Every year, Class 12 students search for one thing before the board exam: which questions will come? Honestly, no one can tell you the exact questions. But CBSE follows a clear pattern, and some question types come up again and again.
In this post, we list the Class 12 Maths most expected questions for CBSE 2026-27, unit by unit, with short answers. Solve them yourself first, then check.
CBSE Class 12 Maths 2026-27: Exam pattern at a glance
- Total marks: 100 (80 theory + 20 internal assessment)
- Theory paper: 3 hours, with five sections: MCQs and assertion-reason (1 mark), very short answer (2 marks), short answer (3 marks), long answer (5 marks) and case-study questions (4 marks)
- No chapter-wise weightage: CBSE expects you to cover every chapter
Unit-wise marks distribution
| Unit | Marks |
|---|---|
| Calculus | 35 |
| Vectors and Three-Dimensional Geometry | 14 |
| Algebra | 10 |
| Relations and Functions | 8 |
| Probability | 8 |
| Linear Programming | 5 |
Calculus alone is almost half of the theory paper, so give it the most time.
Unit I: Relations and Functions (8 marks)
Q1. Let R = {(1,1), (2,2), (3,3), (1,2), (2,3)} be a relation on the set {1, 2, 3}. Check whether R is reflexive, symmetric and transitive.
Answer: Reflexive: yes. Symmetric: no, because (1,2) is in R but (2,1) is not. Transitive: no, because (1,2) and (2,3) are in R but (1,3) is not.
Q2. Find the value of tan⁻¹(1) + cos⁻¹(−1/2) + sin⁻¹(−1/2).
Answer: π/4 + 2π/3 − π/6 = 3π/4.
Unit II: Algebra (10 marks)
Q3. If A = [[2, 1], [5, 3]], find A⁻¹ and use it to solve 2x + y = 4 and 5x + 3y = 11.
Answer: |A| = 1, so A⁻¹ = [[3, −1], [−5, 2]]. Then X = A⁻¹B gives x = 1, y = 2.
Unit III: Calculus (35 marks)
Q4. Find dy/dx if y = xˣ.
Answer: Take logs on both sides (logarithmic differentiation). dy/dx = xˣ(1 + log x).
Q5. Find the value of k so that f(x) = kx + 1 for x ≤ 5 and f(x) = 3x − 5 for x > 5 is continuous at x = 5.
Answer: 5k + 1 = 10, so k = 9/5.
Q6. Find the intervals in which f(x) = 2x³ − 9x² + 12x + 15 is increasing or decreasing.
Answer: f′(x) = 6(x − 1)(x − 2). Increasing for x < 1 and x > 2, and decreasing for 1 < x < 2.
Q7. Evaluate the integral of sin x / (sin x + cos x) from 0 to π/2.
Answer: Use the property f(x) → f(a + b − x). The answer is π/4.
Q8. Find the area of the region bounded by the curve y = x² and the line y = 4.
Answer: Area = integral of (4 − x²) from −2 to 2 = 32/3 square units.
Q9. Solve the differential equation dy/dx + y = e⁻ˣ.
Answer: Integrating factor = eˣ. The solution is y = (x + C)e⁻ˣ.
Unit IV: Vectors and Three-Dimensional Geometry (14 marks)
Q10. Find the shortest distance between the lines r = (i + j) + λ(2i − j + k) and r = (2i + j − k) + μ(3i − 5j + 2k).
Answer: The cross product of the direction vectors is (3, −1, −7), with magnitude √59. The distance is 10/√59 units.
Q11. Find the distance of the point (1, 2, 3) from the plane 2x − y + 2z = 5.
Answer: |2 − 2 + 6 − 5| / √(4 + 1 + 4) = 1/3 unit.
Unit V: Linear Programming (5 marks)
Q12. Maximise Z = 5x + 3y subject to x + y ≤ 6, x ≤ 4, x ≥ 0, y ≥ 0.
Answer: The corner points are (0,0), (4,0), (4,2) and (0,6). Z is 0, 20, 26 and 18 respectively. Maximum Z = 26 at (4, 2).
Unit VI: Probability (8 marks)
Q13. Bag I has 3 red and 2 black balls. Bag II has 2 red and 4 black balls. A bag is chosen at random and a red ball is drawn. Find the probability that it came from Bag I.
Answer: By Bayes’ theorem, P(Bag I | red) = (3/10) ÷ (7/15) = 9/14.
Question types that come again and again
- Matrix inverse and solving equations (Algebra)
- Logarithmic and parametric differentiation
- Maxima, minima and increasing/decreasing functions
- Definite integrals using properties
- Area under curves and first-order differential equations
- Shortest distance between lines, and line and plane problems
- Linear programming with a graph
- Bayes’ theorem and probability distributions
- Case-study questions based on real situations (often on optimisation or probability)
How to prepare in the last weeks
- Finish NCERT first. Solve every example and exercise, especially in Calculus.
- Solve the official CBSE sample paper for 2026-27 in 3 hours, exactly like the exam.
- Practise previous years’ papers and mark the topics where you lose marks.
- Write all the steps. CBSE gives marks for steps, not only for the final answer.
- Revise formulas daily for 10 minutes: derivatives, integrals and vector formulas.
You can find chapter-wise notes on our Study Material page. If you want help with a chapter, contact us with your class and topic.
Frequently asked questions
Which unit has the highest marks in Class 12 Maths?
Calculus, with 35 out of 80 marks.
Are these questions sure to come in the board exam?
No. These are the types of questions that appear most often. The exact questions in your paper will differ, but if you can solve these types, you are well prepared.
How many marks is the Class 12 Maths paper?
The theory paper is 80 marks, and the internal assessment is 20 marks.
Is NCERT enough for Class 12 Maths?
NCERT is the base and covers most of the paper. Adding the CBSE sample paper and previous years’ papers gives you practice with the exam style.
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