The blank in this sentence refers to the purpose for which Rajesh likes books.
"To read" in option A is the to - infinitive of the verb 'read'. This indicates the purpose of the main verb 'likes'. Thus, this is correct.
"Had read" is in tense disagreement with the main verb 'likes' which is in present tense. Thus, this is incorrect.
"Read" in option C is incorrect as the verb requires a preposition to make it grammatical as the blank takes a direct object.
"Has read" is incorrect as it renders the sentence ungrammatical.
Thus, option A is correct.