Question

If $$P,Q,R$$  are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?

A. $$\frac{{\left( {P - Q} \right)}}{R}$$  
B. $$PQ - R$$
C. $$\frac{{PQ}}{R}$$
D. $$\frac{{\left( {PR - {Q^2}} \right)}}{R}$$
Answer :   $$\frac{{\left( {P - Q} \right)}}{R}$$
Solution :
$$\left[ P \right] \ne \left[ Q \right]$$   so, $${P - Q}$$   is not meaningful

Releted MCQ Question on
Basic Physics >> Unit and Measurement

Releted Question 1

The dimension of $$\left( {\frac{1}{2}} \right){\varepsilon _0}{E^2}$$  ($${\varepsilon _0}$$ : permittivity of free space, $$E$$ electric field)

A. $$ML{T^{ - 1}}$$
B. $$M{L^2}{T^{ - 2}}$$
C. $$M{L^{ - 1}}{T^{ - 2}}$$
D. $$M{L^2}{T^{ - 1}}$$
Releted Question 2

A quantity $$X$$ is given by $${\varepsilon _0}L\frac{{\Delta V}}{{\Delta t}}$$   where $${ \in _0}$$ is the permittivity of the free space, $$L$$ is a length, $$\Delta V$$ is a potential difference and $$\Delta t$$ is a time interval. The dimensional formula for $$X$$ is the same as that of-

A. resistance
B. charge
C. voltage
D. current
Releted Question 3

A cube has a side of length $$1.2 \times {10^{ - 2}}m$$  . Calculate its volume.

A. $$1.7 \times {10^{ - 6}}{m^3}$$
B. $$1.73 \times {10^{ - 6}}{m^3}$$
C. $$1.70 \times {10^{ - 6}}{m^3}$$
D. $$1.732 \times {10^{ - 6}}{m^3}$$
Releted Question 4

Pressure depends on distance as, $$P = \frac{\alpha }{\beta }exp\left( { - \frac{{\alpha z}}{{k\theta }}} \right),$$     where $$\alpha ,$$ $$\beta $$ are constants, $$z$$ is distance, $$k$$ is Boltzman’s constant and $$\theta $$ is temperature. The dimension of $$\beta $$ are-

A. $${M^0}{L^0}{T^0}$$
B. $${M^{ - 1}}{L^{ - 1}}{T^{ - 1}}$$
C. $${M^0}{L^2}{T^0}$$
D. $${M^{ - 1}}{L^1}{T^2}$$

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