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
MHT CET Subjects
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12