JEE Main 2019 (Online) 12th April Evening Slot | Trigonometric Equations Question 39 | Mathematics

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JEE Main 2019 (Online) 12th April Evening Slot

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If [x] denotes the greatest integer $$ \le $$ x, then the system of linear equations [sin $$\theta $$]x + [–cos$$\theta $$]y = 0, [cot$$\theta $$]x + y = 0

has a unique solution if $$\theta \in \left( {{\pi \over 2},{{2\pi } \over 3}} \right)$$ and have infinitely many solutions if $$\theta \in \left( {\pi ,{{7\pi } \over 6}} \right)$$

have infinitely many solutions if $$\theta \in \left( {{\pi \over 2},{{2\pi } \over 3}} \right)$$ and has a unique solution if $$\theta \in \left( {\pi ,{{7\pi } \over 6}} \right)$$

have infinitely many solutions if $$\theta \in \left( {{\pi \over 2},{{2\pi } \over 3}} \right) \cup \left( {\pi ,{{7\pi } \over 6}} \right)$$

has a unique solution if $$\theta \in \left( {{\pi \over 2},{{2\pi } \over 3}} \right) \cup \left( {\pi ,{{7\pi } \over 6}} \right)$$

JEE Main 2019 (Online) 12th April Evening Slot

MCQ (Single Correct Answer)

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Let S be the set of all $$\alpha $$ $$ \in $$ R such that the equation, cos2x + $$\alpha $$sinx = 2$$\alpha $$– 7 has a solution. Then S is equal to :

[2, 6]

[3, 7]

[1, 4]

JEE Main 2019 (Online) 12th April Morning Slot

MCQ (Single Correct Answer)

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Out of Syllabus

The number of solutions of the equation
1 + sin⁴ x = cos²3x, $$x \in \left[ { - {{5\pi } \over 2},{{5\pi } \over 2}} \right]$$ is :

JEE Main 2019 (Online) 9th April Morning Slot

MCQ (Single Correct Answer)

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Out of Syllabus

Let S = {$$\theta $$ $$ \in $$ [–2$$\pi $$, 2$$\pi $$] : 2cos²$$\theta $$ + 3sin$$\theta $$ = 0}. Then the sum of the elements of S is

$$\pi $$

2$$\pi $$

$${{13\pi } \over 6}$$

$${{5\pi } \over 3}$$

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