The only one that really seems grammatically wrong to me is #2a. However, the only one whose meaning I understand is #2b. In 1a and 1b, the word "would" confuses me. "Might" seems like a more natural choice for a modal verb. "Would" makes it sound like a habitual search, one that is repeated over and over. But, "they could find nobody" makes it sound like a one time search, so I'm confused. There might be some contexts though in which "would" makes sense. 2a seems ungrammatical because "studied hard" is used to modify "Tom", and that doesn't make sense. "Studied hard" is not an adjective phrase that can modify a person. It could modify a book, but not a person: "That book was studied hard in the class". 2b is a good sentence. The first part of the sentence is an adverbial clause, and "hard" is used as an adverb. That is correct. "Hard" can be used as an adverb. But, if you used a word that LOOKS more like an adverb, the sentence would sound clearer: Diligently as Tom had been studying..., he STILL didn't obtain...

1a and 1b are both potentially correct, depending on the unseen wider context. But if someone is asking you to pick one, 1a is the safer bet, because it is much more likely to match the intended context. 2a and 2b are both bad grammar! Both are roughly as bad as each other, so I can't pick one. Sorry. Whoever wrote this test needs an English lesson themselves. 3: You are probably right, but it depends on the unseen wider context. If this is the limit of the context provided, it would be more accurate to say it means "new techniques were introduced, and it was the introduction itself, which had varying degrees of success" - indeed the varied success is not necessarily referring to the outcomes that the techniques attempted to achieve, although this is most likely the case.

1a I prefer to 1b. However, they both are fine. 2a and 2b are both awful grammar, though 2b is better. Take the IN out of 2b (since 2012 not since in 2012) and it is just about ok. It remains awkwardly wordy. Change something! Jonathan and Dan have suggestions. For 3, I think the 'the' is a mistake. ...with varying degrees of success... is a set expression. The degree of success was anything from 'wow! it works' .... to 'oh dear, try again'. The original does not make sense. Well, you could extract meaning, if you try hard. "With the varying degrees of success (which we tried, tested, recorded, and analysed) we then worked out new techniques.... to try again???? Nah! I think the 'the' is a mistake. I have tried to answer - WITH VARYING DEGREES OF SUCCESS.

Query 1: * 1a. "Search as they would, they could find nobody in the house." * 1b. "Search as they would in the house, they could find nobody." Answer: 1a is the correct option. The phrase "Search as they would" is a set structure that means "No matter how hard they searched." The second version, 1b, is awkward because it interrupts the flow of this fixed phrase. Query 2: * 2a. "Studied hard as he in 2012, Tom still didn't obtain his college diploma." * 2b. "Hard as Tom had been studying English since 2012, he didn't obtain his college English diploma in 2022." Answer: Neither 2a nor 2b is grammatically correct. * Corrected version of 2a: "Hard as he studied in 2012, Tom still didn't obtain his college diploma." * Corrected version of 2b: "Hard as Tom had been studying English since 2012, he still didn't obtain his college English diploma in 2022." Query 3: * Original sentence: "New techniques were introduced with varying the degrees of success." Answer: Your understanding is close but not quite correct. The phrase "with varying degrees of success" is an idiomatic expression that means the success varied—some techniques were more successful than others. The sentence does not imply that the techniques themselves varied the success, but rather that the level of success achieved by using the techniques varied. So, the correct interpretation would be: * "New techniques were introduced, with varying degrees of success" means the new techniques had different levels of success. This phrase is not suggesting that the techniques caused the variation in success; instead, it notes that the outcomes were not uniformly successful.