CBSE Class 12 Maths Important Questions 2026–27 with Solutions

CBSE Class 12 Maths Important Questions help students prepare for board exams by practising important concepts and different types of mathematical problems. These questions cover all 13 chapters of the CBSE Class 12 Maths syllabus, including Relations and Functions, Matrices, Calculus, Vector Algebra, Three-Dimensional Geometry and Probability.

Students looking for 12th Maths important questions can use this chapter-wise collection to revise formulas, practise numerical problems and understand the steps required to solve questions. These questions with solutions are useful for NCERT revision, school tests and CBSE board exam preparation.

Class 12 Maths Important Questions Chapter-wise

The Class 12 Maths important questions chapter-wise collection covers all 13 chapters. Select a chapter to practise questions based on its main concepts, formulas and applications.

These chapters follow the official CBSE Class 12 Mathematics syllabus for 2026–27. CBSE does not specify fixed chapter-wise marks, so students should prepare every chapter.

CBSE Class 12 Maths Important Questions with Solutions

Practising Class 12 Maths important questions with solutions helps students understand how to apply formulas and write step-by-step answers. Try each question before checking its solution.

Important Questions for Class 12 Maths Chapter 1 – Relations and Functions

Question 1. Show that the function f: R → R, defined by f(x) = 2x + 3, is one-one and onto.

Solution:

Step 1: Check whether the function is one-one.

Let f(a) = f(b).

2a + 3 = 2b + 3
2a = 2b
a = b

Since f(a) = f(b) implies a = b, the function is one-one.

Step 2: Check whether the function is onto.

Let y be any real number. We need an x such that y = 2x + 3.

x = (y − 3)/2

For every real y, this value of x is real and satisfies f(x) = y. Therefore, the function is onto.

Final Answer: f(x) = 2x + 3 is both one-one and onto.

Important Questions for Class 12 Maths Chapter 3 – Matrices

Question 2. Find AB for the matrices given below.

Matrix A:

Matrix B:

Solution: Multiply each row of A by the corresponding column of B.

First row, first column: 1 × 2 + 2 × 1 = 4
First row, second column: 1 × 0 + 2 × 3 = 6
Second row, first column: 3 × 2 + 4 × 1 = 10
Second row, second column: 3 × 0 + 4 × 3 = 12

Final Answer: AB =

Important Questions for Class 12 Maths Chapter 4 – Determinants

Question 3. Find the determinant of the matrix A:

Solution: For a 2 × 2 matrix with entries a, b in the first row and c, d in the second row:

Determinant = ad − bc

Substitute the values:

|A| = 3 × 4 − 2 × 5
|A| = 12 − 10
|A| = 2

Final Answer: The determinant is 2.

Important Questions for Class 12 Maths Chapter 5 – Continuity and Differentiability

Question 4. Find k so that f(x) is continuous at x = 2, where f(x) = x² for x ≠ 2, and f(2) = k.

Solution: A function is continuous at x = 2 when the limit as x approaches 2 equals f(2).

lim_x→2 f(x) = lim_x→2 x² = 4
f(2) = k

Therefore, k = 4.

Final Answer: k = 4.

Important Questions for Class 12 Maths Chapter 6 – Applications of Derivatives

Question 5. Find the maximum value of f(x) = 10x − x².

Solution:

Step 1: Differentiate the function.

f′(x) = 10 − 2x

Step 2: Set the first derivative equal to zero.

10 − 2x = 0
x = 5

Step 3: Check the second derivative.

f″(x) = −2

Since f″(5) is negative, the function has a maximum at x = 5.

Step 4: Calculate its value.

f(5) = 10 × 5 − 5² = 50 − 25 = 25

Final Answer: The maximum value is 25, at x = 5.

Important Questions for Class 12 Maths Chapter 7 – Integrals

Question 6. Evaluate the following indefinite integral:

∫ [(2x + 1)/(x² + x + 3)] dx

Solution: Let u = x² + x + 3.

du = (2x + 1) dx

Substitute u into the integral:

∫ (1/u) du = ln|u| + C

Since x² + x + 3 is positive for every real x, the modulus signs can be omitted.

Final Answer:

∫ [(2x + 1)/(x² + x + 3)] dx = ln(x² + x + 3) + C

Here, C is the constant of integration.

Important Questions for Class 12 Maths Chapter 10 – Vector Algebra

Question 7. Find the dot product of vectors a = î + 2ĵ + 2k̂ and b = 2î + k̂.

Solution: The dot product of vectors (a₁, a₂, a₃) and (b₁, b₂, b₃) is:

a · b = a₁b₁ + a₂b₂ + a₃b₃

Substitute the values:

a · b = 1 × 2 + 2 × 0 + 2 × 1
a · b = 2 + 0 + 2 = 4

Final Answer: The dot product is 4.

Important Questions for Class 12 Maths Chapter 13 – Probability

Question 8. A bag has 3 red balls and 2 blue balls. Two balls are drawn one after another without replacement. Find the probability that both balls are red.

Solution: There are 5 balls in total, including 3 red balls.

Step 1: The probability that the first ball is red is 3/5.

Step 2: After one red ball is removed, 2 red balls remain among 4 balls. The probability that the second ball is red, given the first was red, is 2/4.

Step 3: Multiply the probabilities.

P(both red) = (3/5) × (2/4) = 6/20 = 3/10

Final Answer: The probability of drawing two red balls is 3/10.

Students can use NCERT Solutions for Class 12 Maths to revise the methods used in these examples.

Class 12 Maths Important Questions – Chapter-wise Topics for Board Exams

Along with the solved examples, students should practise questions from the following topics in every chapter.

Relations and Functions Class 12 Important Questions with Solutions

Focus on reflexive, symmetric, transitive and equivalence relations. Practise identifying one-one and onto functions and proving the properties of given relations.

Inverse Trigonometric Functions Class 12 Important Questions

Important topics include the domain, range and principal values of inverse trigonometric functions. Practise questions involving identities and simplification.

Matrices and Determinants Class 12 Important Questions

Practise matrix addition, multiplication, transpose and inverse. For Determinants, focus on minors, cofactors, properties of determinants and solving systems of linear equations using matrices.

Continuity and Differentiability Class 12 Important Questions

Prepare questions on continuity at a point, the chain rule, implicit differentiation, logarithmic differentiation and second-order derivatives.

Applications of Derivatives Class 12 Important Questions

Important topics include increasing and decreasing functions, rates of change, and maxima and minima. Practise word problems involving derivatives.

Integrals Class 12 Important Questions with Solutions

Practise indefinite and definite integrals using substitution, partial fractions and integration by parts. Learn the standard formulas and properties of definite integrals.

Applications of Integrals Class 12 Important Questions

Focus on finding the area under a curve and the area of regions bounded by curves. Practise drawing the relevant graph before setting up the integral.

Differential Equations Class 12 Important Questions

Prepare questions on the order and degree of differential equations, general and particular solutions, separation of variables and first-order linear differential equations.

Vector Algebra and 3D Geometry Class 12 Important Questions

For Vector Algebra, practise dot products, cross products and vector operations. In Three-Dimensional Geometry, focus on equations of lines, angles between lines and shortest distance between skew lines.

Linear Programming Class 12 Important Questions

Practise converting word problems into linear programming problems, identifying constraints, drawing feasible regions and finding the optimum value of an objective function.

Probability Class 12 Important Questions with Solutions

Focus on conditional probability, independent events, the multiplication theorem, total probability and Bayes' theorem.

CBSE Class 12 Maths Important Questions – Unit-wise Weightage 2026–27

The CBSE Class 12 Maths theory examination carries 80 marks, while internal assessment carries 20 marks. The official syllabus provides this unit-wise distribution:

Calculus has the highest unit-wise allocation at 35 marks. Students should give sufficient time to its five chapters. However, CBSE does not specify fixed chapter-wise marks. Prepare every chapter rather than skipping topics based on predicted questions. 

Types of CBSE Class 12 Maths Important Questions

Practise different question formats to improve your problem-solving skills.

Refer to the official CBSE Class 12 sample question papers and marking schemes for the current exam format.

How to Prepare Class 12 Maths Important Questions for Board Exams

1. Complete the NCERT textbook: Understand solved examples and complete chapter exercises.
2. Revise formulas daily: Keep a notebook of important formulas and identities.
3. Solve chapter-wise questions: Start with basic problems and move to application-based questions.
4. Write complete solutions: Show formulas, substitutions, calculations and final answers.
5. Practise previous-year questions: Understand earlier CBSE question formats.
6. Solve sample papers: Attempt full papers within the given time.
7. Revise your mistakes: Repeat questions you found difficult until you understand the method.

Use Class 12 Maths Previous Year Question Papers for additional practice.

NCERT Solutions and Class 12 Maths Important Questions

NCERT Solutions for Class 12 Maths and important questions serve different purposes. NCERT Solutions explain textbook exercises and problem-solving methods. Important questions offer additional practice in applying those methods.

• Study the chapter concepts.
• Solve NCERT examples and exercises.
• Attempt chapter-wise important questions.
• Check answers against step-by-step solutions.
• Practise sample papers and previous-year questions.

Read the Infinity Learn NCERT Solutions for Class 12 Maths for chapter-wise explanations.

Class 12 Maths Important Questions PDF

Students often look for a Class 12 Maths important questions PDF to practise questions without an internet connection. An offline practice resource should include chapter-wise questions, important formulas, different question types, step-by-step solutions and clearly written answers.

Students can also download the latest sample papers and marking schemes from the CBSE Academic website.

Practising CBSE Class 12 Maths Important Questions is a useful way to revise concepts and prepare for board exams. Solve chapter-wise questions, understand each solution and practise different question formats.

Complete the NCERT textbook, revise formulas and attempt previous-year papers and sample papers regularly. Cover all 13 chapters to prepare for questions from every unit of the CBSE Class 12 Maths syllabus.