MHT CET 2025 22nd April Morning Shift | Differential Equations Question 27 | Mathematics

The population of a town increases at a rate proportional to the population at that time. If the population increases from forty thousand to eighty thousand in 20 years, then the population in another 40 years will be

240000

160000

320000

640000

MHT CET 2025 21st April Evening Shift

MCQ (Single Correct Answer)

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A particular solution of $3 \mathrm{e}^x \tan y \mathrm{~d} x+\left(1-\mathrm{e}^x\right) \sec ^2 y \mathrm{~d} y=0$ with $y(1)=\frac{\pi}{4}$ is

$\quad \tan y=\left(\frac{1-\mathrm{e}^3}{1-\mathrm{e}^x}\right)^3$

$\quad \tan y=\left(\frac{1-\mathrm{e}^2}{1-\mathrm{e}^x}\right)^3$

$\quad \tan y=\left(\frac{1-\mathrm{e}}{1-\mathrm{e}^x}\right)^3$

$\quad \tan y=\left(\frac{1-\mathrm{e}^x}{1-\mathrm{e}}\right)^3$

MHT CET 2025 21st April Evening Shift

MCQ (Single Correct Answer)

-0

The equation of the curve passing through the origin and satisfying the equation $\left(1+x^2\right) \frac{\mathrm{d} y}{\mathrm{~d} x}+2 x y=4 x^2$, is

$3\left(1+x^2\right) y=4 x^3$

$3\left(1-x^2\right) y=4 x^3$

$3\left(1+x^2\right)=x^3$

$\quad 4\left(1-x^2\right)=x^3$

MHT CET 2025 21st April Evening Shift

MCQ (Single Correct Answer)

-0

The differential equation of all circles having their centres on the line $y=5$ and touching ( X -axis) is $\qquad$

$\quad(5-y) \frac{\mathrm{d} y}{\mathrm{~d} x}+y^2-10 y=0$

$\quad(5-y)^2 \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}+y^2-10 y=0$

$\quad(5-y) \frac{\mathrm{d} y}{\mathrm{~d} x}+y-10=0$

$\quad(5-y)^2\left(\frac{\mathrm{~d} y}{\mathrm{~d} x}\right)^2+y^2-10 y=0$

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