MHT CET 2021 20th September Evening Shift | Differential Equations Question 52 | Mathematics

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

$$10 \sqrt{2}$$ lakhs

$$40 \sqrt{2}$$ lakh

$$30 \sqrt{2}$$ lakhs

None of these

MHT CET 2021 20th September Morning Shift

MCQ (Single Correct Answer)

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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)

$$\mathrm{\frac{dT}{dt}=kT-32}$$

$$\mathrm{\frac{dT}{dt}=kT+32}$$

$$\mathrm{\frac{dT}{dt}=-k(T-32)}$$

$$\mathrm{\frac{dT}{dt}=32kT}$$

MHT CET 2021 20th September Morning Shift

MCQ (Single Correct Answer)

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

$$y=x \log (x+y)+c$$

$$x-y=\log (x+y)+c$$

$$x+y=\log (x+y)+c$$

$$y=x+\log (x+y)+c$$

MHT CET 2021 20th September Morning Shift

MCQ (Single Correct Answer)

-0

The general solution of the differential equation $$x+y \frac{d y}{d x}=\sec \left(x^2+y^2\right)$$ is

$$\sin \left(x^2+y^2\right)=2 x+c$$

$$\sin \left(x^2+y^2\right)+2 x=c$$

$$\sin \left(x^2+y^2\right)+x=c$$

$$\cos \left(x^2+y^2\right)=2 x+c$$

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