1
MHT CET 2021 20th September Morning Shift
+2
-0

An ice ball melts at the rate which is proportional to the amount of ice at that instant. Half the quantity of ice melts in 20 minutes, $$x_0$$ is the initial quantity of ice. If after 40 minutes the amount of ice left is $$\mathrm{Kx}_0$$, then $$\mathrm{K}=$$

A
$$\frac{1}{2}$$
B
$$\frac{1}{8}$$
C
$$\frac{1}{4}$$
D
$$\frac{1}{3}$$
2
MHT CET 2020 16th October Evening Shift
+2
-0

The integrating factor of the differential equation $$\sin y\left(\frac{d y}{d x}\right)=\cos y(1-x \cos y)$$ is

A
$$e^{\sin y}$$
B
$$e^{-x}$$
C
$$e^{-\cos y}$$
D
$$e^{-y}$$
3
MHT CET 2020 16th October Evening Shift
+2
-0

The order and degree of the differential equation $$\left[1+\left[\frac{d y}{d x}\right]^3\right]^{\frac{7}{3}}=7 \frac{d^2 y}{d x^2}$$ are respectively.

A
2, 1
B
1, 2
C
3, 2
D
2, 3
4
MHT CET 2020 16th October Evening Shift
+2
-0

The rate at which the metal cools in moving air is proportional to the difference of temperatures between the metal and air. If the air temperature is 290 K and the metal temperature drops from 370 K to 330 K in 10 min , then the time required to drop the temperature upto 295 K is

A
30 min
B
35 min
C
20 min
D
40 min
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