If a change in current of $0.01\, A$ in one coil produces a change in magnetic flux of $1.2 \times 10^{-2}\,Wb$ in the other coil,then the mutual inductance of the two coils in henries is.....$H$

The mutual inductance between a primary and secondary circuit is $0.5 \, H$. The resistances of the primary and the secondary circuits are $20 \, \Omega$ and $5 \, \Omega$ respectively. To generate a current of $0.4 \, A$ in the secondary,the current in the primary must be changed at the rate of . . . . . . $A/s$.

Two coils $A$ and $B$ have mutual inductance $0.008 \ H$. The current changes in the coil $A$, according to the equation $I = I_{m} \sin \omega t$, where $I_{m} = 5 \ A$ and $\omega = 200 \pi \ rad \ s^{-1}$. The maximum value of the e.m.f. induced in the coil $B$ in volt is (in $\pi$)

The coefficient of mutual inductance,when magnetic flux changes by $2 \times 10^{-2} \ Wb$ and current changes by $0.01 \ A$,is ... $H$.

An electric current $i_1$ can flow in either direction through loop $(1)$ and induces a current $i_2$ in loop $(2)$. Positive $i_1$ is defined when the current flows from $'a'$ to $'b'$ in loop $(1)$,and positive $i_2$ is defined when the current flows from $'c'$ to $'d'$ in loop $(2)$. In an experiment,the graph of $i_2$ against time $'t'$ is as shown below. Which one$(s)$ of the following graphs could have caused $i_2$ to behave as given above?

Two coils have a mutual inductance of $0.005\,H$. The current in the first coil changes according to the equation $I = I_0 \sin \omega t$,where $I_0 = 10\,A$ and $\omega = 100\pi \,rad/s$. The maximum value of $emf$ in the second coil will be: (in $\pi \,V$)