The sentence format is - The Carpathian mountains have none of X and little of Y.

When we say evaluate something on two criteria X and Y, we say - Something has none of X OR little of Y -
That is, we evaluate on EITHER of the checks.

A. have none of the awesome majesties of the Himalayas and little mysticism of
Incorrect for above reason.
B. have none of the awesome majesties of the Himalayas and have little of the mysticism of
Parallelism issue - A of B vs X of Y of Z
C. are neither as awfully majestic as the Himalayas nor as little mystical as
Comparing the mystery of two things (not the minimal mystery). Correct is - The Carpathian mountains are not as mystical as Y.
D. are neither as awesome as the Himalayas nor as mysterious as
it's the majesty and not the awesomeness that is being compared in original sentence. Change in the meaning.
E. have neither the majesty of the Himalayas nor the mystery of
Looks correct.

IMO E

Abhi077
Could you please share the official explanation of this question?

The Carpathian mountains have none of the awesome majesties of the Himalayas and little mysticism of Japan's Mount Fuji.

A. have none of the awesome majesties of the Himalayas and little mysticism of

Eliminate
'awesome majesties' is wrong; (unless we're addressing a group of monarchs) ; 'majesty' is a singular non-countable noun

B. have none of the awesome majesties of the Himalayas and have little of the mysticism of

Keep
The structure is parallel:
...have
none of (something)
and
little of (something else)

C. are neither as awfully majestic as the Himalayas nor as little mystical as

Eliminate
'as little mystical' is not idiomatic. I can't even understand what it's trying to say.

D. are neither as awesome as the Himalayas nor as mysterious as

Eliminate
Changes the meaning; mysterious isn't the same as mystical

E. have neither the majesty of the Himalayas nor the mystery of

Eliminate
Same as D; changes the meaning

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_________________

A. have none of the awesome majesties of the Himalayas and little mysticism of -- This is a bit ambiguous with the parallelism. "have X (none of the awesome..) and (have) Y (little mysticism of..)" OR "have none of the X and (none of the) Y (little mysticism of..)". Eliminate because as we will see B removes this ambiguity.

B. have none of the awesome majesties of the Himalayas and have little of the mysticism of -- Keep for now.

C. are neither as awfully majestic as the Himalayas nor as little mystical as -- Japan's Fuji are not "little mystical". This is changing the meaning. We need to convey that CM do not have even have a small portion of the mystique that Japan's Fuji has.

D. are neither as awesome as the Himalayas nor as mysterious as -- Eliminate. Changes the meaning. "awesome" is only an adjective further describing "majesties" in the original sentence. That is missing here.

E. have neither the majesty of the Himalayas nor the mystery of -- I'm not sure frankly the reason of elimination of this. But B just sounds a whole lot better and accurate. For eg: we aren't saying that both are "equally" mysterious. But we are saying that CM does not even have the little mysticism of Japan's Fuji. There's a difference. I eliminate E for slight change in meaning.