This chapter is currently out of syllabus
1
JEE Main 2023 (Online) 11th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

The number of elements in the set

$$S=\left\{\theta \in[0,2 \pi]: 3 \cos ^{4} \theta-5 \cos ^{2} \theta-2 \sin ^{6} \theta+2=0\right\}$$ is :

A
9
B
8
C
12
D
10
2
JEE Main 2023 (Online) 10th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let $$S=\left\{x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right): 9^{1-\tan ^{2} x}+9^{\tan ^{2} x}=10\right\}$$ and $$\beta=\sum_\limits{x \in S} \tan ^{2}\left(\frac{x}{3}\right)$$, then $$\frac{1}{6}(\beta-14)^{2}$$ is equal to :

A
16
B
32
C
8
D
64
3
JEE Main 2022 (Online) 29th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

The number of elements in the set $$S=\left\{x \in \mathbb{R}: 2 \cos \left(\frac{x^{2}+x}{6}\right)=4^{x}+4^{-x}\right\}$$ is :

A
1
B
3
C
0
D
infinite
4
JEE Main 2022 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let $$S=\left\{\theta \in\left(0, \frac{\pi}{2}\right): \sum\limits_{m=1}^{9} \sec \left(\theta+(m-1) \frac{\pi}{6}\right) \sec \left(\theta+\frac{m \pi}{6}\right)=-\frac{8}{\sqrt{3}}\right\}$$. Then

A
$$ S=\left\{\frac{\pi}{12}\right\} $$
B
$$ S=\left\{\frac{2 \pi}{3}\right\} $$
C
$$ \sum\limits_{\theta \in S} \theta=\frac{\pi}{2} $$
D
$$ \sum\limits_{\theta \in S} \theta=\frac{3\pi}{4} $$
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