1
KCET 2023
+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
$$\frac{1}{2}$$
2
KCET 2023
+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
$$3 \mathrm{~m}^2 / \mathrm{s}$$
3
KCET 2023
+1
-0

A particle moves along the curve $$\frac{x^2}{16}+\frac{y^2}{4}=1$$. When the rate of change of abscissa is 4 times that of its ordinate, then the quadrant in which the particle lies is

A
II or IV
B
III or IV
C
II or III
D
I or III
4
KCET 2023
+1
-0

An enemy fighter jet is flying along the curve, given by $$y=x^2+2$$. A soldier is placed at $$(3,2)$$ wants to shoot down the jet when it is nearest to him. Then, the nearest distance is

A
$$\sqrt{6}$$ units
B
2 units
C
$$\sqrt{5}$$ units
D
$$\sqrt{3}$$ units
EXAM MAP
Medical
NEET