite integral is
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Question 54 of 67
54. Question
The value of is
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Question 55 of 67
55. Question
The value of the integral
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Question 56 of 67
56. Question
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Question 57 of 67
57. Question
The complex number sin x + i cos 2x and cos x – i sin 2x are conjugate to each other for
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Question 58 of 67
58. Question
The inequality z – 4 < z – 2 represents the region given by
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Question 59 of 67
59. Question
The points Z_{1}, Z_{2}, Z_{3}, Z_{4} in the complex plane are the vertices of a parallelogram taken in order if and only if
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Question 60 of 67
60. Question
If are noncoplanar unit vectors such that then the angle between is
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Question 61 of 67
61. Question
The number of vectors of unit length perpendicular to is
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Question 62 of 67
62. Question
The points with position vectors 60i + 3j, ai – 52 are collinear, if
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Question 63 of 67
63. Question
The value of
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Question 64 of 67
64. Question
The function has local minimum at x = ?
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Question 65 of 67
65. Question
Which of the following functions is differentiable at x = 0 ?
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Question 66 of 67
66. Question
The events A, B, C are mutually exclusive events such that
The set of possible values of x are in the intervals
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Question 67 of 67
67. Question
If and then P(B ∩ C) =
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