Answer A is grammatically and logically incorrect. The phrase "attacks recently as dated and culturally biased" does not convey the intended meaning that it is the personality inventory that is dated and culturally biased. Instead it is actually difficult to determine which part of the sentence the phrase following "as" modifies.
B is correct. It conveys the intended meaning and does not contain any flaws.
C is also awkwardly structured. The phrase "revision for receiving much recent attack" is not correct.
Answer D changes the meaning because of the use of the past tense instead of the intended present meaning.
Answer E also changes the meaning as it states that the inventory is going to be revised in the FUTURE.

neer.king wrote:The Minnesota Multiphase personality inventory, a test developed in the 1930s to assess character, attitude, and behavior, is finally being revised after many attacks recently as dated and culturally biased.

A) is finally being revised, after many attacks recently as dated and culturally biased.
B) has recently been attacked as dated and culturally biased and is finally being revised.
C) is finally under revision for receiving much recent attack as dated and culturally biased.
D) was finally revised recently because it is being attacked as dated and culturally biased.
E) is finally to be revised after recent attack as dated and culturally biased.

Please suggest

A. many attacks recently as dated is awkward

C. Same as A. Plus it says that revision is happening for the much recent attack (not for any other attack), while the fact is that MMPI has attracted attacks recently and hence is being revised. Slight change in the meaning here.

D. Was incorrect

E. To be revised is not correct here. It indicates future event while the MMPI is being revised as of now.

B is correct.