In the following sentence, choose the segment that contains an error: Mothers keep on (A) to encouraging their children (B) to study. (C) No Error (D)

Introduction / Context:
This question tests knowledge of verb plus preposition plus gerund patterns. The phrasal verb "keep on" is followed by a gerund form of another verb. The sentence describes mothers repeatedly encouraging their children, and the structure after "keep on" must be grammatically correct.

Given Data / Assumptions:

Sentence parts: (A) Mothers keep on, (B) to encouraging their children, (C) to study, (D) No Error.

The phrase "keep on" suggests continuation of an action.

The word "encouraging" appears with an unnecessary "to" before it.

Concept / Approach:

The phrasal verb "keep on" is followed by a gerund, such as "keep on working" or "keep on smiling".

We do not say "keep on to working"; the preposition "to" is redundant and incorrect here.

Therefore, the natural expression is "keep on encouraging".

Step-by-Step Solution:
Step 1: Look at part A: "Mothers keep on". This is correct because "keep on" introduces a repeated or continuous action. Step 2: Look at part B: "to encouraging their children". The infinitive marker "to" is incorrectly placed before the gerund form "encouraging". Step 3: The standard structure should be "keep on encouraging their children", without "to". Step 4: Part C, "to study", is correct because "encouraging their children to study" is a proper pattern: encourage someone to do something. Step 5: Therefore, the error lies in part B.

Verification / Alternative check:
Correcting the sentence gives: "Mothers keep on encouraging their children to study." This new version follows two correct patterns: "keep on" plus gerund, and "encouraging someone to study". The corrected sentence reads smoothly and conforms to standard English usage.

Why Other Options Are Wrong:
Option a is wrong because "Mothers keep on" is correct and sets up the idea of repeated action. Option c is wrong because "to study" is correctly linked to the verb "encouraging". Option d is wrong because there is indeed an error in the sentence, so "No Error" cannot be chosen.

Common Pitfalls:
Students sometimes mix patterns and add "to" before a gerund where it does not belong, especially after multi word verbs like "keep on". A related mistake is using an infinitive after "keep", for example "keep to work" instead of "keep working". It is useful to remember that "keep on" is followed directly by the "-ing" form when describing ongoing actions.

Final Answer:
The correct answer is: B.