JEE Main 2021 (Online) 16th March Morning Shift | Trigonometric Equations Question 36 | Mathematics

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JEE Main 2021 (Online) 16th March Morning Shift

MCQ (Single Correct Answer)

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The number of roots of the equation, (81)^sin²x + (81)^cos²x = 30 in the interval [ 0, $$\pi$$ ] is equal to :

JEE Main 2021 (Online) 25th February Morning Shift

MCQ (Single Correct Answer)

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Out of Syllabus

All possible values of $$\theta$$ $$\in$$ [0, 2$$\pi$$] for which sin 2$$\theta$$ + tan 2$$\theta$$ > 0 lie in :

$$\left( {0,{\pi \over 4}} \right) \cup \left( {{\pi \over 2},{{3\pi } \over 4}} \right) \cup \left( {{{3\pi } \over 2},{{11\pi } \over 6}} \right)$$

$$\left( {0,{\pi \over 2}} \right) \cup \left( {\pi ,{{3\pi } \over 2}} \right)$$

$$\left( {0,{\pi \over 2}} \right) \cup \left( {{\pi \over 2},{{3\pi } \over 4}} \right) \cup \left( {\pi ,{{7\pi } \over 6}} \right)$$

$$\left( {0,{\pi \over 4}} \right) \cup \left( {{\pi \over 2},{{3\pi } \over 4}} \right) \cup \left( {\pi ,{{5\pi } \over 4}} \right) \cup \left( {{{3\pi } \over 2},{{7\pi } \over 4}} \right)$$

JEE Main 2019 (Online) 12th April Evening Slot

MCQ (Single Correct Answer)

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Out of Syllabus

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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Out of Syllabus

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]

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