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Question 1 of 30
1. Question
The real number k for which the equation, 2x^{3} + 3x + k = 0 has two distinct real roots in [0, 1]
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Question 2 of 30
2. Question
The number of values of k, for which the system of equations :
(k + 1)x + 8y = 4k
kx + (k +3)y = 3k – 1 has no solution, isCorrectIncorrect 
Question 3 of 30
3. Question
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Question 4 of 30
4. Question
Let T_{n} be the number of all possible triangles formed by joining vertices of an nsided regular polygon. If T_{n+1} – T_{n} =10, then the value of n is :
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Question 5 of 30
5. Question
At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by If the firm employs 25 more workers, then the new level of production of items is :
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Question 6 of 30
6. Question
ABCD is a trapezium such that AB and CD are parallel and BC ⊥ CD. If ∠ADB = θ, BC = p and CD = q, then AB is equal to :
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Question 7 of 30
7. Question
All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?
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Question 8 of 30
8. Question
A ray of light along x + √3y = √3 gets reflected upon reaching xaxis, the equation of the reflected ray is :
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Question 9 of 30
9. Question
The area (in square units) bounded by the curves y = √x, 2y – x + 3 = 0, xaxis and lying in the first quadrant is :
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Question 10 of 30
10. Question
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Question 11 of 30
11. Question
If ∫f(x) dx = Ψ(x), then ∫x^{5}f(x^{3}) dx is equal to :
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Question 12 of 30
12. Question
Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is :
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Question 13 of 30
13. Question
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Question 14 of 30
14. Question
The xcoordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1) (1, 1) and (1, 0) is :
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Question 15 of 30
15. Question
Consider :
Statement I : (p ⋀ ~ q) ⋀ (~p ⋀ q) is a fallacy.
Statement II: (p → q) ↔ (~q → ~ p) is a tautology.CorrectIncorrect 
Question 16 of 30
16. Question
If the equations x^{2} + 2x + 3 = 0 and ax^{2} + bx + c = 0, a, b, c ϵ R, have a common root, then a : b : c is :
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Question 17 of 30
17. Question
The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, ….., is :
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Question 18 of 30
18. Question
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Question 19 of 30
19. Question
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Question 20 of 30
20. Question
If x, y, z are in A.P. and tan^{−1} x, tan^{−1} y and tan^{−1} z are also in A.P, then :
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Question 21 of 30
21. Question
The intercepts on xaxis made by tangents to the curve, which are parallel to the line y = 2x, are equal to :
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Question 22 of 30
22. Question
Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is :
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Question 23 of 30
23. Question
The circle passing through (1, −2) and touching the axis of x at (3, 0) also passes through the point :
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Question 24 of 30
24. Question
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Question 25 of 30
25. Question
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Question 26 of 30
26. Question
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Question 27 of 30
27. Question
Given : A circle, 2x^{2} + 2y^{2 }= 5 and a parabola, y^{2} = 4√5x.
Statement – I : An equation of a common tangent to these curves is y = x + √5.
Statement – II : If the line is their common tangent, then m satisfied
m^{4} – 3m^{2} + 2 = 0
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Question 28 of 30
28. Question
A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is :
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Question 29 of 30
29. Question
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Question 30 of 30
30. Question
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