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Distance in the n-th Second Physics
$$S_n = u + \frac{a}{2}(2n - 1)$$

Why: Derived from subtracting total displacement up to (n−1) from total up to n under constant acceleration. How to use: Apply when NEET asks for displacement in a specific second (e.g., '5th second'), not total for first 5 seconds.

Projectile Motion Parameters Physics
$$T = \frac{2u \sin\theta}{g}, \quad H = \frac{u^2 \sin^2\theta}{2g}, \quad R = \frac{u^2 \sin 2\theta}{g}$$

Why: Decomposing 2D projectile into independent vertical and horizontal components. How to use: $R_{max} = u^2/g$ when $\theta = 45°$.

Max Height & Range Relation Physics
$$\tan\theta = \frac{4H}{R}$$

Why: Derived by dividing H by R formulas. How to use: High-yield NEET shortcut! Use directly when both $H$ and $R$ are given, bypassing calculation of initial velocity $u$.

River-Boat Shortest Path Physics
$$\sin\theta = \frac{v_r}{v_b}, \quad t = \frac{d}{\sqrt{v_b^2 - v_r^2}}$$

Why: Swimmer's upstream component must cancel river flow for perpendicular crossing. How to use: Only works when boat speed $v_b > v_r$.

Centripetal & Net Acceleration Physics
$$a_c = \frac{v^2}{r} = \omega^2 r, \quad a_{net} = \sqrt{a_c^2 + a_t^2}$$

Why: $a_c$ changes direction, $a_t = dv/dt$ changes magnitude. How to use: For uniform circular motion $a_t = 0$, so $a_{net} = a_c$. For non-uniform, add vectorially at 90°.

Apparent Weight in Elevator Physics
$$N = m(g \pm a)$$

Why: Non-inertial pseudo force frame. How to use: Accelerating up → $N = m(g+a)$ (heavier). Accelerating down → $N = m(g-a)$ (lighter). Identify acceleration direction, not velocity direction.

Static Friction & Angle of Repose Physics
$$f_{s,max} = \mu_s N, \quad \tan\theta = \mu_s$$

Why: Static friction self-adjusts up to $f_{s,max}$. How to use: If applied force $< f_{s,max}$, friction equals applied force, NOT $\mu_s N$.

Max Speed on Banked Road Physics
$$v_{max} = \sqrt{rg \left( \frac{\mu_s + \tan\theta}{1 - \mu_s \tan\theta} \right)}$$

Why: Normal force + friction provide centripetal force. How to use: If unbanked ($\theta = 0$), reduces to $v_{max} = \sqrt{\mu_s r g}$.

Vertical Circular Motion Speeds Physics
$$v_{bottom} = \sqrt{5gR}, \quad v_{top} = \sqrt{gR}, \quad T_{bottom} - T_{top} = 6mg$$

Why: Energy conservation + centripetal force at extreme points to keep string taut ($T_{top} \ge 0$). How to use: Minimum speeds for completing full vertical circle.

Work-Energy Theorem Physics
$$W_{net} = \Delta K = \frac{1}{2}mv^2 - \frac{1}{2}mu^2$$

Why: Total work by ALL forces = change in kinetic energy. How to use: Extremely versatile NEET solver — avoids complex acceleration integration steps.

1D Head-On Elastic Collision Physics
$$v_1 = \left(\frac{m_1 - m_2}{m_1 + m_2}\right)u_1 + \left(\frac{2m_2}{m_1 + m_2}\right)u_2$$

Why: Simultaneous conservation of momentum and KE ($e=1$). How to use: If $m_1 = m_2$, bodies exchange velocities: $v_1 = u_2, v_2 = u_1$.

Coefficient of Restitution Physics
$$e = \frac{v_2 - v_1}{u_1 - u_2}$$

Why: Measures elasticity ($e=1$ elastic, $0 < e < 1$ inelastic, $e=0$ perfectly inelastic). How to use: Ball bouncing: $e = \sqrt{h'/h}$.

Spring Potential Energy Physics
$$U = \frac{1}{2}kx^2, \quad W_{spring} = -\frac{1}{2}k(x_f^2 - x_i^2)$$

Why: Integration of restoring force $F = -kx$. How to use: Spring work is negative when deformation increases, positive when returning to natural length.

Center of Mass Position Physics
$$\vec{r}_{cm} = \frac{m_1 \vec{r}_1 + m_2 \vec{r}_2}{m_1 + m_2}$$

Why: Weighted mass-average position of system. How to use: COM always lies closer to the heavier object. Distances: $r_1 = \frac{m_2 r}{m_1+m_2}$.

Parallel Axis Theorem Physics
$$I_{axis} = I_{cm} + Md^2$$

Why: Relates MOI about any axis to parallel axis through COM. How to use: $I_{cm}$ MUST be through center of mass. $d$ is perpendicular distance between axes.

Perpendicular Axis Theorem Physics
$$I_z = I_x + I_y$$

Why: Sum of MOI about two in-plane perpendicular axes equals MOI about perpendicular axis. How to use: Applies ONLY to flat 2D objects (discs, rings, sheets), never 3D solid bodies.

Torque & Rotational Newton's Law Physics
$$\tau = rF\sin\theta, \quad \tau_{net} = I\alpha$$

Why: Torque is rotational analog of force. How to use: Calculate $\vec{r}$ from pivot to force point. Use perpendicular component $F_\perp = F\sin\theta$.

Conservation of Angular Momentum Physics
$$L = I\omega = \text{const} \implies I_1\omega_1 = I_2\omega_2$$

Why: If $\tau_{ext} = 0$, angular momentum is conserved. How to use: Diver folding arms → $I$ decreases → $\omega$ increases proportionally. Frequently tested!

KE of Pure Rolling Physics
$$K = \frac{1}{2}Mv^2\left(1 + \frac{k^2}{R^2}\right)$$

Why: Combines translational + rotational KE ($v = \omega R$). How to use: $k^2/R^2$: Ring=1, Disc=1/2, Solid sphere=2/5, Hollow sphere=2/3.

Rolling Down Inclined Plane Physics
$$a = \frac{g\sin\theta}{1 + \frac{k^2}{R^2}}$$

Why: Balancing gravity, friction torque, and rotational inertia. How to use: Solid sphere ($k^2/R^2 = 0.4$) fastest, Ring ($1.0$) slowest down incline.

Gravity at Height & Depth Physics
$$g_h = g\left(1 - \frac{2h}{R}\right), \quad g_d = g\left(1 - \frac{d}{R}\right)$$

Why: Gravity decreases both above and below Earth's surface. How to use: Linear formula valid for $h \ll R$. For large $h$, use $g_h = g\frac{R^2}{(R+h)^2}$.

Escape & Orbital Velocity Physics
$$v_e = \sqrt{2gR}, \quad v_o = \sqrt{gR}, \quad v_e = \sqrt{2}\,v_o$$

Why: Escape velocity is minimum speed to leave gravitational field. How to use: $v_e \approx 11.2$ km/s for Earth. Independent of launched mass.

Kepler's Third Law Physics
$$T^2 \propto r^3 \implies \left(\frac{T_1}{T_2}\right)^2 = \left(\frac{r_1}{r_2}\right)^3$$

Why: Equating gravitational pull to centripetal force. How to use: Ratio form directly solves satellite orbital period comparison problems in NEET.

Young's Modulus & Strain Energy Physics
$$Y = \frac{FL}{A\Delta L}, \quad u = \frac{1}{2} \times \text{Stress} \times \text{Strain}$$

Why: Quantifies elastic stiffness of material under tension. How to use: $Y$ depends ONLY on material type, NOT wire length or thickness. Energy stored $U = u \times \text{Volume}$.

Terminal Velocity (Stokes' Law) Physics
$$v_t = \frac{2r^2(\rho - \sigma)g}{9\eta}$$

Why: Buoyancy + viscous drag balance gravity. How to use: $v_t \propto r^2$ — double the radius, terminal speed increases 4×.

Excess Pressure (Drop & Bubble) Physics
$$\Delta P_{drop} = \frac{2T}{R}, \quad \Delta P_{bubble} = \frac{4T}{R}$$

Why: Soap bubble has 2 free surfaces, doubling excess pressure over single drop. How to use: Pressure inside is always greater on the concave side.

Bernoulli's Equation & Torricelli Physics
$$P + \frac{1}{2}\rho v^2 + \rho gh = \text{const}, \quad v_{efflux} = \sqrt{2gh}$$

Why: Energy conservation per unit volume for ideal fluid. How to use: Speed of efflux from hole at depth $h$ equals free-fall speed from same height.

Capillary Rise Formula Physics
$$h = \frac{2T\cos\theta}{r\rho g}$$

Why: Surface tension forces balance weight of elevated liquid column. How to use: If tube length $L < h$, liquid rises to top and increases meniscus curvature — no overflow.

Newton's Law of Cooling Physics
$$\frac{T_1 - T_2}{t} = K\left(\frac{T_1 + T_2}{2} - T_0\right)$$

Why: Heat loss rate ∝ temperature difference from surroundings. How to use: Average form avoids calculus — ideal for fast NEET numerical solving.

First Law & Work Done Physics
$$\Delta Q = \Delta U + W, \quad W_{iso} = nRT\ln\frac{V_2}{V_1}$$

Why: Conservation of thermal energy. How to use: Isothermal: $\Delta U = 0 \implies Q = W$. Adiabatic: $Q = 0 \implies W = -\Delta U$. $W_{adia} = \frac{P_1V_1 - P_2V_2}{\gamma - 1}$.

Carnot Efficiency & COP Physics
$$\eta = 1 - \frac{T_2}{T_1}, \quad \beta = \frac{T_2}{T_1 - T_2}$$

Why: Maximum theoretical heat engine efficiency. How to use: Temperatures MUST be in Kelvin ($K = °C + 273$). Relation: $\beta = (1 - \eta)/\eta$.

Molecular Speeds of Gas Physics
$$v_{rms} = \sqrt{\frac{3RT}{M}}, \; v_{avg} = \sqrt{\frac{8RT}{\pi M}}, \; v_{mp} = \sqrt{\frac{2RT}{M}}$$

Why: Maxwell-Boltzmann distribution. How to use: Ratio $v_{rms} : v_{avg} : v_{mp} = \sqrt{3} : \sqrt{8/\pi} : \sqrt{2} \approx 1.73 : 1.60 : 1.41$. Remember RAM!

Degrees of Freedom & γ Physics
$$\gamma = \frac{C_p}{C_v} = 1 + \frac{2}{f}$$

Why: Equipartition gives $\frac{1}{2}k_BT$ per degree of freedom. How to use: Mono ($f=3, \gamma=5/3$), Diatomic rigid ($f=5, \gamma=7/5$), Polyatomic ($f=6, \gamma=4/3$).

SHM Kinematics Physics
$$x = A\sin(\omega t), \quad v = \omega\sqrt{A^2 - x^2}, \quad a = -\omega^2 x$$

Why: Acceleration ∝ $-x$ (directed toward mean). How to use: $v_{max} = A\omega$ at $x=0$; $a_{max} = A\omega^2$ at $x = \pm A$.

Spring-Mass & Simple Pendulum Physics
$$T_{spring} = 2\pi\sqrt{\frac{m}{k}}, \quad T_{pendulum} = 2\pi\sqrt{\frac{L}{g}}$$

Why: Period depends on inertia ÷ restoring stiffness. How to use: Pendulum T is independent of bob mass. In elevator accelerating up: $g_{eff} = g + a$, so $T$ decreases.

Doppler Effect Physics
$$f' = f\left(\frac{v \pm v_o}{v \mp v_s}\right)$$

Why: Apparent frequency change due to relative motion. How to use: Upper signs ($+$ top, $-$ bottom) when distance is DECREASING (frequency increases).

Organ Pipe Frequencies Physics
$$f_{open} = n\frac{v}{2L}, \quad f_{closed} = (2n-1)\frac{v}{4L}$$

Why: Open pipe → all harmonics; Closed pipe → odd harmonics only. How to use: Fundamental of open pipe = 2× fundamental of closed pipe of same length.

Coulomb's Law in Medium Physics
$$F_m = \frac{1}{4\pi\varepsilon_0 K}\frac{q_1 q_2}{r^2} = \frac{F_{vacuum}}{K}$$

Why: Dielectric polarization reduces electrostatic force. How to use: $K = \varepsilon_r \ge 1$. Force decreases by factor $K$ in medium.

Dipole Torque & PE in Field Physics
$$\tau = pE\sin\theta, \quad U = -pE\cos\theta$$

Why: Uniform field exerts torque without net force on dipole. How to use: Stable: $\theta = 0°$ ($U_{min} = -pE$). Unstable: $\theta = 180°$ ($U_{max} = +pE$).

Dipole Field (Axial & Equatorial) Physics
$$E_{axial} = \frac{2p}{4\pi\varepsilon_0 r^3}, \quad E_{eq} = \frac{p}{4\pi\varepsilon_0 r^3}$$

Why: Vector addition of $+q$ and $-q$ fields for short dipoles ($r \gg a$). How to use: $E_{axial} = 2 \times E_{equatorial}$. Axial field ∥ $\vec{p}$; equatorial field anti-∥ $\vec{p}$.

Capacitor with Dielectric Slab Physics
$$C = \frac{K\varepsilon_0 A}{d}, \quad C' = \frac{\varepsilon_0 A}{d - t + t/K}$$

Why: Dielectric increases capacitance by factor $K$. How to use: Battery connected → $V$ constant. Battery disconnected → $Q$ constant. Check which scenario before solving!

Drift Velocity & Current Physics
$$I = neAv_d, \quad v_d = \frac{eE\tau}{m}$$

Why: Electric field induces steady drift of free electrons. How to use: ↑ Temperature → ↑ vibrations → ↓ relaxation time $\tau$ → ↑ resistance.

Cell EMF & Internal Resistance Physics
$$V = E - Ir, \quad r = R\left(\frac{E}{V} - 1\right)$$

Why: Potential drop across internal resistance $r$. How to use: Discharging: $V < E$. Charging: $V = E + Ir > E$.

Potentiometer Principle Physics
$$\frac{E_1}{E_2} = \frac{l_1}{l_2}, \quad r = R\left(\frac{l_1 - l_2}{l_2}\right)$$

Why: Measures true EMF at null deflection (no current drawn). How to use: $l_1$ = balance length open circuit; $l_2$ = with shunt resistance $R$.

Magnetic Force & Circular Path Physics
$$F = qvB\sin\theta, \quad r = \frac{mv}{qB}$$

Why: Lorentz force ⊥ velocity, does ZERO work ($W=0$, KE constant). How to use: $\theta = 90°$ → circle. $\theta \ne 90°$ → helix with pitch $p = v\cos\theta \cdot \frac{2\pi m}{qB}$.

Biot-Savart Law Physics
$$B_{center} = \frac{\mu_0 I}{2R}, \quad B_{wire} = \frac{\mu_0 I}{2\pi d}$$

Why: Calculates magnetic field from steady current. How to use: Infinite straight wire simplifies to $B = \mu_0 I / 2\pi d$. Circular loop gives field at center.

Lens Maker's & Thin Lens Formula Physics
$$\frac{1}{f} = (\mu-1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right), \quad \frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$

Why: Relates focal length to refractive index and radii. How to use: Apply Cartesian Sign Convention strictly! Convex: $f > 0$, Concave: $f < 0$.

YDSE Fringe Width Physics
$$\beta = \frac{\lambda D}{d}, \quad y_n = \frac{n\lambda D}{d}$$

Why: Interference from two coherent slits. How to use: $\beta$ is same for bright & dark fringes. In liquid of refractive index $\mu$: $\beta' = \beta/\mu$.

Einstein's Photoelectric & de Broglie Physics
$$h\nu = \phi + K_{max} = h\nu_0 + eV_0, \quad \lambda = \frac{12.27}{\sqrt{V}} \text{ Å}$$

Why: Photoelectric proves particle nature; de Broglie proves wave-particle duality. How to use: $V_0$ is stopping potential. Shortcut $\lambda$ formula saves time when electron accelerated through $V$ volts.

Radioactive Decay Law Physics
$$N = N_0\left(\frac{1}{2}\right)^{t/T_{1/2}}, \quad T_{1/2} = \frac{0.693}{\lambda}$$

Why: Spontaneous statistical decay, rate ∝ nuclei present. How to use: Shortcut: $N = N_0(1/2)^n$ where $n = t/T_{1/2}$ = number of half-lives passed. Avoids exponential calc.

Molarity (M) Chemistry
$$M = \frac{n_{\text{solute}}}{V_{\text{solution (L)}}} = \frac{w \times 1000}{M_{\text{molar}} \times V_{\text{mL}}}$$

Why it matters: Molarity is the primary concentration unit used across physical chemistry, including stoichiometry, titrations, and kinetics. Express solute mass in grams and molar mass in g/mol.

Molality (m) Chemistry
$$m = \frac{n_{\text{solute}}}{W_{\text{solvent (kg)}}} = \frac{w_{\text{solute}} \times 1000}{M_{\text{molar}} \times W_{\text{solvent (g)}}}$$

Why it matters: Molality is temperature-independent, making it essential for colligative property calculations (boiling point elevation, freezing point depression).

Ideal Gas Equation Chemistry
$$PV = nRT$$

Why it matters: Foundational equation for gaseous state problems. $R = 0.0821$ L·atm/(mol·K) or $8.314$ J/(mol·K). Convert temperature to Kelvin before substituting.

Van der Waals Equation Chemistry
$$\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT$$

Why it matters: Corrects ideal gas law for real gases. The constant '$a$' corrects for intermolecular attraction; '$b$' corrects for molecular volume.

Raoult's Law Chemistry
$$P_A = x_A \cdot P_A^{\circ}$$

Why it matters: Partial vapour pressure of a volatile component equals its mole fraction times pure vapour pressure. Applies only to ideal solutions.

Relative Lowering of Vapour Pressure Chemistry
$$\frac{P^{\circ} - P_s}{P^{\circ}} = \frac{n_{\text{solute}}}{n_{\text{solute}} + n_{\text{solvent}}} = x_{\text{solute}}$$

Why it matters: Directly used to find molar mass of non-volatile solutes. The depression is proportional to mole fraction of solute.

Boiling Point Elevation Chemistry
$$\Delta T_b = i \cdot K_b \cdot m$$

Why it matters: $K_b$ is the ebullioscopic constant (solvent-specific), $m$ is molality, $i$ is Van't Hoff factor for electrolyte dissociation.

Freezing Point Depression Chemistry
$$\Delta T_f = i \cdot K_f \cdot m$$

Why it matters: $K_f$ is the cryoscopic constant. Used to determine molar masses. For electrolytes, always multiply by Van't Hoff factor $i$.

Osmotic Pressure Chemistry
$$\pi = iCRT = \frac{inRT}{V}$$

Why it matters: Most sensitive colligative property — preferred for determining molar mass of polymers and biomolecules. $C$ = molarity, $T$ in Kelvin.

Nernst Equation (at 298 K) Chemistry
$$E_{\text{cell}} = E^{\circ}_{\text{cell}} - \frac{0.0591}{n} \log Q$$

Why it matters: Connects standard EMF to non-standard conditions. $n$ = electrons transferred, $Q$ = reaction quotient. At equilibrium, $E_{\text{cell}} = 0$.

Gibbs Free Energy Chemistry
$$\Delta G = \Delta H - T\Delta S$$

Why it matters: If $\Delta G < 0$, the reaction is spontaneous. Also, $\Delta G^{\circ} = -nFE^{\circ}_{\text{cell}} = -RT \ln K$.

Kp – Kc Relation Chemistry
$$K_p = K_c(RT)^{\Delta n_g}$$

Why it matters: $\Delta n_g$ = (moles of gaseous products) − (moles of gaseous reactants). When $\Delta n_g = 0$, $K_p = K_c$.

Degree of Dissociation (α) Chemistry
$$\alpha = \sqrt{\frac{K_c}{C}} \quad \text{(for } \alpha \ll 1 \text{)}$$

Why it matters: Approximation valid for weak electrolytes. Higher dilution increases $\alpha$. For $A \rightleftharpoons B + C$: $K_c = C\alpha^2 / (1-\alpha)$.

pH, pOH, and Kw Chemistry
$$\text{pH} = -\log[\text{H}^+], \quad \text{pH} + \text{pOH} = 14 \;(\text{at 25°C})$$

Why it matters: $K_w = [\text{H}^+][\text{OH}^-] = 10^{-14}$ at 25 °C. For weak acids: $[\text{H}^+] = \sqrt{K_a \cdot C}$.

Henderson–Hasselbalch Equation Chemistry
$$\text{pH} = \text{p}K_a + \log\frac{[\text{Salt}]}{[\text{Acid}]}$$

Why it matters: Calculates the pH of a buffer solution. For basic buffers, use: $\text{pOH} = \text{p}K_b + \log\frac{[\text{Salt}]}{[\text{Base}]}$.

First Order Rate Constant Chemistry
$$k = \frac{2.303}{t} \log\frac{[A]_0}{[A]_t}, \quad t_{1/2} = \frac{0.693}{k}$$

Why it matters: Radioactive decay also follows first-order kinetics. Half-life is concentration-independent for first-order reactions.

Arrhenius Equation Chemistry
$$k = Ae^{-E_a/RT}, \quad \log\frac{k_2}{k_1} = \frac{E_a}{2.303R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)$$

Why it matters: Two-temperature form is frequently tested. $E_a$ is activation energy (J/mol), $A$ is pre-exponential factor.

Hess's Law / Bond Enthalpy Chemistry
$$\Delta H_{\text{rxn}} = \sum \text{BE (reactants)} - \sum \text{BE (products)}$$

Why it matters: Bond enthalpy method gives approximate $\Delta H$. Alternately: $\Delta H = \sum \Delta H_f(\text{products}) - \sum \Delta H_f(\text{reactants})$.

Kirchhoff's Equation Chemistry
$$\Delta H_2 = \Delta H_1 + \Delta C_p(T_2 - T_1)$$

Why it matters: Relates enthalpy change at two different temperatures. $\Delta C_p = \sum C_p(\text{products}) - \sum C_p(\text{reactants})$.

Isothermal Reversible Work Chemistry
$$W = -nRT\ln\frac{V_2}{V_1} = -2.303\,nRT\log\frac{V_2}{V_1}$$

Why it matters: For irreversible expansion: $W = -P_{\text{ext}}(V_2 - V_1)$. Sign convention: negative work = system expands.

First Law of Thermodynamics Chemistry
$$\Delta U = q + W$$

Why it matters: At constant volume: $\Delta U = q_V$. At constant pressure: $\Delta H = q_P$. Relation: $\Delta H = \Delta U + \Delta n_g RT$.

Faraday's Laws of Electrolysis Chemistry
$$w = \frac{M \times I \times t}{n \times F}$$

Why it matters: $w$ = mass deposited (g), $I$ = current (A), $t$ = time (s), $n$ = electrons, $F = 96485$ C/mol. 1 Faraday deposits 1 gram-equivalent.

Molar Conductivity Chemistry
$$\Lambda_m = \frac{\kappa \times 1000}{C}$$

Why it matters: $\kappa$ = specific conductivity (S/cm), $C$ = molarity. Kohlrausch's law: $\Lambda_m^{\circ} = \nu_+ \lambda^{\circ}_+ + \nu_- \lambda^{\circ}_-$.

Bohr Model Formulas Chemistry
$$r_n = 0.529\frac{n^2}{Z} \text{ \AA}, \quad E_n = -13.6\frac{Z^2}{n^2} \text{ eV}$$

Why it matters: Velocity: $v_n = 2.18 \times 10^6 \frac{Z}{n}$ m/s. Energy difference gives spectral line wavelength via $\frac{1}{\lambda} = RZ^2\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$.

Quantum Number Rules Chemistry
$$n \geq 1,\; l = 0 \text{ to } (n-1),\; m_l = -l \text{ to } +l,\; m_s = \pm\frac{1}{2}$$

Why it matters: Max electrons in a shell = $2n^2$. Max electrons in a subshell = $2(2l+1)$. Determines electronic configuration and periodic properties.

Photoelectric Effect Equation Chemistry
$$h\nu = h\nu_0 + \frac{1}{2}m_e v^2$$

Why it matters: $h\nu_0$ = work function (threshold energy), $\nu_0$ = threshold frequency. KE of ejected electron = $h(\nu - \nu_0)$.

Heisenberg's Uncertainty Principle Chemistry
$$\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$$

Why it matters: $\Delta x$ = uncertainty in position, $\Delta p = m \cdot \Delta v$ = uncertainty in momentum. Proves orbits (Bohr) are replaced by orbitals.

Born–Haber Cycle Chemistry
$$\Delta H_f = \Delta H_{\text{sub}} + \text{IE} + \frac{1}{2}\Delta H_{\text{diss}} - \text{EA} + U$$

Why it matters: Calculates lattice energy ($U$) of ionic compounds indirectly. Higher lattice energy → higher melting point and stability.

Steric Number & Hybridization Chemistry
$$\text{SN} = \frac{V + M - C + A}{2}$$

Why it matters: $V$ = valence electrons of central atom, $M$ = monovalent atoms bonded, $C$ = cation charge, $A$ = anion charge. SN 2→sp, 3→sp², 4→sp³, 5→sp³d, 6→sp³d².

Dipole Moment Chemistry
$$\mu = q \times d \quad (\text{Debye, D})$$

Why it matters: $q$ = charge (esu), $d$ = distance (cm). For resultant of two dipoles at angle $\theta$: $\mu_R = \sqrt{\mu_1^2 + \mu_2^2 + 2\mu_1\mu_2\cos\theta}$.

Solubility Product (Ksp) Chemistry
$$K_{sp} = [A^+]^m[B^-]^n \quad \text{for } A_mB_n$$

Why it matters: Precipitation occurs when ionic product $> K_{sp}$. For $AB$-type: $s = \sqrt{K_{sp}}$. For $AB_2$-type: $K_{sp} = 4s^3$.

Graham's Law of Diffusion Chemistry
$$\frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}} = \sqrt{\frac{d_2}{d_1}}$$

Why it matters: Rate of diffusion/effusion is inversely proportional to the square root of molar mass. Used for isotope separation (UF₆).

Henry's Law Chemistry
$$p = K_H \cdot x$$

Why it matters: $p$ = partial pressure of gas, $x$ = mole fraction of dissolved gas, $K_H$ = Henry's constant. Higher $K_H$ → lower solubility. Explains decompression sickness.

Aldol Condensation Chemistry
$$2\text{CH}_3\text{CHO} \xrightarrow{\text{dil. NaOH}} \text{CH}_3\text{CH(OH)CH}_2\text{CHO} \xrightarrow{\Delta} \text{CH}_3\text{CH=CHCHO}$$

Why it matters: Requires at least one α-hydrogen on the carbonyl compound. The aldol product dehydrates on heating to give an α,β-unsaturated aldehyde.

Cannizzaro Reaction Chemistry
$$2\text{HCHO} \xrightarrow{\text{conc. NaOH}} \text{HCOONa} + \text{CH}_3\text{OH}$$

Why it matters: Exclusively for aldehydes with NO α-hydrogen (e.g., HCHO, C₆H₅CHO). One molecule is oxidized, the other reduced — a disproportionation.

Grignard Reagent Reactions Chemistry
$$\text{HCHO} \xrightarrow{\text{RMgX}} 1°\text{-OH}, \quad \text{R'CHO} \xrightarrow{\text{RMgX}} 2°\text{-OH}$$

Why it matters: HCHO gives 1° alcohol, other aldehydes give 2° alcohol, ketones give 3° alcohol. First add RMgX in dry ether, then hydrolyze with dilute acid.

SN1 vs SN2 Key Points Chemistry
$$\text{S}_N\text{1: rate} = k[\text{substrate}], \quad \text{S}_N\text{2: rate} = k[\text{substrate}][\text{Nu}^-]$$

Why it matters: SN1 → racemization (carbocation intermediate, 3° > 2° > 1°). SN2 → Walden inversion (backside attack, CH₃ > 1° > 2°).

Markovnikov's Rule Chemistry
$$\text{CH}_3\text{CH=CH}_2 + \text{HBr} \rightarrow \text{CH}_3\text{CHBrCH}_3$$

Why it matters: In electrophilic addition to unsymmetrical alkenes, H adds to the carbon with more H's. Anti-Markovnikov occurs with HBr/peroxide (Kharasch effect).

Wurtz Reaction Chemistry
$$2\text{R-X} + 2\text{Na} \xrightarrow{\text{dry ether}} \text{R-R} + 2\text{NaX}$$

Why it matters: Used to prepare symmetrical alkanes. Best for preparing even-carbon alkanes. Mixed Wurtz gives a mixture of three products.

Degree of Unsaturation (DBU) Chemistry
$$\text{DBU} = \frac{2C + 2 + N - H - X}{2}$$

Why it matters: Quickly determines rings + double bonds. Each ring or double bond = 1 DBU, each triple bond = 2 DBU. Benzene ring = 4 DBU.

Crystal Field Splitting Energy Chemistry
$$\Delta_t = \frac{4}{9}\Delta_o$$

Why it matters: Tetrahedral splitting is ~4/9 of octahedral. In octahedral: $t_{2g}$ (lower) and $e_g$ (upper). Color arises from d-d transitions absorbing $\Delta_o$ energy.

EAN Rule (Sidgwick) Chemistry
$$\text{EAN} = Z - \text{oxidation state} + 2 \times (\text{coordination number})$$

Why it matters: Stable complexes tend to have EAN = nearest noble gas electron count. Used to predict stability of metal carbonyls and organometallics.

Spin-Only Magnetic Moment Chemistry
$$\mu = \sqrt{n(n+2)} \;\text{BM}$$

Why it matters: $n$ = number of unpaired electrons. Diamagnetic if $n = 0$. Paramagnetism increases with unpaired electrons. Used to determine geometry of complexes.

Ionization Energy Trend Chemistry
$$\text{IE}_1 < \text{IE}_2 < \text{IE}_3 \quad (\text{successive removal})$$

Why it matters: IE increases across a period (↑ nuclear charge) and decreases down a group (↑ atomic radius). Exceptions: Be > B, N > O due to orbital stability.

Electronegativity (Pauling) Chemistry
$$\chi_A - \chi_B = 0.208\sqrt{\Delta E_{A-B}}$$

Why it matters: Where $\Delta E = E_{A-B} - \sqrt{E_{A-A} \cdot E_{B-B}}$ (bond energy excess). F is most electronegative (4.0). Determines bond polarity and % ionic character.

Solubility Product & Common Ion Chemistry
$$\text{If IP} > K_{sp} \Rightarrow \text{precipitation}, \quad \text{If IP} < K_{sp} \Rightarrow \text{no ppt.}$$

Why it matters: Adding a common ion suppresses solubility (Le Chatelier's principle). Used in qualitative analysis and selective precipitation.

Standard Electrode Potential Chemistry
$$E^{\circ}_{\text{cell}} = E^{\circ}_{\text{cathode}} - E^{\circ}_{\text{anode}}$$

Why it matters: Higher $E^{\circ}_{\text{red}}$ = stronger oxidizing agent. Cell is spontaneous when $E^{\circ}_{\text{cell}} > 0$. SHE is the reference (0.00 V).

Le Chatelier's Principle Chemistry
$$\text{Stress applied} \Rightarrow \text{Equilibrium shifts to counteract the stress}$$

Why it matters: ↑ Concentration of reactants → forward shift. ↑ Temperature in exothermic → backward shift. Catalyst does NOT shift equilibrium (only speeds up both directions).

Van't Hoff Factor (i) Chemistry
$$i = 1 + (n - 1)\alpha \quad (\text{dissociation: } n \text{ ions})$$

Why it matters: For association: $i = 1 - (1 - 1/n)\alpha$. Abnormal molar mass = $M_{\text{observed}}/i$. NaCl: $n=2$, CaCl₂: $n=3$.

Beer–Lambert Law Chemistry
$$A = \varepsilon \cdot c \cdot l = \log\frac{I_0}{I}$$

Why it matters: $A$ = absorbance, $\varepsilon$ = molar absorptivity (L·mol⁻¹·cm⁻¹), $c$ = concentration (mol/L), $l$ = path length (cm). Used in colorimetry and spectrophotometry.

Hardy-Weinberg Principle Biology
$$p^2 + 2pq + q^2 = 1 \quad \text{and} \quad p + q = 1$$

Why & How: Hardy-Weinberg equilibrium for allele ($p, q$) and genotype ($p^2, 2pq, q^2$) frequencies in non-evolving populations. NEET Tip: First find $q^2$ from recessive phenotype frequency, take $\sqrt{q^2}$ for $q$, get $p = 1-q$, then $2pq$ for carrier frequency.

Species-Area Relationship Biology
$$\log S = \log C + Z \log A \quad \text{or} \quad S = C A^Z$$

Why & How: Alexander von Humboldt's relationship ($S$: species, $A$: area, $Z$: regression slope). NEET Tip: Small areas: $Z = 0.1 \text{ to } 0.2$. Large continents: $Z = 0.6 \text{ to } 1.2$ (steeper slope).

Exponential Population Growth Biology
$$\frac{dN}{dt} = rN \quad \text{and} \quad N_t = N_0 e^{rt}$$

Why & How: Exponential growth (J-shaped) with unlimited resources. $r = b - d$ (intrinsic rate of natural increase). NEET Tip: If resources are unlimited, growth is exponential. $r$ is always per capita $(b-d)$.

Verhulst-Pearl Logistic Growth Biology
$$\frac{dN}{dt} = rN \left( \frac{K - N}{K} \right)$$

Why & How: Logistic growth (S-shaped / Sigmoid) with limited carrying capacity $K$. NEET Tip: When $N=K$, $dN/dt = 0$ (asymptote). Phases: Lag, Log/Exponential, Deceleration, Asymptote.

Water Potential Equation Biology
$$\Psi_w = \Psi_s + \Psi_p$$

Why & How: Water potential $\Psi_w$, Solute potential $\Psi_s$ (always negative), Pressure potential $\Psi_p$. Pure water at STP $= 0$ (max). NEET Tip: Water moves from HIGH (less negative) to LOW (more negative) $\Psi_w$.

Cardiac Output (CO) Biology
$$\text{CO} = \text{Stroke Volume (SV)} \times \text{Heart Rate (HR)}$$

Why & How: Volume pumped per minute ($70 \text{ mL} \times 72 \text{ bpm} \approx 5 \text{ L/min}$). NEET Tip: Athletes have higher SV, hence lower HR for same CO. $SV = EDV - ESV$.

Glomerular Net Filtration Pressure Biology
$$\text{NFP} = \text{HP}_g - (\text{OP}_g + \text{HP}_c) = 60 - (32 + 18) = 10 \text{ mmHg}$$

Why & How: Drives ultracentrifugation in glomerulus. NEET Tip: $\text{HP}_g$ ($60\text{ mmHg}$) favors filtration; $\text{OP}_g$ ($32\text{ mmHg}$) & $\text{HP}_c$ ($18\text{ mmHg}$) oppose it. Net $= 10\text{ mmHg}$.

Respiratory Quotient (RQ) Biology
$$\text{RQ} = \frac{\text{Vol. of } CO_2 \text{ evolved}}{\text{Vol. of } O_2 \text{ consumed}}$$

Why & How: Indicates oxidized respiratory substrate. NEET Tip: Carbohydrates $= 1.0$, Tripalmitin/Fats $= 0.7$, Proteins $= 0.9$, Organic acids $> 1.0$, Anaerobic $= \infty$.

Chargaff's Rule for dsDNA Biology
$$A + G = T + C \quad \implies \quad \frac{A + G}{T + C} = 1$$

Why & How: Purines equal Pyrimidines in double-stranded DNA. NEET Tip: Only for dsDNA! If $A=20\%$, $T=20\%$, remaining $60\%$ is split equally: $G=30\%, C=30\%$.

Number of Gamete Types Biology
$$N_{\text{gametes}} = 2^n$$

Why & How: $n$ = number of heterozygous gene loci. NEET Tip: Count ONLY heterozygous pairs! E.g. $AaBbCC$ has 2 heterozygous pairs ($Aa, Bb$), so $2^2 = 4$ gamete types.

$F_2$ Phenotypes & Genotypes Biology
$$\text{Phenotypes} = 2^n \quad \text{and} \quad \text{Genotypes} = 3^n$$

Why & How: Yields count of unique phenotypes and genotypes in Mendelian $F_2$. NEET Tip: Monohybrid ($n=1$): 2 phenotypes, 3 genotypes. Dihybrid ($n=2$): 4 phenotypes, 9 genotypes.

$F_2$ Zygotic Combinations Biology
$$\text{Total Combinations in } F_2 = 4^n$$

Why & How: Total Punnett square boxes for $n$ gene loci. NEET Tip: Monohybrid ($n=1$) $= 4$, Dihybrid ($n=2$) $= 16$, Trihybrid ($n=3$) $= 64$ combinations.

PCR DNA Amplification Biology
$$N_t = N_0 \times 2^n$$

Why & How: DNA copies produced after $n$ PCR cycles. NEET Tip: After 30 cycles ($n=30$), 1 DNA molecule yields approximately $2^{30} \approx 10^9$ (1 billion) copies.

Bacterial Population Growth Biology
$$N_t = N_0 \times 2^{(t/g)}$$

Why & How: Population after time $t$ given generation doubling time $g$. NEET Tip: E. coli divides every 20 min. In 2 hrs ($120\text{ min}$), $n = 120/20 = 6 \implies 1 \times 2^6 = 64$ bacteria.

Recombination Frequency & Map Distance Biology
$$\text{RF (\%)} = \frac{\text{Total Recombinants}}{\text{Total Offspring}} \times 100$$

Why & How: $1\% \text{ RF} = 1 \text{ map unit (cM)}$. NEET Tip: Maximum possible recombination frequency between two genes is $50\%$. Higher RF means genes are on separate chromosomes.

Physical Length of DNA Biology
$$\text{Length (m)} = \text{Total bp} \times 0.34 \times 10^{-9} \text{ m}$$

Why & How: Distance between consecutive base pairs in B-DNA $= 0.34\text{ nm}$. NEET Tip: Human diploid ($6.6 \times 10^9 \text{ bp}$) $\approx 2.2 \text{ m}$. E. coli ($4.6 \times 10^6 \text{ bp}$) $\approx 1.36 \text{ mm}$.

Phosphodiester Bonds Count Biology
$$\text{Linear dsDNA} = 2(N - 1), \quad \text{Circular dsDNA} = 2N$$

Why & How: $N$ = base pairs. NEET Tip: Always check if question specifies 'linear' or 'circular', and 'single-stranded' vs 'double-stranded' DNA!

Total Hydrogen Bonds in DNA Biology
$$\text{Total H-Bonds} = 2(n_{A-T}) + 3(n_{G-C})$$

Why & How: $A=T$ has 2 H-bonds; $G \equiv C$ has 3 H-bonds. NEET Tip: Higher G-C content means more H-bonds, greater stability, and higher thermal melting point ($T_m$).

Peptide Bonds & Water Elimination Biology
$$\text{Peptide Bonds} = N_{\text{amino acids}} - \text{Polypeptide Chains}$$

Why & How: Each bond releases $1 \text{ H}_2\text{O}$ via dehydration synthesis. NEET Tip: Unbranched single chain of $N$ amino acids has $(N-1)$ peptide bonds and $(N-1)$ water molecules lost.

Vital Capacity (VC) Biology
$$\text{VC} = \text{ERV} + \text{TV} + \text{IRV}$$

Why & How: Maximum air expired after forced inspiration ($3500 - 4500 \text{ mL}$). NEET Tip: VC does NOT include Residual Volume (RV). Formula: $\text{VC} = \text{TLC} - \text{RV}$.

Total Lung Capacity (TLC) Biology
$$\text{TLC} = \text{VC} + \text{RV} = \text{TV} + \text{IRV} + \text{ERV} + \text{RV}$$

Why & How: Total volume accommodated at end of forced inspiration ($5000 - 6000 \text{ mL}$). NEET Tip: Spirometer CANNOT measure RV, FRC, or TLC.

Functional Residual Capacity (FRC) Biology
$$\text{FRC} = \text{ERV} + \text{RV}$$

Why & How: Air remaining after normal passive expiration ($2100 - 2300 \text{ mL}$). NEET Tip: FRC is air left after NORMAL expiration, while RV is air left after FORCED expiration.

Inspiratory & Expiratory Capacities Biology
$$\text{IC} = \text{TV} + \text{IRV}, \quad \text{EC} = \text{TV} + \text{ERV}$$

Why & How: Total volume inspired/expired after normal expiration/inspiration. NEET Tip: TV $= 500\text{ mL}$, IRV $= 2500-3000\text{ mL}$, ERV $= 1000-1100\text{ mL}$, RV $= 1100-1200\text{ mL}$.

Lindeman's 10% Energy Law Biology
$$E_{n+1} = E_n \times 0.10$$

Why & How: Only 10% of energy transfers to next trophic level. 90% lost as heat/respiration. NEET Tip: Producers capture 1-2% of PAR (Photosynthetically Active Radiation).

Net Primary Productivity (NPP) Biology
$$\text{NPP} = \text{GPP} - R$$

Why & How: GPP minus respiration losses $R$ by producers. NEET Tip: NPP is biomass available for heterotrophs. Total annual global NPP $\approx 170$ billion tons dry weight.

Calvin Cycle Energetics Biology
$$6CO_2 + 18\text{ATP} + 12\text{NADPH} \rightarrow \text{Glucose} + 18\text{ADP} + 12\text{NADP}^+$$

Why & How: Input needed for 1 Glucose molecule. NEET Tip: Per $CO_2$ fixed: $C_3$ plant needs 3 ATP + 2 NADPH; $C_4$ plant needs 5 ATP + 2 NADPH (extra 2 ATP for PEP regeneration).

ATP Yield in Aerobic Respiration Biology
$$1 \text{ Glucose} \rightarrow 36 \text{ or } 38 \text{ ATP} \quad (1\text{NADH} = 3\text{ATP}, 1\text{FADH}_2 = 2\text{ATP})$$

Why & How: Complete oxidation yield from Glycolysis, Link reaction, and Krebs cycle. NEET Tip: NCERT standard: $1\text{NADH} = 3\text{ATP}$, $1\text{FADH}_2 = 2\text{ATP}$. Net gain $= 38$ (or 36) ATP.

Krebs Cycle Yield per Glucose Biology
$$2 \text{ Pyruvate} \rightarrow 6CO_2 + 8\text{NADH} + 2\text{FADH}_2 + 2\text{GTP}$$

Why & How: Matrix reactions for 2 Pyruvates. NEET Tip: Krebs cycle turns TWICE per glucose molecule because 1 glucose splits into 2 pyruvic acid molecules!

Mitotic Divisions for N Cells Biology
$$\text{Mitotic Divisions to form } N \text{ cells} = N - 1$$

Why & How: Number of cell division events needed starting from 1 single cell. NEET Tip: To produce 128 cells from 1 cell, total divisions $= 128 - 1 = 127$. (Generations $= \log_2 128 = 7$).

Meiosis Needed for N Seeds Biology
$$\text{Meiotic Divisions for } N \text{ Seeds} = N + \frac{N}{4} = 1.25N$$

Why & How: Male side needs $N/4$ meiosis; Female side needs $N$ meiosis. NEET Tip: For 100 seeds/grains: Male $= 25$ meiosis; Female $= 100$ meiosis. Total $= 125$ meiotic divisions.

Meiosis for N Pollen Grains Biology
$$\text{Meiotic Divisions for } N \text{ Pollen Grains} = \frac{N}{4}$$

Why & How: 1 Microspore Mother Cell undergoes 1 meiotic division to produce 4 pollen grains. NEET Tip: Check whether question asks for pollen ($N/4$) vs eggs ($N$).

Meiosis for N Female Gametes Biology
$$\text{Meiotic Divisions for } N \text{ Eggs} = N$$

Why & How: 1 MMC yields 4 megaspores, but 3 degenerate leaving only 1 functional egg per meiosis. NEET Tip: Hence $N$ eggs require $N$ meiotic divisions.

Pulse Pressure Biology
$$\text{Pulse Pressure} = \text{Systolic BP} - \text{Diastolic BP}$$

Why & How: Difference between contraction and relaxation pressures. Normal $= 120 - 80 = 40 \text{ mmHg}$. NEET Tip: $140/90$ indicates Hypertension; pulse pressure is $50 \text{ mmHg}$.

Mean Arterial Pressure (MAP) Biology
$$\text{MAP} = \text{Diastolic BP} + \frac{1}{3}(\text{Pulse Pressure})$$

Why & How: Average pressure in arteries during cardiac cycle ($80 + 40/3 \approx 93.3 \text{ mmHg}$). NEET Tip: Diastole lasts twice as long as systole ($0.5\text{s}$ vs $0.3\text{s}$), so don't average directly!

Urine Output & GFR Reabsorption Biology
$$\text{Urine} = \text{GFR} \times 0.01 = 180 \text{ L/day} \times 0.01 = 1.8 \text{ L/day}$$

Why & How: GFR $= 125\text{ mL/min} = 180\text{ L/day}$. 99% of filtrate is reabsorbed by renal tubules. NEET Tip: Final urine output is only $1.5 \text{ to } 1.8 \text{ Liters/day}$.

$O_2$ Carrying Capacity of Blood Biology
$$1\text{g Hb} = 1.34\text{ mL } O_2 \implies 100\text{mL blood (15g Hb)} \approx 20\text{ mL } O_2$$

Why & How: Average blood contains $15\text{g Hb per } 100\text{ mL}$. NEET Tip: Under normal conditions, $100\text{ mL}$ oxygenated blood delivers $5\text{ mL } O_2$ to tissues.

Gas Delivery Rates to Tissues/Alveoli Biology
$$\text{Tissue } O_2 = 5\text{ mL}/100\text{mL blood}, \quad \text{Alveolar } CO_2 = 4\text{ mL}/100\text{mL blood}$$

Why & How: Gas volume delivered per $100\text{ mL}$ blood during resting circulation. NEET Tip: Memorize direct NCERT values: $5\text{ mL } O_2$ to tissues, $4\text{ mL } CO_2$ to alveoli.

Monohybrid Cross Ratios Biology
$$\text{Phenotypic} = 3:1 \quad | \quad \text{Genotypic} = 1:2:1$$

Why & How: Mendelian cross for 1 trait with complete dominance ($Tt \times Tt$). NEET Tip: $1/4$ homozygous dominant ($TT$), $2/4$ heterozygous ($Tt$), $1/4$ recessive ($tt$).

Dihybrid Cross Phenotypic Ratio Biology
$$\text{Dihybrid Ratio} = 9 : 3 : 3 : 1$$

Why & How: For two independent traits ($RrYy \times RrYy$). NEET Tip: Recombinant phenotypes $= 3/16 + 3/16 = 6/16 = 3/8$ of total offspring.

Test Cross Ratios Biology
$$\text{Monohybrid Test} = 1:1, \quad \text{Dihybrid Test} = 1:1:1:1$$

Why & How: Crossing unknown dominant individual with homozygous recessive parent ($aa$). NEET Tip: 1:1 ratio confirms unknown parent is heterozygous.

Incomplete Dominance & Codominance Biology
$$\text{Phenotypic Ratio} = \text{Genotypic Ratio} = 1 : 2 : 1$$

Why & How: Snapdragon (*Antirrhinum*), ABO blood $I^AI^B$, Sickle cell trait. NEET Tip: Whenever Phenotypic ratio equals Genotypic ratio ($1:2:1$), suspect Incomplete Dominance/Codominance!

Polygenic Inheritance (3 Gene Pairs) Biology
$$\text{Ratio} = 1 : 6 : 15 : 20 : 15 : 6 : 1$$

Why & How: Human skin color ($A, B, C$). Bell curve distribution (64 total). NEET Tip: Intermediate phenotype (3 dominant alleles) is maximum ($20/64$). Extremes are $1/64$ each.

Ecological / Transfer Efficiency Biology
$$\text{Efficiency (\%)} = \frac{\text{Energy at Level } n}{\text{Energy at Level } n-1} \times 100$$

Why & How: Energy fraction transferred to next trophic level ($\sim 10\%$). NEET Tip: If Producer has $10,000\text{ J}$, Tertiary consumer gets $10,000 \times 0.1^3 = 10\text{ J}$.

BOD & Dissolved Oxygen Biology
$$\text{BOD} \propto \text{Organic Load} \propto \frac{1}{\text{Dissolved Oxygen (DO)}}$$

Why & How: Microbe oxygen demand to decompose organic matter in water. NEET Tip: High BOD = Heavy sewage pollution = Low Dissolved Oxygen = High fish mortality!

Lincoln-Petersen Mark-Recapture Biology
$$N = \frac{M \times C}{R}$$

Why & How: Estimates total population $N$. $M$: marked initially, $C$: total captured in 2nd sample, $R$: marked recaptured. NEET Tip: Standard method for mobile animals (fish, birds).

Nucleosome Composition Biology
$$1 \text{ Nucleosome} = 200\text{ bp DNA} + \text{Octamer }(H_2A, H_2B, H_3, H_4)_2 + H_1$$

Why & How: Eukaryotic chromatin packaging unit ('beads-on-a-string'). NEET Tip: Octamer has 2 copies each of H2A, H2B, H3, H4. $H1$ binds linker DNA outside the core.

Temperature Coefficient ($Q_{10}$) Biology
$$Q_{10} = \left( \frac{k_2}{k_1} \right)^{\frac{10}{T_2 - T_1}} \approx 2.0$$

Why & How: Biochemical rate doubles for every $10^\circ\text{C}$ rise up to optimum. NEET Tip: Rate doubles per $10^\circ\text{C}$ increase, but beyond optimum temperature enzymes denature rapidly.

Cell Cycle Phase Proportions Biology
$$\text{Interphase} \ge 95\% \quad | \quad \text{M-Phase} \le 5\%$$

Why & How: Human cell cycle $= 24\text{ hrs}$ (Interphase $> 23\text{ hrs}$, M phase $\approx 1\text{ hr}$). NEET Tip: Yeast cell cycle $= 90 \text{ min}$. Interphase comprises $G_1, S, G_2$.

Michaelis-Menten Kinetics Biology
$$v = \frac{V_{\max} [S]}{K_m + [S]}$$

Why & How: $K_m$ is substrate conc. at $\frac{1}{2}V_{\max}$. NEET Tip: Lower $K_m$ = HIGHER enzyme affinity! Competitive inhibitors INCREASE $K_m$ without changing $V_{\max}$.

Ecological Pyramids Rules Biology
$$\text{Energy} = \text{Always Upright} \quad | \quad \text{Aquatic Biomass} = \text{Inverted}$$

Why & How: Pyramid of Energy is ALWAYS upright (2nd law of thermodynamics). NEET Tip: Pyramid of Biomass in sea/aquatic ecosystem is INVERTED ($\text{Phytoplankton} < \text{Fish}$).

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Comprehensive information on the NTA NEET entrance examination structure, section choices, timing, and preparation strategies.

Exam Structure & Marking Rules

SubjectSection A (Compulsory)Section B (Choose 10/15)Total Marks
Physics35 Questions (140 M)15 Questions (Attempt 10 = 40 M)180 Marks
Chemistry35 Questions (140 M)15 Questions (Attempt 10 = 40 M)180 Marks
Botany (Biology)35 Questions (140 M)15 Questions (Attempt 10 = 40 M)180 Marks
Zoology (Biology)35 Questions (140 M)15 Questions (Attempt 10 = 40 M)180 Marks
TOTAL 140 Questions 60 Questions (Attempt 40) 720 Marks (200 Mins)
What is the negative marking scheme in NEET UG?
For every correct answer, you are awarded +4 marks. For every incorrect answer, -1 mark is deducted. Unattempted questions carry 0 marks.
How does Section B optional choice work?
Section B in each subject contains 15 questions, out of which candidates are required to attempt any 10 questions. If more than 10 questions are attempted, only the first 10 evaluated questions are considered.
What is the qualifying percentile for General vs Reserved categories?
General/UR/EWS category candidates must secure at least the 50th percentile. OBC/SC/ST candidates require the 40th percentile, and UR-PwD candidates require the 45th percentile.
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