In this question on Direct and Indirect Speech, convert the sentence "Nasir asked his tutor, 'Do I need to learn these formulas?'" into its correct Indirect Speech form.

Introduction / Context:
This question checks your ability to report a yes or no type question that uses need to or have to to express necessity. The original direct question is: Nasir asked his tutor, "Do I need to learn these formulas?" You must choose the indirect version that correctly handles the question structure, the modal meaning of need and the demonstrative these formulas.

Given Data / Assumptions:

- Speaker: Nasir. - Listener: his tutor. - Direct question: Do I need to learn these formulas? - Reporting verb: asked, already in the past tense. - Demonstrative: these formulas refers to formulas near in context.

Concept / Approach:
A yes or no question in direct speech is reported using if or whether, and the auxiliary do is removed in indirect speech. The structure Do I need to learn changes to whether or if he needed to learn or had to learn. Examinations often prefer had to for necessity in reported speech. The pronoun I refers to Nasir and changes to he. The demonstrative these becomes those to reflect the greater distance in indirect speech. The verb order also changes from question form to normal statement order, with the subject before the verb.

Step-by-Step Solution:

Verification / Alternative check:
To verify, reverse the process. From Nasir asked his tutor if he had to learn those formulas, change he back to I, had to learn back to need to learn, and those formulas back to these formulas. Then reintroduce the auxiliary do and add a question mark. The sentence becomes: Nasir asked his tutor, "Do I need to learn these formulas?" which matches the original. This confirms that the indirect version is correct.

Why Other Options Are Wrong:
Option A uses has to learn, which is present tense, not matching the past reporting. Option C and option D are ungrammatical constructions that misuse did not and had not in strange positions. Option E, using whether he needed to learn those formulas, is grammatically acceptable in many contexts, but the exam version in the options uses had to learn, and the original set of choices makes option B the closest to the textbook rule. Option B correctly uses if, the pronoun he, the phrase had to learn and those formulas, making it the best answer.

Common Pitfalls:
Students sometimes keep do or does in the reported clause, which is incorrect because auxiliary verbs used only for question formation disappear in indirect speech. Another mistake is to keep the pronoun I, forgetting to change it to he or she. Learners also confuse need to with have to, but in reported speech both often move to had to for past necessity. Finally, demonstratives like these and those must be watched carefully so that the sense of distance and time is correctly maintained.

Final Answer:
The correct indirect speech sentence is Nasir asked his tutor if he had to learn those formulas.