ಕನ್ನಡ, हिंदी, मराठि, తెలుగు, தமிழ, ગુજરાતિ, বেংগালি, English Welcome Guest! LOGIN:STUDENT. | COLLEGE  | TUTORIAL | SCHOOL | PARENT | FACULTY Forgot Password?   |   New Student Registration. Online Coaching for CBSE

Welcome Student!

CBSE Class XI / XII, 2021, 2022, 2023 Download CBSE Class XII (NCERT), 2021, 2022, 2023, Maths Syllabus (13687 Downloads so far)
 MATHEMATICS COURSE STRUCTURE CBSE XII (NCERT), 2021, 2022, 2023 (Theory) One Paper Three Hours Max Marks. 80 Unit Titles Weightage I RELATIONS AND FUNCTIONS 10 II ALGEBRA 13 III CALCULUS 44 IV VECTORS AND THREE-DIMENSIONAL GEOMETRY 17 V LINEAR PROGRAMMING 06 VI PROBABILITY 10 Total 100

UNIT I. RELATIONS AND FUNCTIONS
1. Relations and Functions :
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations.
2. Inverse Trigonometric Functions:
Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

UNIT-II: ALGEBRA
1. Matrices:
Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and skew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).
2. Determinants:
Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle.

Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix. Cramer's rule and its applications.

UNIT-III: CALCULUS
1. Continuity and Differentiability:
Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function. Concept of exponential and logarithmic functions to the base. Logarithmic functions as an inverse of exponential functions.
$\underset{x\to 0}{\mathrm{lim}}\frac{1}{x}$, $\underset{x\to \infty }{\mathrm{lim}}\frac{1}{x}$, $\underset{x\to \infty }{\mathrm{lim}}\left(1+\frac{1}{x}{\right)}^{x}$, $\underset{x\to 0}{\mathrm{lim}}\left(1+x{\right)}^{\frac{1}{x}}$, $\underset{x\to 0}{\mathrm{lim}}\frac{\mathrm{log}\left(1+x\right)}{x}$, $\underset{x\to 0}{\mathrm{lim}}\frac{{e}^{x}-1}{x}$

Derivatives of Logarithmic and exponential functions
Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second order derivatives. Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation and simple applications.
2. Applications of Derivatives:
Applications of derivatives: rate of change, increasing/decreasing functions, tangents & normals, approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).
3. Integrals:
Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, only simple integrals of the type as below to be evaluated.

$\int \frac{dx}{{x}^{2}±{a}^{2}}$, $\int \frac{dx}{\sqrt{{x}^{2}±{a}^{2}}}$, $\int \frac{dx}{\sqrt{{a}^{2}-{x}^{2}}}$, $\int \frac{dx}{a{x}^{2}+bx+c}$, $\int \frac{dx}{\sqrt{a{x}^{2}+bx+c}}$, $\int \frac{\left(px+q\right)dx}{a{x}^{2}+bx+c}$, $\int \frac{\left(px+q\right)dx}{\sqrt{a{x}^{2}+bx+c}}$,

, , , ,

,

Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.
4. Applications of the Integrals:
Applications in finding the area under simple curves, especially lines, areas of circles/ parabolas/ellipses (in standard form only), area between the two above said curves (the region should be clearly identifiable).
5. Differential Equations:
Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables, homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type:

$\frac{dy}{dx}+py=q$, where 'p' and 'q' are functions of 'x' and

$\frac{dy}{dx}+px=q$, where 'p' and 'q' are functions of 'y'

UNIT-IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY
1. Vectors:
Vectors and scalars, magnitude and direction of a vector. Direction cosines/ratios of vectors. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Scalar (dot) product of vectors, projection of a vector on a line. Vector (cross) product of vectors.
2. Three - dimensional Geometry:
Direction cosines/ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes. (iii) a line and a plane. Distance of a point from a plane.

UNIT-V: LINEAR PROGRAMMING
1. Linear Programming:
Introduction, definition of related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

UNIT-VI: PROBABILITY
1. Probability:
Multiplication theorem on probability. Conditional probability, independent events, total probability, Baye's theorem, Random variable and its probability distribution, mean and variance of haphazard variable. Repeated independent (Bernoulli) trials and Binomial distribution.

Recommended Textbooks:

CBSE Syllabus

CBSE Class XI Syllabus
Physics
Chemistry
Maths
Biology
CBSE Class XII Syllabus
Physics
Chemistry
Maths
Biology

CBSE eBooks

CBSE Class XI eBooks
Physics
Chemistry
Maths
Biology
CBSE Class XII eBooks
Physics
Chemistry
Maths
Biology

CBSE Notes

Physics Learning Quiz

 CBSE Physics 1.Physical World 2.Units and Measurement Kinematics 3.Motion in a Straight Line 4.Motion in a Plane 5.Laws of Motion 6.Work, Energy and Power 7.Motion of System of Particles and Rotational Motion (Rigid Body) 8.Gravitation Properties of Bulk Matter 9.Mechanical Properties of Solids 10.Mechanical Properties of Fluids 11.Thermal Properties of Matter 12.Thermodynamics 13.Behaviour of Perfect Gas and Kinetic Theory 14.Oscillations 15.Waves Electrostatics 16.Electric Charges and Fields 17.Electrostatic Potential and Capacitance 18.Current Electricity 19.Moving Charges (Magnetic Effect of Current) and Magnetism 20.Magnetism and Matter 21.Electromagnetic Induction 22.Alternating Current 23.Electromagnetic Waves 24.Geometric Optics (Ray Optics) 25.Physical Optics (Wave Optics) 26.Dual Nature of Matter and Radiation 27.Atoms 28.Nuclei 29.Electronic Devices 30.Communication Systems All Chapters

Chemistry Learning Quiz

 CBSE Chemistry 1.Some Basic Concepts of Chemistry 2.Structure of Atom 3.Classification of Elements and Periodicity in Properties 4.Chemical Bonding and Molecular Structure 5.States of Matter 6.Thermodynamics 7.Equilibrium 8.Redox Reactions 9.Hydrogen 10.The s-block Elements 11.The p-block Elements Organic Chemistry 12.Organic Chemistry - Some Basic Principles and Techniques 13.Hydrocarbons 14.Environmental Chemistry 15.The Solid State 16.Solutions 17.Electrochemistry 18.Chemical Kinetics 19.Surface Chemistry 20.General Principles and Processes of Isolation of Elements 21.The p-Block Elements 22.The d-and f-Block Elements 23.Coordination Compounds 24.Haloalkanes and Haloarenes 25.Alcohols, Phenols and Ethers 26.Aldehydes, Ketones and Carboxylic Acids 27.Amines 28.Biomolecules 29.Polymers 30.Chemistry in Everyday Life All Chapters

Maths Learning Quiz

 CBSE Maths 1.Sets 2.Relations and Functions-1 3.Trigonometric Functions 4.Principle of Mathematical Induction 5.Complex Numbers and Quadratic Equations 6.Linear Inequalities 7.Permutations and Combinations 8.Binomial Theorem 9.Sequences and Series 10.Straight Lines 11.Conic Sections 12.Introduction to Three Dimensional Geometry 13.Limits and Derivatives 14.Mathematical Reasoning 15.Statistics 16.Probability-1 17.Infinite Series 18.Mathematical Modeling 19.Relations and Functions-2 20.Inverse Trigonometric Functions 21.Matrices 22.Determinants 23.Continuity and Differentiabilitybr /> 24.Application of Derivatives 25.Integrals 26.Application of Integrals 27.Differential Equations 28.Vector Algebra 29.Three Dimensional Geometry 30.Linear Programming 31.Probability-2 All Chapters

Biology Learning Quiz

 NEET Biology Diversity in the Living World 1.The Living World 2.Biological Classification 3.Plant Kingdom 4.Animal Kingdom Structural Organisation in Plants and Animals 5.Morphology of Flowering Plants 6.Anatomy of Flowering Plants 7.Structural Organisation in Animals Cell: Structure and Functions 8.Cell:The Unit of Life 9.Biomolecules 10.Cell Cycle and Cell Division Plant Physiology 11.Transport in Plants 12.Mineral Nutrition 13.Photosynthesis in Higher Plants 14.Respiration in Plants 15.Plant Growth and Development Human Physiology 16.Digestion and Absorption 17.Breathing and Exchange of Gases 18.Body Fluids and Circulation 19.Excretory Products and their Elimination 20.Locomotion and Movement 21.Neural Control and Coordination 22.Chemical Coordination and Integration Reproduction 23.Reproduction in Organisms 24.Sexual Reproduction in Flowering Plants 25.Human Reproduction 26.Reproductive Health Genetics and Evolution 27.Principles of Inheritance and Variation 28.Molecular Basis of Inheritance 29.Evolution Biology in Human Welfare 30.Human Health and Disease 31.Strategies for Enhancement in Food Production 32.Microbes in Human Welfare Biotechnology 33.Biotechnology : Principles and Processes 34.Biotechnology and its Applications Ecology 35.Organisms and Populations 36.Ecosystem 37.Biodiversity and Conservation 38.Environmental Issues All Chapters

Solved Old Question Papers

Physics
2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012
Chemistry
2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012
Maths
2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012
Biology
2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012

Performance Report

CBSE Video Lessons

CBSE Video Lessons
Physics
Chemistry
Maths
Biology

Lessons' Quick Revision

CBSE Lessons' Quick Revision
Physics
Chemistry
Maths
Biology

Important Formulae/Points

CBSE Important Formulae/Points
Physics
Chemistry
Maths
Biology

Glossary/Dictionary

CBSE Glossary/Dictionary
Physics
Chemistry
Maths
Biology

Scientists & Innovations

Scientists & Innovations
Physics
Chemistry
Maths
Biology

## Online Tutorials

• Computer Languages
• Engg Entrance
• Medical Entrance
• UPSC
• Bank Exams
• Campus Interviews
• More »

## Video Tutorials

• Computer Languages
• Engg Entrance
• Medical Entrance
• UPSC
• Bank Exams
• Campus Interviews
• More »