$A$ force $\overrightarrow F = 6\hat i + 2\hat j - 3\hat k$ acts on a particle,causing a displacement of $\overrightarrow s = 2\hat i - 3\hat j + x\hat k$. If the work done is zero,find the value of $x$.

If $(1, 3), (2, 5),$ and $(3, 3)$ are three elements of $A \times B$ and the total number of elements in $A \times B$ is $6$,then the remaining elements of $A \times B$ are:

During an adiabatic process,the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $C_P / C_V$ for the gas is

Twelve cells,each having emf $E$ volts,are connected in series and are kept in a closed box. Some of these cells are wrongly connected with positive and negative terminals reversed. This $12$-cell battery is connected in series with an ammeter,an external resistance $R$ ohms,and a two-cell battery (two cells of the same type used earlier,connected perfectly in series). The current in the circuit when the $12$-cell battery and $2$-cell battery aid each other is $3 \text{ A}$,and it is $2 \text{ A}$ when they oppose each other. Then,the number of cells in the $12$-cell battery that are connected wrongly is:

The correct order of dipole moment is

In which of the following does the central atom $NOT$ use $sp^3$ hybrid orbitals in its bonding?