CBSE Class 12 · Section E · 2026-27

CBSE Class 12 Maths case study questions, chapter-wise

Case study (case-based) questions are Section E of the Class 12 Maths board paper: three questions of 4 marks, 12 of the 80 marks. Each starts with a real-life passage, then asks three parts worth 1, 1 and 2 marks, with a choice on the 2-mark part. Here are 26 free case studies, two for every chapter, and the 15 in our sample papers, all with worked answers.

26 chapter case studies
15 in our sample papers
12 of the 80 marks
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Start: Continuity and Differentiability case studies

One worked in full: Continuity and Differentiability

Try each part before you open its answer. The marks in brackets are what the part is worth.

Case study 1: Taxi fare (4 marks)

A city taxi charges ₹ $F (d)$ for a trip of $d$ km, where $F (d) = 50 + 12 d$ for $0 \leq d \leq 5$ and $F (d) = k + 10 d$ for $d > 5$ . The transport authority insists that the fare must not jump at $5$ km.

(i) Find

k

so that

F

is continuous at

d = 5

. [1 mark]

Show answer

Answer:

k = 60

F (5) = 110

and

lim_{d \to 5^{+}} (k + 10 d) = k + 50

; so

k + 50 = 110 \Rightarrow k = 60

. A1

(ii) With this

k

, find the fare for an

8

km trip. [1 mark]

Show answer

Answer: ₹

140

F (8) = 60 + 80 = ₹ 140

. A1

(iii) Is

F

differentiable at

d = 5

? Justify. [2 marks]

Show answer

Answer: No

Left derivative at

5

= 12

, right derivative

= 10

M1; they differ, so

F

is not differentiable at

d = 5

(though continuous). A1

OR Find the rate at which the fare increases per km for a

3

km trip and for a

7

km trip. [2 marks]

Show answer

Answer: ₹

12

per km; ₹

10

per km

F^{'} (d) = 12

for

0 < d < 5

M1 and

F^{'} (d) = 10

for

d > 5

: ₹

12

/km at

3

km, ₹

10

/km at

7

km. A1

How to answer a case study

Read the passage once and write down the numbers. Most of the 4 marks depend on setting the situation up correctly: name the quantity, the formula and the values before you start.
Parts (i) and (ii) are 1 mark each. They usually need one idea from the chapter. Give the answer with a line of working and move on; don't spend long here.
Part (iii) holds 2 marks, usually split between the working and the answer. Write the formula or equation you are using before any arithmetic, so a method mark is safe even if a number slips.
Pick the OR option you can finish. Read both versions of part (iii) and choose the one you can complete fully; both are worth the same.

More on reading real-life questions: competency-based questions in Class 12 Maths, and how step marks are given.

Case study questions by chapter

Two for every chapter, in NCERT order. A case study's title opens the chapter's free set, with the answers behind "Show answer"; the chapter name opens its notes.

Chapter	Case study 1	Case study 2
Ch 1: Relations and Functions	School houses Equivalence relations and classes	Temperature converter One-one and onto functions
Ch 2: Inverse Trigonometric Functions	Ramps at the community centre Principal values	Playground swing Domain and range of principal value branches
Ch 3: Matrices	Canteen sales Operations on matrices	Fertiliser mix Invertible matrices
Ch 4: Determinants	Triangular plot Area of a triangle	Tea stall orders Systems of linear equations
Ch 5: Continuity and Differentiability	Taxi fare Continuity	Cooling cup of tea Chain rule and standard derivatives
Ch 6: Application of Derivatives	Fencing a kitchen garden Maxima and minima	Inflating a balloon Rate of change
Ch 7: Integrals	Cyclist's speed Definite integrals and their properties	Revenue from marginal revenue Definite integrals and their properties
Ch 8: Application of Integrals	Elliptical pond Areas of circles and ellipses	Curved flower bed Area under simple curves
Ch 9: Differential Equations	Medicine in the bloodstream Variables separable	Drip infusion Linear equations
Ch 10: Vector Algebra	Pushing a trolley Scalar (dot) product	Sail of a model boat Vector (cross) product
Ch 11: Three Dimensional Geometry	Zip-line cable Equation of a line	Two drone flight paths Shortest distance between two lines
Ch 12: Linear Programming	Wooden toys and boxes Corner points and optimal values	Weekly study plan Feasible regions
Ch 13: Probability	Two filling machines Total probability and Bayes' theorem	Choosing a quiz team Random variable and its mean

Case studies in our sample papers

Questions 36 to 38 of each paper, to sit inside a full 3-hour paper once the chapters are done.

Paper 1, Q36: Screening test (Probability)
Paper 1, Q37: Mall parking (Application of Derivatives)
Paper 1, Q38: Smart-card batches (Relations and Functions)
Paper 2, Q36: School records (Relations and Functions)
Paper 2, Q37: Town population (Differential Equations)
Paper 2, Q38: Spin-the-wheel stall (Probability)
Paper 3, Q36: Monsoon commute (Probability)
Paper 3, Q37: Filling a conical tank (Application of Derivatives)
Paper 3, Q38: Van routes (Relations and Functions)
Paper 4, Q36: Divisor chart (Relations and Functions)
Paper 4, Q37: Reservoir inflow (Integrals)
Paper 4, Q38: Garment quality check (Probability)
Paper 5, Q36: Motor insurance (Probability)
Paper 5, Q37: Giant wheel (Application of Derivatives)
Paper 5, Q38: Square residues (Relations and Functions)

Questions

How many case study questions are in the CBSE Class 12 Maths paper?

Three, in Section E. Each is worth 4 marks, so case studies carry 12 of the 80 marks. Each has a short real-life passage and three parts worth 1, 1 and 2 marks.

Is there a choice in the case study questions?

Yes, inside each one: the 2-mark part (iii) has an OR alternative, and you answer one of the two. There is no choice between the three case studies themselves.

How long should I spend on a case study?

About 9 minutes each. The paper is 180 minutes for 80 marks, a little over 2 minutes a mark, and a 4-mark case study is mostly reading plus one longer part.

Which chapters do case study questions come from?

Any chapter can be set as a case study, so practise all of them. In our 5 sample papers, Probability, Relations and Functions, Application of Derivatives came up most often; CBSE does not publish which chapters it will use.

Are these official CBSE case study questions?

No. They are original questions written by CBSE Math Revision to the CBSE 2026-27 pattern, each checked twice. For CBSE's own, sit the official sample paper linked from our question papers page.

Original questions written by CBSE Math Revision; not taken from NCERT, NCERT Exemplar or CBSE papers. CBSE Math Revision is independent and not affiliated with CBSE or NCERT.