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

a) \frac{(P - Q)}{R}

b) PQ - R

c)\frac{ PQ}{R}
d)\frac{ (PR-Q^{2})}{R}

e) \frac{(R + Q)}{P}

Answers (1)

The answer is the option a) \frac{(P - Q)}{R}  and  e) \frac{(R + Q)}{P}

Explanation:

(i) The different physical quantities (P-Q) & (R+Q) in option a & e and never be added or subtracted. Thus, they will be meaningless.

(ii) In opt (d), dimensions of PR & Q^{2} may be equal.

(iii) in opt (b), the dimension of PQ may be equal to the dimension of R.

(iv) There is no addition or subtraction, which gives the possibility of opt (c).

Hence, opt (a) & (e).

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