Topics
Mathematical Logic
- Statements and Truth Values in Mathematical Logic
- Logical Connectives
- Tautology, Contradiction, and Contingency
- Quantifier, Quantified and Duality Statements in Logic
- Negations of Compound Statements
- Converse, Inverse, and Contrapositive
- Algebra of Statements
- Application of Logic to Switching Circuits
- Overview of Mathematical Logic
Matrices
Trigonometric Functions
Pair of Straight Lines
Vectors
Line and Plane
Linear Programming
Differentiation
- Introduction & Derivatives of Some Standard Functions
- Derivatives of Composite Functions
- Geometrical Meaning of Derivative
- Derivative of Inverse Function
- Logarithmic Differentiation
- Derivative of Implicit Functions
- Derivatives of Functions in Parametric Forms
- Higher Order Derivatives
- Overview of Differentiation
Applications of Derivatives
- Applications of Derivatives in Geometry
- Derivatives as a Rate Measure
- Approximations
- Rolle's Theorem
- Lagrange's Mean Value Theorem (LMVT)
- Increasing and Decreasing Functions
- Maxima and Minima
- Overview of Applications of Derivatives
Indefinite Integration
Definite Integration
- Definite Integral as Limit of Sum
- Integral Calculus
- Methods of Evaluation and Properties of Definite Integral
- Overview of Definite Integration
Application of Definite Integration
- Application of Definite Integration
- Area Bounded by Two Curves
- Overview of Application of Definite Integration
Differential Equations
- Basic Concepts of Differential Equations
- Order and Degree of a Differential Equation
- Formation of Differential Equations
- Methods of Solving Differential Equations> Homogeneous Differential Equations
- Methods of Solving Differential Equations>Linear Differential Equations
- Applications of Differential Equation
- Solution of a Differential Equation
- Overview of Differential Equations
Probability Distributions
- Random Variables
- Probability Distribution of Discrete Random Variables
- Probability Distribution of a Continuous Random Variable
- Variance of a Random Variable
- Expected Value and Variance of a Random Variable
- Overview of Probability Distributions
Binomial Distribution
Estimated time: 3 minutes
Maharashtra State Board: Class 12
Formula: Mean
\[\mathrm{Mean~(\mu)=E(X)=np}\]
Maharashtra State Board: Class 12
Formula: Variance
\[Variance(\sigma^2)=npq\]
Maharashtra State Board: Class 12
Formula: Standard Deviation
\[\text{Standard deviation }(\sigma)=\sqrt{\mathrm{npq}}\]
Related QuestionsVIEW ALL [13]
The probability mass function for X = number of major defects in a randomly selected
appliance of a certain type is
| X = x | 0 | 1 | 2 | 3 | 4 |
| P(X = x) | 0.08 | 0.15 | 0.45 | 0.27 | 0.05 |
Find the expected value and variance of X.
Find the expected value and variance of X using the following p.m.f.
| x | –2 | –1 | 0 | 1 | 2 |
| P(x) | 0.2 | 0.3 | 0.1 | 0.15 | 0.25 |
