IISER IAT cheat sheet

Central dogma: DNA → RNA (transcription, RNA polymerase) → protein (translation, ribosome); the genetic code is degenerate and non-overlapping, with AUG coding methionine and acting as the start codon.

Mendelian ratios: monohybrid F2 gives 3:1 phenotype and 1:2:1 genotype; dihybrid F2 gives 9:3:3:1 when genes are unlinked and assort independently.

Hardy–Weinberg equilibrium requires no mutation, no migration, no selection, random mating, and large population; then p + q = 1 and p² + 2pq + q² = 1.

Enzyme kinetics: Michaelis–Menten v = Vmax[S]/(Km + [S]); Km is the substrate concentration at half Vmax, and a competitive inhibitor raises apparent Km without changing Vmax.

Photosynthesis: light reactions in thylakoid membranes produce ATP and NADPH and split water, releasing O2; the Calvin cycle in the stroma fixes CO2 using RuBisCO.

Cellular respiration yields about 30–32 ATP per glucose in eukaryotes: glycolysis (2 ATP, cytosol), Krebs cycle (mitochondrial matrix), and oxidative phosphorylation via the electron transport chain.

Cell cycle checkpoints occur at G1/S, G2/M, and the spindle-assembly checkpoint in metaphase; failure of these checkpoints is associated with oncogenesis.

Blood flow and gas exchange follow Fick's principle: rate of diffusion is proportional to surface area and concentration gradient and inversely proportional to membrane thickness.

Ideal gas law PV = nRT with R = 8.314 J mol⁻¹ K⁻¹; at STP (273.15 K, 1 bar) one mole occupies about 22.7 L (22.4 L at 1 atm).

First law of thermodynamics: ΔU = q + w; for work done on the system w = −PΔV, and ΔH = ΔU + Δ(PV), so ΔH = q at constant pressure.

Gibbs free energy ΔG = ΔH − TΔS; a reaction is spontaneous when ΔG < 0, and equilibrium gives ΔG° = −RT ln K.

pH = −log[H⁺]; for a weak acid pH ≈ ½(pKa − log C), and a buffer obeys the Henderson–Hasselbalch equation pH = pKa + log([A⁻]/[HA]).

Rate law rate = k[A]^m[B]^n with order determined experimentally; first-order half-life t½ = 0.693/k and is independent of initial concentration.

Quantum numbers: n ≥ 1, l = 0 to n−1, m_l = −l to +l, m_s = ±½; the Pauli exclusion principle forbids identical sets of all four.

Hybridization from steric number: 2 → sp (linear, 180°), 3 → sp² (trigonal planar, 120°), 4 → sp³ (tetrahedral, 109.5°).

Aromaticity requires a planar cyclic conjugated system with 4n + 2 π electrons; benzene (6 π electrons) qualifies, cyclobutadiene (4 π electrons) does not.

Quadratic ax² + bx + c = 0 has roots x = [−b ± √(b² − 4ac)]/(2a); the discriminant b² − 4ac indicates two real, one repeated, or two complex roots.

For an arithmetic progression, a_n = a + (n−1)d and S_n = (n/2)[2a + (n−1)d]; for a geometric progression, a_n = ar^(n−1) and S_n = a(rⁿ − 1)/(r − 1) for r ≠ 1.

Limits: L'Hôpital's rule applies to 0/0 or ∞/∞ forms; the standard limits are lim(x→0) sin x/x = 1 and lim(x→0)(1 + x)^(1/x) = e.

Derivatives: d/dx(xⁿ) = nx^(n−1), d/dx(sin x) = cos x, d/dx(eˣ) = eˣ, d/dx(ln x) = 1/x; the chain rule is dy/dx = (dy/du)(du/dx).

Integration by parts: ∫u dv = uv − ∫v du; definite integrals satisfy ∫ₐᵇ f(x) dx = −∫ᵦᵃ f(x) dx and split at interior points.

Probability: P(A ∪ B) = P(A) + P(B) − P(A ∩ B); conditional probability P(A|B) = P(A ∩ B)/P(B), and Bayes' theorem follows from it.

Binomial theorem: (x + y)ⁿ = Σ C(n,k) x^(n−k) y^k; the general term is C(n,k) x^(n−k) y^k and the middle term occurs at k ≈ n/2.

Vectors: a·b = |a||b|cos θ gives the angle between vectors; a×b is perpendicular to both, with |a×b| = |a||b|sin θ equal to the parallelogram area.

Kinematics for constant acceleration: v = u + at, s = ut + ½at², and v² = u² + 2as; projectile range is R = u² sin 2θ / g for level ground.

Newton's second law F = dp/dt; on an incline of angle θ, the component of gravity along the slope is mg sin θ and the normal force is mg cos θ.

Work–energy theorem: W = ΔKE = ½mv² − ½mu²; conservative forces have potential energy with F = −dU/dx.

Momentum conservation applies when net external force is zero; perfectly inelastic collisions conserve momentum but lose kinetic energy, while elastic collisions conserve both.

Circular motion requires centripetal acceleration a = v²/r directed toward the center; banking angle satisfies tan θ = v²/(rg) without friction.

Simple harmonic motion: x = A sin(ωt + φ) with ω = √(k/m) for a spring and ω = √(g/L) for a pendulum; period T = 2π/ω.

Electric field of a point charge E = kQ/r² with k = 9 × 10⁹ N m² C⁻²; potential V = kQ/r, and field lines run from positive to negative charge.

Ohm's law V = IR; resistors in series add, resistors in parallel satisfy 1/R = Σ1/Rᵢ, and power dissipated is P = VI = I²R = V²/R.

Snell's law n₁ sin θ₁ = n₂ sin θ₂; total internal reflection occurs when the angle exceeds the critical angle sin θc = n₂/n₁ for n₁ > n₂.