CBSE Class 12 Math Exam 2026 Repeated Questions

CBSE Class 12 Math Exam 2026 Repeated Questions from different years' question papers are provided here. The students can refer to the questions after completing the CBSE Class 12 Mathematics Syllabus 2025-26 . It is necessary for students to focus on the repeated questions, as these questions are modified and asked in exams. Solving these questions will also help students in analyzing their preparation. Moreover, they become familiar with the types of questions in exams and the marking scheme followed. By practicing the following questions, students will be able to improve their performance in board exams. Scroll down to check the questions and practice well for final exams.

CBSE Class 12 Math Exam 2026 Repeated Questions

Q1. The length x of a rectangle is decreasing at the rate of 5 cm/min and the width y is increasing at the rate of 4 cm/min. When x = 8 cm and y = 6 cm, find the rate of change of

(i) the perimeter.

(ii) area of rectangle.

Q2. Using integration, find the area of the region bounded by the triangle whose vertices are (- 2, 1), (0, 4) and (2, 3).

Q3. Write the differential equation obtained by eliminating the arbitrary constant C in the equation representing the family of curves xy = C cos x.

Q4. A retired person wants to invest an amount of ₹ 50000. His broker recommends investing in two types of bonds A’ and ‘B’ yielding 10% and 9% return, respectively, on the invested amount. He decides to invest at least ₹ 20000 in bond A’ and at least ₹ 10000 in bond ‘B’. He also wants to invest at least as much in bond A’ as in bond ‘B’. Solve this linear programming problem graphically to maximise his returns.

Q5. A bag contains 3 red and 7 black balls. Two balls are selected at random one by one without replacement. If the second selected ball happens to be red, what is the probability that the first selected ball is also red?

Q6. Show that the height of a closed circular cylinder of a given surface and maximum volume is equal to the diameter of base.

Q7. Water is running into an inverted cone at the rate of π cubic metres per minute. The height of the cone is 10 metres, and the radius of its base is 5 m. How fast the water level is rising when the water stands 7.5 m below the base.

Q8. What is the general solution of the differential equation ey′ =x?
(A) y = xlogx+c
(B) y = xlogx-x+c
(C) y = xlogx+x+c
(D) y = x+c

Q9. The probability that it rains today is 0.4. If it rains today, the probability that it will rain tomorrow is 0.8. If it does not rain today, the probability that it will rain tomorrow is 0.7. If

P ₁ : denotes the probability that it does not rain today.

P ₂ : denotes the probability that it will not rain tomorrow if it rains today.

P ₃ : denotes the probability that it will rain tomorrow if it does not rain today.

P ₄ : denotes the probability that it will not rain tomorrow if it does not rain today.

(i) Find the value of P ₁ x P ₄ - P ₂ x P ₃

(ii) Calculate the probability of rain tomorrow.

Q10. A spherical ball of ice melts in such a way that the rate at which its volume decreases at any instant is directly proportional to its surface area. Prove that the radius of the ice ball decreases at a constant rate.

Students are also advised to check CBSE Class 12 Mathematics Important Questions 2026 while preparing for the final exam. Keep visiting the page to go through the repeated questions for CBSE Class 12 Math.

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