# NCERT solutions for class 12 Mathematics

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## NCERT Solutions for Class 12 Mathematics in PDF Free Download

NCERT Text book solutions for class 12 Maths all chapters in PDF format for free download. NCERT solutions for 12 Class mathematics solved by expert and experienced teachers at myCBSEguide. These ncert book chapter wise questions and answers are very helpful to obtain good marks in CBSE board exam. Ncert solution class 12 Mathematics includes text book solutions . NCERT Solutions for CBSE Class 12 Mathematics have total 13 chapters. Class 12 Mathematics ncert Solutions in pdf for free Download are given in this website. Ncert Mathematics class 12 solutions PDF and Mathematics ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide. In other words cbse guide will also provide an easy learning platform for students. Furthermore, CBSE chapter wise NCERT solution for Mathematics part 1 and Mathematics part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.Download NCERT Solutions for CBSE Class 12 Mathematics 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.

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Download NCERT Solutions for CBSE Class 12 Mathematics Inverse Trigonometric Functions Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

Download NCERT Solutions for CBSE Class 12 Mathematics Matrices Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Noncommutativity 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).

Download NCERT Solutions for CBSE Class 12 Mathematics Determinants Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, co-factors 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.

Download NCERT Solutions for CBSE Class 12 Mathematics Continuity and Differentiability Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions. 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.

Download NCERT Solutions for CBSE Class 12 Mathematics Application of Derivatives Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in 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).

Download NCERT Solutions for CBSE Class 12 Mathematics Integrals Integration as inverse process of differentiation.Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them. Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof).Basic properties of definite integrals and evaluation of definite integrals.

Download NCERT Solutions for CBSE Class 12 Mathematics Application of Integrals Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only), Area between any of the two above said curves (the region should be clearly identifiable).

Download NCERT Solutions for CBSE Class 12 Mathematics 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 solutions of homogeneous differential equations of first order and first degree.

Download NCERT Solutions for CBSE Class 12 Mathematics Vector Algebra Vectors and scalars, magnitude and direction of a vector.Direction cosines and direction ratios of a vector. 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. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors.

Download NCERT Solutions for CBSE Class 12 Mathematics Three Dimensional Geometry Direction cosines and direction ratios of a line joining two points. Cartesian equation 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.

Download NCERT Solutions for CBSE Class 12 Mathematics Linear Programming Introduction, 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(bounded and unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

Download NCERT Solutions for CBSE Class 12 Mathematics Probability Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution.

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**NCERT 12 Mathematics Text book Solutions**

NCERT 12th class Mathematics book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 Mathematics chapter wise NCERT solution for Mathematics part 1 and Mathematics part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.

**NCERT Class 12 Mathematics Chapter-wise Solutions**

**Part I**

- Chapter 1: Relations and Functions
- Chapter 2: Inverse Trigonometric Functions
- Chapter 3: Matrices
- Chapter 4: Determinants
- Chapter 5: Continuity and Differentiability

**Part II**

- Chapter 6: Application of Derivatives
- Chapter 7: Integrals
- Chapter 8: Application of Integrals
- Chapter 9: Differential Equations
- Chapter 10: Vector Algebra
- Chapter 11: Three-Dimensional Geometry
- Chapter 12: Linear Programming
- Chapter 13: Probability

**NCERT Solutions for Class 12th Mathematics**

NCERT Solutions Class 12 Mathematics PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 12 Mathematics includes text book solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 12 Mathematics have total 13 chapters. Class 12 Mathematics ncert Solutions in pdf for free Download are given in this website. Ncert Mathematics class 12 solutions PDF and Mathematics ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.

**NCERT Solutions for Class 12**

**NCERT Solutions for Class 12 Physics****NCERT Solutions for Class 12 Chemistry****NCERT Solutions for Class 12 Mathematics****NCERT Solutions for Class 12 Biology****NCERT Solutions for Class 12 English Core****NCERT Solutions for Class 12 Business Studies****NCERT Solutions for Class 12 Economics**

**NCERT Solutions for Class 11**

**NCERT Solutions for Class 11 Physics****NCERT Solutions for Class 11 Chemistry****NCERT Solutions for Class 11 Mathematics****NCERT Solutions for Class 11 Biology****NCERT Solutions for Class 11 English Core**

**NCERT Solutions for Class 10**

**NCERT Solutions for Class 10 Mathematics****NCERT Solutions for Class 10 Science****NCERT Solutions for Class 10 Social Science****NCERT Solutions for Class 10 English Communicative****NCERT Solutions for Class 10 English Language and Literature****NCERT Solutions for Class 10 Hindi Course A****NCERT Solutions for Class 10 Hindi Course B**

**NCERT Solutions for Class 9**

**NCERT Solutions for Class 9 Mathematics****NCERT Solutions for Class 9 Science****NCERT Solutions for Class 9 Social Science****NCERT Solutions for Class 9 English Communicative****NCERT Solutions for Class 9 English Language and Literature****NCERT Solutions for Class 9 Hindi Course A****NCERT Solutions for Class 9 Hindi Course B**

**NCERT Solutions for Class 8**

**NCERT Solutions for Class 8 Mathematics****NCERT Solutions for Class 8 Science****NCERT Solutions for Class 8 Social Science****NCERT Solutions for Class 8 English****NCERT Solutions for Class 8 Hindi**

**NCERT Solutions for Class 7**

**NCERT Solutions for Class 7 Mathematics****NCERT Solutions for Class 7 Science****NCERT Solutions for Class 7 Social Science****NCERT Solutions for Class 7 English****NCERT Solutions for Class 7 Hindi**

**NCERT Solutions for Class 6**

**NCERT Solutions for Class 6 Mathematics****NCERT Solutions for Class 6 Science****NCERT Solutions for Class 6 Social Science****NCERT Solutions for Class 6 English****NCERT Solutions for Class 6 Hindi**

**NCERT Solutions for Class 5**

**NCERT Solutions for Class 5 Mathematics****NCERT Solutions for Class 5 EVS****NCERT Solutions for Class 5 English****NCERT Solutions for Class 5 Hindi**

**NCERT Solutions for Class 4**

**NCERT Solutions for Class 4 Mathematics****NCERT Solutions for Class 4 EVS****NCERT Solutions for Class 4 English****NCERT Solutions for Class 4 Hindi**

**NCERT Solutions for Class 3**

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