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1
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $y=y(x)$ and $\left(\frac{2+\sin x}{y+1}\right) \frac{\mathrm{d} y}{\mathrm{~d} x}=-\cos x, y(0)=1$, then $y\left(\frac{\pi}{2}\right)=$

A
$\frac{1}{3}$
B
$\frac{2}{3}$
C
$-\frac{1}{3}$
D
1
2
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The degree of the differential equation $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}+3\left(\frac{\mathrm{~d} y}{\mathrm{~d} x}\right)^2=x^2 \log \left(\frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}\right)$ is

A
1
B
2
C
3
D
Not defined
3
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $y+\frac{\mathrm{d}}{\mathrm{d} x}(x y)=x(\sin x+\log x)$ then

A

$y=\cos x+\frac{2 \sin x}{x}+\frac{2}{x^2} \cos x+\frac{x}{3} \log x-\frac{x}{9}+\frac{\mathrm{c}}{x^2}$, where c is the constant of integration.

B

$y=-\cos x-\frac{2}{x} \sin x+\frac{2}{x^2} \cos x+\frac{x}{3} \log x-\frac{x}{9}+\frac{\mathrm{c}}{x^2}$ where c is the constant of integration.

C

$$ \begin{aligned} y=-\cos x+\frac{2}{x} \sin x+ & \frac{2}{x^2} \cos x +\frac{x}{3} \log x-\frac{x}{9}+\frac{c}{x^2}\text { where } \mathrm{c} \text { is the constant of integration. }\end{aligned} $$

D

$y=\cos x-\frac{2}{x} \sin x+\frac{2}{x^3} \cos x+\frac{x}{3} \log x-\frac{x}{9}+\frac{\mathrm{c}}{x^2}$ where $c$ is the constant of intergration.

4
MHT CET 2025 22nd April 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 forty thousand to eighty thousand in 20 years, then the population in another 40 years will be

A
240000
B
160000
C
320000
D
640000
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