NCERT Class 10 Mathematics Exemplar Problem Solution PDF

The NCERT Exemplar Class 10 Maths book is a highly effective resource to improve problem-solving skills and boost board exam scores. It focuses on conceptual clarity, logical thinking, and application-based questions beyond the textbook.

Relying only on NCERT exercises is often not enough for top marks. Exemplar questions are more challenging, involving multi-step and concept-driven problems aligned with the exam pattern.

Here, you’ll find chapter-wise PDFs, key questions with solutions, and effective strategies. For better accuracy, speed, and clarity in Maths, this resource is essential.

Class 10 NCERT Maths Exemplar PDF 

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Download NCERT Class 10 Maths Exemplar: Chapter-wise .

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NCERT Exemplar Class 10: Overview

As per the CBSE curriculum, the NCERT Exemplar Class 10 Maths book is designed to build strong analytical and problem-solving abilities. It goes beyond formulas and focuses on how to apply concepts in different situations.

The Exemplar includes multiple types of questions such as MCQs, very short answer questions, short answer questions and long answer problems. These questions are carefully designed to test reasoning, accuracy and step-wise clarity.

All questions are aligned chapter-wise with the NCERT Maths textbook, allowing students to practice them alongside their regular studies. This ensures better retention and structured revision.

Key Highlights Class 10 NCERT Maths 

• Chapter-wise Exemplar PDFs for easy access
• Important questions with detailed solutions
• Focus on higher-order and application-based problems
• Aligned with CBSE exam pattern
• Helps improve speed, accuracy, and conceptual clarity 

Latest Updates in NCERT Exemplar Class 10 Maths

NCERT Exemplar Maths is aligned with CBSE curriculum, making it relevant for Class 10 preparation.

Alignment with CBSE competency-based pattern

• A larger portion of board exam questions now test application and real-life problem-solving, similar to Exemplar problems. 
• CBSE has case-study and assertion-reason questions, and Exemplar practice helps students adapt to these formats. 

Focus on HOTS and application-based questions

• Exemplar includes a high number of HOTS (Higher Order Thinking Skills) questions that test reasoning and analytical ability.
• Questions are designed to go beyond direct formulas and require multi-step problem solving and logical thinking.
• Helps students prepare for non-routine and twisted questions commonly seen in board exams.

Increased relevance for board exams

• Most CBSE Class 10 Maths papers are directly based on NCERT concepts, making Exemplar a key practice source.
• With no major syllabus changes, Exemplar remains fully aligned with the current curriculum. 
• Units like Algebra, Geometry, and Trigonometry carry the highest weightage, and Exemplar provides strong practice for these.
• Regular practice ensures better performance in case-based, long-answer, and competency-driven questions in boards.

Chapter-wise Exemplar Questions

The NCERT Maths Exemplar contains a wide variety of questions that test conceptual clarity and application skills. Students will find MCQs, case-based problems, short answers and long numerical problems in every chapter.

Below are important Exemplar-style questions (one from each chapter) with clear solutions.

Real Numbers

Q. Prove that √5 is irrational.

Ans. Assume √5 is rational. Then √5 = p/q (where p and q are coprime).

⇒ 5 = p²/q² ⇒ p² = 5q²

So, p² is divisible by 5 ⇒ p divisible by 5
Let p = 5k
⇒ p² = 25k² = 5q² ⇒ q² = 5k² ⇒ q divisible by 5

Thus, p and q have a common factor 5, which contradicts the assumption.
Hence, √5 is irrational.

Polynomials

Q. If α and β are zeroes of x² − 7x + 10, find α + β and αβ.

Ans. For ax² + bx + c:
α + β = −b/a = 7
αβ = c/a = 10

Pair of Linear Equations in Two Variables

Q. Solve graphically: 2x + y = 4 and x − y = 1.

Ans. From second: y = x − 1
Substitute: 2x + (x − 1) = 4
3x = 5 ⇒ x = 5/3
y = 5/3 − 1 = 2/3
Solution = (5/3, 2/3)

Quadratic Equations

Q. Find the nature of roots of 2x² − 4x + 2 = 0.

Ans. D = b² − 4ac = (−4)² − 4×2×2 = 16 − 16 = 0
Roots are real and equal

Arithmetic Progressions

Q. Find the sum of first 20 terms of AP: 3, 7, 11,...

Ans. a = 3, d = 4
Sₙ = n/2 [2a + (n−1)d]
S₂₀ = 20/2 [6 + 19×4]
= 10 [6 + 76] = 10 × 82 = 820

Triangles

Q. Prove that in a triangle, the side opposite to the larger angle is longer.

Ans. Let ΔABC with ∠A > ∠B
Then BC > AC
Hence proved using triangle inequality property.

Coordinate Geometry

Q. Find the coordinates of the midpoint of (2,4) and (6,8). 

Ans. Midpoint = [(2+6)/2, (4+8)/2] = (4,6)

Trigonometry

Q. Prove: (1 − tan²θ)/(1 + tan²θ) = cos2θ

Ans. Using identities:
(1 − tan²θ)/(1 + tan²θ) = cos2θ

Applications of Trigonometry

Q. A ladder leaning against a wall makes an angle of 60° with ground. If ladder length is 10 m, find height reached.

Ans. sin60° = h/10
h = 10 × √3/2 = 5√3 m

Circles

Q. Prove that the tangent at any point of a circle is perpendicular to the radius.

Ans. Let PT be tangent at P and OP radius
Then OP ⟂ PT
(Proved using property of tangents)

Constructions

Q. Construct a triangle with sides 5 cm, 6 cm, 7 cm.

Ans. Draw base = 7 cm
From endpoints draw arcs of radius 5 cm and 6 cm
Intersecting point gives third vertex
Join to complete triangle

Areas Related to Circles

Q. Find the area of a sector of radius 7 cm and angle 60°.

Ans. Area = (θ/360) × πr²
= (60/360) × (22/7 × 49)
= (1/6) × 154 = 25.67 cm²

Surface Areas and Volumes

Q. Find curved surface area of a cylinder with radius 7 cm and height 10 cm.

Ans. CSA = 2πrh
= 2 × 22/7 × 7 × 10 = 440 cm²

Statistics

Q. Find mean of data: 2, 4, 6, 8, 10

Ans. Mean = Sum / n = 30/5 = 6

Probability

Q. A die is thrown. Find the probability of getting a number greater than 4.

Ans. Favourable outcomes = {5,6} = 2
Total outcomes = 6
Probability = 2/6 = ⅓

NCERT Exemplar Maths vs NCERT Textbook (Class 10)

Understanding the difference between the NCERT Textbook and Class 10 NCERT Exemplar is important for smart preparation. Both are essential, but they serve different roles in strengthening your Maths performance.

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For best results, start with the NCERT textbook to build clarity, then move to Exemplar to strengthen accuracy, speed, and problem-solving ability.

The “Reverse Solving” Technique Using NCERT exemplar class 9 Mathematics

Most students solve Maths in a forward direction, but toppers often think differently. They work backward to understand the logic behind every step. The “Reverse Solving” technique helps you break down complex Exemplar problems and truly see how answers are built. It’s a powerful way to sharpen your thinking and improve accuracy in exams.

• Stop jumping straight to solving. Start by reading the final answer first and challenge yourself to figure out how it was reached.
• Work backward step-by-step and identify the exact formula or concept used at each stage.
• Ask yourself: “What must the previous step look like to reach this result?” This builds deep logical thinking.
• Focus on the method, not just the calculation. Reverse solving trains you to see patterns in problem-solving.
• Take one solved Exemplar question and try creating a similar question by reversing the logic.
• Cover the steps and reconstruct the solution from the final answer. This boosts confidence and accuracy.
• Use this technique especially for algebra and trigonometry, where steps matter more than memory.
• When stuck, don’t panic. Reverse thinking often reveals shortcuts you miss in forward solving.
• Practice this regularly, and you’ll start predicting steps before even solving fully.
• This is how toppers develop mathematical intuition, not just speed.

Benefits of Class 9 Maths Exemplar

NCERT Exemplar is a highly useful resource for students aiming to go beyond basic preparation and perform well in exams. It helps strengthen concepts while improving problem-solving ability.

• Builds Strong Conceptual Clarity: Focuses on understanding rather than rote learning.
• Enhances Problem-Solving Skills: Includes multi-step and analytical questions.
• Covers Advanced-Level Questions: Prepares you for difficult and tricky problems.
• Aligned with CBSE Pattern: Matches competency-based and application-focused exams.
• Improves Accuracy and Speed: Regular practice reduces errors and saves time.
• Boosts Confidence: Helps you handle unfamiliar and challenging questions.
• Supports Revision: Useful for revising key concepts through diverse questions.
• Includes Variety of Question Types: MCQs, assertion-reason, case-based, and long answers.

Overall, NCERT Exemplar is essential for students who want better clarity, stronger practice, and higher scores in exams.

FAQs

Q1. What is NCERT Exemplar for Class 10 Maths?

Ans. NCERT Exemplar Class 10 Maths is a practice book by NCERT that contains advanced and application-based questions aligned with the textbook.

Q2. Are NCERT Exemplar questions important for board exams?

Ans. Yes, they are extremely useful as they improve problem-solving skills and help tackle tricky questions in exams.

Q3. Is NCERT Exemplar harder than textbook questions?

Ans. Yes, Exemplar questions are more challenging and focus on conceptual clarity and application.

Q4. Can NCERT Exemplar help in competitive exams?

Ans. Yes, it builds strong fundamentals useful for exams like NTSE, Olympiads and other entrance tests.

Q5. Where can I download NCERT Class 10 Maths Exemplar PDF?

Ans. You can download the full-book and chapter-wise PDFs from the links provided above on this page.