Question

let us do it,..............?(tag question)

Answer 1

Explanation:

Well, it seems quite correct to me. 'Let's' appears to be a contraction of 'let us' (and historically it was, of course), but actually it has quite different grammar. 'Let's' is a first person plural imperative auxiliary. Look at how it forms its negative:

Let's play basketball.

Let's not play basketball.

'Let us', however, is an ordinary second person imperative of the main verb 'let' meaning "allow", followed by a direct object, which happens to be 'us'. So its negative is like any other negative:

Let us/them play basketball.

Don't let us/them play basketball. [cf. Don't make us play basketball.]

So 'let's' is first person, 'let us' second person. Thus the difference in tag questions. (The 'shall'/'will' distinction is a separate issue.)

This is complicated by the fact that 'let us' can be used for 'let's' in ornate speech: in religious or political contexts, for example.