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Absent in Intermediate paper |

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Re: Absent in Intermediate paper
As you are absent in Maths paper of intermediate exam so don’t worry you get another chance by appearing in the supplementary exam of that paper Next time prepare well for Maths exam and score good marks Here I am giving you the syllabus of Maths of intermediate exam Unit I: Relations and functions Relations and Functions Inverse Trigonometric Functions Unit II: Algebra Matrices Determinants Unit III: Calculus Continuity and Differentiability Applications of Derivatives Integrals Applications of the Integrals Differential Equations Unit IV: Vectors and Three-Dimensional Geometry Vectors Three - dimensional Geometry Unit - I: Relations and Functions 1. Relations and Functions: 15 Periods Types of relations: reflexive, symmetric, transitive and equivalence relations. Functions: One to one and onto functions, composite functions, inverse of a function. Binary operations. 2. Inverse Trigonometric Functions: 15 Periods Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions. Unit-II: Algebra 1. Matrices: 25 Periods Concept, notation, order, equality, types of matrices, zero and identity 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: 25 Periods 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. Unit-III: Calculus 1. Continuity and Differentiability: 20 Periods 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. 2. Applications of Derivatives: 10 Periods 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). 3. Integrals: 20 Periods Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts. Evaluation of simple intergrals of the following type 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. 4. Applications of the Integrals: 15 Periods 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). 5. Differential Equations: 15 Periods 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 of first order and first degree by method of separation of variables of homogeneous differential equations. Solutions of linear differential equation of the form. + py = q, where p and q are functions of x or constants + px = q, where p and q are functions of y or constants Unit-IV: Vectors and Three-Dimensional Geometry 1. Vectors: 15 Periods 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, Geomertrical Interpretation, properties and applications of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors projection of a vector on aline. 2. Three - dimensional Geometry: 15 Periods Direction cosines and direction 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: 20 Periods 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, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints). Unit-VI: Probability 1. Probability: 30 Periods Conditional probability, multiplication theorem on probability, independent events, total probability, Baye's theorem, Random variable and its probability distribution, mean and variance of a random variable. Repeated independent (Bernoulli) trials and Binomial distribution. Prescribed Books: 1) Mathematics Part I - Textbook for Class XI, NCERT Publication 2) Mathematics Part II - Textbook for Class XII, NCERT Publication For complete syllabus here is the PDF file
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