1
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Slope of the tangent to the curve $$y=2 e^x \sin \left(\frac{\pi}{4}-\frac{x}{2}\right) \cos \left(\frac{\pi}{4}-\frac{x}{2}\right)$$, where $$0 \leq x \leq 2 \pi$$ is minimum at $$x=$$

A
0
B
$$\pi$$
C
$$2 \pi$$
D
1
2
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If slope of the tangent to the curve $$x y+a x+b y=0$$ at the point $$(1,1)$$ on it is 2, then the value of $$3 a+b$$ is

A
3
B
1
C
2
D
$$-$$1
3
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$A(1,-3), B(4,3)$$ are two points on the curve $$y=x-\frac{4}{x}$$. The points on the curve, the tangents at which are parallel to the chord $$A B$$, are

A
$$(1,2),(-1,-2)$$
B
$$(2,0),(-2,0)$$
C
$$(0,2),(1,-2)$$
D
$$(3,2),(-3,1)$$
4
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Water is running in a hemispherical bowl of radius $$180 \mathrm{~cm}$$ at the rate of 108 cubic decimeters per minute. How fast the water level is rising when depth of the water level in the bowl is $$120 \mathrm{~cm}$$ ? (1 decimeter $$=10 \mathrm{~m}$$)

A
$$16 \pi \mathrm{cm} / \mathrm{sec}$$
B
$$\frac{16}{\pi} \mathrm{cm} / \mathrm{sec}$$
C
$$\frac{1}{16 \pi} \mathrm{cm} / \mathrm{sec}$$
D
$$\frac{\pi}{16} \mathrm{~cm} / \mathrm{sec}$$
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