A length 5.997 m rounded off to three significant figures is written as 

(1) 6.00 m 

(2) 5.99 m

(3) 5.95 m

(4) 5.90 m

What are the dimensions of the change in velocity?

(1) $\left[M^0{L}^0{T}^0\right]$

(2) $<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>\left[L{T}^{-1}\right]<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

(3) $\left[ML{T}^{-1}\right]<mspace\; width="1em"></mspace>$

(4) $<mspace\; width="1em"></mspace>\left[L{T}^{-2}\right]$

The dimensional formula for energy is  

(1) $\left[ML{T}^{-2}\right]$

(2) $<mspace\; width="1em"></mspace>\left[M{L}^2{T}^{-2}\right]$

(3) $<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>\left[M^{-1}{L}^{2}T\right]<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

(4) $<mspace\; width="1em"></mspace>\left[M<mspace\; width="1em"></mspace>L^2<mspace\; width="1em"></mspace>T\right]$

The pair of the quantities having same dimensions is 

(1) Displacement, velocity 

(2) Time, frequency 

(3) Wavelength, focal length 

(4)  Force, acceleration 

The dimensional formula for relative refractive index is 

(1) $\left[M^1{L}^1{T}^1\right]$

(2) $<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>\left[M^0{L}^0{T}^0\right]$

(3) $<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>\left[M^1{L}^0{T}^0\right]$

(4) $\left[ML{T}^{-1}\right]$

The dimensional formula $\left[M{L}^{-1}{T}^{-2}\right]$ is for the quantity 

(1) Force  

(2) Acceleration 

(3) Pressure 

(4) Work 

The dimensionally correct expression for the resistance R among the following is 

[P=electric power, l= electric current, t=time 

V=voltage and E=electric energy]

(1) $R=\sqrt{Pl}$

(2) $R=\frac{E}{l^{2}t}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

(3) $<mspace\; width="1em"></mspace>R=V^{2}P<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

(4) $R=vl$

Which of the following does not have dimensions of force?

(1) Weight 

(2) Rate of change of momentum 

(3) Work per unit length 

(4) Work done per unit charge 

Dimensional analysis cannot be used for:

1. deriving relations

2. deriving relation with four unknown variables

3. converting system of units

4. checking correctness of relations

Which of the following does not have the dimensions of force?

1. Potential gradient

2. Energy gradient

3. Weight

4. Rate of change of momentum