Empty Relations, Universal Relations, Trivial Relations, Reflexive Relations, Symmetric Relations, Transitive Relations, Equivalence Relations, Equivalence Classes, and Questions based on the above topics from NCERT Textbook, Board’s Question Bank, RD Sharma, NCERT Exemplar etc.
One to one andonto functions, composite functions, inverse of a function.
Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions Elementary properties of inverse trigonometric functions.
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).
This course is based on the Assignments by Ashish Kumar (Agam Sir). The assignments have questions from NCERT Exemplar, Board's Question Bank, R. D. Sharma etc., under the syllabus of Class 12 Mathematics.
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.
This course is based on the Assignments by Ashish Kumar (Agam Sir). The assignments have questions from NCERT Exemplar, Board's Question Bank, R. D. Sharma etc., under the syllabus of Class 12 Mathematics.
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.
This course is based on the Assignments by Ashish Kumar (Agam Sir). The assignments have questions from NCERT Exemplar, Board's Question Bank, R. D. Sharma etc., under the syllabus of Class 12 Mathematics.
This course is based on the Assignment - 3 Differentiability by Ashish Kumar (Agam Sir). The assignments have questions from NCERT Exemplar, Board's Question Bank, R. D. Sharma etc., under the syllabus of Class 12 Mathematics.
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).
This course is based on the Assignments by Ashish Kumar (Agam Sir). The assignments have questions from NCERT Exemplar, Board's Question Bank, R. D. Sharma etc., under the syllabus of Class 12 Mathematics.
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. \(\int{\frac{dx}{x^2 \pm a^2}}\), \(\int{\frac{dx}{\sqrt{x^2 \pm a^2}}}\), \(\int{\frac{dx}{\sqrt{a^2 - x^2}}}\), \(\int{\frac{dx}{ax^2+bx+c}}\), \(\int{\frac{dx}{\sqrt{ax^2+bx+c}}}\), \(\int{\frac{px+q}{ax^2+bx+c}}dx\), \(\int{\frac{px+q}{\sqrt{ax^2+bx+c}}}dx\), \(\int{\sqrt{a^2 \pm x^2}}dx\), \(\int{\sqrt{x^2-a^2}}dx\), \(\int{\sqrt{ax^2+bx+c}}dx\), \(\int{(px+q) \sqrt{ax^2+bx+c}}dx\)
Properties of Definite Integrals : Derivations, Assignments, NCERT Exercise 7.11
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).
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: \( \frac{dy}{dx}+ py = q\), where p and q are functions of y or constants \( \frac{dx}{dy}+ px = q\), where p and q are functions of y or constants
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.
This course is based on the Assignments by Ashish Kumar (Agam Sir). The assignments have questions from NCERT Exemplar, Board's Question Bank, R. D. Sharma etc., under the syllabus of Class 12 Mathematics.
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.
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 or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).
Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of random variable.