The magnetic flux linked with a coil varies with time as $\Phi = 4t^2 + 3t + 7$. The magnitude of the induced e.m.f. at $t = 2 \ s$ is: (in $V$)

An aluminium ring $B$ faces an electromagnet $A$. The current $I$ through $A$ can be altered. Which of the following statements is correct?

$A$ conducting loop is placed in a uniform magnetic field with its plane perpendicular to the field. An $emf$ is induced in the loop if:
$(a)$ It is translated (inside the field)
$(b)$ It is rotated about its axis
$(c)$ It is rotated about a diameter
$(d)$ It is deformed

Assertion : An induced current has a direction such that the magnetic field due to the current opposes the change in the magnetic flux that induces the current.
Reason : The above statement is in accordance with the conservation of energy.

$A$ coil of resistance $8 \Omega$,number of turns $250$,and area $120 \ cm^2$ is placed in a uniform magnetic field of $2 \ T$ such that the plane of the coil makes an angle of $\frac{\pi}{6}$ with the direction of the magnetic field. In a time of $100 \ ms$,the coil is rotated until its plane becomes parallel to the direction of the magnetic field. The current induced in the coil 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 $\,mV$)