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Question 1 of 68
1. Question
A single letter is selected at random from the word ‘PROBABILITY’. The probability that it is a vowel is
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Question 2 of 68
2. Question
Two cards are drawn at random from a pack of 52 cards. The probability of these being queens is
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Question 3 of 68
3. Question
If
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Question 4 of 68
4. Question
If log_{10} x = y, then log_{10} 3x^{2} equals
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Question 5 of 68
5. Question
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Question 6 of 68
6. Question
If
= 0, [x] = 0
Where [x] denotes the greatest integer ≤ x, then equals
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Question 7 of 68
7. Question
If is
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Question 8 of 68
8. Question
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Question 9 of 68
9. Question
The maximum value of sin x + cos x =
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Question 10 of 68
10. Question
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Question 11 of 68
11. Question
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Question 12 of 68
12. Question
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Question 13 of 68
13. Question
The value of is
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Question 14 of 68
14. Question
The area between the curve y = 1 – x and Xaxis is
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Question 15 of 68
15. Question
The degree of the differential equation is
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Question 16 of 68
16. Question
The solution set of the inequaiton 2x + y > 5 is
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Question 17 of 68
17. Question
The maximum value of the objective function P = 5x + 3y, subject to the constraints x ≥ 0, y ≥ 0 and 5x + 2y ≤ 10 is
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Question 18 of 68
18. Question
If A = {2, 4, 5}, B = {7, 8, 9} then n(A × B) =
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Question 19 of 68
19. Question
If A & B are sets, then A ∩ (B – A) is
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Question 20 of 68
20. Question
If a set A has a n elements, then the total number of subsets of A is
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Question 21 of 68
21. Question
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Question 22 of 68
22. Question
If x and y are real positive numbers, then
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Question 23 of 68
23. Question
If then z^{69} is equal to
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Question 24 of 68
24. Question
The number is equal to
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Question 25 of 68
25. Question
The value of
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Question 26 of 68
26. Question
If P and P’ be perpendicular from the origin upon the straight lines,
x sec θ + y cosec θ = a and x cos θ – y sin θ = a cos 2θ, then the value of the expression 4P^{2} + P’^{2} is
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Question 27 of 68
27. Question
The lines x + (a – 1)y + 1 = 0 & 2x + a^{2}y – 1 = 0 are perpendicular if
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Question 28 of 68
28. Question
The equation of the line parallel to xaxis bisecting the joint of (1, 4) and (−2, 6) is
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Question 29 of 68
29. Question
The circle x^{2} + y^{2} + 4x – 7y + 12 = 0 cuts an intercept on yaxis equal to
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Question 30 of 68
30. Question
The equation of chord of the circle x^{2} + y^{2} – 4x = 0 whose midpoint is (1, 0) is
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Question 31 of 68
31. Question
The equation of the circle passing through the origin is x^{2} + y^{2} – 6x + 3y = 0. The equation of one of its diameter is
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Question 32 of 68
32. Question
The slope of a chord of the parabola y^{2} = 4ax, which is normal at one end and which subtends a right angle at the origin is
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Question 33 of 68
33. Question
The eccentric angle of a point on the ellipse whose distances from the centre of the ellipse is 2, is
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Question 34 of 68
34. Question
The number of values of c such that the straight line y = 4x + c touches the curve is
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Question 35 of 68
35. Question
If the major axis of an ellipse is thrice the minor axis, then its eccentricity is equal to
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Question 36 of 68
36. Question
For m ≠ n, if tan mθ = tan nθ, then the different values of θ are in
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Question 37 of 68
37. Question
tan 20° + tan 40° + √3 tan 20° tan 40° is equal to
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Question 38 of 68
38. Question
Let sin x+ sin y = a and cos x + cos y = b then sin(x + y) is equal to
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Question 39 of 68
39. Question
If sin A = sin B, cos A = cos B, then the value of A in terms of B is
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Question 40 of 68
40. Question
The number of real solutions of is
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Question 41 of 68
41. Question
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Question 42 of 68
42. Question
The value of is
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Question 43 of 68
43. Question
If sin^{−1} x + sin^{−1} y + sin^{−1} z = π then x^{4} + y^{4} + z^{4} + 4x^{2}y^{2}z^{2} = k(x^{2}y^{2} + y^{2}z^{2} + z^{2}x^{2}) where k = ?
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Question 44 of 68
44. Question
A triangle ABC is rightangled at B. Then the diameter of the incircle of the triangle is
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Question 45 of 68
45. Question
If the angles of triangle are in the ratio 1 : 2 : 3, he corresponding sides are in the ratio
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Question 46 of 68
46. Question
The maximum number of real roots of the equation x^{2n} – 1 = 0 is
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Question 47 of 68
47. Question
We are given b, c & sin B such that B is acute and b < c sin B, then
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Question 48 of 68
48. Question
The expression ax^{2} + bx + c, a > 0 is positive for all real x only if
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Question 49 of 68
49. Question
If α, β are the roots of quadratic equation x^{2} + bx – c = 0 then the equation whose roots are b & c is
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Question 50 of 68
50. Question
If the ratio of the roots of the equation x^{2} + bx + c = 0 is the ratio of the roots of the equation x^{2} + qx + r = 0 then
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Question 51 of 68
51. Question
The roots of the equation 4^{x} – 3 . 2^{x + 3} + 128 = 0 are
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Question 52 of 68
52. Question
If a^{x} = b^{x} = c^{z} and a, b, c are in GP. then x, y, z are in
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Question 53 of 68
53. Question
If , the value of n is
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Question 54 of 68
54. Question
If the sum of n terms of the series 2^{3} + 4^{3} + 6^{3} + …….. ∞ is 3528, then n equals
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Question 55 of 68
55. Question
The 99th term of the series 2 + 7 + 14 + 23 + 34 + , ……. is
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Question 56 of 68
56. Question
The letters of the word RANDOM are written in all possible orders and these words are written out as in a dictionary. Then the rank of the word RANDOM is
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Question 57 of 68
57. Question
How many numbers of five digits can be formed from the digits 2, 0, 4, 3, 8 when repetition of digits is not allowed ?
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Question 58 of 68
58. Question
If the coefficient of mth, (m + 1)th and (m + 2)th terms in the expansion of (1 + x)^{n} are in A.P. then
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Question 59 of 68
59. Question
The middle term in the expansion of is
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Question 60 of 68
60. Question
The value of the determinant is
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Question 61 of 68
61. Question
The inverse of the matrix is
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Question 62 of 68
62. Question
If A and B are any 2 × 2 matrices, then det(A + B) = 0 implies
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Question 63 of 68
63. Question
Value of a for which are coplanar
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Question 64 of 68
64. Question
If the vector form of the component of is
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Question 65 of 68
65. Question
The point which divides the line joining the points (2, 4, 5) & (3, 5, −4) in the ratio −2 : 3 lies on
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Question 66 of 68
66. Question
If θ is an angle given by where α, β & γ are the angles made by a line with the positive directions of the axes of reference, then the measure of θ is
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Question 67 of 68
67. Question
Weighted mean is computed by the formula
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Question 68 of 68
68. Question
The mean and S.D. of 1, 2, 3, 4, 5, 6 is
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