Free online tests on Mathematics class 12

Class 12 Mathematics Online Tests

Free chapter-wise tests based on latest CBSE syllabus

Unit I: Relations and Functions (08 Marks)

Chapter 1: Relations

Topics: Ordered pairs, Cartesian products, types of relations: reflexive, symmetric, transitive, and equivalence relations.

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Chapter 2: Functions

Topics: One-one and onto functions, composition of functions, invertible functions, binary operations.

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Chapter 3: Inverse Trigonometric Functions

Topics: Domains, ranges, principal value branches, graphs, and properties of inverse trigonometric functions.

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Unit II: Algebra (10 Marks)

Chapter 4: Matrices

Topics: Types of matrices, operations, properties, transpose, symmetric and skew-symmetric matrices, invertible matrices.

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Chapter 5: Determinants

Topics: Determinants up to order 3, properties, minors, cofactors, applications, adjoint and inverse, solving systems of equations.

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Unit III: Calculus (35 Marks)

Chapter 6: Continuity and Differentiability

Topics: Continuity, differentiability, derivatives of composite, implicit, inverse trig functions, second-order derivatives, MVT and Rolle’s Theorem.

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Chapter 7: Applications of Derivatives

Topics: Increasing/decreasing functions, tangents and normals, maxima and minima, real-life applications.

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Chapter 8: Integrals

Topics: Indefinite and definite integrals, properties, basic integration techniques, substitution, parts, partial fractions.

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Chapter 9: Applications of Integrals

Topics: Area under curves (lines, parabolas, circles), area between two curves.

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Chapter 10: Differential Equations

Topics: Formation, order, degree, general/particular solutions, variable separable method, linear equations.

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Unit IV: Vectors and Three-Dimensional Geometry (14 Marks)

Chapter 11: Vectors

Topics: Magnitude, direction, types of vectors, operations, dot and cross product, geometric interpretation.

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Chapter 12: Three-Dimensional Geometry

Topics: Direction cosines and ratios, equations of lines and planes, coplanarity, angles, shortest distance.

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Unit V: Linear Programming (05 Marks)

Chapter 13: Linear Programming

Topics: Formulation, feasible and infeasible regions, graphical method, optimization of objective function.

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Unit VI: Probability (08 Marks)

Chapter 14: Probability

Topics: Conditional probability, Bayes’ theorem, random variables, probability distributions, Bernoulli trials, binomial distribution.

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Other Free MCQ Online Tests Class 12 Mathematics

Free mcq online tests class 12 Relations and Functions

Free mcq online tests class 12 Inverse Trigonometric Functions

Free mcq online tests class 12 Matrices

Determinants free mcq online tests class 12

Free mcq online tests class 12 Continuity and Differentiability

Free mcq online tests class 12 Applications of Derivatives

Free mcq online tests class 12 Integrals

Free mcq online tests class 12 Applications of Integrals

Free mcq online tests class 12 Differential Equations

Free mcq online tests class 12 Vector Algebra

Free mcq online tests class 12 Three Dimensional Geometry

Free mcq online tests class 12 Linear Programming

Free mcq online tests class 12 Probability

Frequently Asked Questions (FAQ’s)

Questions

What are free MCQ online tests for Class 12 Relations and Functions and how do they help students?

Answers

Free MCQ online tests class 12 Relations and Functions are designed to help students practice one of the most conceptual chapters of Class 12 Mathematics. These online tests include objective questions based on relations, types of functions, domain, range, and composition of functions. By attempting free MCQ online tests class 12, students can improve conceptual clarity, understand CBSE exam patterns, and strengthen problem-solving speed. Regular practice also boosts confidence and helps identify weak areas before final board examinations.


Questions

How useful are free MCQ online tests class 12 Inverse Trigonometric Functions for board exam preparation?

Answers

Free MCQ online tests class 12 Inverse Trigonometric Functions are extremely useful for mastering formulas, properties, and standard values. This chapter often carries scoring questions in CBSE exams. Practicing inverse trigonometric functions free MCQ online tests class 12 helps students revise concepts like principal values, domains, ranges, and identities efficiently. These online tests are aligned with the latest syllabus and help students prepare for competitive exams while improving accuracy and time management.


Questions

Why should students attempt free MCQ online tests class 12 Matrices regularly?

Answers

Free MCQ online tests class 12 Matrices help students practice important topics such as types of matrices, matrix operations, transpose, and inverse of matrices. Since matrices involve step-wise calculations, MCQ practice improves speed and accuracy. Attempting free MCQ online tests class 12 Mathematics regularly allows students to identify frequently asked questions and common mistakes. These tests are especially helpful for last-minute revision and concept reinforcement before CBSE board exams.


Questions

What is the importance of determinants free MCQ online tests class 12?

Answers

Determinants free MCQ online tests class 12 focus on a crucial chapter that is closely related to matrices and linear equations. These tests help students practice properties of determinants, evaluation methods, and applications such as finding area and solving systems of equations. By attempting determinants free MCQ online tests class 12, students can enhance conceptual understanding and problem-solving efficiency, which is essential for scoring well in Class 12 Mathematics board exams.


Questions

How do free MCQ online tests class 12 Continuity and Differentiability improve performance?

Answers

Free MCQ online tests class 12 Continuity and Differentiability help students master limits, continuity, differentiability, and standard derivatives. This chapter forms the foundation of calculus and has significant weightage in CBSE exams. Practicing free MCQ online tests class 12 Mathematics enables students to quickly recall formulas, understand graphical interpretations, and avoid calculation errors. These online tests are ideal for strengthening basics and improving exam-oriented preparation.


Questions

Why are free MCQ online tests class 12 Applications of Derivatives important?

Answers

Free MCQ online tests class 12 Applications of Derivatives help students understand real-life applications such as rate of change, increasing and decreasing functions, maxima and minima, and tangents. These topics require strong conceptual clarity and practice. By attempting free MCQ online tests class 12, students can learn how to apply derivative concepts effectively and improve logical thinking. These tests also help students prepare for HOTS and case-study-based questions.


Questions

How can free MCQ online tests class 12 Integrals help in scoring higher marks?

Answers

Free MCQ online tests class 12 Integrals provide extensive practice on indefinite and definite integrals, substitution methods, and standard integrals. Integration is often considered challenging, and regular MCQ practice helps students recognize patterns quickly. Attempting free MCQ online tests class 12 Mathematics improves calculation speed and reduces exam stress. These tests are useful for both board exams and competitive exam preparation.


Questions

What are the benefits of free MCQ online tests class 12 Applications of Integrals?

Answers

Free MCQ online tests class 12 Applications of Integrals focus on calculating areas under curves and between curves. These questions require visualization and correct use of limits. Practicing applications of integrals free MCQ online tests class 12 helps students strengthen conceptual understanding and avoid common mistakes. These online tests are designed according to CBSE patterns and help students gain confidence in solving numerical and application-based problems.


Questions

How do free MCQ online tests class 12 Differential Equations support exam preparation?

Answers

Free MCQ online tests class 12 Differential Equations help students practice formation and solution of differential equations using different methods. This chapter is scoring and relatively easy with regular practice. Attempting free MCQ online tests class 12 Mathematics allows students to revise formulas, understand solution techniques, and improve speed. These tests are beneficial for quick revision before exams and for strengthening fundamentals.


Questions

Why should students practice free MCQ online tests class 12 Vector Algebra?

Answers

Free MCQ online tests class 12 Vector Algebra help students understand vector operations, dot product, cross product, and scalar triple product. This chapter is important for both board and competitive exams. Practicing vector algebra free MCQ online tests class 12 improves spatial understanding and formula application. Regular MCQ practice helps students avoid calculation errors and boosts confidence in solving objective questions efficiently.


Questions

What is the role of free MCQ online tests class 12 Three Dimensional Geometry?

Answers

Free MCQ online tests class 12 Three Dimensional Geometry help students master concepts like direction ratios, direction cosines, lines, planes, and angles between them. This chapter involves formula-based and conceptual questions. Practicing free MCQ online tests class 12 Mathematics enhances visualization skills and accuracy. These tests are extremely helpful for quick revision and improving performance in board examinations.


Questions

How do free MCQ online tests class 12 Linear Programming help students?

Answers

Free MCQ online tests class 12 Linear Programming focus on graphical methods, feasible regions, and optimization problems. This chapter is considered easy scoring if concepts are clear. Practicing free MCQ online tests class 12 helps students understand step-wise solutions and graphical interpretations. These tests are useful for quick concept revision and improving accuracy in objective-type questions.


Questions

Why are free MCQ online tests class 12 Probability essential for exam success?

Answers

Free MCQ online tests class 12 Probability help students practice conditional probability, Bayes’ theorem, and random variables. Probability is a high-weightage chapter in Class 12 Mathematics. By attempting probability free MCQ online tests class 12, students can improve logical reasoning, formula application, and numerical accuracy. Regular practice through online tests ensures better performance in CBSE board exams and competitive entrance tests.