Physics
RMS-Peak Relation — For AC voltage/current, RMS = Peak/√2 or 0.707×Peak. Remember "Root-Mean-Square cuts peak by root-two" for quick conversions in circuit problems.
Capacitive Reactance Inverse — Xc = 1/(2πfC). Mnemonic: "Capacitor Chokes DC" — as frequency f→0, Xc→∞, blocking DC. Higher frequency means lower reactance.
Inductive Reactance Direct — XL = 2πfL. Think "Inductor Loves frequency" — reactance increases linearly with frequency, opposite to capacitor behavior.
Bohr Radius Formula — r = n²h²ε₀/(πmZe²). Remember "n-square on top, Z in denominator" — radius grows with orbit number squared, shrinks with atomic number.
Photoelectric Work Function — Maximum KE = hf - φ. Mnemonic: "Energy In minus Work Out" — incident photon energy minus threshold gives electron kinetic energy.
RC Time Constant — τ = RC gives time for capacitor to charge to 63% (or discharge to 37%). Remember "One tau = Two-thirds charged" for quick circuit analysis.
Fleming's Right-Hand Rule — Thumb (motion), First finger (field), Middle finger (induced current). Mnemonic: "ThuMb Middle First" = Motion, eMf, Field for generators.
Lenz Law Direction — Induced current opposes the change causing it. Think "Nature is Lazy" — systems resist change in magnetic flux through them.
Chemistry
Lucas Test Order — 1° alcohols: no reaction, 2° alcohols: 5 min, 3° alcohols: immediate turbidity with ZnCl₂/HCl. Remember "1-2-3 goes Slow-Medium-Fast."
Aldehyde vs Ketone Tests — Aldehydes give positive Tollens' (silver mirror) and Fehling's (red precipitate); ketones don't. Mnemonic: "Aldehydes Are Friendly" — they reduce reagents easily.
Carbylamine Test Specificity — Only 1° amines give isocyanide (foul smell) with CHCl₃ + KOH. Remember "Primary Only Stinks" for nitrogen compound identification.
Aufbau Order — 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p. Mnemonic: draw diagonal arrows from top-right to bottom-left on orbital chart.
Mole Concept Bridge — Moles = Mass/Molecular_weight = Volume/22.4 (at STP) = Number/6.022×10²³. Remember "MMV-N divide by MV-A" for four conversion paths.
Fajan's Rules — Small cation + large anion = more covalent character. Mnemonic: "Small Positive Polarizes Big Negative" for predicting ionic vs covalent nature.
Coordination Number Geometry — CN 2: linear, 4: tetrahedral/square planar, 6: octahedral. Remember "2-Line, 4-Tetra, 6-Octa" for most common geometries.
Biomolecule Reducing Sugars — All monosaccharides + maltose and lactose reduce Fehling's; sucrose doesn't. Remember "Sucrose is Secure" — non-reducing due to glycosidic link.
Mathematics
Derivative Maxima-Minima — At extrema: f'(x)=0. Then f''(x)<0 means maxima, f''(x)>0 means minima. Remember "Negative curves Down, maxima; Positive curves Up, minima."
Area Under Curve Sign — ∫f(x)dx gives signed area; use |f(x)| for actual area when curve dips below x-axis. Always sketch for integration region problems.
Binomial Middle Term — For (a+b)ⁿ: if n even, middle term is (n/2 + 1)th; if n odd, two middle terms at positions (n+1)/2 and (n+3)/2.
i Powers Cycle — i¹=i, i²=-1, i³=-i, i⁴=1, then repeats. Divide exponent by 4; remainder 0,1,2,3 gives 1,i,-1,-i respectively.
Conic Eccentricity Memory — Circle e=0, Ellipse 0<e<1, Parabola e=1, Hyperbola e>1. Remember "CEPH" order with "0, fraction, 1, greater than 1."
Continuity Three Conditions — f(a) exists, lim(x→a)f(x) exists, and both are equal. All three must hold; missing any one means discontinuity at that point.
Determinant Row Operations — Swapping rows: changes sign. Multiplying row by k: determinant multiplies by k. Adding multiple of one row to another: determinant unchanged.
Differential Equation Order-Degree — Order = highest derivative present; Degree = power of highest derivative after removing radicals/fractions. Check both systematically in variable-separable problems.