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

Two concentric circular coils,one of small radius $r$ and the other of large radius $R$,are placed coaxially with their centers coinciding. If the radius $r$ is changed by $2 \%$,then the change in mutual inductance of the arrangement is (assume $r \ll R$). (in $\%$)

Two coils $P$ and $S$ have a mutual inductance of $\pi \text{ mH}$. The secondary coil $S$ has resistance $4 \text{ } \Omega$ and self-inductance $(60/\pi) \text{ mH}$. If the current in the primary is $I_p = 12 \sin(50\pi t)$, then the maximum value of the current induced in coil $S$ is [Take $\pi^2 = 10$] (in $\text{ A}$)

$A$ 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?

$O$ is the centre of two coplanar concentric circular conductors,$A$ and $B$,of radii $r$ and $R$ respectively as shown in the figure. Here $r \ll R$. The mutual inductance of the system of the conductors can be given by . . . . . . .

Derive the formula for mutual inductance of two very long coaxial solenoids. Also,discuss the reciprocity theorem.