Sentence #1
I remember being taken to the zoo.
This is correct and sounds very normal to native ears. Being taken to the zoo functions as a noun phrase denoting the act in which you were taken to the zoo. Being is a gerund here. The passive construction here omits the subject; the implied subject is me (which a person would only say in order to create unusually strong emphasis).
It might help to look at some comparable sentences where the subject of being taken is explicit:
I remember John being taken to the zoo.
I remember him being taken to the zoo.
Notice that the subject of being taken is in the objective case. That's because it's also the object of remember, the main verb of the sentence.
Sorry, I have to tell you this
There's also an older school of thought that says the previous two sentences are incorrect and should instead be:
I remember John's being taken to the zoo.
I remember his being taken to the zoo.
In this parsing, the object of remember is being taken to the zoo. The subject of the gerund in this construction takes the possessive case (strangely enough).
Most fluent speakers today hear both him being taken and his being taken as correct. That is, people can parse both forms. The first form works by analogy with I helped him learn and the second form works by analogy with I helped his education.
Sentence #2
They are remembered taking me to the zoo.
This is actually correct, just a little unusual. Here, taking is a present participle, not a gerund. Taking me to the zoo modifies they, in the manner of a subject-complement. A comparable sentence might make this clearer:
Football players are usually drawn running with the ball.
In other words, in most pictures of football players, the football player is running with the ball.
The reason your example sentence is unusual isn't because of the grammar, it's because it's a little hard to imagine a situation where people would be remembered that way. But it's certainly possible and the sentence can be understood. Perhaps someone took a photograph of "them" while they were taking you to the zoo, they died long ago, and since then, many people have seen this photograph.
1#
Active voice: India expected to win the match.
I think the easiest way to read this sentence is to add one simple verb to act as a copulative:
India (is/was) expected to win the match.
Note that this sentence (or the original headline!) does not in any way indicate who expected India to win! It could be the press, the public at large, the writer of the article or some sports expert that said this in an interview.
Passive voice( book answer): It was expected by India that they would win the match.
Information is added that was not there in the original headline! The headline does not say that India expected to win, it say that India was expected to win. Nothing indicates who expected it!
My answer : India expected the match to be won.
That is an interesting expectation. It is equivalent to:
India did not expect a draw.
The original headline clearly states that expectations exist that India would win the match, your version states that India expect somebody will win.
Both the book and your version are introducing India as the party that expects something, but the headline does not have that information. In my view, both versions are incorrect.
Sentence 2 is more straightforward and I agree with the book version. The original sentence is also a complete sentence, not a headline.
I just realized that the original sentence does not have to be a (newspaper) headline.
The answer above is obviously reading it as if the sentence appeared as a headline, but of course India also simply be the subject in a normal active sentence. In that case, yes, India or the India team are indeed the subject, and they do expect to win the match.
The book answer is completely correct in that case, of course.
Your version still leaves the main verb in the sentence (expects) in the active voice. The main idea of the original sentence is India expects something. You have change something into an (almost) meaningless passive construct and you changed the meaning of the sentence!
The original sentence India expected (to win the match) should be changed into the passive as It was expected by India (that they would win the match).
You version does use a passive construction for (to win the match), but normally in these exercises you are expected (pun intended) to change the voice of the main clause of the sentence.
Apart from the fact that you do not change the main clause of the sentence, you also have removed the important information about who was expected to win the match! In your version, if India's opponent won, that would still be according to the expectation.
Best Answer
The book is giving you some screwy examples. "Let his game be played by him" is correct but weird. You would only say something like that to make very unusual emphasis.
Here are a couple things to know.
How to make the subordinate clause
To make the object of let into the subject of its own clause, you need to put it into the objective case and put the verb into the infinitive. That's why you say:
rather than:
Similarly, you would say Let him be helped by us, not
Let he is helped by us. However, this sentence is equally as weird as Let his game be played by him.Two (or three) senses of let
I think what the book is trying to do is teach two different senses of let at the same time that it's teaching you a tricky form of passive voice. Two of the main senses of the word let mean: (1) allow/permit the clause to happen; (2) suggesting or agreeing that "we" do the clause.
A classic example of the allow/permit sense: Let me go! is what a person who is being held against their will says to their captor.
A classic example of suggesting that "we" do something: Let's go! or Let's get started! is what you say when you want to start doing what you and your listener were just talking about doing together. This sense nearly always has us contracted to 's. (It has to be us rather than we because the subject of the clause has to be in the objective case, as above.)
Those are the most common and simplest examples to remember in order to learn the sound of the language. However, those examples can't be converted to a passive form.
Here's a more-realistic example in both active and passive form:
Possibly your book has confused the suggesting/agreeing sense with a third sense of let, expressing a wish. A classic example of using let to express a wish is: Let peace prevail on Earth. Here's a realistic version of what I think your book is trying to demonstrate:
or, passively again, without using let:
I can see why your book might have confused these senses. They really are a big, muddy mess. They are all variations on the basic sense of allow/permit, stretched to mean different things by repeated usage. The wishing sense can often be understood as the allowing sense and the suggesting sense simultaneously, where the request/suggestion is addressed to a deity, like Oh, God, please let there be peace on Earth.