1
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of $$\tan ^{-1}\left(\frac{1}{8}\right)+\tan ^{-1}\left(\frac{1}{2}\right)+\tan ^{-1}\left(\frac{1}{5}\right)$$ is

A
$$\frac{\pi}{6}$$
B
$$\frac{\pi}{4}$$
C
$$\frac{\pi}{3}$$
D
$$\frac{\pi}{2}$$
2
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The p.m.f. of a random variable $$\mathrm{X}$$ is $$\mathrm{P}(x)=\left\{\begin{array}{cl}\frac{2 x}{\mathrm{n}(\mathrm{n}+1)}, & x=1,2,3, \ldots \mathrm{n} \\ 0, & \text { otherwise }\end{array}\right.$$, then $$\mathrm{E}(\mathrm{X})$$ is

A
$$\frac{\mathrm{n}+1}{6}$$
B
$$\frac{2 \mathrm{n}+1}{6}$$
C
$$\frac{\mathrm{n}+1}{3}$$
D
$$\frac{2 n+1}{3}$$
3
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the lines $$\frac{x-\mathrm{k}}{2}=\frac{y+1}{3}=\frac{\mathrm{z}-1}{4}$$ and $$\frac{x-3}{1}=\frac{y-\frac{9}{2}}{2}=\frac{\mathrm{z}}{1}$$ intersect, then the value of $$\mathrm{k}$$ is

A
$$\frac{1}{2}$$
B
$$-1$$
C
1
D
$$\frac{3}{2}$$
4
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$|\vec{a}|=\sqrt{3} ;|\vec{b}|=5 ; \bar{b} \cdot \bar{c}=10$$, angle between $$\overline{\mathrm{b}}$$ and $$\overline{\mathrm{c}}$$ is $$\frac{\pi}{3}, \overline{\mathrm{a}}$$ is perpendicular to $$\overline{\mathrm{b}} \times \overline{\mathrm{c}}$$. Then the value of $$|\overline{\mathrm{a}} \times(\overline{\mathrm{b}} \times \overline{\mathrm{c}})|$$ is

A
20
B
30
C
60
D
40
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