$A$ current $I = 10 \sin(100 \pi t) \text{ A}$ is passed in a coil, which induces a maximum emf of $5 \pi \text{ V}$ in a neighboring coil. The mutual inductance of the two coils is: (in $\text{ mH}$)

$X$ and $Y$ are two circuits having a coefficient of mutual inductance $3 \text{ mH}$ and resistances $10 \text{ } \Omega$ and $4 \text{ } \Omega$ respectively. To have an induced current of $60 \times 10^{-4} \text{ A}$ in circuit $Y$,the amount of current to be changed in circuit $X$ in $0.02 \text{ s}$ is: (in $A$)

Two conducting circular loops $A$ and $B$ are placed in the same plane with their centres coinciding as shown in the figure. If $b >> a$,the mutual inductance between them is:

Two coils have a mutual inductance of $0.01 \ H$. The current in the first coil changes according to the equation $I = 5 \sin(200 \pi t)$. The maximum value of the e.m.f. induced in the second coil is:

Two coils have a mutual inductance $5 \times 10^{-3} \text{ H}$. The current changes in the first coil according to the equation $I_1 = I_0 \sin \omega t$, where $I_0 = 10 \text{ A}$ and $\omega = 100 \pi \text{ rad/s}$. What is the value of the maximum e.m.f. in the second coil (in $\pi \text{ V}$)?

If the coefficient of mutual induction of the primary and secondary coils of an induction coil is $5\, H$ and a current of $10\, A$ is cut off in $5\times10^{-4}\, s$,the $emf$ induced (in $volt$) in the secondary coil is