Explanation:

Correct Answer is (b).The statement is not correct since ‘though’ is never followed by ‘yet’ in the principal clause. If ‘although’ had been used in its place, it would have been followed by ‘yet’ in the principal clause. Hence, ‘yet’ should be omitted from the given sentence so that the formation becomes correct.
Secondly, the verb 'boast' is followed by the preposition 'of' and not' about'.
The correct sentence will therefore be:
Though he is yet to do something significant in life, his parents always boast of his achievements to each and every person they come across.
This makes Option B the right choice among the given options.