RRB PREP
NTPC ALP Group D

Algebra for RRB Exams

Important Algebraic Identities

Square Formulas

  • (a + b)² = a² + b² + 2ab
  • (a - b)² = a² + b² - 2ab
  • a² - b² = (a + b)(a - b)
  • (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

Cube Formulas

  • (a + b)³ = a³ + b³ + 3ab(a + b)
  • (a - b)³ = a³ - b³ - 3ab(a - b)
  • a³ + b³ = (a + b)(a² - ab + b²)
  • a³ - b³ = (a - b)(a² + ab + b²)

Special Identity

a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)

If a + b + c = 0, then a³ + b³ + c³ = 3abc

Polynomials & Quadratic Equations

Quadratic Equation: ax² + bx + c = 0

  • • Roots (α, β): Values of x that satisfy the equation
  • • Sum of roots (α + β): -b/a
  • • Product of roots (αβ): c/a
  • • Discriminant (D): b² - 4ac

Nature of Roots

  • • D > 0: Real and distinct roots
  • • D = 0: Real and equal roots
  • • D < 0: Imaginary roots

Linear Equations

System of Equations

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂ = 0

  • • Unique Solution (Intersecting Lines): a₁/a₂ ≠ b₁/b₂
  • • No Solution (Parallel Lines): a₁/a₂ = b₁/b₂ ≠ c₁/c₂
  • • Infinite Solutions (Coincident Lines): a₁/a₂ = b₁/b₂ = c₁/c₂

Progressions

Arithmetic Progression (AP)

  • • nth term (Tn): a + (n-1)d
  • • Sum of n terms (Sn): n/2 [2a + (n-1)d] OR n/2 [a + l]
  • • a = first term, d = common difference, l = last term

Geometric Progression (GP)

  • • nth term (Tn): arn-1
  • • Sum of n terms (Sn): a(rn - 1) / (r - 1) [if r > 1]
  • • Sum of infinite GP: a / (1 - r) [if |r| < 1]

Test Your Knowledge

30 random questions • 1 minute per question