1
MHT CET 2025 20th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{d x}{2+\cos x}= $$

A

$2 \tan ^{-1}\left(\frac{1}{\sqrt{3}} \tan \frac{x}{2}\right)+c$, where $c$ is the constant of integration

B

$\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{1}{\sqrt{3}} \tan \frac{x}{2}\right)+c$, where $c$ is the constant of integration

C

$\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{1}{\sqrt{3}} \tan \frac{x}{2}\right)+\mathrm{c}$, where c is the constant of integration

D

$\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}} \tan \frac{x}{2}\right)+c$, where $c$ is the constant of integration

2
MHT CET 2025 20th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $A+B=\frac{\pi}{2}$ then the maximum value of $\cos \mathrm{A} \cdot \cos \mathrm{B}$ is

A
$\frac{1}{\sqrt{2}}$
B
$\frac{1}{2}$
C
$-\frac{1}{2}$
D
$-\frac{1}{\sqrt{2}}$
3
MHT CET 2025 20th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The magnitude of a vector which is orthogonal to the vector $\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and is coplanar with the vectors $\hat{i}+\hat{j}+2 \hat{k}$ and $\hat{i}+2 \hat{j}+\hat{k}$ is

A
$\sqrt{2}$
B
$4 \sqrt{2}$
C
4
D
$2 \sqrt{3}$
4
MHT CET 2025 20th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The distance between the lines represented by the equation $4 x^2+4 x y+y^2-6 x-3 y-4=0$ is

A
$\frac{1}{\sqrt{5}}$ units
B
$\frac{1}{5}$ units
C
$\sqrt{5}$ units
D
5 units

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