Class 11th Mathematics
Algebra • Sets • Functions • Coordinate Geometry • Calculus • Statistics
1. Sets and their Representations
Set का अर्थ, notation तथा representation।
2. Types of Sets
Empty, finite, infinite, singleton और universal sets।
3. Subsets
Subset, proper subset और power set।
4. Operations on Sets
Union, intersection, difference और complement।
5. Venn Diagrams
Sets को Venn diagram की सहायता से समझना और questions solve करना।
1. Ordered Pairs
Ordered pair और Cartesian product।
2. Relations
Relation का अर्थ और विभिन्न representations।
3. Functions
Function, domain, range और co-domain।
4. Types of Functions
One-one, many-one, into और onto functions।
1. Angles
Degree और radian measure।
2. Trigonometric Functions
sin, cos, tan तथा reciprocal functions।
3. Trigonometric Identities
Fundamental identities और transformations।
4. Trigonometric Equations
Basic trigonometric equations और solutions।
1. Principle of Mathematical Induction
Mathematical induction की basic concept।
2. Base Step
Initial statement को verify करना।
3. Induction Step
Induction hypothesis और proof।
1. Complex Numbers
Real और imaginary parts।
2. Algebra of Complex Numbers
Addition, subtraction, multiplication और division।
3. Conjugate
Complex number का conjugate।
4. Quadratic Equations
Roots और nature of roots।
1. Linear Inequalities
Linear inequalities in one variable।
2. Algebraic Solution
Inequality को algebraically solve करना।
3. Graphical Representation
Number line पर solution representation।
1. Fundamental Principle of Counting
Counting principle और applications।
2. Factorial
Factorial notation और properties।
3. Permutations
Arrangement और permutation formula।
4. Combinations
Selection और combination formula।
1. Binomial Theorem
Binomial expansion और theorem।
2. General Term
Expansion का general term।
3. Middle Term
Middle term और related problems।
1. Sequence
Sequence और series की basic concepts।
2. Arithmetic Progression
AP, nth term और sum।
3. Geometric Progression
GP और sum of GP।
4. Special Series
Useful standard series और applications।
1. Coordinate Geometry
Coordinate plane और distance concepts।
2. Slope
Line की slope और angle।
3. Equation of Straight Line
Different forms of straight line equation।
4. Distance of Point from Line
Point और line के बीच distance।
Circle
Circle की basic equation और properties।
Parabola
Parabola की standard forms।
Ellipse & Hyperbola
Standard equations और basic properties।
1. Coordinate Axes and Planes
Three dimensional coordinate system।
2. Coordinates of a Point
3D space में point representation।
3. Distance Formula
Two points के बीच distance।
1. Limits
Limit की basic concept और evaluation।
2. Derivatives
Derivative और rate of change।
3. Derivatives of Functions
Polynomial और basic functions के derivatives।
4. Applications
Derivative के basic applications।
1. Statements
Mathematical statements और truth values।
2. Logical Connectives
AND, OR, NOT आदि।
3. Implications
Implication और converse concepts।
1. Measures of Dispersion
Range, mean deviation और standard deviation।
2. Probability
Probability की basic concepts।
3. Events
Events और their probability।
4. Probability Problems
Basic probability based questions।
Class 12th Mathematics
Relations • Algebra • Calculus • Vectors • 3D Geometry • Probability
1. Types of Relations
Reflexive, symmetric और transitive relations।
2. Equivalence Relation
Equivalence relation की concept।
3. One-One and Onto Functions
Function classification और properties।
4. Composite Functions
Composition of functions।
1. Inverse Trigonometric Functions
sin⁻¹x, cos⁻¹x, tan⁻¹x आदि।
2. Principal Values
Principal value branches।
3. Properties
Inverse trigonometric identities और properties।
1. Matrix
Matrix notation, order और types।
2. Matrix Operations
Addition, subtraction और multiplication।
3. Transpose
Transpose और its properties।
4. Inverse of Matrix
Inverse matrix और related problems।
1. Determinants
Determinant और its properties।
2. Area of Triangle
Determinant की सहायता से triangle का area।
3. Adjoint and Inverse
Adjoint और inverse matrix।
4. Linear Equations
Linear equations को determinants से solve करना।
1. Continuity
Continuity की definition और conditions।
2. Differentiability
Differentiability और continuity relation।
3. Chain Rule
Composite functions का differentiation।
4. Derivatives
Exponential, logarithmic और trigonometric functions।
1. Rate of Change
Quantities के rate of change।
2. Increasing and Decreasing Functions
Function के increasing/decreasing intervals।
3. Maxima and Minima
Maximum और minimum values।
4. Tangents and Normals
Curve से related applications।
1. Indefinite Integrals
Integration की basic concept।
2. Methods of Integration
Substitution और integration by parts।
3. Definite Integrals
Definite integral और properties।
4. Fundamental Theorem
Integration और differentiation का relationship।
1. Area Under Curves
Curve के नीचे area calculate करना।
2. Area Between Curves
दो curves के बीच का area।
1. Differential Equation
Basic concepts और order/degree।
2. Formation
Differential equation formation।
3. Solution
Differential equations को solve करना।
4. Variable Separation
Variable separable differential equations।
1. Vectors
Vector और scalar quantities।
2. Vector Operations
Addition और scalar multiplication।
3. Dot Product
Scalar product और applications।
4. Cross Product
Vector product और applications।
1. Direction Cosines
Direction ratios और direction cosines।
2. Equation of Line
3D में line की equation।
3. Angle Between Lines
दो lines के बीच angle।
4. Distance
Lines और points के बीच distance।
1. Linear Programming Problem
LPP की basic concepts।
2. Constraints
Objective function और constraints।
3. Graphical Method
Graphical method से solution।
4. Optimal Solution
Maximum/minimum value प्राप्त करना।
1. Conditional Probability
Conditional probability की concept।
2. Multiplication Theorem
Multiplication theorem और applications।
3. Bayes' Theorem
Bayes theorem based questions।
4. Random Variable
Random variable और probability distribution।
📌 Mathematics Important Chapters
परीक्षा की तैयारी के दौरान इन chapters की नियमित practice करें।
Matrices
Matrix operations, inverse और problems।
Calculus
Differentiation और Integration।
3D Geometry
Vectors, lines और distances।
Probability
Conditional probability और Bayes theorem।
🧮 Mathematics Preparation Strategy
Concept
पहले formula और concept समझें।
Formula
Important formulas की अलग notebook बनाएं।
Practice
हर chapter के questions solve करें।
Revision
Previous questions और mock tests करें।