1
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The general solution of the equation $\sqrt{3} \cos \theta+\sin \theta=\sqrt{2}$ is

A
$\mathrm{n} \pi+(-1)^{\mathrm{n}} \frac{\pi}{2}+\frac{\pi}{6}, \mathrm{n} \in \mathbb{Z}$
B
$\mathrm{n} \pi+(-1)^{\mathrm{n}} \frac{\pi}{2}-\frac{\pi}{6}, \mathrm{n} \in \mathbb{Z}$
C
$\mathrm{n} \pi+(-1)^{\mathrm{n}} \frac{\pi}{4}-\frac{\pi}{3}, \mathrm{n} \in \mathbb{Z}$
D
$\mathrm{n} \pi+(-1)^{\mathrm{n}} \frac{\pi}{4}+\frac{\pi}{3}, \mathrm{n} \in \mathbb{Z}$
2
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\sin ^{-1}\left(\frac{x}{5}\right)+\operatorname{cosec}^{-1}\left(\frac{5}{4}\right)=\frac{\pi}{2}$, then the value of $x$ is

A
4
B
5
C
1
D
3
3
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

A random variable X takes the values $0,1,2,3$ and its mean is 1.3 . If $\mathrm{P}(\mathrm{X}=3)=2 \mathrm{P}(\mathrm{X}=1)$ and $P(X=2)=0.3$, then $P(X=0)$ is

A
0.2
B
0.1
C
0.3
D
0.4
4
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

Let $\overline{\mathrm{a}}, \overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ be three non-zero vectors such that no two of them are collinear and $(\overline{\mathrm{a}} \times \overline{\mathrm{b}}) \times \overline{\mathrm{c}}=\frac{1}{3}|\overline{\mathrm{~b}}||\mathrm{c}| \overline{\mathrm{a}}$. If $\theta$ is the angle between vectors $\bar{b}$ and $\bar{c}$, then the value of $\sin \theta$ is

A
$\frac{2}{3}$
B
$\frac{-2 \sqrt{2}}{3}$
C
$\frac{2 \sqrt{2}}{3}$
D
$\frac{-\sqrt{2}}{3}$
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