1
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

A biased coin with probability $$\mathrm{p}(0<\mathrm{p}<1)$$ of getting head is tossed until a head appears for the first time. If the probability that the number of tosses required is even is $$\frac{2}{5}$$, then $$\mathrm{p}=$$

A
$$\frac{1}{4}$$
B
$$\frac{1}{3}$$
C
$$\frac{2}{3}$$
D
$$\frac{3}{4}$$
2
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

The expression $$\cos ^2 \phi+\cos ^2(\theta+\phi)-2 \cos \theta \cos \phi \cos (\theta+\phi)$$ is

A
independent of $$\theta$$
B
independent of $$\phi$$
C
independent of $$\theta$$ and $$\phi$$
D
dependent on $$\theta$$ and $$\phi$$
3
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

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
4
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

The equation $$\mathrm{r} \cos \theta=2 \mathrm{a} \sin ^2 \theta$$ represents the curve

A
$$x^3=y^2(2 \mathrm{a}+x)$$
B
$$x^2=y^2(2 \mathrm{a}+x)$$
C
$$x^3=y^2(2 \mathrm{a}-x)$$
D
$$x^3=\mathrm{y}^2(\mathrm{a}+x)$$
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