1
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

Radium decomposes at the rate proportional to the amount present at any time. If $$\mathrm{P} \%$$ of amount disappears in one year, then amount of radium left after 2 years is

A
$$\left(10-\frac{\mathrm{P}}{10}\right)^2$$
B
$$\mathrm{x}_0\left[1+\frac{\mathrm{P}}{100}\right]^2$$
C
$$x_0\left[1-\frac{P}{100}\right]^2$$
D
$$\mathrm{x}_0\left[10-\frac{\mathrm{P}}{10}\right]^2$$
2
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The differential equation obtained by eliminating A and B from $$y=A \cos \omega t+B \sin \omega t$$

A
$$\frac{d^2 y}{d t^2}+\omega^2 y=0$$
B
$$\frac{\mathrm{d}^2 y}{\mathrm{dt}^2}+\omega \mathrm{y}^2=0$$
C
$$\frac{d^2 y}{d t^2}-\omega^2 y=0$$
D
$$\frac{d^2 y}{d t^2}-\omega y^2=0$$
3
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The particular solution of the differential equation $$y(1+\log x) \frac{d x}{d y}-x \log x=0$$ when $$x=e, y=e^2$$ is

A
$$y^2=e^4 \log x$$
B
$$y=e^2 \log x$$
C
$$y=x^2 \log x$$
D
$$y=e x \log x$$
4
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The order and degree of the differential equation $$\frac{d^2 y}{d x^2}=\sqrt{\frac{d y}{d x}}$$ are respectively

A
2, 3
B
3, 3
C
2, 2
D
1, 3
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