General Mental Ability
Divisibility by 11 — Alternating sum of digits must be divisible by 11. For 8910: 8-9+1-0=0, divisible by 11. Quick check for multi-digit numbers without actual division.
Clock Angle Formula — Angle = |11M - 60H|/2 degrees, where M=minutes, H=hours. At 3:15, |11(15) - 60(3)|/2 = 7.5°. Solves clock problems in seconds.
Calendar Day Formula — Odd days method: Count remainder when total days ÷7. 1 ordinary year=1 odd day, leap=2. For day-of-week questions in reasoning.
Dice Opposite Faces — Sum of opposite faces on standard dice always equals 7. If you see 1, opposite is 6; see 2, opposite is 5; see 3, opposite is 4.
Blood Relations Shortcut — Draw gender symbols (○ female, △ male) with connecting lines. Convert complex wordings to instant visual family trees for quick solving.
General Science
VIBGYOR — Violet, Indigo, Blue, Green, Yellow, Orange, Red. Wavelength order of visible spectrum (increasing wavelength). Essential for optics questions.
Vitamin Deficiency (ABCDE-K) — A=Night blindness, B=Beriberi, C=Scurvy, D=Rickets, E=Sterility, K=Blood clotting issues. Covers 90% of vitamin questions.
Reactivity Series (PMASCZIF) — Potassium, Magnesium, Aluminium, Sodium, Carbon, Zinc, Iron, Copper (decreasing reactivity). Higher displaces lower from compounds.
pH Memory — pH<7 Acidic (A comes before N in alphabet), pH=7 Neutral, pH>7 Basic. Acids turn blue litmus red, bases turn red litmus blue.
Newton's Laws Numbers — 1st=Inertia (rest/motion continues), 2nd=F=ma (force calculation), 3rd=Action-Reaction (equal-opposite). Remember by position number.
Human & Plant Biology
Mitosis Phases (PMAT) — Prophase, Metaphase, Anaphase, Telophase. Cell division sequence for questions on genetics and reproduction.
Blood Groups Universal — O negative is universal donor (gives to all), AB positive is universal recipient (receives from all). Critical for transfusion questions.
ABO Compatibility Triangle — A gives to A,AB; B gives to B,AB; AB gives to AB only; O gives to all. Draw arrows for quick reference.
Photosynthesis Equation — 6CO₂ + 6H₂O + Light → C₆H₁₂O₆ + 6O₂. Remember as "6s and 6s make sugar and oxygen." Respiration is exact reverse.
Environmental Science
Greenhouse Gases (COMN) — CO₂, O₃ (Ozone), Methane, NOx. Top contributors to global warming in prelims questions.
Ozone Layer Position — Stratosphere (15-35 km altitude). Ground-level ozone=pollutant, stratospheric ozone=protective shield. Don't confuse the two.
Biodiversity Hotspots India (4 WHE-N) — Western Ghats, Himalayas, Eastern Himalayas, Nicobar Islands. These four regions appear repeatedly in environment questions.
Bihar — Special Knowledge
1857 Leaders Bihar (BKVP) — Babu Kunwar Singh (Jagdishpur), Pir Ali (Patna), Veer Kunwar Singh (Ara). Kunwar Singh was 80 years old, died April 1858.
Champaran Dates — 1917 Satyagraha, Gandhi's first major movement in India. Remember "17=first" (first successful civil disobedience). Against tinkathia (3/20 cultivation) system.
Bihar Districts by Division — Patna=6, Magadh=5, Tirhut=4, Kosi=6, Darbhanga=6, Saran=3, Purnia=4, Bhagalpur=3, Munger=6. Total 38 districts. Remember "Patna-Kosi-Darbhanga-Munger have 6 each."
Nalanda vs Vikramshila — Nalanda=5th century Kumaragupta I (older, Buddhist university), Vikramshila=8th century Dharmapala (later, Tantric Buddhism). Don't mix founding rulers.
Bihar Rivers (GKS-F) — Ganga, Kosi (Sorrow of Bihar), Son, Falgu, Punpun. Kosi changes course frequently, causes devastating floods.
Mauryan Capital Sequence — Pataliputra (modern Patna) was capital of Magadha under Mauryas, Guptas, Palas. Ancient Bihar's political center for 1000+ years.