1
MHT CET 2024 9th 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 cm each and at the sides 50 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
$6 \mathrm{~m}, 3 \mathrm{~m}$
2
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation of the tangent to the curve $x=\operatorname{acos}^3 \theta, y=\operatorname{asin}^3 \theta$ at $\theta=\frac{\pi}{4}$ is

A
$x+y=\frac{\mathrm{a}}{\sqrt{2}}$
B
$x+y=\frac{a}{2}$
C
$x+y=\frac{a}{2 \sqrt{2}}$
D
$x+y=\frac{\mathrm{a}}{8}$
3
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let C be a curve given by $y(x)=1+\sqrt{4 x-3}$, $x>\frac{3}{4}$. If P is a point on C , such that the tangent at P has slope $\frac{2}{3}$, then a point through which the normal at P passes, is

A
$(1,7)$
B
$(4,-3)$
C
$(3,-4)$
D
$(2,3)$
4
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(x)=\frac{\log x}{x}(x>0)$, then it is increasing in

A
$(0, \mathrm{e})$
B
$(\mathrm{e}, \infty)$
C
$(0, \infty)$
D
$(-\infty, \infty)$
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