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The number of solutions of the pair of equations 2sin2θ – cos 2θ = 0
2cos2θ – 3 sinθ = 0 in the interval [0, 2π] isCorrectIncorrect
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 expressionCorrectIncorrect
Solution set of the equation |x2 + 6x + 7| = |x2 + 4x + 4| + |2x + 3| isCorrectIncorrect
The number of ordered triples of non-negative integers are solutions of the equation 3x + y + z = 24 areCorrectIncorrect
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.fCorrectIncorrect
[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 intervalCorrectIncorrect
For 0 < θ < π/2, the solution(s) of
In a triangle ABC, a, b and A are given b > a and c1, c2 are two possible values of the third side c. If ∆1 and ∆2 are areas of two triangles with sides a, b, c1 and a, b, c2 thenCorrectIncorrect
Let a, b, c, p, q be real numbers, Suppose α, β are the roots of the equation x2 + 2px + q = 0 and α, 1/β are the roots of the equation ax2 + 2bxc + c = 0, where β2 ∉(−1, 0, 1)
STATEMENT -1 : (p2 – q) (b2 – ac) ≥ 0
STATEMENT-2 : b ≠ pa or c ≠ qaCorrectIncorrect
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 co-ordinates of A’ areCorrectIncorrect
Co-ordinates of B areCorrectIncorrect
If L1 = 0 is the reflected ray, then it’s equation isCorrectIncorrect
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) = f1(x) + f2(x) + . . .
e.g.(1 – x)−1 = 1 + x + x2 + x3 . . . |x| < 1
Hence the sum of the AGP
1 + 2x + 3x2 + . . . = (1 – x)2 (By differentiation both the side)
The sum of the series isCorrectIncorrect
Sum of the series isCorrectIncorrect
Sum of the series upto infinite terms isCorrectIncorrect
If a1, a2, a3, a4, a5 are in H.P. then find the value ofCorrectIncorrect
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 (x0, y0, z0) with y0z0 ≠ 0, isCorrectIncorrect
Match the statements in Column-I with those in Column-II.
(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.)CorrectIncorrect