What is the maximum marks allocated to the CBSE Class 12 Maths board exam 2025?

The CBSE Class 12 maths theory paper is held for 80 marks.

Where can I find the most important questions for CBSE Class 12th Maths board exam 2025?

Students can find the most important CBSE Class 12 Maths board exam questions from the article above.

CBSE Class 12 Maths Question Paper 2025, Check Most Expected Questions by Experts -

Table of Contents

The Central Board of Secondary Education (CBSE) is all set to hold one of the most important board exam papers of 2025- Mathematics. The CBSE Class 12 Mathematics board exam 2025 is scheduled for March 06, 2025. Students can find the CBSE Class 12th Maths most important and repeated board exam questions for practice here. After the exam, students can access the official CBSE Class 12 Maths Question Paper 2025 with solutions.

CBSE Class 12 Maths Question Paper 2025

The CBSE Class 12 Mathematics theory exam 2025 is held for 80 marks, the rest 20 marks is allocated for Internal assessment. The CBSE Class 12 Maths question paper 2025 is important for both current and upcoming board students. The official question paper for the CBSE Class 12 Board Exam 2025 is issued after the exam conclusion. Students are given 3 hours to solve the mathematics board exam paper.

CBSE Class 12th Maths Question Paper 2025

The Board prepares different sets of question papers for the CBSE 12th Maths board exam 2025. Prior to upcoming board exams, the official question papers assist students in grasping the exam pattern, key topics, and time allocation. Following the exams, the set-wise CBSE Class 12th Maths Question Papers 2025 along with their answers enable students to verify their response and form a rough assessment of their performance.

CBSE Class 12 Maths Most Expected Questions for Board Exam 2025

With just a few time remaining with students, students should practice the CBSE Class 12 Maths Board Exam 2025 Most Expected Questions shared by experts in their final hours before the exam. These model questions have been shared by the veterans of mathematics filed who have also been formulating the CBSE 12th maths Board exam papers in the past. Such questions or the same concepts are certain to be asked in the exam. Practice these questions to ensure your score 95+ marks in CBSE Class 12 maths board exam 2025.

S.No.	Question
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 be 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) =
Q8	Write fog, if f: R → R and g: R → R are given by f(x) = 8x³ and g(x) = x³y.
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?
Q11	Write the value of tan⁻¹(√3) – cot⁻¹(-√3).
Q12	Find the principal value of tan⁻¹(√3) – sec⁻¹(-2).
Q13	Write the principal value of cos⁻¹[cos(680)°].
Q14	Write the value of cos⁻¹(1/2) – 2 sin⁻¹(1/2).
Q15	Using the principal values, write the value of cos⁻¹(1/2) + 2 sin⁻¹(1/2).
Q16	What is the principal value of tan⁻¹(-1)?
Q17	Write the principal value of sin⁻¹(-1/2).
Q18	Write the number of all possible matrices of order 2 × 2 with each entry 1, 2, or 3.
Q19	Write the element a of a 3 × 3 matrix A = [aij], whose elements are given by aij =
Q20	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.
Q21	If a matrix has 5 elements, then write all possible orders it can have.
Q22	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.
Q23	Show that the function f(x) = x³ – 3x² + 6x – 100 is increasing on R.
Q24	Show that the function f(x) = 4x³ – 18x² + 27x – 7 is always increasing on R.
Q25	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?
Q26	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 the rectangle.
Q27	Using integration, find the area of a triangle whose vertices are (2, 3), (3, 5), and (4, 4).
Q28	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.
Q29	Using integration, find the area of the triangular region whose sides have the equations y = 2x + 1, y = 3x + 1, and x = 4.
Q30	Using integration, find the area of the region bounded by the triangle whose vertices are (-2, 1), (0, 4), and (2, 3).
Q31	Using integration, find the area of the region bounded by the curves y = √(4 − x²), x² + y² − 4x = 0, and the x-axis.
Q32	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.
Q33	Using integration, find the area of the region bounded by the line x − y + 2 = 0, the curve x = √y, and the Y-axis.
Q34	Using integration, find the area of the region bounded by the curves y =
Q35	Using integration, find the area of the region bounded by the triangle whose vertices are (-1, 2), (1, 5), and (3, 4).
Q36	Find the area of the region bounded by the parabola y = x² and the line y =
Q37	Find the differential equation representing the family of curves y = ae²ˣ + 5 constant.
Q38	Find the differential equation representing the family of curves V = A/r + B, where A and B are arbitrary constants.
Q39	Write the differential equation obtained by eliminating the arbitrary constant C in the equation representing the family of curves xy = C cos x.
Q40	Write the differential equation representing the family of curves y = mx, where m is an arbitrary constant.
Q41	Find the differential equation of the family of curves y = Ae²ˣ + Be⁻²ˣ, where A and B are arbitrary constants.
Q42	Form the differential equation of the family of parabolas having the vertex at origin and axis along the positive Y-axis.
Q43	Find the differential equation of the family of circles touching the Y-axis at the origin.
Q44	Write the solution of the differential equation dy/dx = 2 − y.
Q45	Find the unit vector in the direction of the sum of the vectors 2î + 3ĵ − k̂ and 4î − 3ĵ + 2k̂.
Q46	Find a vector in the direction of vector 2î − 3ĵ + 6k̂ which has magnitude 21 units.
Q47	Find a vector a of magnitude 5√2, making an angle of π/4 with the X-axis, π/2 with the Y-axis, and an acute angle θ with the Z-axis.
Q48	Find the angle between the X-axis and the vector î + ĵ + k̂.
Q49	Write the direction cosines of vector -2î + ĵ − 5k̂.
Q50	What is the cosine of the angle which the vector √2î + ĵ + k̂ makes with the Y-axis?
Q51	Find the area of a parallelogram whose adjacent sides are represented by the vectors 2î − 3k̂ and 4ĵ + 2k̂.
Q52	If a line makes angles 90°, 135°, 45° with the x, y, and z axes respectively, find its direction cosines.
Q53	What are the direction cosines of a line which makes equal angles with the coordinate axes?
Q54	If a line makes angles 90°, 60°, and θ with X, Y, and Z-axis respectively, where θ is an acute angle, then find θ.
Q55	Write the distance of a point P(a, b, c) from the X-axis.
Q56	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.
Q57	Find the vector equation of the line passing through the point A (1, 2, −1) and parallel to the line 5x − 25 = 14 − 7y = 35z.
Q58	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.
Q59	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 produce at least 60 shirts and 32 pairs of trousers at a minimum labour cost, formulate this as an LPP.
Q60	Maximise and minimise Z = x + 2y subject to the constraints x + 2y ≥ 100, 2x – y ≤ 0, 2x + y ≤ 200, x, y ≥ 0. Solve the above LPP graphically.
Q61	A company produces two types of goods, A and B, that require gold and silver. Each unit of type A requires 3g of silver and 1g of gold, while type B requires 1g of silver and 2g of gold. The company can use at most 9g of silver and 8g of gold. If each unit of A brings ₹40 and B ₹50, find the number of units of each type to maximize profit. Formulate and solve the LPP graphically.
Q62	A retired person wants to invest ₹50,000. His broker recommends investing in two types of bonds A and B yielding 10% and 9% return respectively. He decides to invest at least ₹20,000 in bond A and at least ₹10,000 in bond B, and wants to invest at least as much in bond A as in bond B. Solve this LPP graphically to maximize returns.
Q63	Find graphically, the maximum value of Z = 2x + 5y, subject to the constraints: 2x + 4y ≤ 8; 3x + y ≤ 6; x + y ≤ 4; x ≥ 0, y ≥ 0.
Q64	If P(not A) = 0.7, P(B) = 0.7, and P(B/A) = 0.5, then find P(A/B).
Q65	A and B throw a pair of dice alternately until one of them gets a total of 10 and wins the game. Find their respective probabilities of winning, if A starts first.
Q66	Two groups are competing for positions in the Board of Directors. The probabilities that the first and second groups will win are 0.6 and 0.4, respectively. If the first group wins, the probability of introducing a new product is 0.7, and 0.3 for the second group. Find the probability that the new product was introduced by the second group.
Q67	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, bag A is chosen; otherwise, bag B is chosen. If two balls are drawn from the selected bag, find the probability of one being red and the other black.
Q68	From a lot of 15 bulbs, including 5 defectives, a sample of 2 bulbs is drawn at random (without replacement). Find the probability distribution of the number of defective bulbs.
Q69	Find the mean number of heads in three tosses of a coin.
Q70	Find the probability distribution of the number of doublets in three tosses of a pair of dice.
Q71	A bag contains 3 red and 7 black balls. Two balls are selected randomly without replacement. If the second selected ball is red, what is the probability that the first selected ball is also red?
Q72	Three cards are drawn randomly (without replacement) from a shuffled pack of 52 cards. Find the probability distribution of the number of red cards. Hence, find the mean of the distribution.
Q73	Two numbers are selected randomly (without replacement) from the integers 2, 3, 4, 5, 6, and 7. Let X be the larger of the two numbers. Find the mean and variance of the probability distribution of X.

CBSE 12th Maths Most Repeated Board Questions PDF Download with Solutions

Students can download the CBSE Class 12 Maths most important and most repeated questions for the board exam 2025 in the following PDF. Along with the questions shared by the expert, the PDF also contains the solutions of every question. This will help student know how to write the answer of every question as per the board standard.

CBSE Class 12 Mathematics Most Expected Questions PDF Download

CBSE Class 12 Maths Question Paper 2025 PDF Download All Sets

Students can download the CBSE Class 12 Math board exam 2025 question paper in PDF format here. The official CBSE Class 12 Maths question paper 2025 PDF is presented here after the exam ends. Students can use this question paper to match their responses with the unofficial solution key prepared by the experts. Students can use this paper as a reference to calculate their marks using the marking scheme provided in the paper.

CBSE Class 12 Maths Board Exam Pattern 2025

The CBSE Class 12 Maths question paper 2025 pattern is mentioned below for students.

This board exam paper includes 38 questions. Every question must be answered.
The examination paper consists of five sections – A, B, C, D, and E.
In Section A, Questions 1 to 18 consist of multiple-choice questions (MCQs), while Questions 19 and 20 are Assertion-Reason questions worth 1 mark each.
In Section B, Questions 21 to 25 are categorized as Very Short Answer (VSA) questions, each worth 2 marks.
In Section C, Questions 26 through 31 are Short Answer (SA) questions, each worth 3 marks.
In Section D, Questions 32 to 35 consist of Long Answer (LA) questions, each worth 5 marks.
In Section E, Questions 36 to 38 are based on a case study and are worth 4 marks each.
There is no general option. Nonetheless, an internal option has been included in 2 questions in Section B, 3 questions in Section C, 2 questions in Section D, and one subpart each in 2 questions of Section E.
Calculators are not permitted for use.