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

The equation of plane passing through $(1,0,0)$ and $(0,1,0)$ and making an angle $45^{\circ}$ with the plane $x+y-3=0$ is

A

$x+y \pm \sqrt{2} z-1=0$

B

$3 x+y \pm \sqrt{3} z-3=0$

C

$\quad x+y \pm \sqrt{3} z-1=0$

D

$\quad 2 x+2 y \pm \sqrt{3} z-2=0$

2
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

3
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

4
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

$\frac{28}{169}$

MHT CET Papers

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