This course helps students to understand and correlate the concepts of Class 12th to target CBSE school exams and other entrance exams. Here in this course we cover all units and chapters from subject Physics. It’s a perfect syllabus for school exam and competitive exams. This course has been done using NCERT and other preferred reference books, so this is the perfect study material. This course is available in English Language. Also student will get free eBooks, and Doubt clearing services from our top faculties. Our team of top most faculties are selected with good teaching skill, highly qualified and experienced faculty. Most of our faculty are IITians, NITians and Doctors having decade of experience. They are all expert in their subject and committed to the success of our students. We ensure to provide best results out of all level of students.
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Unit-I: Relations and Functions
1. Relations and Functions 9 Periods Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions.
2. Inverse Trigonometric Functions 8 Periods Definition, range, domain, principal value branch.
Unit-II: Algebra
1. Matrices 17 Periods 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, Invertible matrices; (Here all matrices will have real entries).
2. Determinants 18 Periods Determinant of a square matrix (up to 3 x 3 matrices), minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.
Unit-III: Calculus
Continuity and Differentiability 16 Periods Continuity and differentiability, derivative of composite functions, chain rule, derivative 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.
Applications of Derivatives 7 Periods Applications of derivatives: increasing/decreasing functions, tangents and normal, 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).
Integrals 15 Periods 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.
Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.
Applications of the Integrals 9 Periods Applications in finding the area under simple curves, especially lines, parabolas; area of circles /ellipses (in standard form only) (the region should be clearly identifiable).
Differential Equations 10 Periods Definition, order and degree, general and particular solutions of a differential equation. Solution of differential equations by method of separation of variables, solutions of homogeneous differential equations of first order and first degree of the type: dydx= 𝑓(y/x). Solutions of linear differential equation of the type:
dydx+ py = q, where p and q are functions of x or constant.
Unit-IV: Vectors and Three-Dimensional Geometry
Vectors 13 Periods Vectors and scalars, magnitude and diType equation here.rection 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.
Three - dimensional Geometry 13 Periods 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. Distance of a point from a plane.
Unit-V: Linear Programming
Linear Programming Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems. graphical method of solution for problems in two variables, feasible and infeasible regions (bounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).
Unit-VI: Probability
Probability Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution.