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Question 1 of 30
1. Question
If X = {4^{n} – 3n – 1 : n ∈ N} and Y = {9(n – 1) : n ∈ N}, where N is the set of natural numbers, then X∪Y is equal to :
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Question 2 of 30
2. Question
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Question 3 of 30
3. Question
If a ∈ R and the equation −3(x – [x])^{2} + 2(x – [x]) + a^{2} = 0 (where, [x] denotes the greatest integer ≤ x) has no integral solution, then all possible values of a lie in the interval :
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Question 4 of 30
4. Question
Let α and β be the roots of equation px^{2} + qx + r =0, p ≠ 0. If p, q, r are in A.P. and then the value of α – β is :
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Question 5 of 30
5. Question
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Question 6 of 30
6. Question
If A is an 3 × 3 non – singular matrix such that AA’ = A’A and B = A^{−1}A’, then BB’ equals :
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Question 7 of 30
7. Question
If the coefficients of x^{3} and x^{4} in the expansion of (1 + ax + bx^{2}) (1 – 2x)^{18} in powers of x are both zero, then (a, b) is equal to :
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Question 8 of 30
8. Question
If (10)^{9} + 2(11)^{1} (10)^{8} + 3(11)^{2} (10)^{7} + …. 10(11)^{9} = k(10)^{9}, then k is equal to
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Question 9 of 30
9. Question
Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is :
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Question 10 of 30
10. Question
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Question 11 of 30
11. Question
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Question 12 of 30
12. Question
If f and g are differentiable functions in [0, 1] satisfying f (0) = 2 = g(1), g(0) = 0 and f (1) = 6, then for some c ϵ]0, 1[ :
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Question 13 of 30
13. Question
If x = −1 and x = 2 are extreme points of f (x) = α log x + βx^{2} + x then :
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Question 14 of 30
14. Question
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Question 15 of 30
15. Question
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Question 16 of 30
16. Question
The area of the region described by A={(x, y) : x^{2} + y^{2} ≤ 1 and y^{2} ≤ 1 – x} is :
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Question 17 of 30
17. Question
Let the population of rabbits surviving at a time t be governed by the
If p(0) = 100, then p(t) equals :
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Question 18 of 30
18. Question
Let PS be the median of the triangle with vertices P(2, 2), Q(6, −1) and R(7, 3). The equation of the line passing through (1, −1) and parallel to PS is :
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Question 19 of 30
19. Question
Let a, b, c and d be nonzero numbers. If the point of intersection of the lines 4ax + 2ay + c = 0 and 5bx + 2by + d = 0 lies in the fourth quadrant and is equidistant from the two axes then :
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Question 20 of 30
20. Question
The locus of the foot of perpendicular drawn from the centre of the ellipse x^{2 }+ 3y^{2} = 6 on any tangent to it is :
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Question 21 of 30
21. Question
Let C be the circle with centre at (1, 1) and radius =1. If T is the circle centred at (0, y), passing through origin and touching the circle C externally, then the radius of T is equal to :
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Question 22 of 30
22. Question
The slope of the line touching both the parabolas y^{2} = 4x and x^{2} = −32y is :
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Question 23 of 30
23. Question
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Question 24 of 30
24. Question
The angle between the lines whose direction cosines satisfy the equations l + m + n = 0 and l^{2} = m^{2} + n^{2} is :
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Question 25 of 30
25. Question
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Question 26 of 30
26. Question
Let A and B be two events such that stands for the complement of the event A. Then the events A and B are :
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Question 27 of 30
27. Question
The variance of first 50 even natural numbers is :
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Question 28 of 30
28. Question
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Question 29 of 30
29. Question
A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45°. It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to 30°.
Then the speed (in m/s) of the bird is :
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Question 30 of 30
30. Question
The statement ~(p ↔ ~q) is :
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