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Question 1 of 30
1. Question
Let f be an odd function defined on the set of real numbers such that for x ≥ 0, f(x) = 3 sin x + 4 cos x.
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Question 2 of 30
2. Question
Let P(3 sec θ, 2 tan θ) and Q(sec ϕ, 2 tan ϕ) where be two distinct points on the hyperbola Then the ordinate of the point of intersection of the normals at P and Q is :
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Question 3 of 30
3. Question
The base of an equilateral triangle is along the line given by 3x + 4y = 9. If a vertex of the triangle is (1, 2), then the length of a side of the triangle is :
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Question 4 of 30
4. Question
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Question 5 of 30
5. Question
The proposition ~(p⋁~q) ⋁ ~(p⋁q) is logically equivalent to :
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Question 6 of 30
6. Question
The coefficient of x^{50 }in the binomial expansion of
(1+x)^{1000} + x(1 + x)^{999} + x^{2 }(1 + x)^{998} + ….+x^{1000} is :
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Question 7 of 30
7. Question
A set S contains 7 elements. A nonempty subset A of S and an element x of S are chosen at random. Then the probability that x ∈ A is :
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Question 8 of 30
8. Question
If α and β are roots of the equation, x^{2 }– 4√2 kx + 2e ^{4 ln k }– 1 = 0 for some k, and α^{2} + β^{2} = 66, then α^{3} + β^{3} is equal to :
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Question 9 of 30
9. Question
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Question 10 of 30
10. Question
Two ships A and B are sailing straight away from a fixed point O along routes such that ∠AOB is always 120°. At a certain instance, OA = 8 km, OB = 6 km and the ship A is sailing at the rate of 20 km/hr. while the ship B sailing at the rate of 30 km/hr. Then the distance between A and B is changing at the rate (in km/hr) :
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Question 11 of 30
11. Question
A staircase of length l rests against a vertical wall and a floor of a room,. Let P be a point on the staircase, nearer to its end on the wall, that divides its length in the ratio 1 : 2. If the staircase begins to slide on the floor, then the locus of P is :
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Question 12 of 30
12. Question
The volume of the largest possible right circular cylinder that can be inscribed in a sphere of radius = √3 is :
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Question 13 of 30
13. Question
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Question 14 of 30
14. Question
Let L_{1} be the length of the common chord of the curves x^{2} + y^{2 }= 9 and y^{2} = 8x, and L_{2} be the length of the latus rectum of y^{2 }= 8x, then :
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Question 15 of 30
15. Question
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Question 16 of 30
16. Question
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Question 17 of 30
17. Question
The angle of elevation of the top of a vertical tower from a point P on the horizontal ground was observed to be α. After moving a distance 2 metres from P towards the foot of the tower, the angle of elevation changes to β. Then the height (in metres) of the tower is :
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Question 18 of 30
18. Question
The set of all real values of λ for which exactly two common tangents can be drawn to the circles
x^{2} + y^{2}– 4x – 4y + 6 = 0 and x^{2} + y^{2} – 10x – 10y + λ = 0 is the interval :
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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
Let for i = 1, 2, 3, pi(x) be a polynomial of degree 2 in x, p_{i }´(x) and p_{i }´´(x) be the first and second order derivatives of p_{i}(x) respectively. Let,
and B(x) = [A(x)]^{T }A(x). Then determinant of B(x) :
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Question 22 of 30
22. Question
Let A(2, 3, 5), B(−1, 3, 2) and C (λ, 5, μ) be the vertices of a ΔABC. If the median through A is equally inclined to the coordinate axes, then :
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Question 23 of 30
23. Question
For the curve y = 3 sin θ cos θ, x = e^{θ }sin θ, 0 ≤ θ ≤ π, the tangent is parallel to xaxis when θ is :
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Question 24 of 30
24. Question
An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is :
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Question 25 of 30
25. Question
Let f(x) = xx, g(x) = sin x and h(x) = (gof)(x). Then
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Question 26 of 30
26. Question
In the general solution of the differentiable equation for some function, Φ, is given by y lncx = x, where c is an arbitrary constant, then Φ (2) is equal to :
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Question 27 of 30
27. Question
The sum of the first 20 terms common between the series 3 + 7 + 11 + 15 + … and 1 + 6 + 11 + 16 + … , is :
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Question 28 of 30
28. Question
In a geometric progression, if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49, and the sum of the first and the third term is 35. Then the first term of this geometric progression is :
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Question 29 of 30
29. Question
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Question 30 of 30
30. Question
If X has a binomial distribution, B(n, p) with parameters n and p such that P(X = 2) = P(X = 3), then E(x), the mean of variable X, is :
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