Correct answer is 2

$\begin{array}{rl}& \overrightarrow{\mathrm{A}}=(0.1{)}^2\hat{\mathrm{j}}\\ & \overrightarrow{\mathrm{B}}=\frac{0.2}{\sqrt{2}}\hat{\mathrm{i}}+\frac{0.2}{\sqrt{2}}\hat{\mathrm{j}}\end{array}$

Magnitude of induced emf

$\mathrm{e}=\frac{\mathrm{\Delta }\varphi }{\mathrm{\Delta }\mathrm{t}}=\frac{\overrightarrow{\mathrm{B}}\cdot \overrightarrow{\mathrm{A}}-0}{1}=\sqrt{2}\times {10}^{-3}\mathrm{V}$

Correct Option is (D)

Assertion A is true because a bar magnet dropped through a metallic cylindrical pipe takes more time to come down compared to a non-magnetic bar with the same geometry and mass. This is due to the effect of the magnet's magnetic field on the metallic pipe.

Reason R is also true because when the magnetic bar moves through the metallic pipe, it induces a changing magnetic field in the pipe. This changing magnetic field, in turn, induces Eddy currents in the pipe. According to Lenz's law, these Eddy currents produce their own magnetic field, which opposes the motion of the magnetic bar, causing it to fall more slowly through the pipe.

Since both Assertion A and Reason R are true and R provides the correct explanation for A, the correct answer is Both A and R are true and R is the correct explanation of A.

Correct Option is (B)

If the coil is simply moved at uniform or non-uniform speed in a uniform magnetic field without changing the orientation of the coil or the area of the coil enclosed by the magnetic field, the magnetic flux through the coil does not change, and no emf is induced according to Faraday's Law of electromagnetic induction.

Correct Option is (B)

The magnitude of magnetic flux is given by :

$\mathrm{\Phi }=BA\cos \theta$

where $B$ is the magnitude of the magnetic field, $A$ is the area of the coil, and $\theta$ is the angle between the normal to the area and the direction of the magnetic field.

The correct option is A, B, and C only.

A. The magnetic flux through a coil can be changed by changing the magnitude of the magnetic field within the coil. A stronger magnetic field will increase the magnetic flux, while a weaker magnetic field will decrease the magnetic flux.

B. The magnetic flux through a coil can also be changed by changing the area of the coil within the magnetic field. A larger area of the coil will result in a greater magnetic flux, while a smaller area will result in a smaller magnetic flux.

C. The magnetic flux through a coil can also be changed by changing the angle between the direction of the magnetic field and the plane of the coil. When the angle is perpendicular to the plane of the coil, the magnetic flux is at its maximum. When the angle is parallel to the plane of the coil, the magnetic flux is zero.

D. Reversing the magnetic field direction abruptly without changing its magnitude will not change the magnetic flux through the coil. Magnetic flux is proportional to the dot product of the magnetic field and the area vector of the coil. If the magnitude of the magnetic field remains the same and the direction is reversed, the dot product remains the same and the magnetic flux remains unchanged.

Correct Option is (C)

The correct answer is option C: the insulating ball will reach the earth's surface earlier than the metal ball. When the two balls are dropped from the same height, they will experience the same gravitational force, which will cause them to accelerate downwards. However, According to Faraday’s law of electromagnetic induction motion of metal is opposed by earth magnetic field. Which will slightly reduce its acceleration. On the other hand, the insulating ball will not experience any electromagnetic induction. Therefore, it will accelerate downwards at a slightly faster rate than the metal ball. As a result, the insulating ball will reach the earth's surface earlier than the metal ball. So, option C is the correct statement.