A Lot of work ____ to be done
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remains
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to remain
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remained
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nothing
'A lot of work' is treated as a singular subject, so it takes the singular verb 'remains' (A). The sentence indicates work that is still pending or left to be done. 'Remained' would be past tense, and 'to remain' is grammatically incorrect here.
"A lot of work remains to be done" is correct because "a lot of work" is a singular, uncountable-mass subject taking a singular present-tense verb, and "remains" fits as the finite verb of the main clause. "To remain" is an infinitive and can't stand alone as the sentence's main verb. "Remained" is past tense, which doesn't fit the present, ongoing sense implied (work is still pending now). "Nothing" isn't a verb at all and doesn't belong in the blank. The idiom "much/a lot of work remains to be done" is a standard fixed construction in English.