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1
JEE Main 2024 (Online) 1st February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The number of solutions of the equation $4 \sin ^2 x-4 \cos ^3 x+9-4 \cos x=0 ; x \in[-2 \pi, 2 \pi]$ is :
A
0
B
3
C
1
D
2
2
JEE Main 2024 (Online) 30th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$2 \sin ^3 x+\sin 2 x \cos x+4 \sin x-4=0$$ has exactly 3 solutions in the interval $$\left[0, \frac{\mathrm{n} \pi}{2}\right], \mathrm{n} \in \mathrm{N}$$, then the roots of the equation $$x^2+\mathrm{n} x+(\mathrm{n}-3)=0$$ belong to :

A
$$(0, \infty)$$
B
Z
C
$$\left(-\frac{\sqrt{17}}{2}, \frac{\sqrt{17}}{2}\right)$$
D
$$(-\infty, 0)$$
3
JEE Main 2024 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The sum of the solutions $$x \in \mathbb{R}$$ of the equation $$\frac{3 \cos 2 x+\cos ^3 2 x}{\cos ^6 x-\sin ^6 x}=x^3-x^2+6$$ is

A
3
B
1
C
0
D
$$-$$1
4
JEE Main 2024 (Online) 29th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$\alpha,-\frac{\pi}{2}<\alpha<\frac{\pi}{2}$$ is the solution of $$4 \cos \theta+5 \sin \theta=1$$, then the value of $$\tan \alpha$$ is

A
$$\frac{10-\sqrt{10}}{12}$$
B
$$\frac{\sqrt{10}-10}{6}$$
C
$$\frac{\sqrt{10}-10}{12}$$
D
$$\frac{10-\sqrt{10}}{6}$$
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