The magnetic flux linked with a coil satisfies the relation $\phi = 4t^2 + 6t + 9 \text{ Wb}$, where $t$ is the time in seconds. The emf induced in the coil at $t = 2 \text{ s}$ is (in $\text{ V}$)

$A$ conducting circular coil is placed in a uniform magnetic field with the magnetic field initially directed perpendicular to the plane of the coil. In step $A$,the coil is rotated from its initial position by $60^{\circ}$ about its diameter in time $t$. In step $B$,the coil is further rotated about the same axis in the same sense by another $120^{\circ}$ in time $2t$. The ratio of the emf induced in the coil in step $A$ to that in step $B$ is:

$A$ magnet is moved in the direction indicated by an arrow between two coils $AB$ and $CD$ as shown in the figure. The direction of the induced current in the coils is

The flux associated with a closed loop is $\phi = 3t^2 + 2t + 5 \text{ Wb}$. If the resistance of the loop is $14 \ \Omega$,then the current induced in this coil at $t = 2 \text{ s}$ is . . . . . . . (in $\text{ A}$)

$A$ coil of $n$ turns and resistance $R \ \Omega$ is connected in series with a resistance $R/2$. The combination is moved for time $t$ seconds through a magnetic flux change from $\Phi_1$ to $\Phi_2$. The induced current in the circuit is:

$A$ wire of irregular shape is turning into a circular shape in a magnetic field which is directed into the paper. The direction of the induced current is