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

A body cools according to Newton's law of cooling from $100^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$ in 15 minutes. If the temperature of the surrounding is $20^{\circ} \mathrm{C}$, then the temperature of the body after cooling down for one hour is

A
$30^{\circ} \mathrm{C}$
B
$25^{\circ} \mathrm{C}$
C
$35^{\circ} \mathrm{C}$
D
$40^{\circ} \mathrm{C}$
2
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $y=y(x)$ is the solution of the differential equation $\left(\frac{5+\mathrm{e}^x}{2+y}\right) \frac{\mathrm{d} y}{\mathrm{~d} x}+\mathrm{e}^x=0$ satisfying $y(0)=1$, then a value of $y(\log 13)$ is

A
$-$1
B
0
C
1
D
2
3
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

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

A
$-\frac{2}{3}$
B
$-\frac{1}{3}$
C
$\frac{4}{3}$
D
  $\frac{1}{3}$
4
MHT CET 2024 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

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

A
$\log \left|\frac{2-y}{2-x}\right|=2(y-1)$
B
$-\log \left|\frac{1+x-y}{1-x+y}\right|=x+y-2$
C
$\log \left|\frac{2-x}{2-y}\right|=x-y$
D
$-\log \left|\frac{1-+xy}{1+x-y}\right|=2(x-1)$
MHT CET Subjects
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