An inelastic ball is dropped from a height of $100 \ m$. Due to collision with the earth,$20 \%$ of its energy is lost. To what height will the ball rise?

$A$ hollow conducting sphere is placed in an electric field produced by a point charge placed at $P$ as shown in the figure. Let $V_A, V_B$,and $V_C$ be the potentials at points $A, B$,and $C$ respectively. Then:

If $\int \sqrt{\frac{x}{a^3-x^3}} \, dx = g(x) + c$, then $g(x)$ is equal to:

Identify $A, B$ and $C$ in the following reactions:
$CH_3 Cl$ $\xrightarrow{KCN} A$ $\xrightarrow{H_3 O^{\oplus}} B$ $\xrightarrow{C_2 H_5 OH / H^{+}, \Delta} C$

$10 \ g$ of a radioactive element is disintegrated to $1 \ g$ in $2.303 \ \text{minutes}$. What is the half-life (in minutes) of that radioactive element?

The kinetic energy of an electron and a proton is $10^{-32} \ J$. Then the relation between their de-Broglie wavelengths is