1
MHT CET 2023 12th May Morning Shift
+2
-0

The angle between the tangents to the curves $$y=2 x^2$$ and $$x=2 y^2$$ at $$(1,1)$$ is

A
$$\tan ^{-1}\left(\frac{15}{8}\right)$$
B
$$\tan ^{-1}\left(\frac{7}{8}\right)$$
C
$$\tan ^{-1}\left(\frac{3}{4}\right)$$
D
$$\tan ^{-1}\left(\frac{1}{4}\right)$$
2
MHT CET 2023 12th May Morning Shift
+2
-0

The function $$\mathrm{f}(x)=\sin ^4 x+\cos ^4 x$$ is increasing in

A
$$0 < x < \frac{\pi}{8}$$
B
$$\frac{\pi}{4} < x < \frac{\pi}{2}$$
C
$$\frac{3 \pi}{8} < x < \frac{5 \pi}{8}$$
D
$$\frac{5 \pi}{8} < x < \frac{3 \pi}{4}$$
3
MHT CET 2023 12th May Morning Shift
+2
-0

A ladder 5 meters long rests against a vertical wall. If its top slides downwards at the rate of $$10 \mathrm{~cm} / \mathrm{s}$$, then the angle between the ladder and the floor is decreasing at the rate of ________ rad./s when it's lower end is $$4 \mathrm{~m}$$ away from the wall.

A
$$-0.1$$
B
$$-0.025$$
C
0.1
D
0.025
4
MHT CET 2023 11th May Evening Shift
+2
-0

If the function $$f$$ is given by $$f(x)=x^3-3(a-2) x^2+3 a x+7$$, for some $$\mathrm{a} \in \mathbb{R}$$, is increasing in $$(0,1]$$ and decreasing in $$[1,5)$$, then a root of the equation $$\frac{\mathrm{f}(x)-14}{(x-1)^2}=0(x \neq 1)$$ is

A
$$-$$7
B
6
C
7
D
5
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