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CBSE Class 12 Maths Exam 2025: CBSE Class 12 Maths Exam Date is 08 March 2025, and students across the country have worked hard to perform their best. After the exam, the CBSE Class 12 Maths Paper Analysis 2025 helps students, teachers, and parents understand the difficulty level, question pattern, and overall paper structure.
This detailed CBSE Class 12 Maths Paper Analysis 2025 provides insights into the types of questions asked, weightage of different topics, and student reactions. Whether you are checking the maths board paper 2025 class 12 date for upcoming exams or reviewing the paper to prepare for future attempts, this analysis will be useful.
Additionally, students can download the CBSE Class 12 Maths Paper Analysis 2025 PDF for a complete breakdown of the exam. This report will help them evaluate their performance and compare it with the expected answer key. Along with this, we also cover a Class 12 Physics Sample Paper Analysis to help students get a better idea of how CBSE structures its board exams.
Stay tuned for a detailed section-wise review of the CBSE Class 12 Maths Paper Analysis 2025, covering marks distribution, student feedback, and expert opinions.
This year's maths board paper 2025 class 12 date was set for 08 March 2025, and the question paper followed the usual pattern of CBSE. However, some students found it more challenging than expected, especially in certain sections like Calculus and Algebra.
The exam was moderate to difficult, with a mix of concept-based, formula-based, and tricky application-based questions. While some sections were straightforward, others required deep understanding and strong problem-solving skills. Time management played a crucial role in attempting the paper effectively.
Also Check - CBSE Class 12 Maths Answer Key 2025 PDF Download
Below is a quick summary of the CBSE Class 12 Maths Paper Analysis 2025:
| Aspect | Details |
| Exam Date | 08 March 2025 |
| Total Marks | 80 Marks |
| Total Duration | 3 Hours |
| Question Types | MCQs, Short Answer, Long Answer |
| Overall Difficulty | Moderate to Difficult |
| Toughest Section | Calculus & Algebra |
| Easiest Section | Probability & Statistics |
| Most Time-Consuming | Integration & 3D Geometry |
| Expected Good Score | 65+ Marks |
| Student Reactions | Some found it easy, others struggled with time |
| Expert Review | Well-balanced paper, but some tricky questions |
For a detailed question-wise analysis and solutions, students can download the CBSE Class 12 Maths Paper Analysis 2025 PDF. This will help them evaluate their performance and understand the marking scheme.
| Question Paper Set | Download Link |
| CBSE Class 12 Maths Paper 2025 – Set 1 | Download PDF |
| CBSE Class 12 Maths Paper 2025 – Set 2 | Download PDF |
| CBSE Class 12 Maths Paper 2025 – Set 3 | Download PDF |
| CBSE Class 12 Maths Paper 2025 – Set 4 | Download PDF |
| CBSE Class 12 Maths Paper 2025 – Set 5 | Download PDF |
| Category | Expected Score |
| Top Performers | 90+ Marks |
| Good Score | 65-85 Marks |
| Average Score | 40-60 Marks |
| Passing Marks | 33 Marks |
To help students understand which topics carried the most weight and posed the greatest challenge, here is a detailed breakdown of each section:
The Algebra section was moderate to difficult, featuring a mix of formula-based and logic-based questions. The Matrices & Determinants problems were relatively straightforward, but some sequence and series questions were tricky.
As expected, Calculus was the most challenging part of the exam. Some integration problems required lengthy calculations, while differentiation-based questions had tricky applications.
This section was relatively easy compared to others. Questions on Mean, Variance, and Standard Deviation were direct and formula-based, making it a scoring area for students.
While the questions in Vectors & 3D Geometry were not very tough, they were lengthy and time-consuming. Many students spent extra time solving these questions, which made completing the exam difficult.
This section included formula-based and proof-based questions, with a mix of inverse trigonometric functions and identities. Some students found proof-based questions difficult, but overall, the section was manageable.
Here, you will find the most important questions for CBSE Class 12 Maths that you should practice. The CBSE Class 12 Maths Exam 2025 will include similar questions. These are the types of questions you can expect in the exam.
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.
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. Write the principal value of cos-1 [cos(680)°].
Q4. Write the value of cos-1 (1/2) – 2 sin-1 (1/2)
Q5. Using the principal values, write the value of cos-1(1/2) + 2 sin-1(1/2).
Q6. What is the principal value of tan-1 (- 1)?
Q7. Write the principal value of sin-1(−1/2).
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. If a matrix has 5 elements, then write all possible orders it can have.
4. 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.
5. 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|.
6. 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 = Ae2x + 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
7. 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.
8. 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.
9. 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 ≤ 6
x + y ≤ A; x ≥ 0, y ≥ 0.
10. 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.
The CBSE Class 12 Maths Paper Analysis PDF indicates that this year's paper was slightly more difficult compared to 2024. Below is a comparison of this year’s paper with previous years:
| Year | Overall Difficulty | Most Difficult Section | Easiest Section | Paper Length |
| 2023 | Moderate | Calculus | Probability | Slightly lengthy |
| 2024 | Moderate to Difficult | Algebra & Calculus | Statistics | Lengthy |
| 2025 | Moderate to Difficult | Calculus & Integration | Probability | Very Lengthy |
Students who practiced CBSE sample papers found some similar question patterns in the actual exam. Reviewing Class 12 Physics Sample Paper Analysis also helped students understand CBSE's way of framing papers this year.
CBSE Class 12 Maths Paper Analysis 2025 shows that the exam was moderate to difficult, with time-consuming sections in Calculus and 3D Geometry. Proper time management and practice with previous years' papers were essential for scoring well.
Ans. The CBSE Class 12 Maths Exam 2025 was moderate to difficult, with some lengthy and tricky questions in Calculus and Algebra. Students found Probability & Statistics relatively easier.
Ans. Calculus and Integration were the most challenging sections, requiring strong conceptual understanding and time management skills to solve effectively.
Ans. You can download the CBSE Class 12 Maths Paper Analysis 2025 PDF from our website. The link will be updated soon with a detailed breakdown of the exam.
Ans. Yes, the exam was lengthy, with time-consuming questions in 3D Geometry, Algebra, and Integration. Students had to manage their time effectively to complete all questions.
Ans. A good score is generally 65+ marks, while top scorers are expected to get 90+ marks. The passing marks are 33 out of 80.
