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Question 1 of 30
1. Question
Let A = {x_{1}, x_{2}, ……, x_{7}} and B = {y_{1}, y_{2}, y_{3}} be two sets containing seven and three distinct elements respectively. Then the total number of functions f : A → B that are onto, if there exist exactly three elements x in A such that f(x) = y_{2}, is equal to :
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Question 2 of 30
2. Question
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Question 3 of 30
3. Question
If the two roots of the equation, (a – 1)(x^{4} + x^{2} + 1) + (a + 1)(x^{2} + x + 1)^{2} = 0 are real and distinct, then the set of all values of ‘a’ is :
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Question 4 of 30
4. Question
If A is a 3×3 matrix such that 5.adjA = 5, then A is equal to :
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Question 5 of 30
5. Question
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Question 6 of 30
6. Question
If in a regular polygon the number of diagonals is 54, then the number of sides of this polygon is :
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Question 7 of 30
7. Question
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Question 8 of 30
8. Question
The sum of the 3^{rd} and the 4^{th} terms of a G.P. is 60 and the product of its first three terms is 1000. If the first term of this G.P. is positive, then its 7^{th} term 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
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Question 12 of 30
12. Question
Let k and K be the minimum and the maximum values of the function f(x) = in [0, 1] respectively, then the ordered pair (k, K) is equal to :
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Question 13 of 30
13. Question
From the top of a 64 metres high tower, a stone is thrown upwards vertically with the velocity of 48 m/s. The greatest height (in metres) attained by the stone, assuming the value of the gravitational acceleration g = 32 m/s^{2}, is :
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Question 14 of 30
14. Question
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Question 15 of 30
15. Question
Let f : R → R be a function such that f(2 – x) = f(2 + x) and f(4 – x) = f(4 + x), for all x ϵ R and Then the value of is :
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Question 16 of 30
16. Question
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Question 17 of 30
17. Question
The solution of the differential equation ydx – (x+2y^{2})dy=0 is x = f(y). If f(−1) = 1, then f(1) is equal to :
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Question 18 of 30
18. Question
A straight line L through the point (3, – 2) is inclined at an angle of 60° to the line √3 x + y = 1. If L also intersects the xaxis, then the equation of L is :
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Question 19 of 30
19. Question
If the incentre of an equilateral triangle is (1, 1) and the equation of its one side is 3x + 4y + 3 = 0, then the equation of the circumcircle of this triangle is :
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Question 20 of 30
20. Question
If a circle passing through the point (–1, 0) touches yaxis at (0, 2), then the length of the chord of the circle along the xaxis is :
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Question 21 of 30
21. Question
If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is :
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Question 22 of 30
22. Question
Let PQ be a double ordinate of the parabola, y^{2} = – 4x, where P lies in the second quadrant. If R divides PQ in the ratio 2 : 1 then the locus of R is :
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Question 23 of 30
23. Question
The shortest distance between the zaxis and the line x + y + 2z – 3 = 0 = 2x + 3y + 4z – 4, is :
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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
If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is :
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Question 27 of 30
27. Question
If the mean and the variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than or equal to one is :
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Question 28 of 30
28. Question
If cos∝ + cosβ = 3/2 and sin∝ + sinβ = 1/2 and θ is the arithmetic mean of ∝ and β, then sin 2θ + cos2θ is equal to :
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Question 29 of 30
29. Question
Let 10 vertical poles standing at equal distances on a straight line, subtend the same angle of elevation at a point O on this line and all the poles are on the same side of O. If the height of the longest pole is ‘h’ and the distance of the foot of the smallest pole from O is ‘a’; then the distance between two consecutive poles, is :
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Question 30 of 30
30. Question
Consider the following statements :
P : Suman is brilliant
Q : Suman is rich.
R : Suman is honest
the negation of the statement “Suman is brilliant and dishonest if and only if suman is rich” can be equivalently expressed as :
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