Step 1: Look at what the sentence is describing.
It describes a musician who received a formal award and was given a royal title, Rai Bahadur. Both halves of the sentence are talking about recognition and honour given to this person.
Step 2: Choose the word for the first blank.
A musician who has been given a major award is best described as "accomplished", meaning highly skilled and successful. This is a standard collocation, an "accomplished musician", used to describe someone with a proven, polished body of work.
Step 3: Choose the word for the second blank.
The second half says he received the title of Rai Bahadur. The verb that goes naturally with receiving a title as recognition is "honoured", as in "honoured with the title of", which is exactly how such conferrals are described in English.
Step 4: Eliminate the other options.
"Outstanding ..... popularized" fails because a title is conferred on a person, it does not "popularize" them, that verb describes making something widely known, not bestowing a title. "Underestimated ..... declared" is contradictory, since someone who wins an award is not underestimated, and titles are conferred or bestowed, not simply "declared" on a person. "Impressive ..... assigned" does not fit either, titles are not "assigned" the way a task is assigned. "Effective ..... delivered" is equally awkward, a title is not "delivered" to someone.
Step 5: Conclude.
The pair that fits both halves of the sentence smoothly is Accomplished ..... honoured, option (c).