1
MHT CET 2025 5th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The distance of the point $(5,3,-1)$ from the plane passing through points $(2,1,0),(3,-2,4)$ and $(1,-3,3)$ is

A

$\frac{2}{\sqrt{3}}$ units

B

$\frac{4}{\sqrt{3}}$ units

C

$\sqrt{3}$ units

D

$\frac{1}{\sqrt{3}}$ units

2
MHT CET 2025 5th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{d x}{\cos x(1+\cos x)}= $$

A

$\quad \log (\sec x+\tan x)+2 \tan \left(\frac{x}{2}\right)+\mathrm{c}$, where c is the constant of integration

B

$\quad \log (\sec x+\tan x)-2 \tan \left(\frac{x}{2}\right)+\mathrm{c}$, where c is the constant of integration

C

$\log (\sec x+\tan x)+\tan \left(\frac{x}{2}\right)+\mathrm{c}$, where c is the constant of integration

D

$\log (\sec x+\tan x)-\tan \left(\frac{x}{2}\right)+\mathrm{c}$, where c is the constant of integration

3
MHT CET 2025 5th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Two cards are drawn successively with replacement from fair playing 52 cards. let X denote number of kings obtained when two cards are drawn, then $\mathrm{E}\left(\mathrm{X}^2\right)=$

A

$\frac{24}{169}$

B

$\frac{26}{169}$

C

$\frac{27}{169}$

D

$\frac{28}{169}$

4
MHT CET 2025 5th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The eccentric angle of the point $\mathrm{P}(-6,2)$ of the ellipse $\frac{x^2}{48}+\frac{y^2}{16}=1$ is

A

$30^{\circ}$

B

$135^{\circ}$

C

$150^{\circ}$

D

$120^{\circ}$

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