# Ncert Solutions class 12 Maths free pdf and video

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CBSE | ISC |
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## 1. Relation and FunctionsEx - 1.1Ex - 1.2 Ex - 1.3 Ex - 1.4 Miscellaneous |
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## 2. Inverse Trigonometric FunctionsEx - 2.1Ex - 2.2 Miscellaneous |
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Ex - 3.1 |
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## 4. DeteminantsEx - 4.1Ex - 4.2 Ex - 4.3 Ex - 4.4 Ex - 4.5 Ex - 4.6 Miscellaneous |
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## 5. Continuity and DifferentiabilityEx - 5.1Ex - 5.2 Ex - 5.3 Ex - 5.4 Ex - 5.5 Ex - 5.6 Ex - 5.7 Ex - 5.8 Miscellaneous |
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## 6. Algebra of DerivativesEx - 6.1Ex - 6.2 Ex - 6.3 Ex - 6.4 Ex - 6.5 Ex - 6.6 Miscellaneous |
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## 7. IntegralsEx - 7.1Ex - 7.2 Ex - 7.3 Ex - 7.4 Ex - 7.5 Ex - 7.6 Ex - 7.7 Ex - 7.8 Ex - 7.9 Ex - 7.10 Ex - 7.11 Miscellaneous |
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## 8. Application of IntegralsEx - 8.1Ex - 8.2 Miscellaneous |
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## 9. Differential EquationsEx - 9.1Ex - 9.2 Ex - 9.3 Ex - 9.4 Ex - 9.5 Ex - 9.6 Miscellaneous |
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## 10. Vector AlgebraEx - 10.1Ex - 10.2 Ex - 10.3 Ex - 10.4 Miscellaneous |
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## 11. Three Dimensional GeometryEx - 11.1Ex - 11.2 Ex - 11.3 Miscellaneous |
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## 12. Linear Programming (LPP)Ex - 12.1Ex - 12.2 Miscellaneous |
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## 13. ProbabilityEx - 13.1Ex - 13.2 Ex - 13.3 Ex - 13.4 Ex - 13.5 Miscellaneous |
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__Main Topics to Remember -:__**Chapter 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.

**Chapter 2. Inverse Trigonometric Functions**

Definition, range, domain, principal
value branch. Graphs of inverse trigonometric functions. Elementary properties
of inverse trigonometric functions.

**Chapter 3. 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. 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).

**Chapter 4. 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.

**Chapter 5. 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.

**Chapter 6. Applications 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).

**Chapter 7. 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 types
given in the syllabus 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.

**Chapter 8. Applications of the 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 cures (the region
should be clearly identifiable).

**Chapter 9. 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. Solutions of linear
differential equation of the type given in the syllabus.

**Chapter 10. Vectors**

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.

**Chapter 11. 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.

**Chapter 12: 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.

**Chapter 13. 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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