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Question 1 of 30
1. Question
Let f(x) = 2^{10} ∙ x and g(x) = 3^{10} x ∙ x – 1. If (fog) (x) = x, then x is equal to :
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Question 2 of 30
2. Question
If the sum of the first n terms of the series then n equals :
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Question 3 of 30
3. Question
If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the centre and subtend angles and sec^{−1}(7) at the centre respectively, then the distance between these chords, is :
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Question 4 of 30
4. Question
If then is equal to :
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Question 5 of 30
5. Question
The locus of the point of intersection of the straight lines,
tx – 2y – 3t = 0
x – 2ty + 3 = 0 (t ϵ R), is :
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Question 6 of 30
6. Question
If the arithmetic mean of two numbers a and b, a > b > 0, is five times their geometric mean, then is equal to :
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Question 7 of 30
7. Question
The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If now the mean age of the teachers in this school is 39 years, then the age (in years) of the newly appointed teacher is :
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Question 8 of 30
8. Question
Let A be any 3 × 3 invertible matrix. Then which one of the following is not always true ?
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Question 9 of 30
9. Question
If the common tangents to the parabola, x^{2} = 4y and the circle, x^{2} + y^{2} = 4 intersect at the point P, then the distance of P from the origin, is :
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Question 10 of 30
10. Question
The proposition (~p) ⋁ (p ⋀ ~ q) is equivalent to :
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Question 11 of 30
11. Question
The area (in sq. units) of the parallelogram whose diagonals are along the vectors is :
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Question 12 of 30
12. Question
The curve satisfying the differential equation, ydx – (x + 3y)^{2}dy = 0 and passing through the point (1, 1), also passes through the point :
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Question 13 of 30
13. Question
The integral equals :
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Question 14 of 30
14. Question
The tangent at the point (2, −2) to the curve, x^{2}y^{2} – 2x = 4(1 – y) does not pass through the point :
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Question 15 of 30
15. Question
The integral is equal to :
(where C is a constant of integration)
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Question 16 of 30
16. Question
An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :
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Question 17 of 30
17. Question
The number of real values of λ for which the system of linear equations
2x + 4y – λ z = 0
4x + λ y + 2z = 0
λ x + 2y + 2z = 0
has infinitely many solutions, is :
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Question 18 of 30
18. Question
The coordinates of the foot of the perpendicular from the point (1, −2, 1) on the plane containing the lines, and is :
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Question 19 of 30
19. Question
The line of intersection of the planes and is :
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Question 20 of 30
20. Question
If (27)^{999} is divided by 7, then the remainder is :
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Question 21 of 30
21. Question
If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is :
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Question 22 of 30
22. Question
Let z ϵ C, the set of complex numbers. Then the equation, 2x + 3i − z – i = 0 represents :
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Question 23 of 30
23. Question
If then is equal to :
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Question 24 of 30
24. Question
If a point P h as coordinates (0, −2) and Q is any point on the circle, x^{2} + y^{2} – 5x – y + 5 = 0, then the maximum value of (PQ)^{2} is :
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Question 25 of 30
25. Question
The area (in sq. units) of the smaller portion enclosed between the curves, x^{2} + y^{2} = 4 and y^{2} = 3x, is :
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Question 26 of 30
26. Question
is equal to :
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Question 27 of 30
27. Question
The value of is equal to :
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Question 28 of 30
28. Question
Consider an ellipse, whose centre is at the origin and its major axis is along the xaxis. If its eccentricity is and the distance between its foci is 6, then the area (in sq. units) of the quadrilateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is :
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Question 29 of 30
29. Question
Let p(x) be a quadratic polynomial such that p(0) = 1. If p(x) leaves remainder 4 when divided by x – 1 and it leaves remainder 6 when divided by x + 1; then :
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Question 30 of 30
30. Question
Three persons P, Q and R independently try hit a target. If the probabilities of their hitting the target are respectively, then the probability that the target is hit by P or Q but not by R is :
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