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 the 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.

If radius of the sphere is (5.3 ± 0.1)cm. Then percentage error in its volume will be 

(1) $3+6.01\times \frac{100}{5.3}$

(2) $\frac{1}{3}\times 0.01\times \frac{100}{5.3}$

(3) $\left(\frac{{\displaystyle 3\times 0.1}}{{\displaystyle 5.3}}\right)\times 100$

(4) $\frac{0.1}{5.3}\times 100$

The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate. If the maximum error in the measurement of force and length are respectively 4% and 2%, The maximum error in the measurement of pressure is 

(1) 1%

(2) 2%

(3) 6%

(4) 8%

While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of 1% in the length of the pendulum and a negative error of 3% in the value of time period. His percentage error in the measurement of g by the relation $g=4{\pi }^2(l/T^2)$ will be

(1) 2%

(2) 4%

(3) 7%

(4) 10%

If the unit of force and length each be increased by four times, then the unit of energy is increased by 

(1) 16 times

(2) 8 times

(3) 2 times

(4) 4 times

If energy (\(E\)), velocity (\(v\)) and time (\(T\)) are chosen as the fundamental quantities, the dimensional formula of surface tension will be:
1. \( {\left[E v^{-2} T^{-1}\right]} \)
2. \( {\left[E v^{-1} T^{-2}\right]} \)
3. \( {\left[E v^{-2} T^{-2}\right]} \)
4. \({\left[E^{-2} v^{-1} T^{-3}\right]}\)

If dimensions of critical velocity v_c of a liquid flowing through a tube are expressed as [$\eta$^xρ^yr^z]  , where $\eta$, ρ and r are the coefficent of viscocity of liquid, density of liquid and radius of the tube respectively, then the values of x,y and z are given by

1. 1,-1,-1

2. -1,-1,1

3. -1,-1,-1

4. 1,1,1

If force (F), velocity (v) and time (T) are taken as fundamental units, then the dimensions of mass are:

(a) [FvT^-1]

(b) [FvT^-2]

(c) [Fv^-1T^-1]

(d) [Fv^-1T]

In an experiment four quantities a, b, c and d are measured with percentage error 1%,2%,3% and 4% respectively. Quantity P is calculated as follows P=a³b²/cd %, Error in P is

1. 14%

2. 10%

3. 7%

4. 4%

The dimension of $({\mathrm{\mu }}_0{\mathrm{\epsilon }}_0{)}^{-1/2}$ are 

(1) $\left[{\mathrm{L}}^{-1} \mathrm{T}\right]$

(2) $\left[{\mathrm{LT}}^{-1}\right]$

(3) $\left[{\mathrm{L}}^{-1/2}{\mathrm{T}}^{1/2}\right]$

(4) $\left[{\mathrm{L}}^{1/2}{\mathrm{T}}^{-1/2}\right]$