1
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The differential equation of $y=\mathrm{e}^x\left(\mathrm{a}+\mathrm{bx}+x^2\right)$ is

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

An ice ball melts at the rate which is proportional to the amount of ice at that instant. Half of the quantity of ice melts in 15 minutes. $x_0$ is the initial quantity of ice. If after 30 minutes the amount of ice left is $\mathrm{kx}_0$, then the value of $k$ is

A
$\frac{1}{2}$
B
$\frac{1}{3}$
C
$\frac{1}{4}$
D
$\frac{1}{8}$
3
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
$\frac{\mathrm{e}}{4}$
4
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
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