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
- Vector and Cartesian Equations of a Line
- Distance in Lines (Point & Parallel Lines)
- Distance Between Skew Lines and Parallel Lines
- Equation of a Plane
- Angle Between Planes
- Coplanarity of Two Lines
- Distance of a Point from a Plane
- Overview of Line and Plane
Linear Programming
Differentiation
- Introduction & Derivatives of Some Standard Functions
- Derivative of Composite Functions
- Geometrical Meaning of Derivative
- Derivatives of Inverse Functions
- 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
- Introduction of Distance of a Point from a Line
- Distance between two parallel lines
Maharashtra State Board: Class 12
Formula: Distance of a Point from a Line
For point (x₁, y₁) and line ax + by + c = 0,
\[p=\frac{|ax_1+by_1+c|}{\sqrt{a^2+b^2}}\]
Maharashtra State Board: Class 12
Formula: Distance Between Two Parallel Lines
For lines ax + by + c₁ = 0 and ax + by + c₂ = 0,
P = \[\left|\frac{c_{1}-c_{2}}{\sqrt{a^{2}+b^{2}}}\right|\]
Maharashtra State Board: Class 12
Formula: Distance Between A Pair of Parallel Straight Lines
If ax² + 2hxy + by² + 2gx + 2fy + c = 0 represents a pair of parallel straight lines, then the distance between them is given by
\[2\sqrt{\frac{g^{2}-ac}{a(a+b)}}\mathrm{or}2\sqrt{\frac{f^{2}-bc}{b(a+b)}}\]
