Physics
XL < XC frequency rule — In AC circuits, inductive reactance XL = 2πfL increases with frequency; capacitive reactance XC = 1/(2πfC) decreases with frequency. At resonance XL = XC, impedance is minimum (pure resistance).
Right-hand palm rule for force — For F = qvB sinθ, stretch right palm flat: fingers point in velocity direction, curl toward B-field direction; thumb shows force direction on positive charge (reverse for negative).
VIBGYOR for increasing energy — Electromagnetic spectrum in order of *increasing* frequency/energy: Radio, Microwave, Infrared, Visible (VIBGYOR itself), Ultraviolet, X-ray, Gamma. Remember "RM-I-VUXG."
Capacitor blocks DC, passes AC — At steady DC (f=0), XC = ∞, so capacitor acts as open circuit. At high AC frequency, XC → 0, capacitor becomes short circuit. Inductor does opposite.
Photoelectric threshold trick — Maximum KE = hf - φ (work function). If frequency < threshold, *no* emission occurs regardless of intensity. Stopping potential Vs = KEmax/e, independent of intensity.
Gauss law symmetry shortcut — Use Gauss only for spherical, cylindrical, or infinite planar symmetry. For sphere: E·4πr² = Qenc/ε₀. For cylinder: E·2πrL = λL/ε₀. For plane: E·2A = σA/ε₀.
Chemistry
LEO says GER — Loss of Electrons is Oxidation; Gain of Electrons is Reduction. Oxidizing agent itself gets reduced; reducing agent itself gets oxidized (swap roles).
Alcohols: Lucas test timing — Lucas reagent (ZnCl₂/HCl) with alcohols: Tertiary gives turbidity *immediately*, Secondary in 5 min, Primary doesn't react at room temp. Remember "3-2-1, instant-medium-never."
Aldehydes vs Ketones tests — Aldehydes give positive Tollen's (silver mirror), Fehling's (red ppt), and iodoform if CH₃CO- present. Ketones only give iodoform test if methyl ketone (CH₃COR). Aldehyde = reducing; ketone = not.
Basicity order of amines — In gas phase: 3° > 2° > 1° > NH₃ (more alkyl = more basic). In water: 2° > 1° > 3° > NH₃ (3° bulky, poor solvation). Aromatic amines (aniline) much less basic due to resonance.
Aufbau order: 1s-2s-2p-3s-3p-4s-3d — Filling order by (n+l) rule: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p. When (n+l) equal, lower n fills first. 4s fills before 3d.
SN1 vs SN2 mechanism — SN1: carbocation intermediate, racemization, favored by 3° carbons, polar protic solvent. SN2: backside attack, inversion (Walden), favored by 1° carbons, polar aprotic solvent. Remember "1 = carbocation, 2 = backside."
Zero-order kinetics trap — Rate = k (independent of concentration). Half-life t½ = [A₀]/(2k) – depends on initial concentration. Unlike 1st order (t½ = 0.693/k, concentration-independent). Common in enzyme saturation, surface catalysis.
Mathematics
L'Hospital's rule conditions — Apply only for 0/0 or ∞/∞ indeterminate forms. Differentiate numerator and denominator *separately* (not quotient rule!). Recheck form after each application; stop when determinate.
Conic eccentricity memory — Circle e=0, Ellipse 0<e<1, Parabola e=1, Hyperbola e>1. "CEPH" in alphabetical = increasing eccentricity order. For ellipse a²=b²(1-e²); for hyperbola b²=a²(e²-1).
Determinant row-op rule — Swapping two rows changes sign. Multiplying a row by k multiplies determinant by k. Adding multiple of one row to another keeps determinant unchanged (use for simplification).
Binomial middle term trick — In (a+b)ⁿ, if n is even, middle term is (n/2 + 1)th term. If n is odd, two middle terms: (n+1)/2 and (n+3)/2. Greatest coefficient always at middle term(s).
Integration by parts: ILATE — Choose 'u' in order: Inverse trig, Logarithmic, Algebraic, Trigonometric, Exponential. First in ILATE becomes u; rest becomes dv. Formula: ∫u dv = uv - ∫v du.
Differential equation order-degree — Order = highest derivative present. Degree = power of highest-order derivative *after* removing radicals/fractions. (dy/dx)² is degree 2; √(dy/dx) becomes (dy/dx)^(1/2), not defined for degree.
Biology
Plant tissue "MAPP" — Meristematic (dividing cells at tips/cambium), Permanent tissues are: Assimilatory (parenchyma, storage), Protective (epidermis, cork), Permanent complex (xylem, phloem). Sclerenchyma = dead support tissue.
Animal phyla memory: "PCAN-MAMA" — Porifera, Coelenterata (Cnidaria), Aschelminthes (Nematoda), Annelida—Mollusca, Arthropoda, Echinodermata (MAMA...). Increasing complexity. Remember "No coelom → Pseudocoelom → True coelom."
Heart chambers: 2-3-4 rule — Fish 2-chambered (1A+1V), Amphibians/Reptiles 3-chambered (2A+1V; reptiles have partial septum), Crocodiles/Birds/Mammals 4-chambered (2A+2V, complete double circulation). Evolution = increasing separation.
Biomolecule reducing sugars — All monosaccharides (glucose, fructose, galactose) are reducing. Disaccharides: maltose and lactose reducing; sucrose NOT reducing (no free anomeric carbon). Test: Benedict's/Fehling's gives brick-red precipitate.
DNA vs RNA differences — DNA: deoxyribose, thymine, double helix, stable. RNA: ribose, uracil, usually single strand, less stable. Remember "DNA-T-Double; RNA-U-Single." DNA in nucleus; RNA in nucleus+cytoplasm.
Biodiversity hotspots: WHIMS — India has 4 hotspots: Western Ghats, Himalayas, Indo-Burma, Sundaland (Nicobar). Hotspot criteria: >1500 endemic vascular plants + >70% habitat loss. Western Ghats most questions.