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Question 1 of 20
1. Question
The number of solutions of the pair of equations 2sin^{2}θ – cos 2θ = 0
2cos^{2}θ – 3 sinθ = 0 in the interval [0, 2π] is
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Question 2 of 20
2. Question
If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the side opposite to A, B and C respectively, then the value of the expression
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Question 3 of 20
3. Question
Solution set of the equation x^{2} + 6x + 7 = x^{2} + 4x + 4 + 2x + 3 is
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Question 4 of 20
4. Question
The number of ordered triples of nonnegative integers are solutions of the equation 3x + y + z = 24 are
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Question 5 of 20
5. Question
Let then
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Question 6 of 20
6. Question
If m is a positive integer, then [(√3 + 1)^{2m}] + 1 is divisible by, if it is given that [x] ≤ x denotes the g.i.f
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Question 7 of 20
7. Question
[x] ≤ x denotes the greatest integer, [5 sin x] + [cos x] + 6 = 0 then value of f(x) = sin x + √3 cos x corresponding to the solutions set of the given equation lying in the interval
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Question 8 of 20
8. Question
For 0 < θ < π/2, the solution(s) of
is (are)
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Question 9 of 20
9. Question
In a triangle ABC, a, b and A are given b > a and c_{1}, c_{2} are two possible values of the third side c. If ∆_{1} and ∆_{2} are areas of two triangles with sides a, b, c_{1} and a, b, c_{2} then
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Question 10 of 20
10. Question
Let a, b, c, p, q be real numbers, Suppose α, β are the roots of the equation x^{2} + 2px + q = 0 and α, 1/β are the roots of the equation ax^{2} + 2bxc + c = 0, where β^{2} ∉(−1, 0, 1)
STATEMENT 1 : (p^{2} – q) (b^{2} – ac) ≥ 0
and
STATEMENT2 : b ≠ pa or c ≠ qa
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Question 11 of 20
11. Question
Question number 11 to 13 are based on following statement.
Statement → A ray of light comes along the line L = 0 & strikes the plane mirror kept along the plane P = 0 at B. A(2, 1, 6) is a point on the line L = 0 whose image about P = 0 is A’. If L = 0 is & P = 0 is x + y – 2z = 3.
________
The coordinates of A’ are
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Question 12 of 20
12. Question
Coordinates of B are
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Question 13 of 20
13. Question
If L_{1} = 0 is the reflected ray, then it’s equation is
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Question 14 of 20
14. Question
Question number 14 to 16 are based on following passage.
Sometimes we can find the sum of series by use if differentiation. If we know the sum of a series e.g., if f(x) = f_{1}(x) + f_{2}(x) + . . .
e.g.(1 – x)^{−}^{1} = 1 + x + x^{2} + x^{3} . . . x < 1
Hence the sum of the AGP
1 + 2x + 3x^{2} + . . . = (1 – x)^{2} (By differentiation both the side)
______
The sum of the series is
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Question 15 of 20
15. Question
Sum of the series is
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Question 16 of 20
16. Question
Sum of the series upto infinite terms is
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Question 17 of 20
17. Question
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Question 18 of 20
18. Question
If a_{1}, a_{2}, a_{3}, a_{4}, a_{5} are in H.P. then find the value of
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Question 19 of 20
19. Question
The number of all possible values of θ where 0 < θ < π, for which the system of equations:
(y + z) cos 3θ = (xyz) sin 3θ
(xyz) sin 3θ = (y + 2z) cos 3θ + y sin 3θ
have a solution (x_{0}, y_{0}, z_{0}) with y_{0}z_{0} ≠ 0, is
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Question 20 of 20
20. Question
Match the statements in ColumnI with those in ColumnII.
(Here z takes values in the complex p lane and Im z and Re z denote, respectively, the imaginary part and the real part of z.)
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