Maths Important Questions Class 12 CBSE 2026 — Chapter Wise
Class 12 Maths important questions 2026 — integration, differential equations, vectors, and probability for CBSE board exam.
CBSE Class 12 Maths: 80 marks theory + 20 marks internal assessment. Calculus alone is 35/80 marks — nearly half the paper. Master integration and applications of derivatives first. Below are the most expected questions from each chapter.
Relations & Functions + Inverse Trig (8 marks)
| Question | Marks |
|---|---|
| Show that the relation R on set A = {1,2,3,4,5} defined by R = {(a,b) : |a−b| is even} is an equivalence relation. | 5 |
| Let f: R→R be defined by f(x) = (4x+3)/(6x−4). Show that f is bijective and find f⁻¹. | 5 |
| Prove that: tan⁻¹(1/2) + tan⁻¹(1/5) + tan⁻¹(1/8) = π/4. | 3 |
| Simplify: tan⁻¹[√(1+x²)−1]/x in terms of tan⁻¹x. | 3 |
| Write the principal value of: cos⁻¹(cos 7π/6). | 1 |
Matrices & Determinants (10 marks)
| Question | Marks |
|---|---|
| Using matrices, solve: 2x+3y+3z=5, x−2y+z=−4, 3x−y−2z=3. | 5 |
| Find the inverse of a 3×3 matrix using adjoint method. | 5 |
| If A is a square matrix such that A² = A, show that (I+A)³ = 7A + I. | 3 |
| Using properties of determinants, prove: |a−b−c 2a 2a; 2b b−c−a 2b; 2c 2c c−a−b| = (a+b+c)³. | 5 |
| Find the value of k if the area of triangle with vertices (2,−6), (5,4), (k,4) is 35 sq units using determinant. | 3 |
Continuity & Differentiability
| Question | Marks |
|---|---|
| Find the values of a and b such that f(x) is continuous: f(x) = 5 if x≤2, ax+b if 2<x<10, 21 if x≥10. | 3 |
| If y = (sin⁻¹x)², prove that (1−x²)y₂ − xy₁ − 2 = 0. | 5 |
| Differentiate: xˣ + (sin x)^(log x) with respect to x. | 3 |
| If x = a(cos t + t sin t) and y = a(sin t − t cos t), find d²y/dx². | 5 |
| Verify Rolle's theorem for f(x) = x² + 2x − 8 on [−4, 2]. | 3 |
Applications of Derivatives
| Question | Marks |
|---|---|
| Find the intervals in which f(x) = 2x³ − 3x² − 36x + 7 is strictly increasing or decreasing. | 5 |
| Find the equation of tangent and normal to the curve y = x³ − 3x + 5 at point (2, 7). | 3 |
| Find the maximum and minimum values of f(x) = sin x + cos x on [0, π]. | 3 |
| Show that the semi-vertical angle of a cone of maximum volume inscribed in a sphere of radius r is sin⁻¹(2/3). | 5 |
| A ladder 5m long leans against a wall. Bottom slides at 2 cm/s. How fast is the top sliding when bottom is 4m from wall? | 3 |
Practise Maths chapter-wise
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Start Maths Practice — FreeIntegrals (Most Important)
| Question | Marks |
|---|---|
| Evaluate: ∫ dx / (x² + 4x + 13) | 3 |
| Evaluate: ∫ x² / (x² + 1)(x² + 4) dx using partial fractions. | 5 |
| Evaluate: ∫ eˣ (sin x + cos x) dx. | 3 |
| Evaluate: ∫₀^π x sin x / (1 + cos²x) dx using properties of definite integrals. | 5 |
| Evaluate: ∫ x tan⁻¹x dx using integration by parts. | 3 |
| Evaluate: ∫ (2x + 3) / √(x² + 4x + 1) dx. | 3 |
| Evaluate ∫₀^(π/2) log(sin x) dx. | 5 |
Applications of Integrals
| Question | Marks |
|---|---|
| Find the area bounded by the curve y = x², the line y = x, and the x-axis in the first quadrant. | 5 |
| Find the area of the region enclosed between y² = 4x and x² = 4y. | 5 |
| Find the area of the circle x² + y² = a² using integration. | 5 |
| Find the area bounded by the ellipse x²/a² + y²/b² = 1. | 5 |
Differential Equations
| Question | Marks |
|---|---|
| Solve: dy/dx + y/x = x² (linear DE). | 3 |
| Solve: (1 + x²)dy/dx + 2xy = 1/(1 + x²). | 5 |
| Find the particular solution of dy/dx = y tan x given y = 1 when x = 0. | 3 |
| Form the DE of the family of circles touching the x-axis at origin. | 3 |
| Solve: x dy − y dx = √(x² + y²) dx (homogeneous DE). | 5 |
Vectors & 3D Geometry (14 marks)
| Question | Marks |
|---|---|
| Find the shortest distance between lines: r⃗ = (1+λ)î + (2−λ)ĵ + (λ+1)k̂ and r⃗ = (2+μ)î − (1−μ)ĵ + (−1+2μ)k̂. | 5 |
| Find the equation of the plane through (1,1,1), (1,−1,1), (−7,−3,−5). Also find distance from origin. | 5 |
| Find the angle between planes: 2x − y + z = 4 and x + y + 2z = 3. | 3 |
| If a⃗ × b⃗ = c⃗ × d⃗ and a⃗ × c⃗ = b⃗ × d⃗, show that a⃗ − d⃗ is parallel to b⃗ − c⃗. | 3 |
| Find the image of point (1, 6, 3) in the line x/1 = (y−1)/2 = (z−2)/3. | 5 |
| Find the vector and Cartesian equations of the line passing through (1, 2, −4) and perpendicular to lines (x−8)/3 = (y+19)/−16 = (z−10)/7 and (x−15)/3 = (y−29)/8 = (z−5)/−5. | 5 |
Linear Programming (5 marks)
| Question | Marks |
|---|---|
| Maximise Z = 3x + 2y subject to: x + 2y ≤ 10, 3x + y ≤ 15, x, y ≥ 0. Solve graphically. | 5 |
| A manufacturer makes two types of toys. Type A requires 5 min cutting, 10 min assembling. Type B requires 8 min cutting, 8 min assembling. Available: 3 hrs 20 min cutting, 4 hrs assembling. Profit: ₹50 (A), ₹60 (B). Maximise profit. | 5 |
LP tip: This is 5 easy marks. Always: (1) define variables, (2) write objective function, (3) write constraints, (4) draw graph, (5) find corner points, (6) evaluate Z at each. Show the graph — it carries marks.
Probability (8 marks)
| Question | Marks |
|---|---|
| Bag I has 3 red, 4 black balls. Bag II has 5 red, 6 black. One bag is chosen at random and a ball is drawn. Find probability it is red. If red, find probability it came from Bag I (Bayes' theorem). | 5 |
| A die is thrown 6 times. If getting an odd number is success, find P(at least 5 successes) using binomial distribution. | 5 |
| Find the mean and variance of binomial distribution B(n, p) where n = 6, p = 1/3. | 3 |
| Two cards are drawn from a pack of 52 without replacement. Find probability of getting: (a) both aces, (b) one ace one king. | 3 |
Questions based on CBSE Class 12 Maths papers (2018–2025) and 2026 sample paper. Marks from CBSE 2025–2026 blueprint. Solve all NCERT exercises before practising these. Last updated: February 2026.
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Start preparing — freeFrequently Asked Questions
Which chapters are most important for Class 12 Maths?
Calculus is the most important — 35 out of 80 marks (44% of paper). This includes: Continuity & Differentiability, Applications of Derivatives, Integrals, Applications of Integrals, and Differential Equations. After Calculus: Vectors & 3D Geometry (14 marks), Matrices & Determinants (10 marks), Probability (8 marks).
How to score full marks in Class 12 Maths?
Three rules: (1) Show every step — step marks are generous, even wrong final answers get partial credit. (2) Solve NCERT examples + all exercises — board questions are variations. (3) Practise 10+ sample papers under timed conditions. Linear Programming (5 marks) and Probability (8 marks) are the easiest chapters — never lose marks there.
Is NCERT enough for Class 12 Maths boards?
Yes — 90%+ board questions are from NCERT or slight variations. Solve all examples, all miscellaneous exercises, and NCERT Exemplar for extra practice. RD Sharma is useful for additional practice but not necessary for scoring 90+.
How many marks are from Calculus?
35 marks out of 80 — nearly half the paper. Breakdown: Integration (7-8 marks), Applications of Derivatives (5-6 marks), Continuity & Differentiability (5-6 marks), Differential Equations (5-6 marks), Applications of Integrals (5-6 marks). Master integration techniques and you control 44% of your score.