NCERT Exemplar Solutions Class 11 Maths Chapter 1 Sets

Sets is the chapter where the Exemplar stops asking students to list elements and starts asking them to prove statements. The NCERT Exemplar Solutions for Class 11 Maths Chapter 1 Sets on this page solve all 58 questions of the chapter, step by step, according to the 2026-27 NCERT Exemplar.

Every solution in this Collegedunia set is prepared by subject experts, based on the 2026-27 NCERT Exemplar, and checked line by line against the official answer key.

Chapter 1 has a single long exercise, Exercise 1.3, that mixes six question formats. The solutions PDF runs to 141 pages and covers all of them.

• 58 questions solved: Short Answer, Long Answer, Objective, Fill in the Blanks, Match the Following and True/False.
• Five answer-key errors flagged: the printed key is wrong on Q4(iv), Q12, Q37, Q42 and Q51.
• Exam focus: useful for CBSE Boards, JEE Main, JEE Advanced and CUET.

Topics Covered in the Class 11 Maths Sets Exemplar

The Sets Exemplar reuses the textbook ideas inside harder wrappers. Most questions look short but need a proof or a counter-example, not a list. These are the topics the 58 questions are built on.

• Roster and set-builder form: converting between the two when the rule is a condition on x, not a plain count.
• Subsets and power sets: counting the subsets of a set with n elements, and telling ⊂ apart from ∈.
• Union, intersection and difference: proving set identities instead of only computing A ∪ B.
• Complement and De Morgan's laws: (A ∪ B)′ = A′ ∩ B′ and (A ∩ B)′ = A′ ∪ B′.
• Venn diagrams: shading a region and then naming it in set notation.
• Counting: n(A ∪ B) and the three-set inclusion-exclusion formula.

Important: the Exemplar treats a set identity as something you must prove, usually by taking an element x on the left and showing it lies on the right. A Venn diagram alone does not score full marks.

Exercise 1.3 Question-Type Breakdown for Sets

All 58 questions sit inside Exercise 1.3, grouped by format. The table below shows how the exercise is split, so students can plan practice by question type rather than solving straight through.

The Long Answer block (Q23 to Q28) carries the most marks per question and is the one most students skip. The Objective block is the largest single group, so it is worth a full practice session on its own.

Five Answer-Key Errors in the Sets Exemplar Every Student Must Know

The printed NCERT Exemplar answer key for Chapter 1 has five questions where the given answer is wrong. Each one is checked below against the book's own results. Students who copy the key blindly will learn the wrong answer, so read this section before self-checking.

Q4(iv) and the perfect number 496. The key marks the statement True. But 496 is a perfect number: its factors add to twice itself. Adding 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 + 496 gives 992, which is 2 × 496. So the correct answer is False.

Q12 is a misprint, not a hard proof. The book prints (A − B) ∩ (C − B) = A − (B ∪ C), which is simply not true. The intended statement is (A − B) ∩ (A − C) = A − (B ∪ C). The book contradicts itself here: Q52(iv) of the same exercise gives (A − B) ∩ (C − B) = (A ∩ C) − B, which is the real value of the left side.

Q37, Q42 and Q51. In Q37 the key says the two sets are equal, but 98 belongs to Y and not to X, so Y is strictly bigger and the answer is X ⊂ Y. In Q42 the correct total is n(S) + n(P) = 33 + 8 = 41, and 41 is not among the printed options (34, 31, 33, 30), so the key's 31 cannot be right. In Q51 the key prints A ∪ B′, but the correct fill is A ∩ B′, which is the same as A − B, exactly as Q20 of this exercise proves.

Key Formulas and Results Used in the Sets Exemplar

Sets has few formulas, but the Exemplar uses each of them in a proof. Students should know these by heart before starting Exercise 1.3.

Tip: the single most useful line in the whole chapter is A − B = A ∩ B′. It turns every difference question into a complement question, and it is the result that settles the Q51 error above.

Common Mistakes Students Make in the Sets Exemplar

The Exemplar twists trigger the same wrong reflexes every year. These four cost the most marks in Chapter 1.

• Mixing up ∈ and ⊂. An element belongs to a set; a set is contained in a set. {1} ⊂ A is right, {1} ∈ A usually is not.
• Proving an identity with a Venn diagram only. The Long Answer block wants an element-wise proof. The diagram earns the idea, not the marks.
• Forgetting the empty set. ∅ is a subset of every set, so it must be counted in every power set.
• Dropping the last term in three-set counting. The + n(A ∩ B ∩ C) term is added back, not subtracted, and skipping it is the most common word-problem slip.

How the Sets Exemplar Steps Up from the NCERT Textbook

The Exemplar does not add new topics. It asks the same ideas in a harder way, as the table shows.

How to Use the Sets Exemplar for Boards and JEE Preparation

Treat Exercise 1.3 as four sittings, not one. Finish the NCERT textbook exercises first, because the Exemplar assumes students can already write a set in both forms.

That is about 6 hours for the chapter. For JEE Main and JEE Advanced, the Objective block and the counting formulas matter most. For CBSE Boards and CUET, the Long Answer proofs and De Morgan's laws are the better use of time.

Practice Questions for Class 11 Maths Sets

After reading the solutions, students should test themselves on the same question types. The card below opens a set of solved practice questions with step-by-step answers for Sets.

Other Resources for Class 11 Maths Sets

Pair the Exemplar Solutions with the textbook solutions and the notes for full chapter revision. All the Sets resources are linked below.

NCERT Exemplar Solutions for Other Class 11 Maths Chapters

The full Class 11 Maths Exemplar set covers 14 chapters, 735 questions and 2,625 pages of solutions. Use the table to jump to any other chapter.