The correct answers are: He must have been sleeping soundly to completely miss the sound of shattering glass. He should have been patrolling the main gallery at the exact time the thief entered. He might have been listening to loud music on his headphones, which would explain a lot.
Must/might have been + verb-ing is used to make deductions about continuous actions happening at a specific time in the past.
Should have been + verb-ing expresses an unfulfilled expectation or obligation—something that was supposed to be happening in the past but wasn't.
Why the others are wrong:
Modals must always be followed by the base form of the auxiliary verb (have, not had). Additionally, the active past continuous form requires a present participle (patrolling, not patrolled).
Modal verb
If you've ever struggled with the difference between You must do this (strong command) and You should do this (advice) — or It might rain (possible) and It will rain (certain) — you've felt how much modal verbs do in English. They're how the language signals certainty, obligation, possibility, and politeness, and getting them right is what stops your speech from sounding either pushy or wishy-washy.
A modal verb is an auxiliary — can, could, may, might, must, shall, should, will, would — adding meaning around ability, permission, possibility, obligation, or speculation. Always followed by the bare infinitive (can swim, never can to swim), and never inflected for person.
Perfect tense
If you've ever written I am living here for ten years (should be have lived or have been living) — you've hit the perfect tense's main puzzle. English insists that "started in the past, still true now" lives in the present perfect, not the simple present. Get this clear and a whole class of common errors disappears.
The perfect aspect marks completion relative to a point in time, formed with have + past participle: I have eaten (present perfect), She had finished (past perfect), They will have arrived (future perfect). Combinable with progressive aspect (I have been working).
Progressive tense
If you've ever paused over I work in London vs I'm working in London and not been sure which to pick — you've hit the simple/progressive distinction. The first means it's your usual job; the second means it's temporary, going on right now. Native speakers reach for this distinction constantly without thinking; learners have to make it deliberate.
The progressive aspect marks ongoing action at a time of reference, formed with be + -ing: I am working, She was reading, They will be travelling. Marks temporary or in-progress events. Stative verbs (know, believe, own) don't normally take it.
Past tense
If you've ever told a story in English and felt the timeline get tangled — I came home, the dog ate, the cat slept — you've hit the limits of using simple past for everything. The past tense system has four forms specifically because real stories have layered timing: things that happened before other things, actions caught in progress, sequences of completed events.
The past tense has four English forms: simple past (I walked), past progressive (I was walking), past perfect (I had walked — earlier than another past event), past perfect progressive (I had been walking — ongoing up to a past point). Plus irregular verbs for the simple-past form.
C1 | Advanced
If you've ever sat through a lecture in English, written a complaint letter, or argued a point in a meeting and come out feeling actually understood — not just tolerated — you've felt what C1 looks like. The level matters because it's where most universities, certifications, and skilled-work environments draw their language line.
C1 is the advanced level in the CEFR framework, demanding fluent and flexible language: inversion for emphasis, mixed and advanced conditionals, formal subjunctive, cleft sentences, and complex nominal phrases — all used appropriately across registers.
Difficulty: Hard
If easy and medium questions are clicking but you still feel exposed in real conversation or formal writing, you've outgrown the basics. Hard material is where the gaps you didn't know you had show up: the distractor that "sounds right", the rule that interacts with another rule, the case where context changes the answer. It's where genuine fluency is built.
The Hard difficulty tag marks upper-intermediate to advanced challenges — typically B2 and above. Interacting rules, edge cases, plausible distractors, and contexts that require genuine understanding rather than surface pattern-matching.