Concept:
Grammar questions require identifying errors related to usage, prepositions, articles, punctuation, and sentence structure.
Step 1: Examine sentence A.
\[
\text{The article should not exceed hundred words.}
\]
This sentence is acceptable in competitive exam usage though “a hundred words” is more formal.
Hence, A is treated as correct.
Step 2: Examine sentence B.
\[
\text{I can accept anything than dishonesty.}
\]
The correct expression is:
\[
\text{anything except dishonesty}
\]
Hence, B is incorrect.
Step 3: Examine sentence C.
The comma after “animals” is unnecessary but does not make the sentence grammatically wrong in the intended exam sense.
Hence, C is treated as correct.
Step 4: Examine sentence D.
The phrase:
\[
\text{influence for his family}
\]
is incorrect.
Correct usage:
\[
\text{influence on his family}
\]
Hence, D is incorrect.
Step 5: Examine sentence E.
This sentence is grammatically correct.
Step 6: Identify incorrect sentences.
Incorrect sentences are:
\[
B \text{ and } D
\]
Step 7: Conclusion.
Thus, the correct answer is:
\[
\boxed{\text{B and D Only}}
\]