CBSE Class 12 Maths Board Exam 2025 : Most Repeated Questions from Past Years; Download PDF

Most Repeated Questions in Class 12 Maths: Find the most repeated questions from CBSE board exams for Class 12 Maths. These questions are chosen to help you prepare for the CBSE Board Exam 2025. They include 1-mark, 3-mark, and 4-mark questions based on the latest exam pattern for effective preparation.

Maths needs focus and remembering formulas to solve problems quickly. Practicing these most repeated questions can help you score better and improve your overall marks. Read the full article below for all the details.

Most Repeated Questions in CBSE Class 12 Maths Chapter-Wise

Get chapter-wise most repeated questions for CBSE Class 12 Maths. These questions are important and often appear in exams. Practice them well to prepare for the CBSE Class 12 Maths Exam 2025.

1. Relations and Functions

Q1. If R = {(a, a3): a is a prime number less than 5} be a relation. Find the range of R .

Q2. If f: {1,3, 4} → {1, 2, 5} and g: {1,2, 5} → {1, 3} given by f = {(1,2), (3, 5), (4,1)} and g = {(1,3), (2, 3), (5,1)}. Write down gof.

Q3. Let R is the equivalence relation in the set A = {0,1, 2, 3, 4, 5} given by R = {(a, b) : 2 divides (a – b)}. Write the equivalence class [0].

Q4. If R = {(x, y): x + 2y = 8} is a relation on N, then write the range of R.

Q5. If A = {1, 2, 3}, S = {4, 5,6, 7} and f = {(1, 4), (2, 5), (3, 6)} is a function from A to B. State whether f is one-one or not.

Q6. If f : R → R is defined by f{x) = 3x + 2, then define f[f(x)].

Q7. Write fog, if f: R → R and g:R → R are given by f(x) = |x| and g(x) = |5x – 2|.

Q8. Write fog, if f: R → R and g:R → R are given by f(x) = 8x3 and g(x) = xy3.

Q9. State the reason for the relation R in the set {1, 2, 3} given by R = {(1, 2), (2,1)} not to be transitive.

Q10. What is the range of the function?

2. Inverse Trigonometric Functions

Q1. Write the value of

tan-1 (√3) – cot-1 (- √3).

Q2. Find the principal value of

tan-1√3 – sec-1 (- 2).

Q3.

Q4. Write the principal value of cos-1 [cos(680)°].

Q5. Write the value of cos-1 (1/2) – 2 sin-1 (1/2)

Q6. Using the principal values, write the value of cos-1(1/2) + 2 sin-1(1/2).

Q7. What is the principal value of tan-1 (- 1)?

Q8. Write the principal value of sin-1(−1/2).

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3. Matrices

Q1. Write the number of all possible matrices of order 2 × 2 with each entry 1, 2 or 3.

Q2. Write the element a of a 3 × 3 matrix A = [aij], whose elements are given by aij = |i−j|/2

Q3. If A is a square matrix such that A2 = A, then write the value of 7A — (I + A)3, where I is an identity matrix.

Q4.

Q5. If a matrix has 5 elements, then write all possible orders it can have.

Q6.

4. Determinants

5. Continuity and Differentiability

6. Application of Derivatives

Q1. The total cost C(x) associated with the production of x units of an item is given by C(x) = 0.005x³ – 0.02x² + 30x + 5000. Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

Q2. Show that the function f(x) = x³ – 3x² + 6x – 100 is increasing on R.

Q3. Show that the function f(x) = 4x³ – 18x² + 27x – 7 is always increasing on R.

Q4. The volume of a cube is increasing at the rate of 8 cm³/s. How fast is the surface area increasing when the length of its edge is 12 cm?

Q5. 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.

7. Integrals

8. Application of Integrals

Q1. Using integration, find the area of triangle whose vertices are (2, 3), (3, 5) and (4, 4).

Q2. Using integration, prove that the curves y² = 4x and x² = 4y divide the area of the square bounded by x = 0, x = 4, y = 4 and y = 0 into three equal parts.

Q3. Using integration, find the area of the triangular region whose sides have the equations y = 2x + 1, y = 3x + 1 and x = 4.

Q4. Using integration, find the area of region bounded by the triangle whose vertices are (- 2, 1), (0, 4) and (2, 3).

Q5. Using integration, find the area of the region bounded by the curves y = √4−x², x² + y² – 4x = 0 and the x-axis.

Q6. Using integration, find the area of the region in the first quadrant enclosed by the Y-axis, the line y = x and the circle x² + y² = 32.

Q7. Using integration, find the area of the region bounded by the line x – y + 2 = 0, the curve x = √y and Y-axis.

Q8. Using integration, find the area of the region bounded by the curves y = |x + 1| + 1, x = – 3, x = 3 and y = 0.

Q9. Using integration, find the area of the region bounded by the triangle whose vertices are (- 1, 2), (1, 5) and (3, 4).

Q10. Find the area of the region bounded by the parabola y = x2 and the line y = |x|.

9. Differential Equations

Q1. Find the differential equation representing the family of curves y = ae2x + 5 constant.

Q2. Find the differential equation representing the family of curves V = A/r + B, where A and B are arbitrary constants.

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. Write the differential equation representing the family of curves y = mx, where m is an arbitrary constant.

Q5. Find the differential equation of the family of curves y = Ae^2x + Be^-2x, where A and B are arbitrary constants.

Q6. Form the differential equation of the family of parabolas having vertex at origin and axis along positive Y-axis.

Q7. Find the differential equation of family of circles touching Y-axis at the origin.

Q8. Write the solution of the differential equation dy/dx = 2-y

10. Vector Algebra

Q1. Find the unit vector in the direction of the sum of the vectors 2î + 3ĵ – k̂ and 4î – 3ĵ + 2k̂.

Q2. Find a vector in the direction of vector 2î – 3ĵ + 6k̂ which has magnitude 21 units.

Q3. Find a vector a of magnitude 5√2, making an angle of π4 with X-axis, π2 with Y-axis and an acute angle 0 with Z-axis.

Q4. Find the angle between X-axis and the vector î + ĵ + k̂.

Q5.

Q6. Write the direction cosines of vector -2î + ĵ – 5k̂.

Q7. What is the cosine of angle which the vector √2î + ĵ + k̂ makes with Y-axis?

Q8. Find the area of a parallelogram whose adjacent sides are represented by the vectors 2 î – 3 k̂ and 4 ĵ + 2 k̂.

11. Three Dimensional Geometry

Q1. If a line makes angles 90°, 135°, 45° with the x, y and z axes respectively, find its direction cosines.

Q2. What are the direction cosines of a line which makes equal angles with the coordinate axes?

Q3. If a line makes angles 90°, 60° and θ with X, Y and Z-axis respectively, where θ is acute angle, then find θ.

Q4. Write the distance of a point P(a, b, c) from X-axis.

Q5. Write the vector equation of a line passing through point (1, – 1, 2) and parallel to the line whose equation is x−3/1=y−1/2=z+1/−2.

Q6. Find the vector equation of the line passing through the point A (1, 2, – 1) and parallel to the line 5x – 25 = 14 – 7y = 35 z.

Q7. The x-coordinate of a point on the line joining the points P(2, 2, 1) and Q(5, 1, – 2) is 4. Find its z-coordinate.

12. Linear Programming

Q1. Two tailors A and B, earn ₹ 300 and ₹ 400 per day respectively. A can stitch 6 shirts and 4 pairs of trousers while B can stitch 10 shirts and 4 pairs of trousers per day. To find how many days should each of them work and if it is desired to produce at least 60 shirts and 32 pairs of trousers at a minimum labour cost, formulate this as an LPP.

Q2. Maximise and minimise Z = x + 2y subject to the constraints

x + 2 y ≥ 100
2x – y ≤ 0
2x+ y ≤ 200
x, y ≥ 0

Solve the above LPP graphically.

Q3. A company produces two types of goods, A and B, that require gold and silver. Each unit of type A requires 3 g of silver and 1 g of gold while that of type B requires 1 g of silver and 2 g of gold. The company can use at the most 9 g of silver and 8 g of gold. If each unit of type A brings a profit of ₹ 40 and that of type B ₹ 50, find the number of units of each type that the company should produce to maximize profit. Formulate the above LPP and solve it graphically and also find the maximum profit.

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. Find graphically, the maximum value of Z = 2x + 5y, subject to constraints given below 2x+ 4y ≤ 8; 3x + y ≤ 6x + y ≤ A; x ≥ 0, y ≥ 0.

13. Probability

Q1. If P(not A) = 0.7, P(B) = 0.7 and P(B/A) = 0.5, then find P(A/B).

Q2. A and B throw a pair of dice alternately, till one of them gets a total of 10 and wins the game. Find their respective probabilities of winning, if A starts first.

Q3. Two groups are competing for the positions of the Board of Directors of a corporation. The probabilities that the first and second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of introducing a new product is 0.7 and the corresponding probability is 0.3 if the second group wins. Find the probability that the new product introduced way by the second group.

Q4. A bag A contains 4 black and 6 red balls and bag B contains 7 black and 3 red balls. A die is thrown. If 1 or 2 appears on it, then bag A is chosen, otherwise bag B. If two balls are drawn at random (without replacement) from the selected bag, find the probability of one of them being red and another black.

Q5. From a lot of 15 bulbs which include 5 defectives, a sample of 2 bulbs is drawn at random (without replacement). Find the probability distribution of the number of defective bulbs.

Q6. Find the mean number of heads in three tosses of a coin.

Q7.Find the probability distribution of number of doublets in three tosses of a pair of dice.

Q8. 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?

Q9. Three cards are drawn at random (without replacement) from a well-shuffled pack of 52 playing cards. Find the probability distribution of number of red cards. Hence, find the mean of the distribution.

Q10. Two numbers are selected at random (without replacement) from positive integers 2, 3, 4, 5, 6 and 7. Let X denote the larger of the two numbers obtained. Find the mean and variance of the probability distribution of X.

👉 CBSE Class 12 Study Materials

CBSE Class 12 Syllabus 2024-25	CBSE Class 12 Previous Year Papers
NCERT Books For Class 12 Books	NCERT Class 12 Solutions
CBSE Class 12 Full Study Material	CBSE Class 12 Sample Paper 2024-25