1
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $y=y(x)$ be the solution of the differential equation $(x \log x) \frac{d y}{d x}+y=2 x \log x(x \geq 1)$ then $y(\mathrm{e})$ is equal to

A
2
B
2e
C
e
D
1
2
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\frac{\mathrm{d} y}{\mathrm{~d} x}=y+3, y+3>0$ and $y(0)=2$, then $y(\log 2)$ is equal to

A
13
B
$-$2
C
7
D
5
3
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The assets of a person are reduced in his business such that the rate of reduction is proportional to the square root of the existing assets. If the assets were initially ₹$10,00,000$ and due to loss they reduce to ₹$ 10,000$ after 3 years, then the number of years required for the person to go bankrupt will be

A
$\frac{10}{3}$
B
 $\frac{10}{9}$
C
$\frac{20}{9}$
D
$\frac{20}{3}$
4
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The order of the differential equation, whose solution is $y=\left(C_1+C_2\right) \mathrm{e}^x+C_3 \mathrm{e}^{x+C_4}$, is

A
4
B
1
C
3
D
2
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