Introduction:The Joint Entrance Examination (JEE) is a highly competitive examination conducted in India for students seeking admission into prestigious engineering colleges. To crack the JEE, it is crucial for students to have a strong foundation in mathematics. One of the most popular and reliable resources for JEE mathematics preparation is the RD Sharma Solutions. This article provides a detailed syllabus for JEE mathematics, specifically focusing on the RD Sharma Solutions for Class 11 and Class 12.
Syllabus for JEE RD Sharma Solutions Mathematics for Class 11:The RD Sharma Solutions for Class 11 covers a wide range of topics that are essential for JEE preparation. The syllabus includes:
1. Sets:
- Sets and their representations
- Operations on sets
- Venn diagrams
- Union, intersection, and complement of sets
- Power set
- Cardinality of sets
2. Relations and Functions:
- Ordered pairs
- Cartesian product of sets
- Relations
- Functions
- Types of functions
- Composition of functions
- Inverse functions
- Binary operations
3. Trigonometric Functions:
- Trigonometric ratios
- Trigonometric functions
- Trigonometric identities
- Trigonometric equations
- Inverse trigonometric functions
- Heights and distances
4. Principle of Mathematical Induction:
- Motivation for mathematical induction
- The principle of mathematical induction
- Application of the principle of mathematical induction
5. Complex Numbers and Quadratic Equations:
- Complex numbers
- Algebraic properties of complex numbers
- Modulus and argument
- Quadratic equations
- Quadratic equations in real and complex number system
- Solutions of quadratic equations
6. Linear Inequalities:
- Linear inequalities
- Algebraic solutions of linear inequalities in one variable and their graphs
- Graphical solution of linear inequalities in two variables
- Solution of system of linear inequalities in two variables
7. Permutations and Combinations:
- Fundamental principle of counting
- Permutations
- Combinations
- Mathematical induction and its application
8. Binomial Theorem:
- Binomial theorem for a positive integral index
- General term and middle term
- Binomial theorem for any index
- Properties of binomial coefficients
9. Sequences and Series:
- Sequences and their types
- Arithmetic progressions (AP)
- Geometric progressions (GP)
- Harmonic progressions (HP)
- Arithmetic mean (AM)
- Geometric mean (GM)
- Harmonic mean (HM)
- Special series: sums of squares, cubes, etc.
10. Straight Lines:
- Brief recall of two-dimensional geometry
- Cartesian system of rectangular coordinates
- Distance formula
- Section formula
- Area of a triangle
- Condition of collinearity of three points
- Slope of a line
- Parallel and perpendicular lines
- Intercepts of a line
- Equation of a line in various forms
- Angle between two lines
- Distance of a point from a line
Syllabus for JEE RD Sharma Solutions Mathematics for Class 12:The RD Sharma Solutions for Class 12 builds upon the concepts learned in Class 11 and covers advanced topics that are crucial for JEE preparation. The syllabus includes:
1. Relations and Functions:
- Relations and their types
- Functions and their types
- Inverse trigonometric functions
2. Inverse Trigonometric Functions:
- Definition, range, domain, principal value branch
- Graphs of inverse trigonometric functions
- Elementary properties of inverse trigonometric functions
3. Matrices:
- Concept, notation, order, equality, types of matrices
- Addition, multiplication, scalar multiplication, transpose, and adjoint of matrices
- Inverse of a matrix
- Properties of determinants
- Consistency, inconsistency, and solvability of a system of linear equations by determinants and matrices
4. Determinants:
- Determinant of a square matrix (up to 3x3 matrices)
- Properties of determinants
- Area of triangles using determinants
5. Continuity and Differentiability:
- Continuity and differentiability of a function
- Derivatives of composite functions, implicit functions, logarithmic and exponential functions
- Derivative of functions expressed in parametric forms
- Second order derivatives
- Rolle's and Lagrange's mean value theorems
6. Applications of Derivatives:
- Rate of change of quantities
- Increasing and decreasing functions
- Tangents and normals
- Approximations
- Maxima and minima
7. Integrals:
- Integration as an inverse process of differentiation
- Methods of integration
- Definite integrals and their properties
- Areas under simple curves
8. Applications of Integrals:
- Area under simple curves
- Differential equations
- Formation of differential equations
- Solutions of linear differential equations
9. Differential Equations:
- Definition, order, and degree of a differential equation
- Formation of a differential equation
- General and particular solutions of a differential equation
- Methods of solving first order, first degree differential equations
10. Vector Algebra:
- Vectors and scalars
- Addition of vectors
- Components of a vector in two dimensions and three-dimensional space
- Scalar and vector products
- Scalar and vector triple products
- Application of vectors to plane geometry
11. Three Dimensional Geometry:
- 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 two lines and angle between two planes
- Distance of a point from a plane
12. Linear Programming:
- Introduction to linear programming
- Mathematical formulation of linear programming problems
- Graphical method of solution for problems in two variables
- Feasible and infeasible regions
- Solving linear programming problems using graphical method
13. Probability:
- Conditional probability
- Multiplication theorem on probability
- Independent events
- Bayes' theorem
- Random variables and probability distributions
- Bernoulli trials and binomial distribution
Conclusion:The RD Sharma Solutions for Class 11 and Class 12 provide a comprehensive coverage of the mathematics syllabus for JEE preparation. By following these solutions and mastering the concepts, students can enhance their problem-solving skills and increase their chances of cracking the JEE with flying colors.
This course is helpful for the following exams: Class 11, Class 12, Commerce, Humanities/Arts, JEE