Consider the following sentences: (i) After his surgery. Raja hardly could walk. (ii) After his surgery. Raja could barely walk. (iii) After his surgery. Raja barely could walk. (iv) After his surgery. Raja could hardly walk. Which of the above sentences are grammatically CORRECT?

The grammatically correct sentences are (ii) and (iv).

Detailed Explanation:
In English grammar, adverbs of degree or limitation such as "barely" and "hardly" have a standard position when used in sentences containing auxiliary or modal verbs (such as "could") and a main verb (such as "walk").

The standard word order is:
Subject + Auxiliary/Modal Verb + Adverb + Main Verb

Let's apply this rule to the given sentences:
1. In sentence (ii), "Raja could barely walk", the adverb barely is placed correctly between the modal verb could and the main verb walk.
2. In sentence (iv), "Raja could hardly walk", the adverb hardly is placed correctly between the modal verb could and the main verb walk.
3. In sentences (i) and (iii), the adverbs hardly and barely are placed before the modal verb could (i.e., "hardly could walk" and "barely could walk"), which violates the standard English word order and is grammatically incorrect in this context.

Therefore, only sentences (ii) and (iv) are grammatically correct.