Pascal's triangle: the binomial coefficientsपास्कल त्रिभुज: द्विपद गुणांकPascal's triangle: the binomial coefficients

Section 7.2 · Class 11 Maths Ch 7 · interactive diagram

Parts and what they mean

• n = 0: (a + b)⁰ = 1 (n = 0: (a + b)⁰ = 1) — The top row is just 1.
• n = 1: 1 1 (n = 1: 1 1) — (a + b)¹ = a + b.
• n = 2: 1 2 1 (n = 2: 1 2 1) — (a + b)² = a² + 2ab + b².
• n = 3: 1 3 3 1 (n = 3: 1 3 3 1) — (a + b)³ = a³ + 3a²b + 3ab² + b³.
• n = 4: 1 4 6 4 1 (n = 4: 1 4 6 4 1) — Coefficients of (a + b)⁴. They are ⁴C₀, ⁴C₁, ⁴C₂, ⁴C₃, ⁴C₄.
• n = 5: 1 5 10 10 5 1 (n = 5: 1 5 10 10 5 1) — Coefficients of (a + b)⁵ — used in Exercise 7.1 Q1, Q2, Q4.
• n = 6: 1 6 15 20 15 6 1 (n = 6: 1 6 15 20 15 6 1) — Coefficients of (a + b)⁶. Row sum = 2⁶ = 64.
• Each entry = sum of the two above (हर संख्या = ऊपर की दो संख्याओं का योग) — This is Pascal’s rule ⁿCᵣ₋₁ + ⁿCᵣ = ⁿ⁺¹Cᵣ. Row n also sums to 2ⁿ.

Original diagram drawn by Simple Learning Hub for NCERT Class 11 Maths Ch 7. Report a mistake