1
KCET 2024
MCQ (Single Correct Answer)
+1
-0

For the function $f(x)=x^3-6 x^2+12 x-3$; $x=2$ is

A
A point of minimum
B
A point of inflexion
C
Not a critical point
D
A point of maximum
2
KCET 2024
MCQ (Single Correct Answer)
+1
-0

The function $x^x ; x>0$ is strictly increasing at

A
$\forall x \in R$
B
$x<\frac{1}{e}$
C
$x>\frac{1}{e}$
D
$x<0$
3
KCET 2024
MCQ (Single Correct Answer)
+1
-0

The maximum volume of the right circular cone with slant height 6 units is

A
$4 \sqrt{3} \pi$ cu units
B
$16 \sqrt{3} \pi \mathrm{cu}$ units
C
$3 \sqrt{3} \pi$ cu units
D
$6 \sqrt{3} \pi$ cu units
4
KCET 2024
MCQ (Single Correct Answer)
+1
-0

If $f(x)=x e^{x(1-x)}$, then $f(x)$ is

A
increasing in $R$
B
decreasing in $R$
C
decreasing in $\left[-\frac{1}{2}, 1\right]$
D
increasing in $\left[-\frac{1}{2}, 1\right]$
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