I have some questions if you don't mind...

1) ..............., he decided not to swim.

a) The lake is very hot

b) the pond being so cold

c) he has been feeling very ill.

d) since the weather is quite good

e) As he doesn't like going out.

The answer key shows "b" is correct. But I don't understand why. That sentence seems wrong to me. (c can be acceptable to me)

The tense used in c is wrong – if it was “As he HAD been feeling very ill”, then it would have been correct as well. Since the pond was so cold, he decided not to swim is correct and is basically what choice b means by “The pond being so cold”. The “since/as in choice b is not stated or implicit.
2) If you had taken my advice those days .................. now.

a) You wouldn't be living in the streets.

b) You could be rich.

I know "a" is correct but not "b"? Again, it’s to do with the tense being used. “If you HAD taken my advice in those days, then you COULD HAVE been rich now” would be the correct form of choice b. The only way “you COULD be rich” is a correct answer would be the following: “If you take my advice, you could be rich”
So choice b would only hold in the present tense. Notice “those days” doesn’t come in then.
3) The fact that space exploration has increased since the 1960s............................................. ..... ....

a) is a representative of our small desire to learn more about our solar system.

b) Indicates that we are very enthusiastic to learn about our solar system.

The answer is "a" but I think "b" is correct.

Ok over here, I don’t think either choice is very good. I think in choice a, the “a” needs to be dropped out so the sentence would read as: “The fact that space exploration has increased since the 1960s is representative of our small desire to learn more about our solar system” Maybe the “a” being there is a typing error.

For b to be correct, it should be “we have become very enthusiastic” so it would read as “indicates that we have become very enthusiastic to learn about our solar system.”
4) ..........everyone developing many different skills, specialization came about as a result of agriculture and this gave rise

to the beginning of technology.

a) Notwithstanding b) Even though c) Nevertheless d) Although e) Instead of

Which one is correct I couldn't find.

None of these choices are correct. For this sentence to be correct, it has to be because of everyone developing new skills, or due to the fact that everyone was developing new skills, that specialization came about.

So the correct choice would be any of the following:
- As everyone was developing many different skills, specialization came about…
- Since everyone was developing many different skills, specialization came about…
- Due to the fact that everyone was developing many different skills, specialization came about…
- Because everyone was developing many different skills, specialization came about…

Thanks.


Hope that helps! Ask me in case you don’t understand any of this. 
AFFAN RASHID