Progressions — A.P., G.P. & H.P.

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Sequence A sequence is an ordered list of numbers a₁, a₂, a₃, …, aₙ formed by a definite rule. Arithmetic Progression (A.P.) Sequence with constant...

Binomial Theorem

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Statement of Binomial Theorem (x + a)n = nC0xn + nC1xn−1a + nC2xn−2a2 + … + nCnan, where n ∈ N Binomial coefficients: nCr = n! / r!(n−r)! General...

Permutations & Combinations

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Fundamental Principle of Counting Multiplication Principle: If one operation can be done in m ways and the next in n ways, then total ways = m × n. Addition...

Complex Numbers

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Complex Numbers: Basics A complex number is of the form z = a + ib, where a, b ∈ R and i² = −1. Set of complex numbers: C = {a + ib | a, b ∈ R} Real...

Quadratic Equations & Expressions

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Quadratic Equation General form: ax² + bx + c = 0, where a ≠ 0 Coefficients: a, b, c Roots: α, β Sum of roots: α + β = −b/a Product of roots: αβ =...

Heights & Distances

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Introduction Heights and distances problems use trigonometric ratios to find lengths that are not directly measurable. Assumption: The line of sight,...

Properties & Solution of a Triangle

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Notation & Basics In ΔABC: sides opposite to angles A, B, C are a, b, c respectively. Semi-perimeter: s = (a + b + c)/2 Area: Δ Sine Rule a/sinA =...

Trigonometric Equations

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Trigonometric Equations: Basics Equations involving trigonometric functions of an unknown angle are called trigonometric equations. A solution is a value of θ...

Trigonometric Ratios & Identities

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Trigonometry: Basics Trigonometry deals with measurement of triangles. Angle measurement systems: Sexagesimal (Degree): 1° = 60′, 1′ = 60″ Centesimal...

Functions & Relations

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Numbers & Their Sets Natural Numbers (N) = {1, 2, 3, 4, …} Whole Numbers (W) = {0, 1, 2, 3, …} Integers (Z) = {…, −3, −2, −1, 0,...

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