1
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
2
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 $\left[-\frac{1}{2}, 1\right]$
3
KCET 2023
MCQ (Single Correct Answer)
+1
-0

If $$u=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)$$ and $$v=\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)$$, then $$\frac{d u}{d v}$$ is

A
2
B
$$\frac{1-x^2}{1+x^2}$$
C
1
D
$$\frac{1}{2}$$
4
KCET 2023
MCQ (Single Correct Answer)
+1
-0

The distance '$$s$$' in meters travelled by a particle in '$$t$$' seconds is given by $$s=\frac{2 t^3}{3}-18 t+\frac{5}{3}$$. The acceleration when the particle comes to rest is :

A
$$10 \mathrm{~m}^2 / \mathrm{s}$$
B
$$12 \mathrm{~m}^2 / \mathrm{s}$$
C
$$18 \mathrm{~m}^2 / \mathrm{s}$$
D
$$3 \mathrm{~m}^2 / \mathrm{s}$$
KCET Subjects
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