1
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $\overline{\mathrm{a}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$ and $\overline{\mathrm{b}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$. If $\overline{\mathrm{c}}$ is a vector such that $\overline{\mathrm{a}} \cdot \overline{\mathrm{c}}=|\overline{\mathrm{c}}|,|\overline{\mathrm{c}}-\overline{\mathrm{a}}|=2 \sqrt{2}$ and the angle between $(\overline{\mathrm{a}} \times \overline{\mathrm{b}})$ and $\overline{\mathrm{c}}$ is $30^{\circ}$, then the value of $|(\bar{a} \times \bar{b}) \times \bar{c}|$ is equal to

A
$\frac{\sqrt{3}}{2}$
B
$\frac{3}{2}$
C
$\frac{1}{\sqrt{2}}$
D
$\frac{\sqrt{3}}{4}$
2
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\theta$ and $\alpha$ are not odd multiples of $\frac{\pi}{2}$ then $\tan \theta=\tan \alpha$ implies principal solution is

A
$\theta=\alpha+\frac{\mathrm{n} \pi}{2}, \mathrm{n} \in \mathbb{Z}$
B
$\quad \theta=\alpha+\frac{3 \mathrm{n} \pi}{2}, \mathrm{n} \in \mathbb{Z}$
C
$\theta=\mathrm{n} \pi+\alpha, \mathrm{n} \in \mathbb{Z}$
D
$\quad \theta=\frac{\mathrm{n} \pi}{4}+\alpha, \mathrm{n} \in \mathbb{Z}$
3
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The approximate value of $\cos \left(30^{\circ}, 30^{\prime}\right)$ is given that $1^{\circ}=0.0175^{\circ}$ and $\cos 30^{\circ}=0.8660$

A
0.8778
B
0.7666
C
0.7916
D
0.8616
4
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Let X denote the random variable of number of jacks obtained in the two drawn cards. Then $P(X=1)+P(X=2)$ equals

A
$\frac{24}{169}$
B
$\frac{52}{169}$
C
$\frac{25}{169}$
D
$\frac{49}{169}$
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