Physics
VIBGYOR for EM Spectrum — Visible light order (Red longest wavelength → Violet shortest): Violet, Indigo, Blue, Green, Yellow, Orange, Red. For full spectrum: Radio, Microwave, Infrared, Visible, Ultraviolet, X-ray, Gamma (increasing frequency/energy).
Right-Hand Thumb Rule — For current direction and magnetic field: Thumb = current direction, curled fingers = magnetic field direction around conductor. For force on conductor: First finger = Field, seCond = Current, thuMb = Motion (Fleming's Left-Hand Rule).
SUVAT Equations Trick — Remember v² = u² + 2as first; derive others. For free fall, use g = 10 m/s² (not 9.8) for quick calculations unless precision needed. Time to max height = u/g, total time = 2u/g.
Series/Parallel Resistance — Series: resistances ADD directly (R_total = R₁ + R₂). Parallel: reciprocals add (1/R = 1/R₁ + 1/R₂). For two equal resistances in parallel, total = R/2. Opposite rules for capacitors.
Lens Formula Sign Convention — Real is positive, virtual is negative for image distance (v). For lens: focal length f is positive (converging), negative (diverging). Object distance u always negative (New Cartesian convention). Formula: 1/f = 1/v - 1/u.
Chemistry
Electronegativity Order — Father Of Naughty Children Brought Ice-cream Close: F > O > N > Cl > Br > I > C > H (most electronegative to least). Fluorine most electronegative element (4.0), Francium least (0.7).
Reactivity Series Mnemonic — Please Send Charlie's Monkeys And Zebras In Large Cages Having Strong Guards: K, Na, Ca, Mg, Al, Zn, Fe, Pb, H, Cu, Hg, Ag, Au, Pt (decreasing reactivity).
Homologous Series Formula — Alkanes: C_nH_{2n+2}, Alkenes: C_nH_{2n}, Alkynes: C_nH_{2n-2}, Alcohols: C_nH_{2n+1}OH. Each -CH₂- group adds 14 to molecular mass.
pH Scale Quick Values — pH 7 = neutral (pure water). pH < 7 acidic, pH > 7 alkaline. Each unit change = 10× concentration change. Stomach acid ~2, lemon ~2-3, blood ~7.4, soap ~9-10.
Oxidation Number Rules — Group 1 always +1, Group 2 always +2, F always -1, O usually -2 (except peroxides -1), H usually +1 (except metal hydrides -1). Sum equals charge on species.
Mathematics
Divisibility by 3 or 9 — Sum all digits; if sum divisible by 3, number divisible by 3. If digit-sum divisible by 9, number divisible by 9. Example: 12345 → 1+2+3+4+5=15 (÷3 yes, ÷9 no).
Trigonometric Ratios Hand Trick — Palm up, fingers 0°-90° (thumb=0°, index=30°, middle=60°, ring=90°). sin θ = √(finger_number/4). sin 30° = √(1/4) = 1/2, sin 45° = √(2/4) = 1/√2, sin 60° = √(3/4) = √3/2.
Quadratic Formula Quick Check — For ax² + bx + c = 0: discriminant Δ = b² - 4ac. If Δ > 0 (two real roots), Δ = 0 (one root), Δ < 0 (no real roots). Sum of roots = -b/a, product = c/a.
CAST Diagram for Trig Signs — Draw quadrants anticlockwise from 0°: All positive (0-90°), Sine only (90-180°), Tan only (180-270°), Cos only (270-360°). Add, Sugar, To, Coffee for easy recall.
Slope Formula Direction — Positive slope: line rises left→right. Negative slope: falls left→right. Zero slope: horizontal line. Undefined slope: vertical line. Parallel lines have equal slopes; perpendicular slopes multiply to -1.
Area of Triangle (Heron's) — When three sides a,b,c known: s = (a+b+c)/2, then Area = √[s(s-a)(s-b)(s-c)]. For coordinate geometry: Area = ½|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)|.
Biology
Mitosis Phases IPMAT — Interphase, Prophase, Metaphase, Anaphase, Telophase. Mnemonic: I Passed My Anatomy Test. In prophase chromosomes condense, metaphase align at equator, anaphase separate, telophase two nuclei form.
Taxonomy Hierarchy — King Phillip Came Over For Good Soup: Kingdom, Phylum, Class, Order, Family, Genus, Species (broad to specific). Human example: Animalia, Chordata, Mammalia, Primates, Hominidae, Homo, sapiens.
Blood Group Compatibility — O negative = universal donor (can give to all). AB positive = universal recipient (can receive from all). Remember: O gives to All, AB takes from All. For plasma reverse: AB plasma universal donor.
Plant Transport Mnemonic — Xylem carries Water upward (wood), Phloem carries Food bidirectionally (bast). Xylem = dead cells, Phloem = living cells. Root pressure, transpiration pull, capillarity move xylem sap.
History
1857 Revolt Centers — Meerut (start), Delhi, Lucknow, Kanpur, Jhansi, Bareilly: Many Daring Leaders Killed Justly Battled. Began May 10, 1857. Leaders: Bahadur Shah (Delhi), Nana Sahib (Kanpur), Rani Lakshmibai (Jhansi), Begum Hazrat Mahal (Lucknow).
Indian National Congress Presidents — 1885 W.C. Bonnerjee (first), 1893 Dadabhai Naoroji (first Indian), 1911 Bishan Narayan Dar (youngest at 35). Moderates (1885-1905), Extremists (1905-1918), Gandhian Era (1918-1947).
Gupta Empire Chronology — Chandragupta I (320-335 CE) founded empire, Samudragupta (335-375 CE) "Napoleon of India", Chandragupta II (375-415 CE) golden age. Remember C-S-C sequence. Fahien visited during Chandragupta II