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

Let $y=y(x)$ be the solution of the differential equation $x \frac{\mathrm{~d} y}{\mathrm{~d} x}+y=x \log x,(x>1)$ If $2(y(2))=\log 4-1$ then the value of $y(\mathrm{e})$ is

A
$\frac{\mathrm{e}^2}{4}$
B
$\frac{-\mathrm{e}^2}{2}$
C
$\frac{-\mathrm{e}}{2}$
D
$\frac{\mathrm{e}}{4}$
2
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $y(x)$ is the solution of the differential equation $(x+2) \frac{\mathrm{d} y}{\mathrm{~d} x}=x^2+4 x-9, x \neq-2$ and $y(0)=0$, then $y(-4)$ is equal to

A
0
B
1
C
$-$1
D
2
3
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
4
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
$\log \tan \left(\frac{y}{2}+\frac{\pi}{4}\right)=\mathrm{C}-2 \sin \left(\frac{x}{2}\right)$
MHT CET Subjects
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