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1
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The function $f(x)=\frac{\log _e(\pi+x)}{\log _e(e+x)}$ is

A
increasing on $(0, \infty)$.
B
increasing on $\left(0, \frac{\pi}{\mathrm{e}}\right)$, decreasing on $\left(\frac{\pi}{\mathrm{e}}, \infty\right)$.
C
decreasing on $(0, \infty)$.
D
decreasing on $\left(0, \frac{\pi}{\mathrm{e}}\right)$, increasing on $\left(\frac{\pi}{\mathrm{e}}, \infty\right)$
2
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The sum of intercepts on coordinate axes made by tangent to the curve $\sqrt{x}+\sqrt{y}=\sqrt{a}$ is

A
$a$
B
$2 a$
C
$2 \sqrt{a}$
D
$\sqrt{2} a$
3
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A wire of length 2 units is cut into two parts, which are bent respectively to form a square of side $x$ units and a circle of radius of r units. If the sum of the areas of square and the circle so formed is minimum, then

A
$2 x=(\pi+4) \mathrm{r}$
B
$(4-\pi) x=\pi \mathrm{r}$
C
$x=2 \mathrm{r}$
D
$2 x=\mathrm{r}$
4
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If sum of two numbers is 3 , then the maximum value of the product of first number and square of the second number is

A
6
B
4
C
5
D
3
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