1
MHT CET 2021 20th September Evening Shift
+2
-0

The general solution of $$\left(x \frac{d y}{d x}-y\right) \sin \frac{y}{x}=x^3 e^x$$ is

A
$$e^x(x-1)+\cos \frac{y}{x}+c=0$$
B
$$x e^x+\cos \frac{y}{x}+c=0$$
C
$$e^x(x+1)+\cos \frac{y}{x}+c=0$$
D
$$e x^x-\cos \frac{y}{x}+c=0$$
2
MHT CET 2021 20th September Evening Shift
+2
-0

The population of a city increases at a rate proportional to the population at that time. If the population of the city increase from 20 lakhs to 40 lakhs in 30 years, then after another 15 years the population is

A
$$10 \sqrt{2}$$ lakhs
B
$$40 \sqrt{2}$$ lakh
C
$$30 \sqrt{2}$$ lakhs
D
None of these
3
MHT CET 2021 20th September Morning Shift
+2
-0

A differential equation for the temperature 'T' of a hot body as a function of time, when it is placed in a bath which is held at a constant temperature of 32$$^\circ$$ F, is given by (where k is a constant of proportionality)

A
$$\mathrm{\frac{dT}{dt}=kT-32}$$
B
$$\mathrm{\frac{dT}{dt}=kT+32}$$
C
$$\mathrm{\frac{dT}{dt}=-k(T-32)}$$
D
$$\mathrm{\frac{dT}{dt}=32kT}$$
4
MHT CET 2021 20th September Morning Shift
+2
-0

The general solution of the differential equation $$\frac{d y}{d x}=\frac{x+y+1}{x+y-1}$$ is given by

A
$$y=x \log (x+y)+c$$
B
$$x-y=\log (x+y)+c$$
C
$$x+y=\log (x+y)+c$$
D
$$y=x+\log (x+y)+c$$
MHT CET Subjects
Physics
Mechanics
Optics
Electromagnetism
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Calculus
Coordinate Geometry
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