The CBSE Class 12 Mathematics syllabus for 2025 emphasizes conceptual understanding and application, making case study-based questions a significant part of the exam. These questions test a student’s ability to apply mathematical concepts to real-life scenarios, enhancing their analytical and problem-solving skills. Here, we present 20+ case study-based questions, complete with scenarios, tables, and a mix of question types to help students prepare effectively.
What Are Case Study-Based Questions?
Case study-based questions are designed around real-world contexts or hypothetical situations. These questions combine multiple concepts, requiring students to:
- Analyze given information.
- Apply relevant mathematical concepts.
- Solve problems using logical reasoning.
These questions may include scenarios, data tables, or graphical representations, and are often divided into sub-parts.
Case Study 1: Revenue Analysis
Scenario: A company produces two types of gadgets, A and B. The profit on each gadget A is ₹500, while the profit on each gadget B is ₹700. The production is subject to the following constraints:
- At most 300 units of gadget A can be produced.
- At least 200 units of gadget B must be produced.
- The combined production should not exceed 500 units.
Data Table:
| Gadget | Profit (in ₹) | Production Limit |
|---|---|---|
| A | 500 | At most 300 |
| B | 700 | At least 200 |
Questions:
- Formulate the given problem as a Linear Programming Problem (LPP).
- Determine the feasible region using the graphical method.
- Find the maximum profit and the corresponding production plan.
- If the profit per gadget B increases by ₹200, how does the solution change?
- Analyze the impact on production limits if both gadgets have to be produced equally.
Case Study 2: Population Growth
Scenario: A town’s population is modeled by the equation: where is the initial population, is the growth rate, and is the time in years. The initial population in 2020 was 50,000, and it grows at a rate of 2% annually.
Questions:
- Write the expression for the population in terms of .
- Find the population in 2025.
- How long will it take for the population to double?
- Plot the population growth curve for to .
- Discuss the implications of a 3% growth rate instead of 2%.
Case Study 3: Traffic Flow
Scenario: A traffic monitoring system records the number of vehicles passing through a junction every hour. The data for a 6-hour period is shown below:
| Time (hours) | Number of Vehicles |
| 6 AM – 7 AM | 120 |
| 7 AM – 8 AM | 150 |
| 8 AM – 9 AM | 200 |
| 9 AM – 10 AM | 180 |
| 10 AM – 11 AM | 170 |
| 11 AM – 12 PM | 190 |
Questions:
- Find the mean and standard deviation of the number of vehicles.
- Calculate the probability of having more than 180 vehicles in a randomly chosen hour.
- Using calculus, determine the hour during which the rate of vehicle arrival is highest.
- Create a histogram to represent the data and interpret the peak traffic hours.
- Predict the number of vehicles for the next hour using a linear regression model.
Case Study 4: Manufacturing Costs
Scenario: A factory manufactures two products, X and Y, with cost functions: where and are the quantities produced.
Questions:
- Find the critical points of .
- Determine the production levels that minimize the cost.
- Calculate the minimum cost.
- Analyze the cost function if the coefficient of changes from 10 to 15.
- Find the cost when production levels are doubled for both products.
Case Study 5: Probability in Games
Scenario: A bag contains 5 red balls, 3 blue balls, and 2 green balls. A ball is drawn at random.
Questions:
- Find the probability of drawing a red ball.
- If two balls are drawn without replacement, find the probability that both are blue.
- If two balls are drawn with replacement, calculate the probability that one is red and the other is green.
- Compute the expected number of red balls in three draws with replacement.
- Discuss the changes in probability if an additional green ball is added to the bag.
Additional Case Study-Based Questions
Case Study 6: Investment Analysis
Scenario: An investor allocates funds between two schemes, A and B. Scheme A offers a return of 10% annually, while scheme B offers 8%. The total investment is ₹1,00,000, with at least ₹40,000 in scheme A.
Questions:
- Formulate this as an LPP.
- Determine the investment plan that maximizes the return.
- Analyze the return if scheme B’s rate increases to 9%.
- Calculate the total return if the investment is split equally.
- Discuss the impact of reducing the total investment to ₹80,000.
Case Study 7: Water Tank Geometry
Scenario: A water tank is in the shape of a cuboid with a square base. The height is three times the side length of the base.
Questions:
- Derive the volume of the tank in terms of the side length of the base.
- If the side length is 5 m, calculate the volume.
- Find the rate of change of volume if the side length increases at 2 m/s.
- Calculate the surface area of the tank.
- Discuss the implications of increasing the height-to-base ratio.
Summary Table of Concepts Covered
| Topic | Case Study Examples | Key Concepts Tested |
| Linear Programming | Revenue Analysis, Investment Analysis | Constraints, Feasible Region |
| Exponential Growth | Population Growth | Logarithms, Exponential Functions |
| Statistics | Traffic Flow | Mean, Standard Deviation, Probability |
| Calculus Optimization | Manufacturing Costs, Water Tank Geometry | Partial Derivatives, Minima/Maxima |
| Probability | Probability in Games | Basic and Conditional Probability |
Why Practice Case Study-Based Questions?
- Exam Relevance: CBSE focuses on case studies to assess application-based learning.
- Improved Understanding: These questions integrate multiple concepts, reinforcing overall understanding.
- Higher Scores: Practicing such questions enhances problem-solving speed and accuracy, ensuring better exam performance.
Conclusion
Case study-based questions are an integral part of the CBSE Class 12 Maths Exam, bridging the gap between theoretical knowledge and practical application. By practicing these questions, students can enhance their conceptual understanding and analytical skills. Regular practice of diverse scenarios, along with a strategic focus on critical topics, will empower students to tackle the 2025 exam confidently and excel in their academic journey. Prepare thoroughly, stay consistent, and success will follow.