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Question 1 of 68
1. Question
The number of real solution of the equation is
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Question 2 of 68
2. Question
The total number of terms in the expansion of (x + y)^{100} + (x – y)^{100} after simplification is
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Question 3 of 68
3. Question
Let A and B be 3 × 3 matrices. The AB = 0 implies
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Question 4 of 68
4. Question
The derivative of w.r.t. at x = 0 is
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Question 5 of 68
5. Question
Three identical dice are rolled. The probability that the same number will appear on each of them is
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Question 6 of 68
6. Question
If then is equal to
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Question 7 of 68
7. Question
If then
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Question 8 of 68
8. Question
Two tangents are drawn from the point (−2, −1) to the parabola y^{2} = 4x. If α be the angle between these tangents, then tan α = ?
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Question 9 of 68
9. Question
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Question 10 of 68
10. Question
where p and q are integers, is equal to
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Question 11 of 68
11. Question
The value of is ([ ] denotes the greatest integer function)
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Question 12 of 68
12. Question
On the interval [0, 1] the function x^{25}(1 – x)^{75} takes its maximum value at the point
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Question 13 of 68
13. Question
The general solution of the differential equation is
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Question 14 of 68
14. Question
The area of parallelogram having diagonals and is
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Question 15 of 68
15. Question
If for x ≠ 1 and if f is continuous oat x = 1 then f(1) is
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Question 16 of 68
16. Question
If y = log_{a}x + log_{x}a + log_{x}x + log_{a}a, then dy/dx =
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Question 17 of 68
17. Question
The sin θ of the angle between the straight line and the plane 2x – 2y + z = 5 is
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Question 18 of 68
18. Question
Domain of the function
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Question 19 of 68
19. Question
If the mean of a Binomial distribution is 3 and its variance is 3/2, then the number of trials is
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Question 20 of 68
20. Question
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Question 21 of 68
21. Question
The integrating factor of differential equation y log y dx = (log y – x) dy is
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Question 22 of 68
22. Question
The value of is
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Question 23 of 68
23. Question
The area between the curve y = 1 − x and x – ax is equal to
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Question 24 of 68
24. Question
The equation of tangent of the curve y = 4e^{−x/4} at the point where the curve crosses Yaxis is equal to
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Question 25 of 68
25. Question
The maximum value of z = 10x + 6y subject to constraints x ≥ 0, y ≥ 0, x + y ≤ 12, 2x + y ≤20 is
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Question 26 of 68
26. Question
If then k = 0
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Question 27 of 68
27. Question
Find a polynomial f(x) of degree 2 where f(0) = 8, f(1) = 12, f(2) = 18.
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Question 28 of 68
28. Question
Given, P(A) = 0.5, P(B) = 0.4, P(A ∩ B) = 0.3, then is
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Question 29 of 68
29. Question
The number of complex numbers z such that z – 1 = z + 1 = z – i equals
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Question 30 of 68
30. Question
The circles x^{2} + y^{2} = 4x + 8y + 5 intersect the line 3x – 4y = m at two distinct points if
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Question 31 of 68
31. Question
If the three point (3q, 0), (0, 3p) and (1, 1) are collinear, then which one is TRUE?
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Question 32 of 68
32. Question
If yʹʹ − 3yʹ + 2y = 0 where y(0) = 1, yʹ(0) = 0 then the value of y at x = log 2 is
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Question 33 of 68
33. Question
The solution of the differential equation xdy – ydx = 0 represents a
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Question 34 of 68
34. Question
If the angles A, B and C are in A.P., then
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Question 35 of 68
35. Question
Value of is
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Question 36 of 68
36. Question
The sum of n terms of the following series 1^{3} + 3^{3} + 5^{3} + 7^{3}+….. is
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Question 37 of 68
37. Question
The quadratic equation x^{2} + 15x + 14 = 0 has
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Question 38 of 68
38. Question
The coefficient of the (r – 1)th , rth and (r + 1)th terms in the expansion of (x + 1)^{n} are in the ratio 1 : 3 : 5. The pair (n, r) is
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Question 39 of 68
39. Question
The number of solutions of the equations of the equation tan x + sec x = 2 cos x lying in the interval [0, 2π] is
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Question 40 of 68
40. Question
If the function f(x) satisfy then is
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Question 41 of 68
41. Question
The value of is
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Question 42 of 68
42. Question
If ax^{2} + 4xy + y^{2} + ax + 3y + 2 = 0 represents a parabola, then a is
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Question 43 of 68
43. Question
The value of (tan 70° − tan 50° + tan 10°) is
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Question 44 of 68
44. Question
If a, b, c, are in A.P. then 3^{a}, 3^{b}, 3^{c} are in
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Question 45 of 68
45. Question
Variance of the numbers 2, 4, 6, 8 is
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Question 46 of 68
46. Question
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Question 47 of 68
47. Question
7 persons to be seated in a row. Probability that 2 particular persons to sit next to each other is
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Question 48 of 68
48. Question
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Question 49 of 68
49. Question
If and then α + β = ?
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Question 50 of 68
50. Question
The range of the function is
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Question 51 of 68
51. Question
If then the locus of z = x + iy is
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Question 52 of 68
52. Question
sin^{4} x + cos^{4} x + sin 2x + α = 0 is solvable if
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Question 53 of 68
53. Question
The inequality does NOT hold good for which of the following values of x ?
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Question 54 of 68
54. Question
If then the value of Z_{1} . Z_{2}……∞ is
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Question 55 of 68
55. Question
If the roots of ax^{2} + bx + c = 0 are in their ratio m : n, then
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Question 56 of 68
56. Question
The equation (cos p – 1)x^{2} + (cos p)x + sin p = 0, where x is a variable, has real roots. Then p lies in
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Question 57 of 68
57. Question
If then is equal to
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Question 58 of 68
58. Question
The coefficient of x^{r}(0 ≤ r ≤ n – 1) in the expansion of (x + 3)^{n – 1 }+ (x + 3)^{n }^{– 2}(x+ 2) + (x + 3)^{n – 3}(x + 2)^{2} + ….. … + (x + 2)^{n – 1 } is
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Question 59 of 68
59. Question
If all permutation of the letters of the word AGAIN are arranged as in dictionary, then fiftieth word is
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Question 60 of 68
60. Question
If the system of equations x + 2y – 3z = 1, (p + 2)z = 3, (2p + 1)y + z = 2 is inconsistent then the value of p is
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Question 61 of 68
61. Question
If sin^{−1} a + sin^{−1} b + sin^{−1} c = π, then
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Question 62 of 68
62. Question
If tan pθ + cos qθ = 0, then general value of θ is
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Question 63 of 68
63. Question
If Z_{1}, Z_{2}, Z_{3} are vertices of an equilateral triangle with Z_{0} its centroid, then Z_{1}^{2} + Z_{2}^{2} + Z_{3}^{2} = ?
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Question 64 of 68
64. Question
The number of ways in which one or more balls can be selected out of 10 white, 9 green and 7 blue balls is
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Question 65 of 68
65. Question
The integer k for which the inequality x^{2} – 2(4k – 1) x + 15k^{2} – 2k – 7 > 0 is valid for any real x, is
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Question 66 of 68
66. Question
If S_{1}, S_{2} and S_{3} denote the sum of first n_{1}, n_{2}, n_{3} terms of an A.P. respectively, then the value of is
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Question 67 of 68
67. Question
p ⇒ q can also be written as
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Question 68 of 68
68. Question
If (sec α + tan α) (sec β + tan β) (sec γ + tan γ) = tan α tan β tan γ, then the value of (sec α – tan α) (sec β – tan β) (sec γ – tan γ) is
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