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Question 1 of 30
1. Question
The eccentricity of the conjugate hyperbola of the hyperbola x^{2} – 3y^{2} = 1 is
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Question 2 of 30
2. Question
Given that X = A ∩ B & Y = A ∪ B. The no. of subsets of B is 4 times the no. of subsets of A and no of subsets of A is 4 times the no. of subsets of X. It is given that n(X) = 5. Let p, q, r, s be the no. of subsets of A, B, X & Y respectively. Then from the following statements
(i) n(A) = 7 (ii) n (B) = 9
(iii) n(Y) = 11 (iv) pq = rs
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Question 3 of 30
3. Question
The shortest distance of the line xy2=0 from the curve y = x^{2} + 3x + 2 is
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Question 4 of 30
4. Question
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Question 5 of 30
5. Question
S – 1 – If sin^{2}θ_{1} + sin^{2}θ_{2} + …… + sin^{2}θ_{n} = 0, then the different sets of values of (θ_{1}, θ_{2}……θ_{n}) for which cos θ_{1} + cos θ_{2} + ….. + cos θ_{n} = n – 4 is n(n – 1).S – 2 – If sin^{2}θ_{1} + sin^{2}θ_{2} + …… + sin^{2}θ_{n} = 0, then cos θ_{1}.cos θ_{2}. ….. cos θ_{n} = ± 1CorrectIncorrect 
Question 6 of 30
6. Question
If f be any one of the six trigonometric functions. Let A, B ∈ R satisfying f(2A) = f(2B)
S 1 − A = nπ + B, ∀ n ∈ R
S 2 − 2π is one of the period of f.
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Question 7 of 30
7. Question
S –1 – If diagonals of the quadrilateral formed by the lines px + qy + r = 0 & p’x + q’y + r = 0 are at right angles, then p^{2} + q^{2} = q’^{2} + p’^{2}.
S –2− Diagonals of a rhombus bisect perpendicularly each other.
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Question 8 of 30
8. Question
Consider circles x^{2} + y^{2} – 4x – 6y − 8 = 0 & x^{2} + y^{2} – 2x – 3 = 0
S 1− Both the circles intersect each other at two distinct points.
S2−Sum of two radii of the circles is greater than distance between centres of circles.
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Question 9 of 30
9. Question
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Question 10 of 30
10. Question
If x^{2} + 3x + 5 = 0 & ax^{2} + bx + c = 0 have a root in common, a, b, c ϵ N, then least value of a + b + c is
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Question 11 of 30
11. Question
The 100^{th} place digit of the number 17^{256} is
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Question 12 of 30
12. Question
The equation x^{2} + ax + b = 1 has roots which are positive integers, then a^{2} + b^{2} may be equal to
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Question 13 of 30
13. Question
If 1 is a twice repeated root of the equation ax^{3} + bx^{2} +bx + d = 0 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 function f(x) = max{(2 –x), (2 + x), 4}, x ∈ (−∞, ∞) is
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Question 17 of 30
17. Question
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Question 18 of 30
18. Question
Number of distinct normals can be drawn from (–2, 1) to the parabola y^{2} – 4x – 2y – 3 = 0 is
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Question 19 of 30
19. Question
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Question 20 of 30
20. Question
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Question 21 of 30
21. Question
For what value of λ, the following system of linear equations have a non trivial solution?
(3 + λ) x + 3y + 4z = 0
x – y + 4z = 0
λx + y + 3z = 0
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Question 22 of 30
22. Question
Equation of the circle having centre at (3, −1) and cutting intercept of length 6 unit on the line 2x – 5y + 18 = 0 is
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Question 23 of 30
23. Question
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Question 24 of 30
24. Question
If A, G & H are A.M, G.M & H.M of a, b, c then the equation with roots a, b, c is
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Question 25 of 30
25. Question
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Question 26 of 30
26. Question
Three persons work independently on a problem. If respective probabilities of solving problem is 1/3, 1/4, & 1/5. Then the probability that the problem is unsolved
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Question 27 of 30
27. Question
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Question 28 of 30
28. Question
Let A = {1, 2, 3, 4}, B = {5, 6, 7, 8}, then which of the followings is a relation from A to B?
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Question 29 of 30
29. Question
If x = secθ – tanθ & y = cosecθ + cotθ then
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Question 30 of 30
30. Question
In triangle ABC, greatest value of is, if it is given that ‘R’ is the circum radius and ‘s’ is semiperimeter.
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