In a pair of adjacent coils, for a change of current in one of the coils from 0 A to 10 A in 0.25 s, the magnetic flux in the adjacent coil changes by 15 Wb. The mutual inductance of the coils is _______.

The correct option is 1.5 H.

Mutual inductance ($M$) between two adjacent coils is defined as the ratio of the magnetic flux linkage in the second coil to the change in current in the first coil. Mathematically, the relationship is given by:
$N\Delta {\Phi }_2=M\Delta I_1$
where:
- $N\Delta {\Phi }_2$ is the change in magnetic flux linkage in the adjacent coil (which is given as 15 Wb),
- $\Delta I_1$ is the change in current in the first coil,
- $M$ is the mutual inductance.

First, we calculate the change in current ($\Delta I_1$):
$\Delta I_1=I_{\text{final}}-I_{\text{initial}}$
$\Delta I_1=10\text{A}-0\text{A}=10\text{A}$

We are given that the change in magnetic flux linkage is:
$\Delta \Phi =15\text{Wb}$

Substituting these values into the mutual inductance formula:
$15=M\times 10$

Solving for $M$:
$M=\frac{15}{10}=1.5\text{H}$
Therefore, the mutual inductance of the coils is 1.5 H.