Explanation:

Correct Option 4: to provide

Let’s look at the sentence containing blank 4 in context:

"The inter-city transport of parcels by road (3)______ amid the inability of the railways (4)______ adequate space..."

We are focusing on the phrase:

"the inability of the railways ___ adequate space"

Step-by-step:
The noun "inability" is typically followed by "to + base verb"

So the correct construction is:
"inability to provide"

Option analysis:
providing – Incorrect (gerund; doesn’t follow "inability")

provide – Incorrect (bare verb; needs "to")

provided – Incorrect (past tense; doesn't fit)

to provide – Correct (infinitive verb form used after "inability")

Correct Answer: to provide