Class 11 Maths Formulas Handbook (All Chapters)

This is a single running reference for every important formula, definition and result across the Class 11 Maths (CBSE, 2026-27 rationalised syllabus) NCERT textbook — built to be used for quick lookups while solving problems or revising before an exam, without having to dig through full chapter notes. We are building this handbook chapter by chapter, and it currently covers Chapter 1: Sets. New chapters will be appended below as they are published, so bookmark this page and check back as your syllabus progresses.

Chapter 1: Sets

• Set: a well-defined collection of distinct objects; x ∈ A means x belongs to A, x ∉ A means it does not.
• Empty set: φ, with n(φ)=0. Singleton set: exactly one element.
• Equal sets: A=B when both contain exactly the same elements.
• Subset: A⊂B if every element of A is in B; proper subset if additionally A≠B.
• Power set: P(A) = set of all subsets of A. Number of subsets of an n-element set = 2ⁿ; proper subsets = 2ⁿ-1.
• If A⊂B, then P(A)⊂P(B).
• Intervals: (a,b) open; [a,b] closed; [a,b) and (a,b] semi-open/closed.
• Union: A∪B={x: x∈A or x∈B}. Intersection: A∩B={x: x∈A and x∈B}.
• Difference: A-B={x: x∈A and x∉B} = A∩B′.
• Complement: A′=U-A.
• Disjoint sets: A∩B=φ.
• Commutative: A∪B=B∪A; A∩B=B∩A.
• Associative: (A∪B)∪C=A∪(B∪C); (A∩B)∩C=A∩(B∩C).
• Distributive: A∪(B∩C)=(A∪B)∩(A∪C); A∩(B∪C)=(A∩B)∪(A∩C).
• Identity: A∪φ=A; A∩U=A; A∪U=U; A∩φ=φ.
• Complement: A∪A′=U; A∩A′=φ; (A′)′=A; U′=φ; φ′=U.
• De Morgan’s Laws: (A∪B)′=A′∩B′; (A∩B)′=A′∪B′.
• A=(A∩B)∪(A-B); A∪B=A∪(B-A).
• If A⊂B: A-B=φ, A∪B=B, A∩B=A.
• n(A∪B)=n(A)+n(B)-n(A∩B) (two sets); if disjoint, n(A∪B)=n(A)+n(B).
• n(A-B)=n(A)-n(A∩B).
• n(A∪B∪C)=n(A)+n(B)+n(C)-n(A∩B)-n(B∩C)-n(A∩C)+n(A∩B∩C) (three sets).

More chapters will be added to this handbook progressively — check back for Relations & Functions, Trigonometric Functions, and further chapters as they are published.

Related NCERT Content for Class 11 Maths Chapter 1

• NCERT Solutions for Sets
• Extra Questions (HOTS) for Sets
• Revision Notes for Sets
• Class 11 Maths NCERT Book (Download PDF)

Chapter 2: Relations and Functions

• Function: each domain element → exactly 1 output.

Chapter 3: Trigonometric Functions

• π rad = 180°; sin²θ+cos²θ=1; sin(A±B)=sinAcosB±cosAsinB.

Chapter 4: Complex Numbers and Quadratic Equations

• i²=−1; z=a+bi; |z|=√(a²+b²); D<0 → complex roots.

Chapter 5: Linear Inequalities

• Multiply/divide by negative → reverse inequality.

Chapter 6: Permutations and Combinations

• ⁿP_r=n!/(n−r)!; ⁿC_r=n!/[r!(n−r)!].

Chapter 7: Binomial Theorem

• (a+b)ⁿ=∑ⁿC_ka^n−kb^k; T_k+1=ⁿC_ka^n−kb^k.

Chapter 8: Sequences and Series

• GP: a_n=arⁿ⁻¹; S∞=a/(1−r) for |r|<1.

Chapter 9: Straight Lines

• m=(y2−y1)/(x2−x1); Perpendicular: m1m2=−1; y=mx+c.

Chapter 10: Conic Sections

• Circle: (x−h)²+(y−k)²=r². Parabola: y²=4ax. Ellipse: x²/a²+y²/b²=1.

Chapter 11: Introduction to Three Dimensional Geometry

• d=√[(x2−x1)²+(y2−y1)²+(z2−z1)²]; 8 octants.

Chapter 12: Limits and Derivatives

• f'(x)=lim_h→0[f(x+h)−f(x)]/h; d/dx(xⁿ)=nxⁿ⁻¹.

Chapter 13: Statistics

• Variance=∑(xi−mean)²/n; SD=√variance.

Chapter 14: Probability

• P(A)=n(A)/n(S); P(A∪B)=P(A)+P(B)−P(A∩B).

Written by Satish

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