1
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The general solution of the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{y+\sqrt{x^2-y^2}}{x}$ is

A
$\sin ^{-1} y=\log x+c$, where c is a constant of integration.
B
$\frac{y}{x}=\sin ^{-1} x+\mathrm{c}$, where c is a constant of integration.
C
$\frac{y}{x}=\sqrt{x^2-y^2}+\mathrm{c}$, where c is a constant of integration.
D
$\sin ^{-1}\left(\frac{y}{x}\right)=\log x+\mathrm{c}$, where c is a constant of integration.
2
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

In a certain culture of bacteria, the rate of increase is proportional to the number present. If there are $10^4$ at the end of 3 hours and $4 \cdot 10^4$ at the end of 5 hours, then there were _________ the beginning.

A
$10^4$
B
$\frac{10^4}{4}$
C
$410^4$
D
$\frac{10^4}{8}$
3
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Integrating factor of the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}+y=\frac{1+y}{x}$ is

A
$\frac{x}{\mathrm{e}^x}$
B
$x e^x$
C
$e^x$
D
$\frac{\mathrm{e}^x}{x}$
4
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The population of a town increases at a rate proportional to the population at that time. If the population increases from 40 thousand to 80 thousand in 40 years, then the population in another 40 years will be

A
180000
B
128000
C
160000
D
256000
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