1
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The bacteria increase at the rate proportional to the number of bacteria present. If the original number N doubles in 8 hours, then the number of bacteria in 24 hours will be

A
8 N
B
16 N
C
32 N
D
64 N
2
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The general solution of $\frac{\mathrm{d} y}{\mathrm{~d} x}+\sin \left(\frac{x+y}{2}\right)=\sin \left(\frac{x-y}{2}\right)$ is

A
$\log \tan \left(\frac{y}{2}\right)=\mathrm{C}-2 \sin x$
B
$\log \tan \left(\frac{y}{4}\right)=\mathrm{C}-2 \sin \left(\frac{x}{2}\right)$
C
$\log \tan \left(\frac{y}{2}+\frac{\pi}{4}\right)=\mathrm{C}-2 \sin x$
D
$\log \tan \left(\frac{y}{2}+\frac{\pi}{4}\right)=\mathrm{C}-2 \sin \left(\frac{x}{2}\right)$
3
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The particular solution of the differential equation, $x y \frac{\mathrm{~d} y}{\mathrm{~d} x}=x^2+2 y^2$ when $y(1)=0$ is

A
$\frac{x^2+y^2}{x^3}=1$
B
$x^2+y^2=x$
C
$x^2+y^2=x^4$
D
$x^2+2 y^2=x^4$
4
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The general solution of the differential equation $\mathrm{e}^{y-x} \frac{\mathrm{~d} y}{\mathrm{~d} x}=y\left(\frac{\sin x+\cos x}{1+y \log y}\right)$ is

A
$\mathrm{e}^y \log y=\mathrm{e}^{\mathrm{x}} \sin x+\mathrm{c}$, where c is a constant of integration.
B
$\mathrm{e}^y=\mathrm{e}^x \sin x+\mathrm{c}$, where c is a constant of integration.
C
$\log y=\mathrm{e}^x \sin x+\mathrm{c}$, where c is a constant of integration.
D
$y \log y=\mathrm{e}^x \sin x+\mathrm{c}$, where c is a constant of integration.
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