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
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
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: 4 minutes
Maharashtra State Board: Class 12
Key Points : Partial Fractions
| Type | Rational Form | Partial Form |
|---|---|---|
| Type I (Non-repeated linear factors) | \[\frac{\mathrm{p}x+\mathrm{q}}{(x-\mathrm{a})(x-\mathrm{b})}\] | \[\frac{\mathrm{A}}{x-\mathrm{a}}+\frac{\mathrm{B}}{x-\mathrm{b}}\] |
| \[\frac{\mathrm{p}x^{2}+\mathrm{q}x+\mathrm{r}}{(x-\mathrm{a})(x-\mathrm{b})(x-\mathrm{c})}\] | \[\frac{\mathrm{A}}{x-\mathrm{a}}+\frac{\mathrm{B}}{x-\mathrm{b}}+\frac{\mathrm{C}}{x-\mathrm{c}}\] | |
| Type II (Repeated linear factors) | \[\frac{\mathrm{p}x+\mathrm{q}}{\left(x-\mathrm{a}\right)^2}\] | \[\frac{\mathrm{A}}{(x-\mathrm{a})}+\frac{\mathrm{B}}{(x-\mathrm{a})^{2}}\] |
| \[\frac{\mathrm{p}x^{2}+\mathrm{q}x+\mathrm{r}}{\left(x-\mathrm{a}\right)^{2}\left(x-\mathrm{b}\right)}\] | \[\frac{\mathrm{A}}{(x-\mathrm{a})}+\frac{\mathrm{B}}{(x-\mathrm{a})^{2}}+\frac{\mathrm{C}}{(x-\mathrm{b})}\] | |
| Type III (Linear × Quadratic) | \[\frac{\mathrm{p}x^{2}+\mathrm{q}x+\mathrm{r}}{(x-\mathrm{a})(x^{2}+\mathrm{b}x+\mathrm{c})}\] | \[\frac{\mathrm{A}}{(x-\mathrm{a})}+\frac{\mathrm{B}x+\mathrm{C}}{(x^{2}+\mathrm{b}x+\mathrm{c})}\] |
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