Class 12 Maths

In this self study course, you will learn Empty Relations, Universal Relations, Trivial Relations, Reflexive Relations, Symmetric Relations, Transitive Relations, Equivalence Relations, Equivalence Classes. For further understanding of concepts and for examination preparation, practice questions based on the above topics are discussed in the form of assignments that have questions from NCERT Textbook exercise, NCERT Examples, Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignments can be downloaded within the course.

In this self study course, you will learn One to one and onto functions, composite functions and inverse of a function. For further understanding of concepts and for examination preparation, practice questions based on the above topics are discussed in the form of assignments that have questions from NCERT Textbook exercise, NCERT Examples, Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignments can be downloaded within the course.

In this self study course, you will learn definition, range, domain, principal value branch, graphs of inverse trigonometric functions and elementary properties of inverse trigonometric functions. For further understanding of concepts and for examination preparation, practice questions based on the above topics are discussed in the form of assignments that have questions from NCERT Textbook exercise, NCERT Examples, Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignments can be downloaded within the course.

In this self study course, you will learn 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). For further understanding of concepts and for examination preparation, this course has explanation of all NCERT Exercise questions and important NCERT Examples.

In this self study course, you will learn 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

For further understanding of concepts and for examination preparation, practice questions based on the above topics are discussed in the form of assignments that has questions from NCERT Textbook exercise, NCERT Examples, Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignments can be downloaded within the course.
“Limit of Sum” and “Properties of Integrals” are not included in this course.

This self study course is an extended part of chapter 7 Integrals of Class 12 Maths. In this course, you will learn properties of definite Integrals and their derivations. For further understanding of concepts and for examination preparation, practice questions based on the above topics are discussed in the form of assignments that has questions from NCERT Textbook exercise 7.11, Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignments can be downloaded within the course.

In this self study course, you will learn limit of sum, 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). For further understanding of concepts and for examination preparation, practice questions based on the above topics are discussed in the form of assignments that has questions from NCERT Textbook exercise, NCERT Examples, Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignments can be downloaded within the course.

In this self study course, you will learn 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

For further understanding of concepts and for examination preparation, this course has explanation of all NCERT Exercise questions. Also, there are practice assignments that has questions from Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignments can be downloaded within the course.

In this self study course, you will learn 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). For further understanding of concepts and for examination preparation, this course has explanation of all NCERT Exercise questions (except Exercise 12.1). Also, there is practice assignment that has questions from Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignment can be downloaded within the course.

In this self study course, you will learn conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of random variable. For further understanding of concepts and for examination preparation, practice questions based on the above topics are discussed in the form of assignments that have questions from NCERT Textbook exercise, NCERT Examples, Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignments can be downloaded within the course.

In this self study course, you will learn 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. Concept of elementary row and column operations and Invertible matrices. This course also has solutions of NCERT Exercise questions.
Please note, this course comprises of live session recordings of Ashish Kumar (Agam Sir). Please ignore, if you have heard Agam Sir discussing about live session or doubts session in the course. Live sessions or doubts sessions are no longer offered.

This self study course is an extended part of Ch03. Matrices Class 12 Maths. The course is based on the assignments by Ashish Kumar (Agam Sir), which have questions from NCERT Exemplar, Board’s Question Bank, R. D. Sharma etc. The PDF of assignments can be downloaded within the course. Please note, the assignments do not have questions based on elementary operations.

In this self study course, you will learn 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, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.. This course also has solutions of NCERT Exercise questions.
Please note, this course comprises of live session recordings of Ashish Kumar (Agam Sir). Please ignore, if you have heard Agam Sir discussing about live session or doubts session in the course. Live sessions or doubts sessions are no longer offered.

This self study course is an extended part of Ch04. Determinants Class 12 Maths. The course is based on the assignments by Ashish Kumar (Agam Sir), which have questions from NCERT Exemplar, Board’s Question Bank, R. D. Sharma etc. The PDF of assignments can be downloaded within the course. Please note, the assignments do not have questions based on properties of determinants.

The whole chapter Continuity and Differentiability is divided into three courses. This course is the part one. In this self study course, you will learn continuity, 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 also has NCERT Exercise solutions, some important NCERT Examples and assignment based on NCERT Exemplar, R.D. Sharma, board’s question bank etc. Please note, all three courses based on Continuity and Differentiability do not have Rolle’s Theorem, Mean Value Theorem, NCERT Exercise 5.8 and questions based on them in Miscellaneous exercise.

The whole chapter Continuity and Differentiability is divided into three courses. This course is the part 2. In this self study course, you will learn about differentiability. This course also has assignment that has questions from NCERT Exemplar, R.D. Sharma, board’s question bank etc. Please note, all three courses based on Continuity and Differentiability do not have Rolle’s Theorem, Mean Value Theorem, NCERT Exercise 5.8 and questions based on them in Miscellaneous exercise. The PDF of assignment can be downloaded within the course.

The whole chapter Continuity and Differentiability is divided into three courses. This course is the part 3. The course is based on the assignments on Derivatives by Ashish Kumar (Agam Sir), which have questions from NCERT Exemplar, Board’s Question Bank, R. D. Sharma etc. The PDF of assignments can be downloaded within the course. Please note, all three courses based on Continuity and Differentiability do not have Rolle’s Theorem, Mean Value Theorem, NCERT Exercise 5.8 and questions based on them in Miscellaneous exercise.

This self study course is an extended part of Ch06. Applications of Derivatives. The course is based on the assignments by Ashish Kumar (Agam Sir), which have questions from NCERT Exemplar, Board’s Question Bank, R. D. Sharma etc. The PDF of assignments can be downloaded within the course.

In this self study course, you will learn 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 also has solutions of NCERT Exercise and a few important examples. Please note, some of the part of this course comprises of live session recordings of Ashish Kumar (Agam Sir). Please ignore, if you have heard Agam Sir discussing about live session or doubts session in the course. Live sessions or doubts sessions are no longer offered.

This self study course is an extended part of Ch10. Vector Algebra Class 12 Maths. The course is based on the assignments by Ashish Kumar (Agam Sir), which have questions from NCERT Exemplar, Board’s Question Bank, R. D. Sharma etc. The PDF of assignments can be downloaded within the course.

In this self study course, you will learn 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. For further understanding of concepts and for examination preparation, practice questions based on the above topics are discussed in the form of assignments that have questions from NCERT Textbook exercise, NCERT Examples, Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignments can be downloaded within the course. Please note, this course comprises of live session recordings of Ashish Kumar (Agam Sir). Please ignore, if you have heard Agam Sir discussing about live session or doubts session in the course. Live sessions or doubts sessions are no longer offered.