$A$ vertical bar magnet is dropped from the shown position on the axis of a fixed metallic coil as shown in Fig-$I$. In Fig-$II$,the magnet is fixed and a horizontal coil is dropped. If the acceleration of the magnet and coil are $a_1$ and $a_2$ respectively,then:

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 having effective area '$A$' is held with its plane normal to a magnetic field of induction '$B$'. The magnetic induction is quickly reduced to $25\%$ of its initial value in $1 \text{ s}$. The e.m.f. induced in the coil (in volt) will be

Assertion $(A):$ The bar magnet falling vertically along the axis of the horizontal coil will have an acceleration less than $g$.
Reason $(R):$ Clockwise current is induced in the coil.

The induced $emf$ can be produced in a coil by:
$A.$ Moving the coil with uniform speed inside a magnetic field.
$B.$ Moving the coil with non-uniform speed inside a uniform magnetic field.
$C.$ Rotating the coil inside a uniform magnetic field.
$D.$ Changing the area of the coil inside a uniform magnetic field.
Choose the correct answer from the options given below:

The flux linked with a coil at any instant $t$ is given by $\phi = 10t^2 - 50t + 250$. The induced $emf$ at $t = 3 \ s$ is ....... $V$.