NEET UG cheat sheet

Projectile range R = u²sin2θ/g is maximum at θ = 45°; maximum height H = u²sin²θ/(2g) and time of flight T = 2u sinθ/g.

For uniform circular motion, centripetal acceleration a = v²/r = ω²r; angular momentum L = Iω and torque τ = Iα for a rigid body about a fixed axis.

Work-energy theorem: net work equals change in kinetic energy, W_net = ΔKE; conservative forces give F = −dU/dx and mechanical energy is conserved when only conservative forces act.

Moment of inertia values: solid cylinder/disc about central axis I = ½MR²; solid sphere I = (2/5)MR²; thin ring/hoop I = MR²; rod about centre I = ML²/12.

Doppler effect for sound: apparent frequency f' = f(v ± v_o)/(v ∓ v_s), with upper signs for approach; the medium velocity v is relative to still air.

Lens and mirror formulae: 1/v − 1/u = 1/f for lenses (Cartesian sign convention) and 1/v + 1/u = 1/f for mirrors; magnification m = v/u for mirrors, m = v/u for lenses.

Photoelectric effect: maximum kinetic energy K_max = hν − φ, threshold frequency ν₀ = φ/h; stopping potential V₀ satisfies eV₀ = hν − φ.

Radioactive decay: N = N₀e^(−λt), half-life t½ = 0.693/λ, activity A = λN; after n half-lives the remaining fraction is (1/2)^n.

Series LCR resonance occurs at f = 1/(2π√(LC)); at resonance impedance is purely resistive (Z = R) and current is maximum.

Ideal gas equation PV = nRT with R = 8.314 J K⁻¹ mol⁻¹; at STP one mole of an ideal gas occupies 22.4 L.

pH = −log[H⁺] and pOH = −log[OH⁻]; at 25 °C pH + pOH = 14, and for a weak acid pH ≈ ½(pKa − log C).

Henderson–Hasselbalch equation for a buffer: pH = pKa + log([salt]/[acid]).

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

First-order kinetics: k = (2.303/t) log(a/(a − x)); half-life t½ = 0.693/k is independent of initial concentration.

Nernst equation at 298 K: E = E° − (0.0591/n) log([products]/[reactants]) for the cell reaction with n electrons transferred.

Markovnikov's rule: in HX addition to an unsymmetrical alkene, H adds to the carbon bearing more hydrogens; peroxide effect gives anti-Markovnikov addition of HBr.

SN1 proceeds via a carbocation intermediate with first-order kinetics and racemisation; SN2 is a single-step backside attack with second-order kinetics and inversion of configuration.

Crystal field: in an octahedral field the d orbitals split into lower t2g and higher eg sets; high-spin versus low-spin depends on the magnitude of Δ₀ relative to pairing energy.

Photosynthesis light reactions occur in thylakoid membranes; the Calvin cycle occurs in the stroma and fixes CO₂ via RuBisCO onto RuBP.

C4 plants fix CO₂ first into oxaloacetate in mesophyll cells using PEP carboxylase, then decarboxylate in bundle-sheath cells; they lack photorespiration and show low CO₂ compensation point.

In C3 plants, photorespiration occurs because RuBisCO oxygenates RuBP at high O₂/CO₂ ratios, wasting carbon and reducing net photosynthesis.

Translocation in phloem follows the pressure-flow (Münch) hypothesis: sugar loading lowers water potential at the source, and unloading raises it at the sink.

Root pressure, driven by active ion transport into xylem, causes guttation; transpiration pull is the main driver of water ascent according to the cohesion-tension theory.

Plant hormones: auxin (IAA) promotes apical dominance and cell elongation; gibberellin promotes stem elongation and seed germination; ABA closes stomata and induces dormancy; ethylene ripens fruit.

Alternation of generations: the sporophyte (2n) produces spores by meiosis, the gametophyte (n) produces gametes by mitosis; in angiosperms the gametophyte is highly reduced.

Double fertilisation in angiosperms: one male gamete fuses with the egg (2n zygote), the other with two polar nuclei to form triploid (3n) endosperm.

Mendelian dihybrid cross F₂ phenotypic ratio is 9:3:3:1; a test cross with a heterozygous individual gives a 1:1 ratio for a monohybrid.

Human cardiac cycle: SA node is the pacemaker; normal rate 72 beats/min, cardiac output = stroke volume × heart rate (about 5 L/min at rest).

Nephron function: glomerular filtration in the glomerulus, selective reabsorption mainly in the proximal convoluted tubule, and counter-current concentration in the loop of Henle.

Respiratory gas transport: about 97% of O₂ is carried by haemoglobin; CO₂ travels mostly as bicarbonate (~70%), with carbaminohaemoglobin and dissolved CO₂ forming the rest.

Nerve impulse: resting potential about −70 mV maintained by the Na⁺/K⁺ pump; depolarisation by Na⁺ influx, repolarisation by K⁺ efflux; conduction is saltatory in myelinated fibres.

Hormones: insulin from pancreatic β-cells lowers blood glucose; glucagon from α-cells raises it; thyroid hormones regulate basal metabolic rate via T3 and T4.

Blood groups follow ABO and Rh systems; a mother who is Rh-negative carrying an Rh-positive fetus is at risk of erythroblastosis fetalis in later pregnancies.

DNA replication is semi-conservative; the human genome has about 3 × 10⁹ base pairs, and the human diploid chromosome number is 46 (23 pairs).

Human digestion: pepsin acts on proteins in the acidic stomach; trypsin and chymotrypsin act in the alkaline small intestine; bile emulsifies fats without enzymatic action.

Immunity: B lymphocytes produce antibodies (humoral immunity); T lymphocytes mediate cell-mediated immunity, and memory cells give the secondary response.