Which of the following pairs of compounds are positional isomers?

First, we recall the definition of positional (position) isomerism. Two compounds are called positional isomers when (i) both possess the same molecular formula, (ii) both contain the same functional group, and (iii) the only difference between the two is the position of that functional group or of a multiple bond on the same carbon skeleton.

Now we inspect the two substances given in option 1. The first molecule in that pair is written as $$CH_3CH_2CH_2OH$$. Counting all atoms, we have

$$C:3,\; H:8,\; O:1 \;\; \Longrightarrow \;\; \text{molecular formula } C_3H_8O.$$

The second molecule in the same pair is written as $$CH_3CH(OH)CH_3$$. Again, counting every atom explicitly, we get

$$C:3,\; H:8,\; O:1 \;\; \Longrightarrow \;\; \text{molecular formula } C_3H_8O.$$

So both substances definitely satisfy the first requirement of having an identical molecular formula. Next we note that both contain the hydroxyl functional group $$-OH$$, so the functional group is also common. The only remaining point to check is the position of this $$-OH$$ group on the parent carbon chain.

In $$CH_3CH_2CH_2OH$$ the $$-OH$$ is attached to the terminal (number 1) carbon, giving the name propan-1-ol. In $$CH_3CH(OH)CH_3$$ the $$-OH$$ is bonded to the middle (number 2) carbon, giving the name propan-2-ol. Therefore the two differ solely in the location of the same functional group on an unchanged three-carbon skeleton; this is exactly the hallmark of positional isomerism.

For completeness, we compare this situation with the remaining options. In each of the other three pairs, either the molecular formula is different (violating condition (i)), or the carbon skeleton is rearranged (giving chain isomers rather than positional isomers), or the functional groups themselves are different (giving functional isomers). Hence none of those remaining pairs satisfies all three criteria listed at the outset.

Because only the pair in option 1 fulfils every one of the requirements for positional isomerism, we can confidently conclude that this is the correct choice.

Hence, the correct answer is Option 1.