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 differential equation obtained by eliminating arbitrary constant from the equation $y^2=(x+c)^3$ is

A
$\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)^3=27 y$
B
$\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)^3=-27 y$
C
$8\left(\frac{\mathrm{~d} y}{\mathrm{~d} x}\right)^3=27 y$
D
$ 8\left(\frac{\mathrm{~d} y}{\mathrm{~d} x}\right)^3+27 y=0$
3
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The decay rate of radium is proportional to the amount present at any time $t$. If initially 60 gms was present and half life period of radium is 1600 years, then the amount of radium present after 3200 years is

A
20 grams
B
15 grams
C
12 grams
D
10 grams
4
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The particular solution of differential equation $\left(1+y^2\right)(1+\log x) \mathrm{d} x+x \mathrm{~d} y=0$ at $x=1, y=1$ is

A
$\log x-\frac{1}{2}(\log x)^2-\tan ^{-1} y=-\frac{\pi}{4}$
B
$\log x+\frac{1}{2}(\log x)^2+\tan ^{-1} y=\frac{\pi}{4}$
C
$\log x-\frac{1}{2}(\log x)^2+\tan ^{-1} y=\frac{\pi}{4}$
D
$\log x+\frac{1}{2}(\log x)^2-\tan ^{-1} y=\frac{\pi}{4}$
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