In the following question, the sentence has a part given in brackets. Choose the alternative which best improves the bracketed part; if no improvement is required, select “no improvement”: You must (be mistake).

Introduction / Context:
This sentence improvement question checks your ability to use the correct verb form and pattern after the modal verb must. The sentence is expressing a strong logical conclusion that someone is wrong about something. You need to pick the grammatically correct way of saying this in English.

Given Data / Assumptions:

• Original sentence: “You must (be mistake).”
• We must improve “be mistake” so that the full sentence is natural and correct.
• Options: be mistakenly, be mistaken, be mistook, no improvement.
• Common usage: “You must be mistaken” is a standard expression meaning “I am sure you are wrong.”

Concept / Approach:
After modal verbs like must, we use the base form of a verb or an appropriate complement. In this context, we need an adjective describing the subject you. The correct adjective derived from the noun mistake is mistaken, meaning wrong in one's judgment or belief. Therefore, “You must be mistaken” is the correct form. “Be mistakenly” uses an adverb incorrectly, “be mistook” mixes tenses and forms, and “be mistake” is ungrammatical because mistake is a noun, not an adjective.

Step-by-Step Solution:
Recognise that must expresses strong logical probability or conclusion: “I am sure that …”.The phrase “You must be …” is followed by an adjective describing the state of the subject.Mistaken is the correct adjective meaning wrong, as in “I was mistaken.”Thus, “You must be mistaken” is the natural and grammatically correct expression.Eliminate the options that use incorrect word forms: mistakenly (adverb), mistook (past tense verb), or the original “be mistake” (noun).

Verification / Alternative check:
Read the corrected sentence: “You must be mistaken.” This clearly means that the speaker believes the other person is wrong about something. It is a standard polite formula in English. If we say “You must be mistakenly”, the sentence becomes incomplete and incorrect because an adverb cannot serve as the complement of be. “You must be mistook” mixes the structure and does not follow normal grammar rules. Keeping “You must be mistake” is plainly wrong because mistake is a noun in this position, not an adjective.

Why Other Options Are Wrong:
“Be mistakenly” is incorrect because mistakenly is an adverb and cannot describe the subject directly after be. It would need a structure like “You must have spoken mistakenly,” where it modifies a verb, not be. “Be mistook” tries to use the past tense of the verb mistake as a complement, which does not fit after be. “No improvement” leaves the ungrammatical phrase “be mistake” untouched. Therefore, these options cannot be correct in a standard English grammar test.

Common Pitfalls:
When learners see the noun mistake, they sometimes try to attach it directly after be, but English typically requires the adjective mistaken to describe a person who is wrong. Remember pairs like mistake (noun) vs mistaken (adjective), hope (noun/verb) vs hopeful (adjective), and care (noun/verb) vs careful (adjective). In this specific modal pattern, “must be mistaken” is a fixed, very common phrase that you should recognise instantly in exams.

Final Answer:
The correct improvement is be mistaken, so the full sentence should read: “You must be mistaken.”