The activity of a radioactive sample reduces from $A_0$ to $\frac{A_0}{\sqrt{3}}$ in $1 \text{ hour}$. What will be the activity after $3 \text{ hours}$ more?

$\sum_{k=1}^{2n+1} (-1)^{k-1} k^2$ is equal to

Which of the following salts increases the rate of the setting process of Plaster of Paris?

If $f(x) = \begin{cases} \frac{1-\sqrt{2} \sin x}{\pi-4x} & \text{if } x \neq \frac{\pi}{4} \\ a & \text{if } x = \frac{\pi}{4} \end{cases}$ is continuous at $x = \frac{\pi}{4}$, then $a$ is equal to

If $\frac{1-x+6x^2}{x-x^3} = \frac{A}{x} + \frac{B}{1-x} + \frac{C}{1+x}$,then $A$ is equal to

There are two holes,one each along the opposite sides of a wide rectangular tank. The cross-section of each hole is $0.01 ~m^2$ and the vertical distance between the holes is $1 ~m$. The tank is filled with water. The net force on the tank in newtons when the water flows out of the holes is (Density of water $= 1000 ~kg/m^3$,$g = 10 ~m/s^2$):