The number of significant figures in all the given numbers 25.12, 2009, 4.156 and $1.217\times {10}^{-4}$ is 

1. 1

2. 2

3. 3

4. 4

The dimensions of physical quantity X in the equation Force $=\frac{X}{\text{Density}}$ is given by 

(1) $M^1{L}^4{T}^{-2}$

(2) $M^2{L}^{-2}{T}^{-1}$

(3) $M^2{L}^{-2}{T}^{-2}$

(4) $M^1{L}^{-2}{T}^{-1}$

A force F is given by F = at + bt², where t is time. What are the dimensions of a and b 

(1) $ML{T}^{-3}$ and $M{L}^2{T}^{-4}$

(2) $ML{T}^{-3}$ and $ML{T}^{-4}$

(3) $ML{T}^{-1}$ and $ML{T}^0$

(4) $ML{T}^{-4}$ and $ML{T}^1$

Two quantities A and B have different dimensions. Which mathematical operation given below is physically meaningful 

(1) A/B

(2) A + B

(3) A – B

(4) None

The decimal equivalent of 1/20 upto three significant figures is

(1) 0.0500

(2) 0.05000

(3) 0.0050

(4) 5.0 × 10^-2

A small steel ball of radius \(r\) is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity \(\eta\). After some time the velocity of the ball attains a constant value known as terminal velocity \(v_T\). The terminal velocity depends on \((\text{i})\) the mass of the ball \(m\) \((\text{ii})\) \(\eta\) \((\text{iii})\) \(r\) and \((\text{iv})\) acceleration due to gravity \(g\). Which of the following relations is dimensionally correct:

The quantity $X=\frac{{\epsilon }_{0}LV}{t}:{\epsilon }_0$ is the permittivity of free space, L is length, V is the potential difference and t is time. The dimensions of X are the same as that of  

(1) Resistance

(2) Charge

(3) Voltage

(4) Current

Assertion: Out of three measurements l = 0.7 m; l = 0.70 m and l = 0.700 m, the last one is most accurate.

Reason: In every measurement, only the last significant digit is not accurately known.

Accuracy of measurement is determined by

(1) Absolute error

(2) Percentage error

(3) Both

(4) None of these