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1
JEE Main 2022 (Online) 30th June Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language

Let $${S_1} = \{ x \in [0,12\pi ]:{\sin ^5}x + {\cos ^5}x = 1\} $$

and $${S_2} = \{ x \in [0,8\pi ]:{\sin ^7}x + {\cos ^7}x = 1\} $$

Then $$n({S_1}) - n({S_2})$$ is equal to ______________.

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2
JEE Main 2022 (Online) 29th June Evening Shift
Numerical
+4
-1
Out of Syllabus
Change Language

The number of solutions of the equation $$\sin x = {\cos ^2}x$$ in the interval (0, 10) is _________.

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3
JEE Main 2022 (Online) 29th June Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language

The number of elements in the set $$S = \{ \theta \in [ - 4\pi ,4\pi ]:3{\cos ^2}2\theta + 6\cos 2\theta - 10{\cos ^2}\theta + 5 = 0\} $$ is __________.

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4
JEE Main 2022 (Online) 29th June Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language

The number of solutions of the equation

$$2\theta - {\cos ^2}\theta + \sqrt 2 = 0$$ in R is equal to ___________.

Your input ____
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