In this English grammar question on pronoun agreement, identify the incorrect part of the sentence: "Every student should be asked to give their ideas on the subject."

Introduction / Context:
This question tests agreement between singular indefinite nouns and pronouns in English. The sentence is "Every student should be asked to give their ideas on the subject." While this form is common in conversational English, traditional grammar rules treat "Every student" as singular and expect a singular pronoun. Competitive exams usually follow this traditional rule and require agreement in number between antecedent and pronoun.

Given Data / Assumptions:

• The sentence refers to each individual student being invited to share ideas.
• Segment (a) is "Every student".
• Segment (b) is "should be asked to give".
• Segment (c) is "their ideas on the subject.".
• Segment (d) is "No error".
• We assume an examination context following conservative agreement rules.

Concept / Approach:
"Every student" is grammatically singular, similar to "each student". Under traditional rules, a singular pronoun such as "his", "her", or a combination like "his or her" should follow. The plural pronoun "their" does not agree in number with the singular subject. Therefore, the standard exam correction would be "Every student should be asked to give his or her ideas on the subject." Segment (c) is thus considered incorrect because of this mismatch.

Step-by-Step Solution:
Step 1: Identify the subject phrase "Every student", which refers to each student taken individually. Step 2: Recall that "every" and "each" normally take singular verbs and singular pronouns in formal grammar. Step 3: Check segment (b) "should be asked to give" and see that it correctly uses the modal "should" followed by passive infinitive. Step 4: Focus on segment (c) "their ideas on the subject." The pronoun "their" is plural. Step 5: Note that plural "their" does not agree with singular "Every student" under traditional exam rules. Step 6: Conclude that segment (c) is the incorrect part and that "his or her ideas" would be the exam preferred correction.

Verification / Alternative check:
Rewrite the sentence in a fully acceptable exam style: "Every student should be asked to give his or her ideas on the subject." Now the singular subject matches the singular pronoun. Compare with similar sentences like "Each employee must submit his or her report" or "Every candidate should bring his or her admit card." These patterns are widely taught in exam oriented grammar books. Although modern informal English often uses singular "they", competitive exams usually still treat it as incorrect in such structures, confirming that segment (c) carries the error.

Why Other Options Are Wrong:
Option (a) "Every student" is a standard way to speak about all students individually. Option (b) "should be asked to give" is a correct passive construction in the modal form. Option (d) "No error" is not acceptable because traditional agreement rules are not followed in segment (c).

Common Pitfalls:
In everyday conversation, many speakers use "they" and "their" as gender neutral singular pronouns, which is increasingly accepted in modern English. However, examination boards often continue to test older prescriptive rules, expecting forms like "his or her" after singular generic nouns. Candidates must be aware of this difference between natural speech and exam standards to score well in grammar sections.

Final Answer:
The incorrect part is option (c) "their ideas on the subject." Under exam rules it should be "his or her ideas on the subject." Therefore, the correct answer is "their ideas on the subject.".