$X$ 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 . . . . . . $H$.

Consider $I_1$ and $I_2$ are the currents flowing simultaneously in two nearby coils $1$ and $2$,respectively. If $L_1$ is the self-inductance of coil $1$ and $M_{12}$ is the mutual inductance of coil $1$ with respect to coil $2$,then the value of the induced emf in coil $1$ will be:

$A$ coil of radius '$r$' is placed on another coil (whose radius is '$R$' and current flowing through it is changing) so that their centres coincide $(R \gg r)$. If both the coils are coplanar,then the mutual inductance between them is $(\mu_0 = \text{permeability of free space})$

When a current of $4 \,A$ changes to $8 \,A$ in $0.6 \,s$ in a primary coil, it induces an e.m.f. of $50 \,mV$ in the secondary coil. The mutual inductance between the two coils is: (in $\,mH$)

$A$ square loop of side length $a$ is moving away from an infinitely long current-carrying conductor at a constant speed $v$ as shown. Let $x$ be the instantaneous distance between the long conductor and side $AB$. The mutual inductance $M$ of the square loop-long conductor pair changes with time $t$ according to which of the following graphs?

$A$ pair of adjacent coils has a mutual inductance of $1.5 \ H$. If the current in one coil changes from $0 \ A$ to $10 \ A$ in $0.5 \ s$,what is the change of flux linkage with the other coil (in $Wb$)?