Mathematics
Divisibility by 11 — Alternating sum of digits must be 0 or divisible by 11. For 4356: (4+5) – (3+6) = 0, so divisible by 11.
BODMAS Left-to-Right Trap — Division and Multiplication have equal priority; solve left-to-right. Same for Addition and Subtraction. 20÷5×2 = (20÷5)×2 = 8, NOT 20÷10.
Percentage-Fraction Quick Converts — 12.5%=⅛, 16.67%=⅙, 20%=⅕, 25%=¼, 33.33%=⅓, 50%=½, 66.67%=⅔, 75%=¾. Instant mental calculation shortcuts.
Profit Loss CP Formula — If SP > CP: Profit% = [(SP-CP)/CP]×100. If marked price MP with discount: SP = MP×(100-d%)/100, then compare to CP.
SI vs CI First Year Trick — Simple Interest and Compound Interest are identical for the first year. Difference appears only from Year 2 onwards when CI compounds on interest.
Speed-Distance-Time Triangle — Draw triangle: D on top, S and T at bottom. Cover what you need: D=S×T, S=D/T, T=D/S. Palm-cover method works instantly.
Time and Work Man-Days — Total work = Men × Days. If M₁ men do work in D₁ days, then M₂ men need D₂ = (M₁×D₁)/M₂ days. Cross-multiply shortcut.
Calendar Odd Days Count — Ordinary year=1 odd day, Leap year=2 odd days. Century divisible by 400 is leap, else not. For day-finding, sum odd days, divide by 7.
Pipes and Cisterns Sign Rule — Inlet pipes: positive (+), Outlet/leak pipes: negative (–). Net fill rate = Sum of rates. Time = 1/Net rate. Use LCM for easy calculation.
LCM-HCF Product Rule — For two numbers A and B: A × B = LCM × HCF. If any three values known, find the fourth instantly.
Ratio Simplification Trick — Convert ratios to same multiplier. If A:B=2:3 and B:C=4:5, make B equal: A:B:C = 8:12:15 (multiply first by 4, second by 3).
Age Calculation Timeline — Draw timeline with "now" as reference. Mark past/future positions. "n years ago" and "n years hence" create equations with consistent +n or –n.
General Intelligence and Reasoning
Coding: Letter Position — A=1, B=2...Z=26. For reverse: A=26, B=25...Z=1. Remember EJOTY at positions 5,10,15,20,25 as anchors for quick counting.
Direction Sense: NESW Clock — Visualize clock: North=12, East=3, South=6, West=9. Right turn=clockwise 90°, Left turn=anticlockwise 90°. About turn=180°.
Blood Relations: Generation Method — Maternal side=Mother's family, Paternal=Father's family. Brother's wife=Sister-in-law. Father's brother=Uncle. Mother's sister=Aunt. Draw family tree upward for clarity.
Venn Diagram Only Formula — Only A = Total A – (A∩B). For three sets: Only A = Total A – (A∩B) – (A∩C) + (A∩B∩C).
Series: Difference of Differences — If first differences unclear, check second differences. 2,5,10,17,26: differences are 3,5,7,9 (themselves in +2 pattern). Common in number series.
Analogy Relationship Types — Check: Part-Whole, Tool-Work, Worker-Product, Cause-Effect, Male-Female, Young-Old, Synonym-Antonym, Symbol-Representation. Identify pattern type first.
General Science
VIBGYOR Spectrum — Violet, Indigo, Blue, Green, Yellow, Orange, Red. Increasing wavelength order. Violet has shortest wavelength, Red has longest. Rainbow color sequence.
pH Scale Memory: 7-7-7 — pH 7 = Neutral (water). pH < 7 = Acidic (lemon, vinegar). pH > 7 = Basic/Alkaline (soap, baking soda). Range 0-14.
Mitosis vs Meiosis — Mitosis: body cells, 2 daughter cells, same chromosome number (growth/repair). Meiosis: sex cells, 4 daughter cells, half chromosomes (gamete formation).
Valency Shortcut — Group 1=1, Group 2=2, Group 13=3, Group 14=4, Group 15=3, Group 16=2, Group 17=1, Group 18=0. For common elements in competitive exams.
Photosynthesis Equation — 6CO₂ + 6H₂O + Sunlight → C₆H₁₂O₆ + 6O₂. Occurs in chloroplast, needs chlorophyll. Opposite of respiration. Raw materials: CO₂ and water.
Acids Turn Litmus Red — Acids: red litmus stays red, blue litmus turns red. Bases: blue litmus stays blue, red litmus turns blue. Simple indicator memory.
Carbon Bonding: Catenation — Carbon forms 4 covalent bonds, can bond with itself in long chains (catenation). Explains millions of organic compounds. Valency = 4 always.
Food Components: CPFVMW — Carbohydrates, Proteins, Fats, Vitamins, Minerals, Water. Six essential nutrients. Energy-giving: CPF. Protective: VM. Regulatory: MW.
General Awareness and Current Affairs
Indian History Dates: 1857-1947-1950 — 1857 First War of Independence, 1947 Independence (Aug 15), 1950 Republic Day (Jan 26). 90-year gap, then 3-year gap for Constitution.
Monsoon Months: JJAS — June, July, August, September. Southwest monsoon brings 75% of India's annual rainfall. Critical for agriculture, economy questions.
Bharat Ratna Firsts — C. Rajagopalachari, Sarvepalli Radhakrishnan, CV Raman (1954, first three together). Mother Teresa first naturalized citizen (1980). Sachin Tendulkar first sportsperson (2014).
Indian Geography: BIMARU States — Bihar, Madhya Pradesh, Rajasthan, Uttar Pradesh. Historically backward states acronym. Now MP split (Chhattisgarh), UP split (Uttarakhand). Still used in economics questions.
Five-Year Plan Memory — First Plan (1951): Agriculture focus. Second (1956): Industry focus. Plans discontinued after 12th (2017), replaced by NITI Aayog's 3-year action agenda.
Railway Zones: 18 Total — Remember major HQs: Northern (Delhi), Southern (Chennai), Eastern (Kolkata), Western (Mumbai), Central (Mumbai). 18 zones total since 2003 reorganization including Metros.