Which of the following can be used to extinguish a fire caused by alkali metals?

If $x = \frac{1 - t^2}{1 + t^2}$ and $y = \frac{2at}{1 + t^2}$,then $\frac{dy}{dx} = $

Match the following (Take the relative strength of the strongest fundamental forces in nature as $1$):
| List-$I$ (Fundamental forces in nature) | List-$II$ (Relative strength) |
| :--- | :--- |
| $(A)$ Strong nuclear force | $(e)$ $10^{-2}$ |
| $(B)$ Weak nuclear force | $(f)$ $1$ |
| $(C)$ Electromagnetic force | $(g)$ $10^{10}$ |
| $(D)$ Gravitational force | $(h)$ $10^{-13}$ |
| | $(i)$ $10^{-39}$ |
The correct match is:

If $A$ and $B$ are two independent events such that $P(B)=\frac{2}{7}$ and $P(A \cup B^c)=0.8$, then $P(A)$ is equal to:

What is the percentage of lead in a lead pencil (in $,\%$)?

At a certain instant, a stationary transverse wave is found to have maximum kinetic energy. The appearance of the string at that instant is: