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.

1. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
2. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
3. If the assertion is true but the reason is false
4. If both the assertion and reason are false

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

From the equation $\tan \theta =\frac{rg}{v^2}$, one can obtain the angle of banking θ for a cyclist taking a curve (the symbols have their usual meanings). Then say, it is

1. Both dimensionally and numerically correct

2. Neither numerically nor dimensionally correct

3. Dimensionally correct only

4. Numerically correct only