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
- Derivative of Composite Functions
- Geometrical Meaning of Derivative
- Derivative of Inverse Function
- Logarithmic Differentiation
- Derivatives of Implicit Functions
- Derivatives of Parametric Functions
- 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
- Indefinite Integration with Standard Indefinite Integral Formulae
- Methods of Integration> Integration by Substitution
- Methods of Integration> Integration by Parts
- Methods of Integration> Integration Using Partial Fraction
- Overview of 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
- Differential Equations
- Order and Degree of a Differential Equation
- Formation of Differential Equations
- Homogeneous 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
- Bernoulli Trial
- Mean and Variance of Binomial Distribution
- Probability using Binomial Distribution
- Overview of Binomial Distribution
Estimated time: 3 minutes
- The necessary conditions for a general second degree equation
ax2 + 2hxy + by2 + 2gx + 2fy + c = 0
- abc + 2fgh - af2 - bg2 - ch2 = 0
- h2 - ab ≥ 0
Maharashtra State Board: Class 12
Definition: General Second Degree Equation
Equation of the form ax² + 2hxy + by² + 2gx + 2fy + c = 0 is called a general second-degree equation.
- The necessary conditions for a general second-degree equation to represent a pair of lines are: (i) abc + 2fgh − af² − bg² − ch² = 0, (ii) h² − ab ≥ 0
Maharashtra State Board: Class 12
Key Points: Nature of Pair of Lines
| Condition | Type of Lines |
|---|---|
| \[\Delta=0,h^2>ab\] | Intersecting lines |
| \[\Delta=0,h^2 = ab\] | Coincident lines |
| \[\Delta=0,h^2<ab\] | Imaginary lines |
| (\[\Delta=0,h^2=ab\] and \[bg^{2}=af^{2}\] | Parallel lines |
