NCERT Class 11 Mathematics Exemplar Problem Solution PDF

The NCERT Exemplar Class 11 for Maths is a resource important for the students to help them with extra practice. The questions in exemplar are challenging and so prepare students for both CBSE boards and competitive exams properly. 

The exemplar focuses on application and high-level thinking questions which are designed to improve analytical thinking and logical reasoning ability of the students. 

Download NCERT Exemplar Class 11 Maths 

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Complete Overview: NCERT Maths Exemplar Class 11

The Class 11 Maths Exemplar is a supplementary resource for practice which is made by NCERT. It is to support students to understand maths in depth with the help of challenging questions. It provides questions that are beyond the textbook questions and focus more on competency-based, activity-based and HOTS questions. 

These questions are importantly useful for students to set the base for higher classes and competitive exams. 

Key highlights of the NCERT Class 11 Maths Exemplar:

• Covers all chapters from the NCERT Class 11 Mathematics syllabus
• Includes MCQs, very short answer, short answer, and long answer questions
• Focuses on concept-based and application-oriented problems
• Improves logical reasoning and analytical thinking skills
• Recommended by teachers for advanced practice and exam readiness

Chapter-wise Maths Exemplar Questions

The Maths Exemplar for Class 11 includes different types of questions that test the thinking level along with application skills of the students. 

Below are some questions with solutions:

Chapter 1: Sets

Q: Let A = (1,2,3,4) and B = (3,4,5,6). Then (A − B) ∪ (B − A) =

1. (1,2,5,6)
2. (1,2)
3. (3,4)
4. (5,6)

Answer: A
Reason:
A − B = (1,2), B − A = (5,6) - Union = (1,2,5,6)

Chapter 2: Relations and Functions

Q: Which of the following relations is both symmetric and transitive?

1. ((1,2), (2,3))
2. ((1,2), (2,1))
3. ((1,2), (2,1), (1,1))
4. ((1,1), (2,2))

Answer: D
Reason:
Only identity relation satisfies both properties fully.

Chapter 3: Trigonometric Functions

Q: If sinθ + cosθ = √2, then θ =

1. 30°
2. 45°
3. 60°
4. 90°

Answer: B
Reason:
sin45° + cos45° = √2

Chapter 4: Mathematical Induction

Q: The sum 1³ + 2³ + … + n³ equals:

1. [n(n+1)/2]²
2. n²(n+1)/2
3. n(n+1)/2
4. n(n+1)(2n+1)/6

Answer: A
Reason: Known identity: sum of cubes = square of sum

Chapter 5: Complex Numbers

Q: If z = (1 + i)/(1 − i), then |z| =

1. 1
2. √2
3. 2
4. 0

Answer: A
Reason:
Simplify - z = i - |z| = 1

Chapter 6: Linear Inequalities

Q: The solution of |x − 2| < 3 is:

1. x > 5
2. −1 < x < 5
3. x < −1
4. −5 < x < 1

Answer: B
Reason:
|x−2| < 3 - −3 < x−2 < 3 - −1 < x < 5

Chapter 7: Permutations and Combinations

Q: Number of ways to arrange the letters of “LEVEL” is:

1. 20
2. 30
3. 60
4. 120

Answer: B
Reason:
5! / (2!×2!) = 120/4 = 30

Chapter 8: Binomial Theorem

Q: The middle term in (1 + x)⁶ is:

1. 20x³
2. 15x³
3. 10x³
4. 6x³

Answer: A
Reason:
Middle term = 6C3 x³ = 20x³

Chapter 9: Sequences and Series

Q: Sum of first n odd numbers is:

1.  n²
2. n(n+1)
3. n(n−1)
4. n³

Answer: A
Reason:
Standard result: sum of n odd numbers = n²

Chapter 10: Straight Lines

Q: Equation of line with slope 2 passing through (1,3):

1. y = 2x − 1
2. y = 2x + 1
3. y = x + 2
4. y = 3x + 1

Answer: B
Reason:
y−3 = 2(x−1) - y = 2x + 1

Chapter 11: Conic Sections

Q: Eccentricity of a circle is:

1. <1 but not 0
2. >1
3. 1
4. 0

Answer: D
Reason:
Circle has e = 0

Chapter 12: 3D Geometry

Q: Distance between (0,0,0) and (1,2,2):

1. 3
2. √5
3. √9
4. √6

Answer: A
Reason:
Distance = √(1+4+4) = √9 = 3

Chapter 13: Limits and Derivatives

Q: lim x-0 (1 − cosx)/x² =

1. 2
2. 1
3. 1/2
4. 0

Answer: C
Reason:
Standard limit = 1/2

Chapter 14: Mathematical Reasoning

Q: The negation of “All A are B” is:

1. Some A are B
2. No A are B
3. Some A are not B
4. All B are A

Answer: C
Reason:
Logical negation rule

Chapter 15: Statistics

Q: If mean = 10 and number of observations = 5, sum =

1. 50
2. 15
3. 10
4. 5

Answer: A
Reason:
Mean = sum/n - sum = 10×5 = 50

Chapter 16: Probability

Q: Probability of getting a prime number on a die:

1. 1/3
2. 1/6
3. 1/2
4. 2/3 

Answer: C
Reason:
Primes = (2,3,5) - 3/6 = 1/2

More Resources for Class 11

NCERT Exemplar Class 11

‍NCERT Books Class 11 Maths

‍CBSE Syllabus Class 11 Maths‍

Important Questions Class 11 Maths‍

Class 11 Maths Practice Papers

How to Create a Week-wise Plan for Exemplar Practice 

Creating a weak-wise practice for Maths exemplar for 11 is important as it will help them get in the habit of solving questions. What is even more important is that, it will break the pattern when it will get boring by just studying through the NCERT Textbook Class 11 Maths. Solving exemplar questions will give them a feeling of accomplishment every week. 

• Choose chapters that you are studying from the textbook now and practice them. This will help in remembering the content in a better way. 
• Pick one chapter from the exemplar and give it focused 30-45 minutes. Go one by one. 
• Go from easy to medium to difficult questions as that will help make a better flow of practice. You will gain confidence and then move to the next stage with the confidence gained. 
• Do not do mixed practice on the weekdays. Keep that for the weekends when you have more time. 

Some Benefit of NCERT Exemplar Maths Class 11

Class 11 Maths Exemplar does not contain just questions but also level-wise support to students so that the practice does not feel scary. It helps in concept retention and also trains the mind of students for any challenges that they have to face in the exam. It also trains them to think logically and solve problems in a more organised manner. 

Here are some more benefits of using the Maths exemplar:

• Increase hold on maths concepts by making students practice something different than the basic textbook problems. 
• Get students ready for competitive exams like JEE by providing challenging questions, which increases the capacity of  thinking. 
• Increased accuracy and speed as regular practice of critical problems trains the mind to solve questions efficiently. 
• Increase confidence by helping students move from easy to difficult questions in an organised manner. By this, students can start slow and move smoothly to the next level at their own pace.  

FAQs

Q1. What is NCERT Exemplar for Class 11 Maths?

Ans. NCERT Exemplar Class 11 Maths is a supplementary book that contains advanced and application-based questions designed to improve conceptual understanding.

Q2. Are NCERT Exemplar questions important for Class 11 exams?

Ans. Yes, they help students practice higher-order thinking questions and improve exam performance.

Q3. Is the NCERT Class 11 Maths Exemplar available chapter-wise?

Ans. Yes, students can download it as a full book or chapter-wise PDFs.

Q4. Are exemplar questions tougher than NCERT textbook questions?

Ans. Yes, they are generally more challenging and focus on deeper understanding.

Q5. When should students solve NCERT Exemplar?

Ans. Students should solve it after completing the NCERT textbook to strengthen their concepts.