Topics
11th Std
Mathematical Logic
- Concept of Statements
- Truth Value of Statement
- Logical Connective, Simple and Compound Statements
- Statement Patterns and Logical Equivalence
- Tautology, Contradiction, and Contingency
- Duality
- Quantifier and Quantified Statements in Logic
- Negations of Compound Statements
- Converse, Inverse, and Contrapositive
- Algebra of Statements
- Application of Logic to Switching Circuits
Trigonometry - II
- Compound Angle
- Trigonometric Functions of Sum and Difference of Angles
- Trigonometric Functions of Allied Angels
- Trigonometric Functions of Multiple Angles
- Trigonometric Functions of Double Angles
- Trigonometric Functions of Triple Angle
- Factorization Formulae
- Formulae for Conversion of Sum Or Difference into Product
- Formulae for Conversion of Product in to Sum Or Difference
- Trigonometric Functions of Angles of a Triangle
- Angles of Elevation and Depression
- Fundamental Identities
Matrices
- Elementary Transformations
- Properties of Matrix Multiplication
- Application of Matrices
12th Std
Straight Line
- Locus
- Shift of Origin
- Concept of Slope (or, gradient)
- The Angle Between Two Intersecting Lines
- Distance of a Point from a Line
- Locus of a Points in a Co-ordinate Plane
- Equation of a Straight Line
- Family of Lines
- Equations of Line in Different Forms
Circle
- Equation of a Circle in Different Forms
- Equation of Tangent to a Circle
- Different Forms of Equation of a Circle
- General Equation of a Circle
- Parametric Form of a Circle
- Secant and Tangent
- Condition of tangency
- Director circle
- Tangent and Secant Properties
Trigonometric Functions
- Trigonometric Equations and Their Solutions
- Solutions of Triangle
- Inverse Trigonometric Functions
Pair of Straight Lines
- Combined Equation of a Pair Lines
- Homogeneous Equation of Degree Two
- Angle between lines represented by ax2 + 2hxy + by2 = 0
- General Second Degree Equation in x and y
- Equation of a Line in Space
- Formation of Joint Equation and Separation of Equations from a Given Equation
- Sum and Product of Slopes
- Acute Angle Between a Pair of Straight Lines
- General 2nd Degree Equation to Represent a Pair of Lines
Measures of Dispersion
- Range, Variance and Standard Deviation
- Coefficient of Variation
- Standard Deviation for Combined Data
- Meaning and Definition of Dispersion
- Measures of Dispersion
- Quartiles and Range in Statistics
- Variance
- Standard Deviation
- Change of Origin and Scale of Variance and Standard Deviation
- Standard Deviation for Combined Data
- Coefficient of Variation
- Mean Deviation
Vectors
- Vector
- Algebra of Vectors
- Collinearity and Coplanarity of Vectors
- Vector in Two Dimensions (2-D)
- Three Dimensional (3-D) Coordinate System
- Position Vector of a Point P(X, Y, Z) in Space
- Components of Vector
- Component Form of a Position Vector
- Vector Joining Two Points
- Section Formula
- Scalar Product(Dot Product)
- Vector Product (Cross Product)
- Scalar Triple Product of Vectors
- Vector Triple Product
- Direction Angles
- Direction Ratios
- Direction Cosines
- Vector Operations>Addition and Subtraction of Vectors
Probability
- Concept of Probability
- Basic Terminologies
- Elementary Types of Events in Probability
- Addition Theorem for Two Events
- Conditional Probability
- Multiplication Theorem on Probability
- Independent Events
- Bayes’ Theorem
- Odds (Ratio of Two Complementary Probabilities)
Line and Plane
- Vector and Cartesian Equations of a Line
- Distance of a Point from a Line
- Distance Between Skew Lines and Parallel Lines
- Equation of a Plane
- Angle Between the Planes
- Coplanarity of Two Lines
- Distance of a Point from a Plane
Complex Numbers
- Introduction of Complex Number
- Concept of Complex Numbers
- Algebraic Operations of Complex Numbers
- Equality of Two Complex Numbers
- Conjugate of a Complex Number
- Powers of i
- Square Root of a Complex Number
- Fundamental Theorem of Algebra
- Modulus of a Complex Number
- Argument, Polar Form and Exponential Form of a Complex Number
- Argand Diagram Or Complex Plane
- Cube Root of Unity
- DeMoivre's Theorem
- Set of Points in Complex Plane
Permutations and Combinations
- Factorial Notation
- Fundamental Principles of Counting
- Invariance Principle
- Factorial Notation
- Permutations
- Permutations When All Objects Are Distinct
- Permutations When Repetitions Are Allowed
- Permutations When Some Objects Are Identical
- Circular Permutations
- Properties of Permutations
- Combination
- Properties of Combinations
Linear Programming
- Linear Inequations in Two Variables
- Linear Programming Problem (L.P.P.)
- Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
- Formulation of LPP
- Terminologies Related to the Solution of LPP
- Graphical Method of Solving Linear Programming Problems
- Special Cases of LPP
- Linear Programming Problem in Management Mathematics
Differentiation
- Differentiation
- Derivative of Composite Functions
- Derivatives of Composite Functions - Chain Rule
- Geometrical Meaning of Derivative
- Derivative of Inverse Functions
- Logarithmic Differentiation
- Derivative of Implicit Functions
- Derivative of Parametric Functions
- Higher Order Derivatives
Functions
- Algebra of Functions
Applications of Derivatives
- Application of Derivative to Tangents and Normals
- Derivative as a Rate Measure
- Velocity, Acceleration and Jerk
- Approximations
- Rolle's Theorem
- Lagrange's Mean Value Theorem (LMVT)
- Increasing and Decreasing Functions
- Maxima and Minima
Limits
- Concept of Limits
- Algebra of Limits
- Factorization Method
- Rationalization Method
- Limits of Trigonometric Functions
- Substitution Method
- Limits of Exponential and Logarithmic Functions
- Limit at Infinity
- Limit at Infinity
Indefinite Integration
- Indefinite Integration
- Algebra of Integration and Standard Results
- Methods of Integration: Integration by Substitution
- Methods of Integration: Integration by Parts
- Methods of Integration: Integration Using Partial Fractions
- Integrals of Trignometric Functions
- Some Special Integrals
Continuity
- Continuous and Discontinuous Functions
- Definition of Continuity
- Continuity of a Function at a Point
- Discontinuity of a Function
- Types of Discontinuity
- Continuity in the Domain of the Function
- Algebra of Continuous Functions
- Continuity in Interval - Definition
- Continuity of Some Standard Functions - Polynomial Function
- Continuity of Some Standard Functions - Rational Function
- Continuity of Some Standard Functions - Trigonometric Function
Definite Integration
- Definite Integral as Limit of Sum
- Integral Calculus
- Evaluation of Definite Integrals by Substitution
- Evaluation of Definite Integrals by Parts Rule and by Partial Fraction
- Properties of Definite Integrals
Conics
- Double Cone
- Conic Sections
- Parametric Form of an Ellipse
- Parabola
- Ellipse
- Hyperbola
Application of Definite Integration
- Area Under Simple Curves
- Symmetrical Area
- Area Bounded by Two Curves
Sets and Relation
- Concept of Sets
- Classification of Sets
Sequences and Series
- Sequence, Series, and Progression
- nth Term of A.G.P
- Expressing Recurring Decimals as Rational Numbers
- Arithmetic Progression (A.P.)
- Geometric Progression (G. P.)
- Sum to' n' Terms of a Geometric Progression
- Harmonic Progression (H. P.)
- Types of Means
- Arithmetico Geometric Series
- Power Series
Differential Equations
- Order and Degree of a Differential Equation
- Solution of a Differential Equation
- Formation of Differential Equations
- Equations in Variable Separable Form
- Homogeneous Differential Equations
- Linear Differential Equations
- Application of Differential Equations
Methods of Induction and Binomial Theorem
- Principle of Mathematical Induction
- General Term in Expansion of (a + b)n
- Middle term(s) in the expansion of (a + b)n
Probability Distribution
Binomial Distribution
- Bernoulli Trial
- Binomial Distribution
- Mean of Binomial Distribution (P.M.F.)
- Variance of Binomial Distribution (P.M.F.)
Determinants and Matrices
- Minors and Cofactors of Elements of Determinants
- Properties of Matrix Multiplication
Shaalaa.com | Probability Mass Function
to track your progress
Related QuestionsVIEW ALL [3]
The probability mass function (p.m.f.) of X is given below:
| X=x | 1 | 2 | 3 |
| P (X= x) | 1/5 | 2/5 | 2/5 |
find E(X2)
