1
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

The Cartesian equation of a line passing through $$(1,2,3)$$ and parallel to $$x-y+2 z=5$$ and $$3 x+y+z=6$$ is

A
$$\frac{x-1}{-3}=\frac{y-2}{5}=\frac{z-3}{4}$$
B
$$\frac{x-1}{3}=\frac{y-2}{1}=\frac{z-3}{1}$$
C
$$\frac{x-1}{1}=\frac{y-2}{-1}=\frac{z-3}{1}$$
D
$$\frac{x-1}{-3}=\frac{y-2}{-5}=\frac{z-3}{4}$$
2
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the lines $$3 x-4 y-7=0$$ and $$2 x-3 y-5=0$$ pass through diameters of a circle of area $$49 \pi$$ square units, then the equation of the circle is

A
$$x^2+y^2-2 x+2 y-47=0$$
B
$$x^2+y^2-2 x+2 y+51=0$$
C
$$x^2+y^2+2 x-2 y-51=0$$
D
$$x^2+y^2+2 x+2 y+47=0$$
3
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

A spherical iron ball of $$10 \mathrm{~cm}$$ radius is coated with a layer of ice of uniform thickness that melts at the rate of $$50 \mathrm{~cm}^3 / \mathrm{min}$$. If the thickness of ice is $$5 \mathrm{~cm}$$, then the rate at which the thickness of ice decreases is

A
$$\frac{-1}{18 \pi} \mathrm{cm} / \mathrm{min}$$
B
$$\frac{2}{9 \pi} \mathrm{cm} / \mathrm{min}$$
C
$$\frac{1}{18 \pi} \mathrm{cm} / \mathrm{min}$$
D
$$\frac{1}{3 \pi} \mathrm{cm} / \mathrm{min}$$
4
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{\sin \frac{5 x}{2}}{\sin \frac{x}{2}} d x=$$

(where $$C$$ is a constant of integration.)

A
$$x+\sin x+\sin 2 x+C$$
B
$$x+\sin x+\sin 2 x-C$$
C
$$x+2 \sin x+2 \sin 2 x+C$$
D
None of these
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