Usage of evidence of and evidence that depends on the context.
evidence of - supports something
evidence that - proves something. Hope you get that.

A - them - them can refer to north american indians or calendars - wrong, no clear referent. Basing them is redundant, them here referring to the calendars again is unnecessary.
B - The calendar stick provide evidence of North America Indians - Totally absurd - changes the meaning as if the calendar stick is the evidence for the existence of North American Indians
C - them - same problem as in A - no clear referrant
D - same problem as in B - Calender stick as the evidence for two things X (North American Indians) and Y (their development of calendars) - wrong as it changes the meaning

E is the only choice which is error free

IMO E.

First of all I would request you to underline the relevant parts under study. As I can infer from B,C,D and E - "on systematic astronomical observation" cannot be in underline portion. So please check before posting to avoid confusion.

Now coming to you doubt:

nikhilgupta wrote:
1) Should evidence be followed by 'of'

This is dependent what you want to convey.

Here B,C and D ( I am just approaching this problem from your perspective, there are other error in B,C and D, I am ignoring that), is wrong because we are not sure what the prepositional modifier : "of the development of .... " is modifying. IS it an adverb modifier for the verb "provide" or is it a noun modifier of the noun - "evidence" ?

As per the meaning of the sentence : X provided the first evidence Y.

Please note here : X is the subject and Y completes the sentence by telling us what is the first evidence.
X did not only provided the "first evidence" but it provided the "first evidence of something" - the technical name for this is called object complement. So we need a noun clause here and "that...." exactly is suitable here.

When you are using evidence as a verb, you can use a prepositional phrase (by, of, for, with... ) to modify "evidence" -

So we can go for A and E.

nikhilgupta wrote:
2)Is usage of 'them' incorrect in A,B and C

There are two plural noun here : From meaning point , yes "them " do refer to "calendars". This is not a split here anyway.
I think there is a meaning issue in this : the first one is more logical from what I can get from the meaning wants to convey.

1. I created a rock sculpture based on my past experience.
2. I created a rock sculpture and based them on my past experience.
3. I created a rock sculpture, basing them on my past experience.

2 and 3 are quiet different and illogical in meaning from 1.

Hope this helps !!

Thank you guys, BTW I cannot find the "thank" button

sam2304 wrote:Usage of evidence of and evidence that depends on the context.
evidence of - supports something
evidence that - proves something. Hope you get that.

IMO E.

Hii sam,

After long, I got the privilege to comment on your post. Great explanation. But I have a doubt here.

I could not realize the difference between supporting something and proving something - We prove a theory X to support the fact that theory X exists. Isn't it ?

Thanks !!

Hey avik

Welcome back after the new year break.

evidence of
e.g His trembling was evidence of his fear - Here we support/indicate something

evidence that
e.g the above sentence is to prove something or arrive at a conclusion
A calendar stick is the evidence that North American Indians used advanced full year calendars

Hope that makes sense and i am right. Maybe i used inappropriate words.

sam2304 wrote:Hey avik

Welcome back after the new year break.

evidence of
e.g His trembling was evidence of his fear - Here we support/indicate something

evidence that
e.g the above sentence is to prove something or arrive at a conclusion
A calendar stick is the evidence that North American Indians used advanced full year calendars

Hope that makes sense and i am right. Maybe i used inappropriate words.

Ok...I got the structural difference now ( apart from the one i mentioned above)

If you want to modify the noun "evidence" with a clause : use "that".

A calendar stick is the evidence that North American Indians used advanced full year calendars
The broken window was evidence that a burglary had taken place.

If its just a noun phrase use a preposition as desired :

His trembling was evidence of his fear.
Scientists weigh the evidence for and against a hypothesis.

The meaning difference mentioned by you is quiet subtle. If you can understand the difference, go for it.