$A$ coil of resistance $250 \Omega$ is placed in a magnetic field. If the magnetic flux $(\phi)$ linked with the coil varies with time $t$ $(s)$ as $\phi = 50t^2 + 7$,the current in the coil at $t = 4 \ s$ is: (in $A$)

$A$ metal loop of area $10 \,cm^2$ is placed in a region such that its area vector points along $\hat{k}$. The region contains a uniform magnetic field of magnitude $1.73 \,T$ that points in the direction $\hat{i}+\hat{j}+\hat{k}$. When the magnetic field is switched off, the field decreases to zero at a steady rate in $10 \,s$, then the magnitude of emf induced in the loop is (in $\,mV$)

$A$ circular coil of area $2 \text{ cm}^2$ is placed in a magnetic field of $3 \text{ T}$ perpendicularly. The coil has $10$ turns and $5 \text{ } \Omega$ resistance. Now,the coil is removed from the magnetic field in $0.2 \text{ s}$. The value of induced charge flowing through the coil is . . . . . . .

Out of the following,which law obeys the law of conservation of energy?

Magnetic flux in a circuit containing a coil of resistance $2\,\Omega$ changes from $2.0\,Wb$ to $10\,Wb$ in $0.2\,s$. The charge passed through the coil in this time is......$C$

$A$ square wire loop of side $10.0 \, cm$ is placed in a uniform perpendicular magnetic field of $20 \, T.$ The magnetic field decreases to zero in time interval $\Delta t.$ The bulb will glow with full brightness if the value of $\Delta t$ is.....$ms.$ (Assume the bulb requires $10 \, V$ to glow with full brightness.)