Preparing for the CBSE Class 12 Mathematics Viva can seem daunting, but with the right strategy, it turns into an opportunity to showcase your knowledge and confidence. The Mathematics practical exam, an essential part of the curriculum, assesses students on both their theoretical grasp and the practical application of concepts.
Viva questions play a significant role, where students are evaluated based on their experiments, records, and the concepts related to the subject. For the 2025 session, students need to prepare diligently for the viva, which is worth 4 out of the total 30 marks, with additional marks allocated for the investigatory project and viva related to it.
Grasping the underlying concepts and practicing key experiments is crucial. This article offers important CBSE Class 12 Mathematics Viva Questions with Answers, including downloadable PDFs, to help students excel in their practical exams and confidently impress their examiners.
1. What is the importance of the derivative in mathematics?
Answer: The derivative represents the rate of change of a function. It is fundamental in calculus as it helps in finding the slope of a curve, understanding motion, and solving problems related to maxima and minima. In practical applications, derivatives are used to analyze the behavior of functions and solve real-world problems in physics, economics, and engineering.
2. What is the chain rule in differentiation?
Answer: The chain rule is a method for differentiating composite functions. It states that if a function y = f(g(x)) is a composition of two functions f and g, the derivative is given by: dy/dx = (dy/dg) * (dg/dx)
3. Explain the concept of a limit.
Answer: A limit is a fundamental concept in calculus that describes the behavior of a function as its input approaches a particular point. It helps in defining continuity, derivatives, and integrals. For example, the limit of a function f(x) as x approaches a value a is written as: lim (x -> a) f(x) If this value exists, it indicates the behavior of the function near x = a.
4. What is the Fundamental Theorem of Calculus?
Answer: The Fundamental Theorem of Calculus connects differentiation and integration. It states that if f(x) is continuous over the interval [a, b] and F(x) is its antiderivative, then: ∫ab f(x) dx = F(b) - F(a)
5. What is the application of integration in finding areas under curves?
Answer: Integration is used to find the area under a curve by calculating the integral of the function between two points. For a curve defined by the function y = f(x), the area between the curve and the x-axis from x = a to x = b is given by the integral: Area = ∫ab f(x) dx
6. How do you calculate the area between two curves?
Answer: The area between two curves y = f(x) and y = g(x), from x = a to x = b, is calculated by finding the integral of the difference of the functions: Area = ∫ab [f(x) - g(x)] dx
7. What is the difference between definite and indefinite integrals?
Answer: - **Definite Integral**: It has limits of integration and gives the exact numerical value of the area under the curve between those limits. - **Indefinite Integral**: It does not have limits of integration and represents the general form of antiderivatives, including a constant of integration.
8. Explain the concept of matrices and their operations.
Answer: A matrix is a rectangular array of numbers arranged in rows and columns. Operations on matrices include addition, subtraction, multiplication, and finding the determinant and inverse. Matrix operations are fundamental in solving systems of linear equations and have applications in areas such as computer graphics, economics, and engineering.
9. What is the determinant of a matrix and how is it useful?
Answer: The determinant is a scalar value that can be calculated from a square matrix. It is used to determine if a matrix is invertible and helps in solving systems of linear equations. The determinant of a 2x2 matrix is calculated as: det (a b; c d) = ad - bc
10. What is the significance of vectors in mathematics?
Answer: Vectors represent quantities that have both magnitude and direction, such as velocity and force. They are essential in geometry and physics. Operations like addition, subtraction, and scalar multiplication are performed on vectors. Dot product and cross product are special vector operations used in calculating angles and areas.
1. What is the importance of the derivative in mathematics?
Answer: The derivative represents the rate of change of a function. It is fundamental in calculus as it helps in finding the slope of a curve, understanding motion, and solving problems related to maxima and minima. In practical applications, derivatives are used to analyze the behavior of functions and solve real-world problems in physics, economics, and engineering.
2. What is the chain rule in differentiation?
Answer: The chain rule is a method for differentiating composite functions. It states that if a function y = f(g(x)) is a composition of two functions f and g, the derivative is given by: dy/dx = (dy/dg) * (dg/dx)
3. Explain the concept of a limit.
Answer: A limit is a fundamental concept in calculus that describes the behavior of a function as its input approaches a particular point. It helps in defining continuity, derivatives, and integrals. For example, the limit of a function f(x) as x approaches a value a is written as: limx→a f(x) If this value exists, it indicates the behavior of the function near x = a.
4. What is the Fundamental Theorem of Calculus?
Answer: The Fundamental Theorem of Calculus connects differentiation and integration. It states that if f(x) is continuous over the interval [a, b] and F(x) is its antiderivative, then: ∫ab f(x) dx = F(b) - F(a) This theorem establishes the link between the process of differentiation and the evaluation of integrals.
5. What is the application of integration in finding areas under curves?
Answer: Integration is used to find the area under a curve by calculating the integral of the function between two points. For a curve defined by the function y = f(x), the area between the curve and the x-axis from x = a to x = b is given by the integral: Area = ∫ab f(x) dx This application is widely used in physics and engineering to calculate quantities like distance, work, and probability.
6. How do you calculate the area between two curves?
Answer: The area between two curves y = f(x) and y = g(x), from x = a to x = b, is calculated by finding the integral of the difference of the functions: Area = ∫ab [f(x) - g(x)] dx This method helps in finding the region enclosed by two curves.
7. What is the difference between definite and indefinite integrals?
Answer:
8. Explain the concept of matrices and their operations.
Answer: A matrix is a rectangular array of numbers arranged in rows and columns. Operations on matrices include addition, subtraction, multiplication, and finding the determinant and inverse. Matrix operations are fundamental in solving systems of linear equations and have applications in areas such as computer graphics, economics, and engineering.
9. What is the determinant of a matrix and how is it useful?
Answer: The determinant is a scalar value that can be calculated from a square matrix. It is used to determine if a matrix is invertible and helps in solving systems of linear equations. The determinant of a 2x2 matrix is calculated as: det [a b] = ad - bc
10. What is the significance of vectors in mathematics?
Answer: Vectors represent quantities that have both magnitude and direction, such as velocity and force. They are essential in geometry and physics. Operations like addition, subtraction, and scalar multiplication are performed on vectors. Dot product and cross product are special vector operations used in calculating angles and areas.
In CBSE Class 12 Biology, the viva questions are a part of the practical examination, which carries 30 marks out of the total 100 marks in the subject. The practical exam is divided into different components, including experiments, spotting, practical records, and viva voce.
| Component | Marks |
|---|---|
| One Major Experiment | 5 |
| One Minor Experiment | 4 |
| Slide Preparation | 5 |
| Spotting | 7 |
| Practical Record + Project + Model | 5 |
| Viva Voce | 4 |
| Total | 30 |
The viva session tests conceptual understanding, practical skills, and knowledge of the performed experiments. It includes:
Yes, in CBSE Class 12, viva is a part of the practical examination for subjects like Biology, Physics, Chemistry, Computer Science, and others. The viva carries 4-5 marks and assesses your conceptual understanding, practical knowledge, and project work.
The difficulty of topics varies for students, but some commonly considered challenging topics in Class 12 Maths are:
Scoring 95%+ in Maths requires a strategic approach:
The practical viva includes:
The Maths viva is conducted during the Maths Practical/Project assessment and may include:
The most challenging topics for many students are: