1
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+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
2
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$a$$ and $$b$$ are positive number such that $$a>b$$, then the minimum value of $$a \sec \theta-b \tan \theta\left(0 < \theta < \frac{\pi}{2}\right)$$ is

A
$$\frac{1}{\sqrt{a^2-b^2}}$$
B
$$\frac{1}{\sqrt{a^2+b^2}}$$
C
$$\sqrt{a^2+b^2}$$
D
$$\sqrt{a^2-b^2}$$
3
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$A$$ rod $$A B, 13$$ feet long moves with its ends $$A$$ and $$B$$ on two perpendicular lines $$O X$$ and $$O Y$$ respectively. When $$A$$ is 5 feet from $$O$$, it is moving away at the rate of $$3 \mathrm{feet} / \mathrm{sec}$$. At this instant, $$\mathrm{B}$$ is moving at the rate

A
$$\frac{5}{4} \mathrm{ft} / \mathrm{sec}$$ upwards.
B
$$\frac{4}{5} \mathrm{ft} / \mathrm{sec}$$ upwards.
C
$$\frac{5}{4} \mathrm{ft} / \mathrm{sec}$$ downwards.
D
$$\frac{4}{5} \mathrm{ft} / \mathrm{sec}$$ downwards.
4
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation of the tangent to the curve $$y=\sqrt{9-2 x^2}$$, at the point where the ordinate and abscissa are equal, is

A
$$2 x+y+\sqrt{3}=0$$
B
$$2 x+y+3 \sqrt{3}=0$$
C
$$2 x-y-3 \sqrt{3}=0$$
D
$$2 x+y-3 \sqrt{3}=0$$
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