General Knowledge & Current Affairs
- Bharat Ratna chronology — Remember first three: CV Raman (1954), Rajagopalachari (1954), Radhakrishnan (1954) as "CRR-54". Helps anchor timeline for awards questions.
- Indian Ocean island nations — MMSS: Maldives, Mauritius, Seychelles, Sri Lanka. Quick recall for geography questions on island nations near India.
- Monsoon months — June-September: JJAS (sounds like "Jazz"). Covers SW monsoon period for Indian Geography climate questions.
- Five-Year Plan landmarks — 1st Plan (1951) agriculture focus, 2nd (1956) industry (Mahalanobis), 5th (1974) Garibi Hatao. Remember "A-I-G" sequence for themes.
Bihar Geography
- Bihar neighbors — "UP-WaNts-JharKhand": Uttar Pradesh (West), Nepal (North), Jharkhand (South). West Bengal on East completes the boundary memory.
- Major rivers of Bihar — "GSK-P" (Ganges, Sone, Kosi, Punpun). Ganges is main, Kosi is "Sorrow of Bihar", Sone from south.
- Bihar divisions — Nine divisions: "Patna-Magadh-Tirhut" are three major ones to remember first, covers 50% of geography questions about administrative divisions.
Indian History
- Vedas sequence — RYSA: Rigveda, Yajurveda, Samaveda, Atharvaveda. Chronological order of composition in Ancient India.
- 1857 revolt centers — "Delhi-Meerut-Kanpur-Lucknow-Jhansi" (north to south line). Remember as DMKLJ for uprising locations.
- Gupta rulers — Chandragupta I → Samudragupta → Chandragupta II. "C-S-C" golden age sequence, Samudragupta was "Napoleon of India".
- Mauryan chronology — Chandragupta (322 BCE), Bindusara, Ashoka (268 BCE). Remember "CBC" and 322-268 = 54 years gap for Ashoka.
Indian Polity & Constitution
- Fundamental Rights articles — Articles 14-32. "14 to 32 = FR". Article 32 is "Right to Constitutional Remedies" (Dr. Ambedkar's "heart and soul").
- Union List subjects — "DART": Defence, Atomic energy, Railways, Telecommunications. Core Central subjects from 7th Schedule.
- President's ordinance power — Article 123. Remember "1-2-3, Ordinance-free" (when Parliament not in session, valid 6 weeks after reassembly).
- Money Bill definition — Article 110. Only in Lok Sabha, RS can only recommend. "110 = Money's Solo" (no RS equality here).
Indian Geography
- Western Ghats states — "GaMKaT": Gujarat, Maharashtra, Karnataka, Tamil Nadu (+ Kerala, Goa). North to south sequence along Arabian Sea.
- Tropic of Cancer states — "RAMPJAM": Rajasthan, Gujarat (Raj-Guj), Madhya Pradesh, Chhattisgarh, Jharkhand, West Bengal, Tripura, Mizoram. 8 states at 23.5°N.
- Major soil types — "ARBDL": Alluvial, Red, Black, Desert, Laterite. Five main Indian soil categories for agriculture questions.
Mathematics - Number System
- Divisibility by 11 — Alternating digit sum difference divisible by 11. Example: 121 → (1+1)−2=0, divisible. Quick mental check trick.
- Unit digit patterns — Powers of 2: cycle 2-4-8-6 repeats every 4; Powers of 3: 3-9-7-1; Powers of 7: 7-9-3-1. Memorize these four cycles.
- Perfect squares ending — Only end in 0,1,4,5,6,9. Never 2,3,7,8. Eliminates wrong options instantly in competitive exams.
- Divisibility by 9 — Sum of digits divisible by 9. Example: 729 → 7+2+9=18, divisible. Faster than actual division.
Mathematics - Algebra
- Quadratic formula memory — x = [−b ± √(b²−4ac)] / 2a. Remember as "minus b plus-minus root-delta by 2a" where delta = b²−4ac.
- (a+b)² and (a−b)² trap — (a+b)² = a²+2ab+b²; (a−b)² = a²−2ab+b². Middle term sign follows outer sign. Common mistake area.
- a³ ± b³ identity — a³+b³ = (a+b)(a²−ab+b²); a³−b³ = (a−b)(a²+ab+b²). Middle sign opposite for sum, same for difference in factor.
Mathematics - Average
- Average speed formula — For equal distances at speeds S₁, S₂: Average = 2S₁S₂/(S₁+S₂). Harmonic mean, NOT (S₁+S₂)/2. Critical difference.
- Age average shift — When one leaves (age X) and another joins (age Y): Average change = (Y−X)/n. Direct formula avoids long calculation.
Mathematics - Percentage
- Percentage to fraction — 12.5%=1/8, 16.67%=1/6, 20%=1/5, 25%=1/4, 33.33%=1/3. Memorize these six for rapid calculation in profit/discount problems.
- Successive percentage — Two changes of a% and b%: Net = a+b+(ab/100). The ab/100 term is the compounding effect, often forgotten.
Mathematics - Profit & Loss
- Marked Price formula — MP = CP × (100+P)/(100−D) where P=profit%, D=discount%. One-step formula when both CP and percentages given.
- False weight trick — If uses 900g instead of 1kg: Profit% = [(1000−900)/900]×100 = 11.11%. Formula: (Error/True weight)×100.
Mathematics - Time & Work
- Work formula — If A does in 'a' days, B in 'b' days: Together = ab/(a+b) days. Product over sum for two workers.
- Man-days constant — M₁D₁ = M₂D₂ (when work same). If men increase, days decrease proportionally. Use cross-multiplication directly.
Mathematics - Time & Distance
- Relative speed — Same direction: |S₁−S₂|; Opposite direction: S₁+S₂. Subtract when chasing, add when meeting head-on.
- Train crossing — Time = (L₁+L₂)/S for two trains; Time = L/S for pole/man. Add lengths for platform/train, single length for point objects.
Mathematics - Geometry
- Triangle angle sum — Always 180°. If two angles given, third = 180−(sum of two). Simplest yet most frequently used property.
- Pythagoras triplets — 3-4-5, 5-12-13, 8-15-17, 7-24-25. Memorize these four; saves calculation time in right triangle problems.
- Circle theorems — Angle in semicircle = 90°; Angle at center = 2× angle at circumference (same arc). Two most tested properties.
Mathematics - Mensuration
- **Area formulas