Choose any one of the following four responses :

(1) If both assertion and reason are true and the reason is the correct explanation of the assertion.

(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.

(3) If assertion is true but reason is false.

(4) If the assertion and reason both are false.

Assertion :The time period of a pendulum is given by the formula, $T=2\pi \sqrt{\text{l}/\text{g}}$.

Reason : According to the principle of homogeneity of dimensions, only that formula is correct in which the dimensions of L.H.S. is equal to dimensions of R.H.S.

Assertion :In the relation $f=\frac{1}{2l}\sqrt{\frac{T}{m},}$ where symbols have standard meaning, m represent linear mass density.

Reason : The frequency has the dimensions of inverse of time.

Choose any one of the following four responses :

(1) If both assertion and reason are true and the reason is the correct explanation of the assertion.

(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.

(3) If the assertion is true but the reason is false.

(4) If the assertion and reason both are false.

Assertion: Avogadro number is the number of atoms in one gram mole.

Reason: Avogadro number is a dimensionless constant.

Choose any one of the following four responses :

(1) If both assertion and reason are true and the reason is the correct explanation of the assertion.

(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.

(3) If assertion is true but reason is false.

(4) If the assertion and reason both are false.

Assertion : The quantity $(1\text{}/\text{}\sqrt{{\mu }_0{\epsilon }_0})$ is dimensionally equal to velocity and numerically equal to velocity of light.

Reason : ${\mu }_0$ is permeability of free space and ${\epsilon }_0$ is the permittivity of free space.

The surface tension of a liquid is 70 dyne/cm. In MKS system its value is 

1. 70 N/m

2. 7 × 10^–2 N/m

3. 7 × 10³ N/m

4. 7 × 10² N/m

The SI unit of universal gas constant (R) is

1. Watt K^–1 mol^–1

2. Newton K^–1 mol^–1

3. Joule K^–1 mol^–1

4. Erg K^–1 mol^–1

The unit of permittivity of free space ${\epsilon }_0$ is

1. Coulomb/Newton-metre

2. Newton-metre²/Coulomb²

3. Coulomb²/(Newton-metre)²

4. Coulomb²/Newton-metre²

What are the units of $K=1\text{}/\text{}4\pi {\epsilon }_0$

1. C²N^–1m^–2

2. Nm²C^–2

3. Nm²C²

4. Unitless

The SI unit of surface tension is

1. Dyne/cm

2. Newton/cm

3. Newton/metre

4. Newton-metre

E, m, l and G denote energy, mass, angular momentum and gravitational constant respectively, then the dimension of $\frac{E{l}^2}{m^5{G}^2}$ are

1. Angle

2. Length

3. Mass

4. Time