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Question 1 of 30
1. Question
If and S = {x ∈ R : f(x) = f(−x)}; then S:
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Question 2 of 30
2. Question
A value of θ for which is purely imaginary, is:
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Question 3 of 30
3. Question
The sum of all real value of x satisfying the equation is :
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Question 4 of 30
4. Question
If and A adj A = AA^{T}, then 5a + b is equal to:
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Question 5 of 30
5. Question
The system of linear equations
x + λy – z = 0
λx – y – z = 0
x + y – λz = 0
has a nontrivial solution for.
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Question 6 of 30
6. Question
If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is:
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Question 7 of 30
7. Question
If the number of terms in the expansion of is 28, then the sum of the coefficients of all the terms in this expansion, is:
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Question 8 of 30
8. Question
If the 2nd, 5th and 9th terms of a nonconstant A.P. are in G.P., then the common ratio of this G.P. is:
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Question 9 of 30
9. Question
If the sum of the first ten terms of the series then m is equal to:
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Question 10 of 30
10. Question
Let then long p is equal to:
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Question 11 of 30
11. Question
For x ∈ R, f(x) = log 2 – sin x and g(x0 = f(f(x)), then:
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Question 12 of 30
12. Question
Consider
A normal to y = f(x) at x = π/6 also passes through the point:
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Question 13 of 30
13. Question
A wire of length 2 units is cut into two parts which are bent respectively to form a square of side = x units and a circle of radius = r units. If the sum of the areas of the square and the circle so formed is minimum, then:
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Question 14 of 30
14. Question
The integral is equal to:
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Question 15 of 30
15. Question
is equal to:
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Question 16 of 30
16. Question
The area(in sq. units) of the region {(x, y) : y^{2} ≥ 2x and x^{2} + y^{2} ≤ 4x, x ≥ 0, y ≥ 0} is:
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Question 17 of 30
17. Question
If a curve y = f(x) passes through the point (1, −1) and satisfies the differential equation, y(1 + xy) dx = x dy, then is equal to:
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Question 18 of 30
18. Question
Two sides of a rhombus are along the lines, x − y + 1 = 0 and 7x − y − 5 = 0. If its diagonals intersect at (−1, −2), then which one of the following is a vertex of this rhombus?
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Question 19 of 30
19. Question
The centres of those circles which touch the circle, x^{2} + y^{2} − 8x − 8y − 4 = 0, externally and also touch the xaxis, lie on:
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Question 20 of 30
20. Question
If one of the diameters of the circle, given by the equation, x^{2} + y^{2} −4x + 6y −12 = 0, is a chord of a circle S, whose centre is at (−3, 2), then the radius of S is:
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Question 21 of 30
21. Question
Let P be the point on the parabola, y^{2} = 8x which is at a minimum distance from the centre C of the circle, x^{2} + (y + 6)^{2} = 1. Then the equation of the circle, passing through C and having its centre at P is:
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Question 22 of 30
22. Question
The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half the distance between its foci, is:
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Question 23 of 30
23. Question
The distance of the point (1, −5, 9) from the plane x − y + z = 5 measured along the line x = y = z is :
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Question 24 of 30
24. Question
If the line, ℓx + my – z = 9, then ℓ^{2} + m^{2} is equal to:
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Question 25 of 30
25. Question
Let be three unit vectors such that If is not parallel to then the angle between is :
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Question 26 of 30
26. Question
If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?
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Question 27 of 30
27. Question
Let two fair six−faced dice A and B be thrown simultaneously. If E_{1} is the event that die A shows up four, E_{2} is the event that die B shows up two and E_{3} is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?
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Question 28 of 30
28. Question
If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x = cos 3x + cos 4x = 0, is :
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Question 29 of 30
29. Question
A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30°. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60°. Then the time taken (in minutes) by him, from B to reach the pillar, is :
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Question 30 of 30
30. Question
The Boolean Expression (p ⋀ ~ q) ⋁ q ⋁ (~p ⋀ q) is equivalent to:
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