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Question 1 of 68
1. Question
If X = {4^{n} – 3n – 1 : n ∈ N} and Y = {9(n – 1) : n ∈ N} then X ∪ Y =
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Question 2 of 68
2. Question
Let A be a nonvoid set of the children in a family. The relation ‘X is a brother of Y’ on Y is
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Question 3 of 68
3. Question
A mapping f : R → R which is defined as f(x) = cos x, x ∈ R is
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Question 4 of 68
4. Question
Let α, β be the roots of the equation x^{2} – tx + r = 0 and be the roots of their equation x^{2} – tx + r = 0, then the value of r is
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Question 5 of 68
5. Question
If sin α, cos α are the roots of the equation ax^{2} + bx + c = 0, then
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Question 6 of 68
6. Question
The product of cube roots of −1 is equal to
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Question 7 of 68
7. Question
The Point in sphere which corresponds to is
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Question 8 of 68
8. Question
The region of the Argand diagram defined by z – 3 > 0 is
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Question 9 of 68
9. Question
How many numbers between 5000 and 10000 can be formed with the digits if each digit NOT appearing more than once in each number?
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Question 10 of 68
10. Question
The unit digit of 2^{100} is
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Question 11 of 68
11. Question
The minimum value of cos 2θ + cos θ for real values of θ is
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Question 12 of 68
12. Question
The number of solutions of the pair of the equations 2sin^{2} θ – cos 2θ = 0
3cos^{2} θ – 3 sin θ = 0 in the interval [0, 2π] is
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Question 13 of 68
13. Question
The solution of the differential equation y[x^{2} + y^{2} + 1]dy + [2x(x^{2} + y^{2}) – 1]dx = 0 is
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Question 14 of 68
14. Question
Consider the following differential equations:
The sum of the order of 2nd differential equation and the degree of the 1st differential equation is
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Question 15 of 68
15. Question
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Question 16 of 68
16. Question
Probability that A speaks truth is 4/5, while this probability for B is 3/4. The probability that they contradict each other when asked to speak on a fact is
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Question 17 of 68
17. Question
A bag contains unlimited number of black, blue, red and orange balls. The number of ways to select 10 balls so that the selection includes at least one ball of each colour is
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Question 18 of 68
18. Question
The number of diagonals of nsided polygon is
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Question 19 of 68
19. Question
The middle term of (1 + x)^{2n} is
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Question 20 of 68
20. Question
The product of the series is
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Question 21 of 68
21. Question
If a variable line passes through the point of intersection of the lines x + 2y – 1 = 0 and 2x – y – 1 = 0 and meets the coordinate axes at A and B, then the locus of midpoint of AB is
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Question 22 of 68
22. Question
If M is 7 × 5 matrix of rank 3 and N is a 5 × 7 matrix of rank 5, then rank of MN is
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Question 23 of 68
23. Question
If A is a 3 × 3 matrix with det A = 5 and if B = A^{2} then det B – ?
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Question 24 of 68
24. Question
If then det(A^{−1}) = ?
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Question 25 of 68
25. Question
Five horses are in a race. Mr. A selects two of them at random and bets on them. The probability that Mr. A selected the winning horse is
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Question 26 of 68
26. Question
The relationship between mean, median and mode for a moderately skewed distribution is
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Question 27 of 68
27. Question
If two lines of regression are 3x + 12y = 19 and 9x + 3y = 46, the correlation coefficient is
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Question 28 of 68
28. Question
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Question 29 of 68
29. Question
∫{xf ʹ(x) + f(x)}dx = ?
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Question 30 of 68
30. Question
If then Fʹ(x) = ?
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Question 31 of 68
31. Question
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Question 32 of 68
32. Question
If x = f(t) cost – f ʹ(t) sin t and y = f(t) sin t + f ʹ(t) cost t then
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Question 33 of 68
33. Question
If f(x) is a differentiable function on [0, 3], and f(3) = 2 then
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Question 34 of 68
34. Question
log_{3}sinx – log_{3} cos x – log_{3}(1 – tan x) – log_{3}(1 + tan x) = −1 then tan 2x = ?
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Question 35 of 68
35. Question
then the value of is
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Question 36 of 68
36. Question
The coefficient of x^{99} in the expansion of (x – 1) (x – 2) (x – 3) …. (x – 100) is
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Question 37 of 68
37. Question
The number of solutions of the equation 2 sin(e^{x}) = 5^{x} + 5^{−x} is
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Question 38 of 68
38. Question
The straight li ne y = mx + c cuts the circle x^{2} + y^{2} = a^{2} in real points if
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Question 39 of 68
39. Question
If are two vectors such that and , then
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Question 40 of 68
40. Question
Let P, Q, R, and S be the points on the plane with position vectors and respectively. The quadrilateral PQRS must be a
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Question 41 of 68
41. Question
The value of
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Question 42 of 68
42. Question
Let and be three vectors. A vector in the plane , whose projection on is given by
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Question 43 of 68
43. Question
Let P = {θ : sin θ – cos θ = √2 cos θ} and Q = {θ : sin θ + cos θ = √2 sin θ} be two sets. Then
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Question 44 of 68
44. Question
If the cardinality of a set A is 4 and that of a set B is 3, then what is the cardinality of the set A ∆ B?
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Question 45 of 68
45. Question
The total number of subsets of a finite set A has 56 more elements than the total number of subsets of another finite set B. What is the number of elements in the set A?
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Question 46 of 68
46. Question
The number of continuous functions on R which satisfy (f(x))^{2} = x^{2}, ∀x ∈ R, is
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Question 47 of 68
47. Question
The value of C of Lagrange’s Mean Value Theorem if f(x) = x(x – 1)(x – 2); a = 0, b = 1/2 is
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Question 48 of 68
48. Question
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Question 49 of 68
49. Question
Let f(x) = x^{2} – 5x + 6 and then f(A) = ?
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Question 50 of 68
50. Question
Multiplication of matrices E and G is F where and Then the value of F is
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Question 51 of 68
51. Question
What is the value of following determinant?
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Question 52 of 68
52. Question
The real part of complex number (1 + i)n is
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Question 53 of 68
53. Question
If 1, ω, ω^{2} are the cube roots of unity, then the roots of the equation (x – 1)^{3} + 8 = 0 are
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Question 54 of 68
54. Question
The remainder when 2^{50} is divided by 7 is
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Question 55 of 68
55. Question
Solution of is
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Question 56 of 68
56. Question
A fair dice is tossed 7 times. The probability that a 5 or a 6 occurs atleast once is
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Question 57 of 68
57. Question
The maximum value of Z = 2x + 3y, subject to constraints x + y ≤ 30, y ≥ 3, 0 ≤ 12, 0 ≤ x ≤ 20 and x – y ≥ 0 is
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Question 58 of 68
58. Question
Consider the LP problem : max z = x + y subject x – 2y ≤ 10
y – 2x ≤ 10
x, y ≥ 0
Then the LP problem
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Question 59 of 68
59. Question
Which of the following is the convex set?
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Question 60 of 68
60. Question
The reflection of the point A(1, 0, 0) in the line is
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Question 61 of 68
61. Question
If α, β are roots of the equation 8x^{2} – 3x + 27 = 0 then the value of is
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Question 62 of 68
62. Question
In decimal system, the number (362)_{16} is equivalent to
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Question 63 of 68
63. Question
The least value of n for which the sum of the series 3 + 6 + 9 +…to n terms exceeds 1000 is
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Question 64 of 68
64. Question
(1 – x)^{3/2} can be expanded in ascending power of x if
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Question 65 of 68
65. Question
The angle made by a double ordinate of length 8a at the vertex of the parabola y^{2} = 4ax is
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Question 66 of 68
66. Question
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Question 67 of 68
67. Question
Let [x] denote the greatest integer less than or equal to x and f(x) = [tan^{2}x] then
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Question 68 of 68
68. Question
If f(x) = (x – p)^{2} + (x – q)^{2} + (x – r)^{2}, then f(x) has a minimum at
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