In which of the following reactions does $HNO_3$ $NOT$ act as an oxidizing agent?

For a cell,the terminal potential difference $(P.D.)$ is $2.2 \, V$ when the circuit is open and reduces to $1.8 \, V$ when the cell is connected to an external resistance of $R = 5 \, \Omega$. Determine the internal resistance of the cell $(r)$.

With a standard rectangular bar magnet,the time period of a vibration magnetometer is $4 ~s$. The bar magnet is cut parallel to its length into four equal pieces. The time period of the vibration magnetometer when one piece is used (in seconds) (bar magnet breadth is small) is

$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ horizontal force $F$ is applied at one end of the rod perpendicular to its length. The acceleration of the centre of mass of the rod is:

$\sin ^{-1} \frac{4}{5} + 2 \tan ^{-1} \frac{1}{3}$ is equal to

The number of electrons in the valence shell of the central atom of a molecule is $8$. The molecule is