1
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

A cylindrical tank of radius $$10 \mathrm{~m}$$ is being filled with wheat at the rate of $$200 \pi$$ cubic metre per hour. Then, the depth of the wheat is increasing at the rate of

A
0.5 m/h
B
2 m/h
C
0.2 m/h
D
2.2 m/h
2
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

If $$\left(1+x^2\right) d y+2 x y d x=\cot x d x$$, then the general solution be

A
$$y=\frac{\log |\sin x|}{1+x^2}+\frac{C}{1+x^2}$$
B
$$y=\frac{\log |\sin x|}{1-x^2}+\frac{C}{1-x^2}$$
C
$$y=\frac{\log |\cos x|}{1+x^2}+\frac{C}{1+x^2}$$
D
$$y=\frac{\log |\cos x|}{1-x^2}+\frac{C}{1-x^2}$$
3
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

If the straight line $$y=m x+c$$, touches the circle $$x^2+y^2=a^2$$ at a point, then $$c^2$$ is

A
$$m^2\left(1-a^2\right)$$
B
$$m^2\left(1+a^2\right)$$
C
$$a^2\left(1-m^2\right)$$
D
$$a^2\left(1+m^2\right)$$
4
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

A normal is drawn at the point $$P$$ to the circle $$x^2+y^2=25$$, which is inclined at $$45^{\circ}$$ with the straight line $$y=6$$. Then, the point lies on the straight line

A
$$y=x$$
B
$$y=-x$$
C
$$y=\sqrt{3} x$$
D
$$\sqrt{3} y=x$$
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