1
WB JEE 2024
+1
-0.25

If $$0< \theta<\frac{\pi}{2}$$ and $$\tan 3 \theta \neq 0$$, then $$\tan \theta+\tan 2 \theta+\tan 3 \theta=0$$ if $$\tan \theta \cdot \tan 2 \theta=\mathrm{k}$$ where $$\mathrm{k}=$$

A
1
B
2
C
3
D
4
2
WB JEE 2024
+2
-0.5

If $$A$$ and $$B$$ are acute angles such that $$\sin A=\sin ^2 B$$ and $$2 \cos ^2 A=3 \cos ^2 B$$, then $$(A, B)=$$

A
$$\left(\frac{\pi}{6}, \frac{\pi}{4}\right)$$
B
$$\left(\frac{\pi}{6}, \frac{\pi}{6}\right)$$
C
$$\left(\frac{\pi}{4}, \frac{\pi}{6}\right)$$
D
$$\left(\frac{\pi}{4}, \frac{\pi}{4}\right)$$
3
WB JEE 2023
+1
-0.25

If $${1 \over 6}\sin \theta ,\cos \theta ,\tan \theta$$ are in G.P, then the solution set of $$\theta$$ is

(Here $$n \in N$$)

A
$$2n\pi \, \pm \,{\pi \over 6}$$
B
$$2n\pi \, \pm \,{\pi \over 3}$$
C
$$n\pi + {( - 1)^n}{\pi \over 3}$$
D
$$n\pi + {\pi \over 3}$$
4
WB JEE 2022
+1
-0.25

If $$(\cot {\alpha _1})(\cot {\alpha _2})\,......\,(\cot {\alpha _n}) = 1,0 < {\alpha _1},{\alpha _2},....\,{\alpha _n} < \pi /2$$, then the maximum value of $$(\cos {\alpha _1})(\cos {\alpha _2}).....(\cos {\alpha _n})$$ is given by

A
$${1 \over {{2^{n/2}}}}$$
B
$${1 \over {{2^n}}}$$
C
$${1 \over {2n}}$$
D
1
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