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Which option correctly pairs a dimensionally similar quantity to \(x\) in \(e^x\)?

1. (a) (I) (i) (R)
2. (b) (II) (iii) (S)
3. (c) (III) (i) (R)
4. (d) (IV) (iii) (S)

Correct answer: (b) (II) (iii) (S)

Solution

In \(e^x\), the exponent must be dimensionless, so the quantity corresponding to \(x\) must have no dimensions. The correct pair is the one that matches this requirement. Hence option (b) is correct.

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