The potential energy between two atoms in a molecule is given by $U(x) = \frac{a}{x^{12}} - \frac{b}{x^6}$,where $a$ and $b$ are positive constants and $x$ is the distance between the atoms. The atoms are in stable equilibrium when:

The number of radial nodes of $3s$ and $2p$ orbitals respectively are

There is some change in length when a $33000 ~N$ tensile force is applied on a steel rod of area of cross-section $10^{-3} ~m^2$. The change of temperature required to produce the same elongation,if the steel rod is heated,is (The modulus of elasticity is $3 \times 10^{11} ~N/m^2$ and the coefficient of linear expansion of steel is $1.1 \times 10^{-5} /{ }^{\circ} C$). (in $^{\circ} C$)

Let $P(3, 2, 6)$ be a point in space and $Q$ be a point on the line $\vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \mu(-3\hat{i} + \hat{j} + 5\hat{k})$. Then the value of $\mu$ for which the vector $\vec{PQ}$ is parallel to the plane $x - 4y + 3z = 1$ is:

The total charge induced in a conducting loop when it is moved in a magnetic field depends on

Which of the following is a pair of functional isomers?