IF \(P, Q\) and \(R\) are physical quantities, having different dimensions, which of the following combination/s can never be a meaningful quantity?
(a) \((P – Q)/R\)
(b) \(PQ – R\)
(c) \(PQ /R\)
(d) \((PR – Q^2)/R\)
(e) \((R + Q)/P\)
Choose the correct option:
1. (a), (e)
2. (a), (d), (e)
3. (a), (c), (d)
4. (b), (d)
(1) Hint: In addition or subtraction, the quantities should have the same dimensions.
Step 1: Find the inappropriate operations.
In this question, it is given that P, Q and A are having different dimensions, hence they cannot be added or subtracted, so we can say that (a) and (e) is not meaningful. We cannot say about the dimension of the product of these quantities, hence (b), (c), and (d) may be meaningful.
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