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This mock test of Test : Trigonometric Functions And Identities - 3 for Mathematics helps you for every Mathematics entrance exam.
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QUESTION: 1

The equation kcos x.- 3sin x = k + 1 is solvable only if k belongs to the interval

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QUESTION: 2

The number of solutions of cosθ + √3 sinθ = 5, 0 ≤ 0 ≤ 5π, is

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QUESTION: 3

If the equation a_{1} - a_{2}, cos 2x + a_{3}, sin^{2}x = 1 is satisfied by every real value of x then the number of possible values of the triplet (a_{1},a_{2}, a_{3}) is

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QUESTION: 4

The number of solutions of the equation tan x - sec x = 2cos x lying in the interval [0.2π] is

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QUESTION: 5

The number of values of x in [0, 5π] satisfying the equation 3cos 2x - 10cos x + 7 = 0 is

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QUESTION: 6

The smallest positive integral value of p for which the equation cos (p sin a) = sin(p cos x) in x has a solution in [0. 2π] is

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QUESTION: 7

If sin^{2}θ - 2sinθ - 1 = 0 is to be satisfied for exactly 4 distinct values of θ ∈ [0,nπ], n ∈ N, then the least value of n is

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QUESTION: 8

If 2 tan2 x-5 sec x is equal to 1 for exactly 7 distinct values of n ∈ N, then the greatest value of n is

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QUESTION: 9

The number of value of x ∈ [0, 2π] that satisfy cot x - cosec x = 2 sin x is

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QUESTION: 10

If sin a, 1 and cos 2a are in GP then a is equl to

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QUESTION: 11

If 1/6 sinθ, cosθ and tanθ are in GP then the general value of θ is

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QUESTION: 12

The general values of x for which cos 2x, 1/2 and sin 2x are in AP are given by

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QUESTION: 13

The most general values of θ satisfying

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QUESTION: 14

The most general solutions of the equation sec x - 1 - (√2 - 1) tan x are given by

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QUESTION: 15

The most general solutions of the equation sec^{2}x √2(1 - tan^{2}x) are given by

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QUESTION: 16

The most general values of x for which sin x + cos x, are given by

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QUESTION: 17

then the set of possible values of α is

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QUESTION: 18

Let α, β, be any two positive values of x for which 2cos x, |cosx| and 1- 3cos^{2} x are in GP. The minimum value of |α-β| is

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QUESTION: 19

The sum of all the solutions of the equation cos x.cos is

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QUESTION: 20

The values of x ∈ [-2π, 2π] such that _{ is purely imaginary, are given by}

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