1
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

A body at an unknown temperature is placed in a room which is held at a constant temperature of $$30^{\circ} \mathrm{F}$$. If after 10 minutes the temperature of the body is $$0^{\circ} \mathrm{F}$$ and after 20 minutes the temperature of the body is $$15^{\circ} \mathrm{F}$$, then the expression for the temperature of the body at any time $$\mathrm{t}$$ is

A
$$\mathrm{T}=-60 \mathrm{e}^{-0.069 \mathrm{t}}-30$$
B
$$\mathrm{T}=-60 \mathrm{e}^{-0.03010 \mathrm{t}}+30$$
C
$$\mathrm{T}=60 \mathrm{e}^{-0.069 t}+30$$
D
$$\mathrm{T}=60 \mathrm{e}^{-0.069 \mathrm{t}}-30$$
2
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

A stone is thrown into a quite lake and the waves formed move in circles. If the radius of a circular wave increases at the rate of 4 cm/sec, then the rate of increase in its area, at the instant when its radius is 10 cm, is _________ cm$$^2$$/sec.

A
80 $$\pi$$
B
10 $$\pi$$
C
8 $$\pi$$
D
40 $$\pi$$
3
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The function $$f(x)=\cot ^{-1} x+x$$ is increasing in the interval.

A
$$(-\infty, \infty)$$
B
$$(0,3)$$
C
$$(1, \infty)$$
D
$$(-1, \infty)$$
4
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The curves $$\frac{x^2}{a^2}+\frac{y^2}{4}=1$$ and $$y^3=16 x$$ intersect each other orthogonally, then $$a^2=$$

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