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Question 1 of 30
1. Question
In a certain town, 25% of the families own a phone and 15% own a car; 65% families own neither a phone nor a car and 2,000 families own both a car and a phone. Consider the following three statements : (a) 5% families own both a car and a phone, (b) 35% families own either a car or a phone, (c)40,000 families live in the town. Then,
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Question 2 of 30
2. Question
The largest value of r for which the region represented by the set {ω ϵ C/ω−4−i≤r} is contained in the region represented by the set {z ϵ C/z−1≤z+i}, is equal to :
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Question 3 of 30
3. Question
If 2 + 3i is one of the roots of the equation 2x^{3} – 9x^{2} + kx – 13 = 0, k ϵ R, then the real root of this equation :
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Question 4 of 30
4. Question
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Question 5 of 30
5. Question
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Question 6 of 30
6. Question
The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is :
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Question 7 of 30
7. Question
Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is :
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Question 8 of 30
8. Question
If the coefficients of the three successive terms in the binomial expansion of (1 + x)^{n} are in the ratio 1 : 7 : 42, then the first of these terms in the expansion is :
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Question 9 of 30
9. Question
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Question 10 of 30
10. Question
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Question 11 of 30
11. Question
The distance, from the origin, of the normal to the curve, x = 2 cos t + 2t sin t, y = 2 sin t – 2t cos t at is :
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Question 12 of 30
12. Question
If Roll’s theorem holds for the function f (x) = 2x^{3}+bx^{2}+cx, x ϵ [−1, 1], at the point then 2b+c equals :
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Question 13 of 30
13. Question
Let the tangents drawn to the circle, x^{2} + y^{2} = 16 from the point P(0, h) meet the xaxis at points A and B. If the area of ∆APB is minimum, then h is equal to :
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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 (in square units) of the region bounded by the curves y + 2x^{2} = 0 and y + 3x^{2} = 1, is equal to :
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Question 17 of 30
17. Question
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Question 18 of 30
18. Question
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Question 19 of 30
19. Question
Let L be the line passing through the point P(1, 2) such that its intercepted segment between the coordinate axes is bisected at P. If L_{1} is line perpendicular to L and passing through the point (–2, 1), then the point of intersection of L and L_{1} is :
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Question 20 of 30
20. Question
If y + 3x = 0 is the equation of a chord of the circle, x^{2} + y^{2} – 30x = 0, then the equation of the circle with this chord as diameter is :
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Question 21 of 30
21. Question
If the tangent to the conic, y – 6 = x^{2} at (2, 10) touches the circle, x^{2} + y^{2} + 8x – 2y = k (for some fixed k) at a point (∝, β) ; then (∝, β ) is :
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Question 22 of 30
22. Question
An ellipse passes through the foci of the hyperbola, 9x^{2} – 4y^{2} = 36 and its major and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. if the product of eccentricities of the two conics is 1/2, then which of the following points does not lie on the ellipse ?
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Question 23 of 30
23. Question
If the points (1, 1, λ) and (–3, 0, 1) are equidistant from the plane, 3x + 4y – 12z + 13 = 0, then λ satisfies the equation :
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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
Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X), with replacement, then the probability that A and B have equal number of elements, is :
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Question 27 of 30
27. Question
A factory is operating in two shifts, day and night, with 70 and 30 workers respectively. If per day mean wage of the day shift workers is Rs. 54 and per day mean wage of all the worker is Rs. 60, then per day mean wage of the night shift workers (in Rs.) is :
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Question 28 of 30
28. Question
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Question 29 of 30
29. Question
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Question 30 of 30
30. Question
The contrapositive of the statement “If it is raining, then I will not come”, is :
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