〜ますか

1. 1Asks politely about someone's actions or habits, either as a yes/no question or with a question word such as 何時.Ex. 2
2. 2Asks politely about the listener's intention or plans, which can also serve as a direct invitation or offer.Ex. 1

This is the standard polite question form for verbs, used with strangers, colleagues, teachers, and in most everyday conversation that calls for です/ます speech. Because it asks about the listener's will, it can also invite or offer (一緒に食べますか), but it is more direct than ませんか, the usual softer invitation form. For noun or adjective predicates, 〜ですか is used instead.

• ませんかN5「ませんか」 is a negative question form used mainly to gently invite someone to do something together, and it can also politely ask 'is there...? / do you have...?'. 「〜ますか」 is for ordinary yes/no questions and wh-questions; for invitations, 「ませんか」 sounds softer and more natural.
• かN5「か」 is the sentence-final question particle, and 「〜ますか」 is simply 「ます」 plus 「か」. 「か」 can also follow 「です」, plain forms, nouns, and adjectives, and it forms the alternative question 「〜か、〜か」, whereas 「〜ますか」 is used only for polite verb questions.
• 〜は〜ですかN5「〜は〜ですか」 is used with noun predicates to ask 'Is X Y?' or 'Who/what/where is X?', while 「〜ますか」 attaches to verbs. Both are polite questions and both can take question words, but whether the predicate is a noun or a verb decides which one to use — they are not interchangeable.
• かいN4「かい」 attaches to verbs, adjectives, and nouns and is casual spoken language used with people you know well and juniors, while 「ますか」 attaches only to verbs and is polite. In yes/no questions the two are close in meaning but not freely interchangeable; with a question word 「かい」 usually switches to 「だい」, and it can also convey a rhetorical negative.
• でしょうN5「〜ますか」 politely puts a direct question to the listener, while 「でしょう」 with rising intonation seeks the listener's agreement with the speaker's own judgment and can also express conjecture. 「でしょう」 attaches to verbs, adjectives, and nouns, but 「ますか」 attaches only to a verb's 連用形 (continuative form), so the two are not interchangeable.

か is the question particle itself and attaches to many forms, 〜は〜ですか asks about noun and adjective predicates, and ますか is the polite question form for verbs; ませんか, the negative form, is the softer standard invitation. かい is a casual question on plain forms, and でしょう expresses conjecture or, with rising intonation, seeks confirmation of something the speaker already assumes, rather than asking neutrally.