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

The area (in sq. units) of the region bounded by curves $$y=3 x+1, y=4 x+1$$ and $$x=3$$ is

A
$$\frac{7}{2}$$
B
$$\frac{9}{5}$$
C
$$\frac{9}{2}$$
D
$$\frac{7}{5}$$
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 13th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A vector $$\bar{a}$$ has components 1 and $$2 p$$ with respect to a rectangular Cartesian system. This system is rotated through a certain angle about origin in the counter clock wise sense. If, with respect to the new system, $$\bar{a}$$ has components 1 and $$(p+1)$$, then

A
$$\mathrm{p}=1$$ or $$\mathrm{p}=\frac{1}{3}$$
B
$$\mathrm{p}=-1$$ or $$\mathrm{p}=\frac{-1}{3}$$
C
$$\mathrm{p}=\frac{-1}{3}$$ or $$\mathrm{p}=1$$
D
$$\mathrm{p}=\frac{1}{3}$$ or $$\mathrm{p}=-1$$
4
MHT CET 2023 13th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A line is drawn through the point $$(1,2)$$ to meet the co-ordinate axes at $$\mathrm{P}$$ and $$\mathrm{Q}$$ such that it forms a $$\triangle \mathrm{OPQ}$$, where $$\mathrm{O}$$ is the origin. If the area of $$\triangle \mathrm{OPQ}$$ is least, then the slope of the line $$\mathrm{PQ}$$ is

A
$$-2$$
B
2
C
$$\frac{-1}{2}$$
D
$$\frac{1}{2}$$
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