The average emf induced in a coil is 2 V when current is changed in 0.4 s (A) from 5 A to 2 A and the self-inductance of the coil is 0.266 mH (B) from 4 A to 4 A in the opposite direction, the self-inductance of the coil is 0.10 mH

The correct option is: Both (A) and (B) are incorrect

To understand why both statements are incorrect, let us analyze the formula for the average electromotive force (emf) induced in a coil due to self-induction.

The magnitude of the average induced emf ($e$) in a coil of self-inductance $L$ when the current changes by $\Delta I$ in a time interval $\Delta t$ is given by Faraday's law of electromagnetic induction:
$e=L·\frac{\left|\Delta I\right|}{\Delta t}$
Rearranging the formula to solve for the self-inductance $L$ gives:
$L=\frac{e·\Delta t}{\left|\Delta I\right|}$

We are given that the average induced emf is $e=2\text{V}$ and the time interval is $\Delta t=0.4\text{s}$.

Analyzing Statement (A):
The current changes from $5\text{A}$ to $2\text{A}$.
The change in current is:
$\left|\Delta I\right|=\left|2\text{A}-5\text{A}\right|=3\text{A}$
Using the formula for $L$:
$L=\frac{2\text{V}·0.4\text{s}}{3\text{A}}=\frac{0.8}{3}\text{H}\approx 0.2667\text{H}$
Converting this to millihenries ($\text{mH}$):
$L\approx 266.7\text{mH}$
Statement (A) claims that the self-inductance is $0.266\text{mH}$ (which is off by a factor of 1000). Thus, statement (A) is incorrect.

Analyzing Statement (B):
The current changes from $4\text{A}$ to $4\text{A}$ in the opposite direction (from $+4\text{A}$ to $-4\text{A}$).
The magnitude of the change in current is:
$\left|\Delta I\right|=\left|-4\text{A}-4\text{A}\right|=8\text{A}$
Using the formula for $L$:
$L=\frac{2\text{V}·0.4\text{s}}{8\text{A}}=\frac{0.8}{8}\text{H}=0.10\text{H}$
Converting this to millihenries ($\text{mH}$):
$L=100\text{mH}$
Statement (B) claims that the self-inductance is $0.10\text{mH}$ (which is also off by a factor of 1000). Thus, statement (B) is incorrect.

Consequently, both statements (A) and (B) are incorrect.