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

The slope of the normal to the curve $$x=\sqrt{t}$$ and $$y=t-\frac{1}{\sqrt{t}}$$ at $$t=4$$ is

A
$$\frac{-17}{4}$$
B
$$\frac{4}{17}$$
C
$$\frac{-4}{17}$$
D
$$\frac{17}{4}$$
2
MHT CET 2023 13th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Values of $$c$$ as per Rolle's theorem for $$f(x)=\sin x+\cos x+6$$ on $$[0,2 \pi]$$ are

A
$$\frac{\pi}{3}, \frac{5 \pi}{3}$$
B
$$\frac{\pi}{6}, \frac{5 \pi}{6}$$
C
$$\frac{\pi}{4}, \frac{5 \pi}{4}$$
D
$$\frac{\pi}{4}, \frac{7 \pi}{4}$$
3
MHT CET 2023 12th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A poster is to be printed on a rectangular sheet of paper of area $$18 \mathrm{~m}^2$$. The margins at the top and bottom of $$75 \mathrm{~cm}$$ each and at the sides $$50 \mathrm{~cm}$$ each are to be left. Then the dimensions i.e. height and breadth of the sheet, so that the space available for printing is maximum, are ________ respectively.

A
$$2 \sqrt{3} \mathrm{~m}, 3 \sqrt{3} \mathrm{~m}$$
B
$$3 \sqrt{3} \mathrm{~m}, 2 \sqrt{3} \mathrm{~m}$$
C
$$3 \mathrm{~m}, 6 \mathrm{~m}$$
D
$$6 \mathrm{~m}, 3 \mathrm{~m}$$
4
MHT CET 2023 12th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation of the normal to the curve $$3 x^2-y^2=8$$, which is parallel to the line $$x+3 y=10$$, is

A
$$x+3 y+6=0$$
B
$$x+3 y-3=0$$
C
$$x+3 y+8=0$$
D
$$x+3 y-4=0$$
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