Which of the following is an amphoteric hydroxide?

$A$ man standing on a road has to hold his umbrella at $30^{\circ}$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10 ~km/h$. He finds that raindrops are hitting his head vertically. The actual speed of raindrops is:

Which of the following methods is used to remove hardness from water?

Two long conductors,separated by a distance $d$,carry currents $I_1$ and $I_2$ in the same directions. They exert a force $F$ on each other. Now,the current in one of them is increased to two times its original value and its direction is reversed. The distance is also increased to $3d$. The new value of the force between them is:

$\int_0^{\frac{\pi}{4}} \frac{\cos ^2 x}{\cos ^2 x+4 \sin ^2 x} d x=$

The foci of the ellipse $\frac{x^2}{16} + \frac{y^2}{b^2} = 1$ and the hyperbola $\frac{x^2}{144} - \frac{y^2}{81} = \frac{1}{25}$ coincide. Then the value of $b^2$ is