Match List-I with List-II (Symbols have their usual meanings)

List-I (Physical Quantity)	List-II (Expression)
(A) Current density	(I) \( \frac{e E \tau}{m} \)
(B) Drift velocity	(II) \( \frac{n e^2 \tau}{m} \)
(C) Conductivity	(III) \( \frac{e \tau}{m} \)
(D) Mobility	(IV) \( n e v_d \)

Choose the correct answer from the options given below:

According to the Biot- Savart law, the magnetic field due to a current element is
(A) inversely proportional to the square of the distance from the current element to the point of interest.
(B) produced by a vector source.
(C) perpendicular to the plane containing the displacement vector and the current element.
(D) non-zero at any point in the direction of the current element.
Choose the correct answer from the options given below:

An infinite plane sheet of charge density \(10^{-8} \text{ C m}^{-2}\) is held in air. In this situation, the distance between two equipotential surfaces, whose potential difference is 10 V, will be (Given: Permittivity of vacuum\(\epsilon_0 \approx 8.85 \times 10^{-12} F / m\))

A proton enters a uniform magnetic field of 0.2 T with speed v. It describes a semicircular path of radius 5 cm and comes out of the field. The final speed of the proton will be

The magnetic flux linked to a coil changes from 10 \(\times 10^{-3}\) Wb to 6 \(\times 10^{-3}\) Wb in 0.01 s. The induced emf will be :

A current of 2 A flows through a plane circular coil of radius 3 cm and having 50 turns. The coil has been placed in a uniform magnetic field of 0.6 T. The minimum potential energy of the coil will be

The ratio of the radius of the third orbit to that of the second orbit in a hydrogen atom is

The values of \(a\) for which the function \(f(x)=a^x\) is increasing on \(R\) are given by :

Choose the correct statement.

A piece of copper and a piece of germanium are cooled from room temperature 20 C down to 80 K. The resistance of

If the straight lines \(x=1+s, y=-3-\lambda s, z=1+\lambda s\) and \(x=\frac{t}{2}, y=1+t, z=2-t\) with parameters s and \(t\) respectively, are coplanar, then \(\lambda\) is equal to :

Choose the correct statements:
(A) The angle of incidence corresponding to an angle of refraction \(90^{\circ}\) is called critical angle (i).
(B) Refractive index of denser medium \(\mu=\frac{1}{\sin \left(i_c\right)}\).
(C) For \(i>i_c\), Snell's law of refraction cannot be satisfied.
(D) The refractive index of air increases with decrease in density.
(E) Rainbow is the combined effect of dispersion, refraction and reflection of sunlight by droplets.
Choose the correct answer from the options given below :

The properties which depend on the number of solute particles irrespective of their nature relative to the total number of particles in the solution are called colligative properties. These are relative lowering of vapour pressure of the solvent, depression of freesing point of the solvent, elevation of boiling point of the solvent and osmotic pressure of the solution. All of these properties help in calculating the observed molar mass of the solute.
Determination of osmotic pressure is considered best for the determination of molecular mass of the solute.
A solution of \(12.5\) g of an unknown solute in \(170\) g of water gave a boiling point elevation of 0.63 K .
\(k_b\) for water is \(0.53 K kg mol ^{-1}\).
The molar mass of the solute is :