$A$ pair of adjacent coils has a mutual inductance of $1.5\; H$. If the current in one coil changes from $0$ to $20\; A$ in $0.5\; s$,what is the change of flux (in $Wb$) linkage with the other coil?

Consider two coils in which a current in one coil carrying $6$ $A$ causes the change in the flux in the second coil $12 \times 10^{-4}$ $Wb/turn$. The second coil has $2000$ turns. The mutual inductance between the coils is (in $H$)

With the decrease of current in the primary coil from $2\,A$ to zero in $0.01\,s$,the $emf$ generated in the secondary coil is $1000\,V$. The mutual inductance of the two coils is......$H$.

Two concentric circular coils with radii $1\,cm$ and $1000\,cm$,and number of turns $10$ and $200$ respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be $.........\times 10^{-8}\,H$ (Take,$\pi^2=10$).

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?

$X$ and $Y$ are two metallic coils arranged in such a way that when the steady change in current flowing in coil $X$ is $4 \ A$,the change in magnetic flux associated with coil $Y$ is $0.4 \ Wb$. The mutual inductance of the system of these coils is . . . . . . $H$.