1
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The general solution of the differential equation $\frac{1}{x} \frac{\mathrm{~d} y}{\mathrm{~d} x}=\tan ^{-1}$ is

A
$y+\frac{x^2 \tan ^{-1} x}{2}+\mathrm{c}=0$, where c is a constant of integration.
B
$y+x \tan ^{-1} x+\mathrm{c}=0$, where c is a constant integration.
C
$y-x-\tan ^{-1} x+\mathrm{c}=0$, where is a constant of integration.
D
$y=\frac{x^2 \tan ^{-1} x}{2}-\frac{1}{2}\left(x-\tan ^{-1} x\right)+\mathrm{c}$, where c is constant of integration.
2
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The area (in square units) in the first quadrant bounded by the curve $y=x^2+2$ and the lines $y=x+1, x=0$ and $x=3$, is

A
$\frac{15}{4}$
B
$\frac{21}{2}$
C
$\frac{17}{4}$
D
$\frac{15}{2}$
3
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The co-ordinates of the point where the line through $\mathrm{A}(3,4,1)$ and $\mathrm{B}(5,1,6)$ crosses the $x y$-plane are

A
$\left(\frac{13}{5}, \frac{23}{5}, 0\right)$
B
$\left(-\frac{13}{5}, \frac{23}{5}, 0\right)$
C
$\left(\frac{13}{5},-\frac{23}{5}, 0\right)$
D
$\left(-\frac{13}{5},-\frac{23}{5}, 0\right)$
4
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\frac{\tan ^{-1}(\sqrt{3})-\sec ^{-1}(-2)}{\operatorname{cosec}^{-1}(-\sqrt{2})+\cos ^{-1}\left(\frac{-1}{2}\right)}$

A
$\frac{4}{5}$
B
$\frac{-4}{5}$
C
$\frac{3}{5}$
D
0
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