In short: Competency-Based Questions (CBQs) make up 50% of your CBSE Class 10 Maths paper — that is 40 marks out of 80. These include MCQs (20%), case-based questions in Section E (12 marks from 3 questions × 4 marks), and assertion-reason questions in Section A. This post gives you chapter-wise practice material in the exact board format.

What Are Competency-Based Questions in CBSE Class 10 Maths?

Competency-Based Questions test whether you can apply mathematical concepts to real-world situations rather than just reproduce formulas. CBSE introduced this format to shift away from rote learning, and it now accounts for half of your total marks.

Here is how CBQs are distributed across the paper:

Question Type	Section	Marks Per Question	Number of Questions	Total Marks
Competency MCQs	Section A	1 mark	~10 out of 20	~10
Assertion-Reason	Section A	1 mark	4 questions	4
Case Study Questions	Section E	4 marks	3 questions	12
Application-based SA/LA	Sections B-D	2-5 marks	~6-8 questions	~14-16
Total CBQ marks				~40 out of 80

The CBSE Class 10 Maths chapter-wise marks weightage shows that Algebra (20 marks) and Geometry (15 marks) dominate the paper. CBQs appear from every high-weightage unit, so you need chapter-wise practice.

Chapter-Wise Case Study Questions

Case Study 1: Real Numbers — The School Library Problem

The librarian of a school wants to arrange 1260 English books and 945 Hindi books on shelves such that each shelf contains books of only one language, and every shelf has the same number of books. She also wants the maximum number of books on each shelf.

(i) What is the HCF of 1260 and 945? (a) 315 (b) 105 (c) 45 (d) 63

(ii) What is the maximum number of books on each shelf? (a) 45 (b) 315 (c) 105 (d) 63

(iii) How many shelves are needed for English books? (a) 3 (b) 4 (c) 5 (d) 6

(iv) If 1260 = 2² × 3² × 5 × 7, and 945 = 3³ × 5 × 7, what is the LCM of 1260 and 945? (a) 3780 (b) 7560 (c) 2520 (d) 5040

Answers: (i) a — 315 (ii) b — 315 (iii) b — 4 shelves (1260 ÷ 315) (iv) a — 3780

Case Study 2: Arithmetic Progressions — Monthly Savings Plan

Reema starts saving money from her pocket allowance. In the first month, she saves ₹100. Every subsequent month, she increases her savings by ₹50. Her father promises to double her total savings once she has saved for 12 months.

(i) The savings form an AP. What is the common difference? (a) ₹100 (b) ₹50 (c) ₹150 (d) ₹200

(ii) How much does Reema save in the 8th month? (a) ₹350 (b) ₹400 (c) ₹450 (d) ₹500

(iii) What is the total amount saved by Reema in 12 months? (a) ₹3600 (b) ₹4500 (c) ₹5100 (d) ₹4200

(iv) After her father doubles the amount, how much does Reema have? (a) ₹7200 (b) ₹9000 (c) ₹10200 (d) ₹8400

Answers: (i) b — ₹50 (ii) c — a₈ = 100 + 7(50) = ₹450 (iii) d — S₁₂ = 12/2 [2(100) + 11(50)] = 6 × 750 = ₹4200 (Note: recalculated: 6[200+550] = 6×750 = 4500. Answer is (b) ₹4500) (iv) b — ₹9000

Case Study 3: Trigonometry — Height and Distance

Two friends Ankit and Bhavna are standing on opposite sides of a 30-metre-high tower. Ankit observes the top of the tower at an angle of elevation of 60° and Bhavna observes it at an angle of elevation of 30°.

(i) What is the distance of Ankit from the base of the tower? (a) 10√3 m (b) 30√3 m (c) 15√3 m (d) 20√3 m

(ii) What is the distance of Bhavna from the base of the tower? (a) 10√3 m (b) 30√3 m (c) 60√3 m (d) 15√3 m

(iii) What is the total distance between Ankit and Bhavna? (a) 40√3 m (b) 20√3 m (c) 50√3 m (d) 60√3 m

(iv) If a bird sits at the top of the tower and Ankit looks at it, what is the line-of-sight distance? (a) 20√3 m (b) 60 m (c) 20 m (d) 30/sin 60° m

Answers: (i) a — tan 60° = 30/d, so d = 30/√3 = 10√3 m (ii) b — tan 30° = 30/d, so d = 30√3 m (iii) a — 10√3 + 30√3 = 40√3 m (iv) a — hypotenuse = 30/sin 60° = 30/(√3/2) = 60/√3 = 20√3 m

Case Study 4: Statistics — Class Performance Data

A teacher recorded the marks of 50 students in a mathematics test. The data is presented below:

Marks	0-20	20-40	40-60	60-80	80-100
Number of Students	4	8	16	14	8

(i) What is the modal class? (a) 60-80 (b) 40-60 (c) 80-100 (d) 20-40

(ii) What is the mean marks of the class using the direct method? (a) 52.4 (b) 55.6 (c) 58.0 (d) 48.8

(iii) What is the median class? (a) 20-40 (b) 40-60 (c) 60-80 (d) 80-100

(iv) The cumulative frequency just before the median class is: (a) 4 (b) 12 (c) 28 (d) 42

Answers: (i) b — 40-60 has the highest frequency (16) (ii) b — Σfx/Σf = 2780/50 = 55.6 (iii) b — N/2 = 25, cf before 40-60 is 12, median class is 40-60 (iv) b — 12

Case Study 5: Coordinate Geometry — City Map Problem

A city planner is designing a park on a coordinate grid. Three lamp posts are located at points A(2, 4), B(6, 4), and C(6, 8). A fourth lamp post D must be placed to form a rectangle ABCD.

(i) What are the coordinates of D? (a) (2, 8) (b) (4, 6) (c) (8, 2) (d) (2, 6)

(ii) What is the length of side AB? (a) 4 units (b) 6 units (c) 8 units (d) 2 units

(iii) What is the area of the rectangle ABCD? (a) 12 sq. units (b) 16 sq. units (c) 20 sq. units (d) 24 sq. units

(iv) What is the length of diagonal AC? (a) 4√2 units (b) 4√5 units (c) 6 units (d) 8 units

Answers: (i) a — D(2, 8) (ii) a — AB = |6-2| = 4 units (iii) b — 4 × 4 = 16 sq. units (iv) a — AC = √[(6-2)² + (8-4)²] = √(16+16) = 4√2 units

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Assertion-Reason Questions: Chapter-Wise Practice

In assertion-reason questions, you are given two statements and must identify the relationship between them.

Options for all questions:

(a) Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.

Quadratic Equations

Q1. Assertion: The equation x² + 3x + 5 = 0 has no real roots. Reason: If the discriminant D = b² − 4ac < 0, the quadratic equation has no real roots.

Answer: (a) — D = 9 − 20 = −11 < 0. Both statements are true, and the reason correctly explains the assertion.

Q2. Assertion: The roots of 2x² − 5x + 3 = 0 are x = 1 and x = 3/2. Reason: The sum of roots of ax² + bx + c = 0 is −b/a.

Answer: (b) — Both are true. The roots are indeed 1 and 3/2 (sum = 5/2 = −(−5)/2), but the reason talks about the sum of roots formula, which does not directly explain why the roots are specifically 1 and 3/2.

Q3. Assertion: Every quadratic equation has exactly two roots. Reason: A polynomial of degree n has at most n roots.

Answer: (d) — A is false (a quadratic equation can have two equal roots, which means technically one distinct root), R is true.

Circles (Tangent Properties)

Q4. Assertion: The tangent at any point of a circle is perpendicular to the radius through the point of contact. Reason: The length of tangents drawn from an external point to a circle are equal.

Answer: (b) — Both are true, but the reason does not explain the assertion. These are two independent theorems.

Q5. Assertion: If PA and PB are tangents from point P to a circle with centre O, then ∠APB + ∠AOB = 180°. Reason: The tangent at any point is perpendicular to the radius at the point of contact.

Answer: (a) — Since OA ⊥ PA and OB ⊥ PB, in quadrilateral OAPB, ∠OAP + ∠OBP = 180°. Therefore ∠APB + ∠AOB = 180°. The reason is the correct explanation.

Triangles (Similarity)

Q6. Assertion: If two triangles are similar, then their corresponding sides are proportional. Reason: The ratio of areas of two similar triangles is equal to the ratio of their corresponding sides.

Answer: (c) — A is true (definition of similar triangles). R is false (the ratio of areas equals the square of the ratio of corresponding sides, not the ratio itself).

Q7. Assertion: In triangle ABC, if DE ∥ BC and AD/DB = 2/3, then AE/EC = 2/3. Reason: A line drawn parallel to one side of a triangle divides the other two sides in the same ratio (Basic Proportionality Theorem).

Answer: (a) — Both true, and BPT directly explains why the ratio is preserved.

Application-Based MCQs

These MCQs go beyond direct formula use and test whether you understand concepts in context. They appear throughout Section A.

Q1. A rectangular park is 80 m long. A path of uniform width runs along two adjacent sides. If the area of the path is 780 m², the width of the path is: (a) 5 m (b) 6 m (c) 4 m (d) 8 m

Answer: (b) — Let width = x. If path runs along length and breadth: 80x + bx − x² = 780. This requires the breadth value, which leads to a quadratic equation — a classic CBQ pattern.

Q2. The sum of first n terms of an AP is 3n² + 5n. The common difference is: (a) 3 (b) 5 (c) 6 (d) 8

Answer: (c) — a₁ = S₁ = 8, a₂ = S₂ − S₁ = 22 − 8 = 14, d = 14 − 8 = 6.

Q3. The probability of getting at most 2 heads when three coins are tossed is: (a) 3/8 (b) 7/8 (c) 1/2 (d) 5/8

Answer: (b) — P(at most 2 heads) = 1 − P(3 heads) = 1 − 1/8 = 7/8.

Q4. From a point on the ground, the angle of elevation of the top of a 20 m tall building is 45°. The distance of the point from the base of the building is: (a) 20 m (b) 10 m (c) 20√2 m (d) 10√2 m

Answer: (a) — tan 45° = 20/d, so d = 20 m.

How to Approach Competency-Based Questions

CBQs have a specific answering strategy that differs from traditional questions. Follow these steps:

For Case Study Questions (4 marks each)

Read the passage first, completely. Do not jump to the sub-questions. The passage contains all the data you need.
Identify what mathematical concept is being tested. Is it AP? Trigonometry? Probability? This tells you which formulas to use.
Extract numerical data from the passage and write it down separately. Convert the real-world scenario into mathematical terms.
Solve each sub-question independently. Sub-questions are usually not dependent on each other. If you get stuck on one, move to the next.
Check your answer against the MCQ options. If your calculated value does not match any option, recheck your working.

For Assertion-Reason Questions (1 mark each)

Evaluate the Assertion first. Is the statement mathematically correct? Verify with an example if needed.
Evaluate the Reason independently. Is this statement true on its own?
Only then check the connection. If both are true, does the reason actually explain why the assertion is true?
Beware of option (b) — this is where most students lose marks. Two true statements do not automatically mean one explains the other.

For more on the overall paper strategy, see the board exam time management guide.

Common Mistakes in CBQ Maths Questions

Not reading the full passage. Students jump to sub-questions and miss crucial data embedded in the scenario. The answer is always in the passage.
Confusing assertion-reason option (a) with (b). Both have "A true, R true" — the difference is whether R explains A. Practise distinguishing correlation from causation.
Applying wrong formulas to real-world problems. A savings problem might look like simple addition but is actually an AP. A shadow problem is trigonometry. Train yourself to recognize the concept behind the scenario.
Calculation errors under pressure. Case study MCQs have fixed options — a small arithmetic mistake means zero marks. Use rough work for every calculation.
Spending too much time on one case study. Each case study is 4 marks. Do not spend more than 8-10 minutes on one. If stuck, mark and return.
Ignoring units and context. If the question asks for distance in metres, ensure your answer is in metres. Real-world questions often mix units.

Check the CBSE sample paper practice sets to practise full papers with CBQs in the actual exam format.

FAQs

How many marks are competency-based in CBSE Class 10 Maths 2027?

Approximately 40 marks out of 80 (50% of the paper) are competency-based. This includes competency MCQs, assertion-reason questions, and case-based questions in Section E. The SQP 2027 released by CBSE confirms this split.

What chapters do case study questions come from in Class 10 Maths?

Case study questions in Section E typically come from Arithmetic Progressions, Trigonometry (height and distance), Statistics (data interpretation), Coordinate Geometry, and Probability. These are the chapters that lend themselves to real-world application scenarios.

Are assertion-reason questions difficult in Class 10 Maths?

They are not difficult if you understand the underlying concepts. The challenge is in distinguishing between options (a) and (b) — both have true assertion and true reason, but only (a) means the reason explains the assertion. Regular practice with 20-30 assertion-reason pairs builds this skill.

How should I prepare for CBQs if I have only 2 months left?

Focus on practising the format, not memorising content. Solve at least 5 case studies per chapter and 10 assertion-reason pairs per chapter. Use the CBSE Class 10 Maths important questions collection for targeted practice.

Do case study sub-questions depend on each other?

Usually no. Each sub-question within a case study is independent and can be answered separately. If you cannot solve part (ii), you can still answer parts (iii) and (iv). Attempt all sub-questions.

Is the CBQ pattern for 2027 the same as 2025-26?

Yes. CBSE released the SQP 2027 in September, and the pattern is the same as 2025-26. The 50% competency-based split, Section E case studies, and assertion-reason format remain unchanged.

CBSE Class 10 Maths Competency-Based Questions Chapter-Wise Practice 2027