Mathematics

Area Formulas
Rectangle: A = l × w
Square: A = s²
Circle: A = πr²
Triangle: A = ½ × b × h
Volume Formulas
Cube: V = s³
Cuboid: V = l × w × h
Sphere: V = (4/3)πr³
Cylinder: V = πr²h
Algebraic Identities
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
a² - b² = (a+b)(a-b)

Physics

Motion
v = u + at
s = ut + ½at²
v² = u² + 2as
Force and Energy
F = ma
W = Fs
KE = ½mv²
PE = mgh
Electricity
V = IR
P = VI
E = VIt

Chemistry

Important Equations
2H₂ + O₂ → 2H₂O
NaOH + HCl → NaCl + H₂O
CaCO₃ → CaO + CO₂
Gas Laws
PV = nRT
P₁V₁ = P₂V₂
V₁/T₁ = V₂/T₂
Solutions
Molarity = moles/liter
pH = -log[H⁺]
Kw = [H⁺][OH⁻]

Biology

  • Cell is the basic unit of life - discovered by Robert Hooke
  • DNA structure: Double helix model by Watson and Crick
  • Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
  • Cellular Respiration: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + Energy
  • Human body has 206 bones and over 600 muscles
  • Blood Types: A, B, AB, and O (Universal donor: O-, Universal recipient: AB+)

    • Notes For Exams

    General Awareness

    Key points to remember:

    • Indian Constitution was adopted on 26 November 1949
    • First Five Year Plan was launched in 1951
    • RBI was established on April 1, 1935
    • UN was established on October 24, 1945
    • First Battle of Panipat was fought in 1526
    • Ganga Action Plan was launched in 1985
    History Notes

    Important Historical Events:

    • Quit India Movement started in 1942
    • First War of Independence: 1857
    • Partition of Bengal: 1905
    • Formation of INC: 1885
    Geography Notes

    Geographical Facts:

    • Largest State by Area: Rajasthan
    • Largest State by Population: Uttar Pradesh
    • Highest Peak: Mount Everest (8,848m)
    • Longest River: Ganga
    Economics Notes

    Economic Concepts:

    • GDP: Total value of goods & services
    • Inflation: Rise in general price level
    • Fiscal Policy: Government's revenue & expenditure
    • Monetary Policy: RBI's money supply control
    Polity Notes

    Constitutional Framework:

    • Fundamental Rights: Articles 12-35
    • Directive Principles: Articles 36-51
    • Fundamental Duties: Article 51A
    • Emergency Provisions: Articles 352-360
    Current Affairs

    Key Areas to Focus:

    • National & International Events
    • Sports & Awards
    • Science & Technology
    • Important Days & Themes

    Details Syllabus

    General Knowledge (GK)
    • Indian History
      • Ancient India (Indus Valley, Vedic Age, Mauryan Empire)
      • Medieval India (Delhi Sultanate, Mughal Empire)
      • Modern India (British Rule, Freedom Struggle)
    • Geography
      • Physical Geography of India
      • World Geography
      • Climate and Natural Resources
    • Indian Polity
      • Constitution and Its Features
      • Governance Structure
      • Rights and Duties
    • Economics Basics
      • Indian Economy
      • Economic Policies
      • Banking and Finance
    • Science & Technology
      • Latest Developments
      • Space Technology
      • Digital India
    • Current Affairs
      • National Events
      • International Relations
      • Sports and Awards
    Quantitative Aptitude
    • Number System
      • Natural Numbers and Properties
      • Divisibility Rules
      • HCF and LCM
    • Algebra
      • Basic Operations
      • Equations and Inequalities
      • Quadratic Equations
    • Geometry
      • 2D and 3D Shapes
      • Circles and Triangles
      • Coordinate Geometry
    • Data Interpretation
      • Tables and Graphs
      • Pie Charts
      • Bar Diagrams
    • Probability & Statistics
      • Basic Probability
      • Mean, Median, Mode
      • Standard Deviation
    • Time, Speed & Distance
      • Basic Concepts
      • Relative Speed
      • Trains and Boats
    Logical Reasoning
    • Puzzles
      • Number Series
      • Letter Series
      • Visual Reasoning
    • Syllogisms
      • Basic Rules
      • Venn Diagrams
      • Conclusions
    • Blood Relations
      • Family Tree
      • Complex Relations
      • Coded Relations
    • Coding-Decoding
      • Letter Coding
      • Number Coding
      • Symbol Coding
    • Seating Arrangements
      • Linear Arrangement
      • Circular Arrangement
      • Square Arrangement
    • Logical Sequences
      • Pattern Recognition
      • Analogies
      • Classifications
    English Language
    • Grammar Rules
      • Parts of Speech
      • Tenses
      • Voice and Narration
    • Vocabulary Development
      • Word Formation
      • Idioms and Phrases
      • Commonly Confused Words
    • Reading Comprehension
      • Main Ideas
      • Inference
      • Author's Tone
    • Sentence Rearrangement
      • Paragraph Formation
      • Coherence
      • Sentence Types
    • Error Spotting
      • Subject-Verb Agreement
      • Article Usage
      • Preposition Usage
    • Synonyms & Antonyms
      • Word Meanings
      • Contextual Usage
      • Word Pairs
    General Science
    • Physics
      • Motion and Forces
      • Energy and Work
      • Light and Sound
    • Chemistry
      • Matter and States
      • Chemical Reactions
      • Periodic Table
    • Biology
      • Human Body Systems
      • Ecosystem and Environment
      • Genetics
    • Environmental Science
      • Pollution Control
      • Conservation
      • Climate Change
    • Everyday Science
      • Common Phenomena
      • Scientific Principles
      • Modern Applications