NEET Revision List

SI and CGS Conversion Relations

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Physics Units and Systems of Units

1 \text{ N} = 10^5 \text{ dyn}

1 \text{ J} = 10^7 \text{ erg}

Parameters & Definitions

N is Newton, dyn is dyne, J is Joule, and erg is erg.

Physical conversions for force (Newton to dyne) and energy (Joules to ergs) between SI and CGS systems.

General Dimensional Representation

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Physics Dimensional Representation

[Q] = M^a L^b T^c I^d \theta^e N^f J^g

Parameters & Definitions

$[Q]$ represents the dimensions of physical quantity $Q$ ; $M, L, T, I, \theta, N, J$ are the seven fundamental dimensions.

Expressing any physical quantity in terms of base dimensions (Mass, Length, Time, etc.).

Mean Absolute Error

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Physics Absolute and Relative Errors

a_{mean} = \frac{1}{n} \sum_{i=1}^n a_i

\Delta a_{mean} = \frac{1}{n} \sum_{i=1}^n |a_{mean} - a_i|

Parameters & Definitions

$a_i$ is the $i$ -th measurement, $a_{mean}$ is the arithmetic mean, and $\Delta a_{mean}$ is the mean absolute error.

The mean of the absolute values of the differences between individual measurements and the true mean value.

Relative and Percentage Error

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Physics Absolute and Relative Errors

e_r = \frac{\Delta a_{mean}}{a_{mean}}

e_p = \frac{\Delta a_{mean}}{a_{mean}} \times 100\%

Parameters & Definitions

$e_r$ represents relative error, and $e_p$ represents percentage error.

Relative error is the fractional value of absolute error relative to the mean, and percentage error is its value expressed as a percentage.

Propagation of Errors in Calculations

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Physics Propagation of Errors

Z = A \pm B \implies \Delta Z = \Delta A + \Delta B

Z = A^p B^q C^{-r} \implies \frac{\Delta Z}{Z} = p \frac{\Delta A}{A} + q \frac{\Delta B}{B} + r \frac{\Delta C}{C}

Parameters & Definitions

$A, B, C$ are measured quantities with errors $\Delta A, \Delta B, \Delta C$ ; $Z$ is the resulting calculated quantity.

Formulas to calculate the maximum absolute and relative errors propagated through arithmetic combinations.

Average Speed and Velocity Inequality

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Physics Frame of Reference & Displacement

v_{avg} = \frac{\text{Total Distance}}{\text{Total Time}}

\vec{v}_{avg} = \frac{\Delta \vec{r}}{\Delta t} \implies |\vec{v}_{avg}| \le v_{avg}

Parameters & Definitions

$v_{avg}$ is average speed, $\vec{v}_{avg}$ is average velocity vector, $\Delta \vec{r}$ is displacement vector, and $\Delta t$ is total elapsed time.

Defines average speed and average velocity vector, establishing that the magnitude of average velocity is always less than or equal to average speed.

Average and Instantaneous Velocity

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Physics Average & Instantaneous Velocity

v_{avg} = \frac{\Delta x}{\Delta t}

v_{inst} = \frac{dx}{dt}

Parameters & Definitions

$v_{avg}$ is the average velocity, $v_{inst}$ is the instantaneous velocity, $x$ represents position, and $t$ represents time.

Average velocity is displacement divided by time interval, while instantaneous velocity is the time derivative of position.

Equations of Motion for Uniform Acceleration

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Physics Equations of Motion

v = u + at

s = ut + \frac{1}{2}at^2

v^2 - u^2 = 2as

s_n = u + \frac{a}{2}(2n - 1)

Parameters & Definitions

$u$ is initial velocity, $v$ is final velocity, $a$ is constant acceleration, $t$ is elapsed time, $s$ is displacement, and $s_n$ is the displacement in the $n$ -th second.

Relationships between velocity, displacement, time, and acceleration for constant acceleration.

Relative Velocity in One Dimension

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Physics Relative Velocity in 1D

v_{AB} = v_A - v_B

Parameters & Definitions

$v_{AB}$ is the velocity of object A relative to B, $v_A$ is the velocity of A, and $v_B$ is the velocity of B.

The velocity of an object A as observed from the reference frame of an object B.

Parallelogram Law of Vector Addition

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Physics Vector Operations

R = \sqrt{A^2 + B^2 + 2AB\cos\theta}

\tan\alpha = \frac{B\sin\theta}{A + B\cos\theta}

Parameters & Definitions

$R$ is magnitude of resultant vector, $A, B$ are magnitudes of the individual vectors, $\theta$ is angle between them, and $\alpha$ is angle of resultant with vector $A$ .

Calculates the magnitude and direction of the resultant vector of two vectors added at angle $\theta$ .

Dot and Cross Products of Vectors

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Physics Dot and Cross Products

\vec{A} \cdot \vec{B} = AB \cos\theta

|\vec{A} \times \vec{B}| = AB \sin\theta

Parameters & Definitions

$\vec{A}$ and $\vec{B}$ are vectors, $A$ and $B$ are their magnitudes, and $\theta$ is the angle between them.

Mathematical representations of scalar (dot) and vector (cross) products of two vectors.

Formulas for Projectile Motion under Gravity

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Physics Projectile Motion

T = \frac{2u \sin\theta}{g}

H = \frac{u^2 \sin^2\theta}{2g}

R = \frac{u^2 \sin 2\theta}{g}

y = x \tan\theta - \frac{gx^2}{2u^2 \cos^2\theta}

Parameters & Definitions

$u$ is the launch speed, $\theta$ is the launch angle with the horizontal, $T$ is time of flight, $H$ is max height, $R$ is range, and $g$ is acceleration due to gravity.

Time of flight, maximum height, horizontal range, and the equation of the trajectory for a projectile launched from ground level.

Centripetal Acceleration and Angular Velocity Relations

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Physics Uniform Circular Motion

v = \omega r

\omega = 2\pi f = \frac{2\pi}{T}

a_c = \frac{v^2}{r} = \omega^2 r

Parameters & Definitions

$v$ is linear speed, $\omega$ is angular velocity, $r$ is circular radius, $f$ is frequency, $T$ is time period, and $a_c$ is centripetal acceleration.

Relations linking linear speed, angular velocity, frequency, and centripetal acceleration in uniform circular motion.

Newton's Second Law

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Physics Forces & Newton's Laws

\vec{F} = \frac{d\vec{p}}{dt} = m\vec{a}

Parameters & Definitions

$\vec{F}$ is force, $\vec{p}$ is linear momentum, $m$ is mass, and $\vec{a}$ is acceleration.

Definition of force as the rate of change of linear momentum.

Momentum and Impulse

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Physics Momentum & Impulse

\vec{p} = m\vec{v}

\vec{J} = \int \vec{F} dt = \Delta \vec{p}

Parameters & Definitions

$\vec{p}$ is linear momentum, $m$ is mass, $\vec{v}$ is velocity, $\vec{J}$ is impulse, and $\Delta \vec{p}$ is the change in momentum.

Definition of momentum and impulse as the change in momentum.

Static and Kinetic Friction Limits

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Physics Friction Forces

f_{s,max} = \mu_s N

f_k = \mu_k N

Parameters & Definitions

$f_{s,max}$ is limiting static friction, $f_k$ is kinetic friction, $\mu_s$ and $\mu_k$ are coefficients of static and kinetic friction respectively, and $N$ is normal force.

Formulas to calculate maximum static friction and kinetic friction.

Critical Speeds on Level and Banked Circular Roads

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Physics Circular Roads & Banking

v_{level} = \sqrt{\mu_s rg}

v_{opt} = \sqrt{rg \tan\theta}

v_{max} = \sqrt{rg \left( \frac{\mu_s + \tan\theta}{1 - \mu_s \tan\theta} \right)}

Parameters & Definitions

$r$ is circular radius, $g$ is acceleration due to gravity, $\mu_s$ is coefficient of static friction, $\theta$ is banking angle, $v_{opt}$ is friction-free optimum speed, and $v_{max}$ is maximum safe speed.

Formulas for maximum safe speed on flat and banked roads.

Work Done by Forces

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Physics Work Done by Forces

W = \vec{F} \cdot \vec{d}

W = \int \vec{F} \cdot d\vec{r}

Parameters & Definitions

$W$ is work done, $\vec{F}$ is force, $\vec{d}$ is constant displacement, and $d\vec{r}$ is differential displacement.

Definition of work done by constant and variable forces.

Work-Energy Theorem and Power

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Physics Kinetic Energy & Work-Energy Theorem

W_{net} = \Delta K = K_f - K_i

P = \frac{dW}{dt} = \vec{F} \cdot \vec{v}

Parameters & Definitions

$W_{net}$ is net work done, $\Delta K$ is change in kinetic energy, $P$ is power, $\vec{F}$ is force, and $\vec{v}$ is velocity.

The work-energy theorem (net work equals change in kinetic energy) and instantaneous power.

Relation Between Force and Potential Energy

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Physics Conservative Forces

F_x = -\frac{dU}{dx}

Parameters & Definitions

$F_x$ is the conservative force along the x-axis, and $U$ is the potential energy as a function of position $x$ .

Formula relating a conservative force to the spatial gradient of its potential energy.

Potential Energy of a Hookean Spring

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Physics Spring Potential Energy

U = \frac{1}{2} k x^2

Parameters & Definitions

$U$ is the stored potential energy, $k$ is the spring constant, and $x$ is the extension or compression.

Potential energy stored in a spring stretched or compressed by an displacement $x$ .

Critical Speeds in Vertical Circular Motion

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Physics Vertical Circular Motion

v_{\text{lowest}} = \sqrt{5gR}

v_{\text{highest}} = \sqrt{gR}

T_{\text{lowest}} - T_{\text{highest}} = 6mg

Parameters & Definitions

$v$ is the critical speed, $T$ is the tension in the string, $R$ is the radius of the circle, $m$ is the mass, and $g$ is the acceleration due to gravity.

Minimum speeds required at the lowest and highest points for a mass on a string to complete a vertical circle.

Coefficient of Restitution and Collision Speeds

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Physics Collisions & Restitution

e = \frac{v_2 - v_1}{u_1 - u_2}

v_1 = \left( \frac{m_1 - e m_2}{m_1 + m_2} \right) u_1 + \left( \frac{(1+e) m_2}{m_1 + m_2} \right) u_2

Parameters & Definitions

$e$ is the coefficient of restitution, $u_1, u_2$ are velocities before collision, $v_1, v_2$ are velocities after collision, and $m_1, m_2$ are the colliding masses.

Definition of coefficient of restitution ( $e$ ) and final velocities after a 1D elastic or inelastic collision.

Position of Centre of Mass

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Physics Centre of Mass of Particle Systems

\vec{r}_{cm} = \frac{\sum m_i \vec{r}_i}{\sum m_i}

Parameters & Definitions

$\vec{r}_{cm}$ is the center of mass position vector, and $m_i$ and $\vec{r}_i$ are the mass and position of the $i$ -th particle.

Weighted average position of a discrete system of particles.

Centre of Mass for Continuous Media

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Physics Centre of Mass of Rigid Bodies

\vec{r}_{cm} = \frac{1}{M} \int \vec{r} dm

Parameters & Definitions

$\vec{r}_{cm}$ is the center of mass position vector, $M$ is total mass, and $dm$ is a differential mass element.

Weighted average position for a continuous mass distribution.

Torque and Angular Acceleration Relation

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Physics Torque and Equilibrium

\vec{\tau} = \vec{r} \times \vec{F} = I\vec{\alpha}

Parameters & Definitions

$\vec{\tau}$ is torque, $\vec{r}$ is position vector, $\vec{F}$ is force vector, $I$ is moment of inertia, and $\vec{\alpha}$ is angular acceleration.

Definition of torque and the relation linking net torque to angular acceleration.

Angular Momentum and Net Torque

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Physics Angular Momentum

\vec{L} = \vec{r} \times \vec{p} = I\vec{\omega}

\vec{\tau}_{net} = \frac{d\vec{L}}{dt}

Parameters & Definitions

$\vec{L}$ is angular momentum, $\vec{r}$ is position, $\vec{p}$ is linear momentum, $I$ is moment of inertia, $\vec{\omega}$ is angular velocity, and $\vec{\tau}_{net}$ is net torque.

Definition of angular momentum and the relation linking net torque to the rate of change of angular momentum.

Moment of Inertia and Radius of Gyration

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Physics Moment of Inertia & Radius of Gyration

I = \sum m_i r_i^2 = \int r^2 dm

I = MK^2

Parameters & Definitions

$I$ is moment of inertia, $r$ represents distance from axis of rotation, $M$ is total mass, and $K$ is the radius of gyration.

General definition of moment of inertia and its relation to the radius of gyration.

Parallel and Perpendicular Axes Theorems

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Physics Axes Theorems

I_z = I_{cm} + Md^2

I_z = I_x + I_y

Parameters & Definitions

$I_z$ is moment of inertia about the target axis, $I_{cm}$ is moment of inertia about parallel center-of-mass axis, $M$ is total mass, $d$ is perpendicular distance between axes, and $I_x, I_y$ are moments of inertia about perpendicular axes in the plane of a laminar sheet.

Mathematical expressions of the parallel axes theorem and perpendicular axes theorem for moments of inertia.

Universal Gravitational Force and Kepler's Third Law

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Physics Kepler's Laws & Newton's Law

F = G \frac{m_1 m_2}{r^2}

T^2 = \left( \frac{4\pi^2}{GM_s} \right) r^3

Parameters & Definitions

$F$ is gravitational force, $G$ is gravitational constant, $m_1, m_2$ are masses, $r$ is orbital radius, $T$ is orbital period, and $M_s$ is mass of the central star/Sun.

Newton's force equation for gravity and the mathematical relation for Kepler's third law of planetary motion.

Variation of g with Altitude, Depth, and Rotation

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Physics Gravity (g) and its Variations

g_h \approx g \left( 1 - \frac{2h}{R} \right)

g_d = g \left( 1 - \frac{d}{R} \right)

g' = g - \omega^2 R \cos^2\phi

Parameters & Definitions

$g$ is gravity at sea level, $g_h$ and $g_d$ are gravity values at height $h$ and depth $d$ , $R$ is Earth's radius, $\omega$ is Earth's rotational speed, and $\phi$ is the latitude.

Formulas calculating how earth's gravitational acceleration changes at heights ( $h \ll R$ ), depths ( $d$ ), and latitudes ( $\phi$ ).

Gravitational Potential Energy and Potential

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Physics Gravitational Potential & Energy

U = -G \frac{M m}{r}

V = -G \frac{M}{r}

Parameters & Definitions

$U$ is gravitational potential energy, $V$ is gravitational potential, $M, m$ are masses, and $r$ is the separation distance.

Potential energy of a two-mass system and the potential due to a point mass.

Escape Velocity and Satellite Orbital Velocity

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Physics Orbital & Escape Velocities

v_e = \sqrt{\frac{2GM}{R}} = \sqrt{2gR}

v_o = \sqrt{\frac{GM}{R}} = \sqrt{gR}

Parameters & Definitions

$v_e$ is escape velocity, $v_o$ is orbital velocity, $M$ is Earth's mass, $R$ is Earth's radius, and $g$ is acceleration due to gravity.

Formulas to calculate escape speed from Earth and the speed required for circular orbit close to Earth.

Hooke's Law of Elasticity

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Physics Stress & Strain

\text{Stress} = E \times \text{Strain} \implies \frac{F}{A} = E \frac{\Delta L}{L_0}

Parameters & Definitions

$F$ is applied deforming force, $A$ is cross-sectional area, $E$ is modulus of elasticity, $\Delta L$ is elongation, and $L_0$ is original length.

Fundamental linear relationship of elasticity indicating stress is directly proportional to strain within the elastic limit.

Young's and Bulk Moduli

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Physics Elastic Moduli

Y = \frac{F L}{A \Delta L}

B = -\frac{\Delta P}{\Delta V / V}

Parameters & Definitions

$Y$ is Young's Modulus, $B$ is Bulk Modulus, $F$ is stretching force, $L$ is length, $A$ is area, $\Delta L$ is extension, $\Delta P$ is pressure change, and $\Delta V$ is volume change.

Definitions of Young's and Bulk Moduli of elasticity.

Poisson's Ratio and Elastic Constants Relations

Physics Elastic Moduli

\sigma = \frac{\text{Lateral Strain}}{\text{Longitudinal Strain}} = -\frac{\Delta d / d_0}{\Delta L / L_0}

Y = 3B(1 - 2\sigma) = 2\eta(1 + \sigma)

\frac{9}{Y} = \frac{1}{B} + \frac{3}{\eta}

Parameters & Definitions

$\sigma$ is Poisson's ratio (theoretical limits: $-1 \le \sigma \le 0.5$ ), $Y$ is Young's modulus, $B$ is Bulk modulus, and $\eta$ is Shear modulus (rigidity modulus).

Defines Poisson's ratio and the fundamental mathematical relations between Young's, Bulk, and Shear moduli.

Elastic Strain Energy Density

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Physics Elastic Energy Density

u_{energy} = \frac{1}{2} \times \text{Stress} \times \text{Strain}

Parameters & Definitions

$u_{energy}$ is energy density, Stress represents applied force per unit area, and Strain is fractional deformation.

The elastic strain energy stored per unit volume of a stretched body.

Hydrostatic Pressure variation

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Physics Hydrostatic Pressure

P = P_0 + \rho g h

Parameters & Definitions

$P$ is total pressure at depth $h$ , $P_0$ is atmospheric pressure at surface, $\rho$ is fluid density, and $g$ is acceleration due to gravity.

Formula for pressure at depth $h$ in a fluid of density $\rho$ .

Buoyant Force (Archimedes' Principle)

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Physics Buoyancy & Archimedes Principle

F_B = \rho_f V_{\text{sub}} g

Parameters & Definitions

$F_B$ is the buoyant force, $\rho_f$ is the density of the fluid, $V_{\text{sub}}$ is the volume of the submerged part of the body, and $g$ is the acceleration due to gravity.

Formula to calculate the upward buoyant force acting on a body fully or partially submerged in a fluid.

Stokes' Law and Terminal Velocity

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Physics Viscosity & Stokes' Law

F_d = 6\pi \eta r v

v_t = \frac{2}{9} \frac{r^2(\rho_{body} - \rho_{fluid})g}{\eta}

Parameters & Definitions

$F_d$ is viscous drag, $\eta$ is coefficient of viscosity, $r$ is sphere radius, $v$ is speed, $v_t$ is terminal velocity, $\rho_{body}$ is density of sphere, and $\rho_{fluid}$ is fluid density.

Viscous drag force on a sphere and its ultimate terminal speed through a viscous medium.

Reynolds Number Flow Regime

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Physics Streamline & Turbulent Flow

R_e = \frac{\rho v d}{\eta} \implies \begin{cases} R_e < 1000 & \text{Laminar Flow} \\ R_e > 2000 & \text{Turbulent Flow} \end{cases}

Parameters & Definitions

$R_e$ is Reynolds number, $\rho$ is fluid density, $v$ is flow velocity, $d$ is diameter of tube, and $\eta$ is coefficient of viscosity.

Dimensionless quantity determining whether fluid flow is laminar (streamline) or turbulent.

Equation of Continuity and Bernoulli's Theorem

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Physics Bernoulli's Principle & Continuity

A_1 v_1 = A_2 v_2

P + \frac{1}{2}\rho v^2 + \rho g h = \text{constant}

Parameters & Definitions

$A$ represents cross-sectional area, $v$ represents flow velocity, $P$ is pressure, $h$ is height, and $\rho$ is fluid density.

Conservation of mass and mechanical energy principles in streamline fluid flow.

Relation Between Surface Tension and Surface Energy

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Physics Surface Energy & Surface Tension

W = T \cdot \Delta A

Parameters & Definitions

$W$ is the work done (stored as surface energy), $T$ is the surface tension of the liquid, and $\Delta A$ is the increase in surface area (taking both surfaces into account for a film).

Formula for the work done in increasing the surface area of a liquid film.

Excess Pressure in Drops/Bubbles

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Physics Excess Pressure

\Delta P_{drop} = \frac{2T}{R}

\Delta P_{bubble} = \frac{4T}{R}

Parameters & Definitions

$T$ is surface tension, $R$ is radius of curved interface, and $\Delta P$ is the excess pressure.

Formulas calculating excess internal pressure in curved interfaces.

Height of Capillary Rise

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Physics Capillary Rise

h = \frac{2T \cos\theta}{\rho g r}

Parameters & Definitions

$T$ is surface tension, $h$ is capillary height, $\theta$ is contact angle, $\rho$ is density of liquid, $g$ is acceleration due to gravity, and $r$ is tube radius.

Formula calculating height of capillary liquid column.

Temperature Scale Conversions

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Physics Heat & Temperature Scale

\frac{C}{5} = \frac{F-32}{9} = \frac{K-273.15}{5}

Parameters & Definitions

$C$ is temperature in degrees Celsius, $F$ is in degrees Fahrenheit, and $K$ is in Kelvin.

Formula to convert temperatures between Celsius, Fahrenheit, and Kelvin scales.

Linear Expansion

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Physics Thermal Expansion

L = L_0 (1 + \alpha \Delta T)

Parameters & Definitions

$L$ is final length, $L_0$ is initial length, $\alpha$ is linear expansion coefficient, and $\Delta T$ is temperature change.

Formula for linear dimension changes with temperature.

Specific Heat Capacity and Latent Heat

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Physics Specific Heat & Calorimetry

Q_{heat} = m s \Delta T

Q_{latent} = m L

Parameters & Definitions

$Q$ is heat exchanged, $m$ is mass, $s$ is specific heat, $L$ is latent heat, and $\Delta T$ is temperature change.

Basic heat transfer calculations for temperature and phase changes.

Conduction Rate

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Physics Conduction & Conductivity

\frac{dQ}{dt} = \frac{kA(T_{hot} - T_{cold})}{L}

Parameters & Definitions

$k$ is thermal conductivity, $A$ is area, $L$ is length, and $T$ is temperature.

Formula for conductive heat current through a material.

Wien's Displacement Law

Physics Convection & Radiation

\lambda_{\text{max}} T = b

Parameters & Definitions

$\lambda_{\text{max}}$ is wavelength of maximum radiation intensity, $T$ is absolute temperature, and $b$ is Wien's displacement constant ( $2.898 \times 10^{-3} \text{ m K}$ ).

Relates the peak wavelength of blackbody radiation to the absolute temperature of the body.

Stefan's Law and Wien's Law

Physics Black Body Radiation, Stefan & Wien Laws

E = \sigma e A T^4

\lambda_m T = b

Parameters & Definitions

$E$ is radiative power, $\sigma$ is Stefan-Boltzmann constant, $e$ is emissivity, $A$ is area, $T$ is temperature, $\lambda_m$ is peak wavelength, and $b$ is Wien's constant.

Formulas for total radiative power of a blackbody and wavelength of maximum emission.

Newton's Law of Cooling

Physics Newton's Law of Cooling

\frac{dT}{dt} = -K(T - T_s)

Parameters & Definitions

$T$ is body temperature, $T_s$ is surrounding temperature, $K$ is positive constant, and $t$ is time.

Approximate rate of temperature fall of a hot body to its surroundings.

Temperature Scale Conversions

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Physics Thermal Equilibrium & Zeroth Law

\frac{T_C}{100} = \frac{T_F - 32}{180} = \frac{T_K - 273.15}{100}

Parameters & Definitions

$T_C$ is Celsius temperature, $T_F$ is Fahrenheit temperature, and $T_K$ is Kelvin (absolute) temperature.

Conversion equations among Celsius, Fahrenheit, and Kelvin temperature scales.

First Law Equation

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Physics First Law of Thermodynamics

\Delta Q = \Delta U + W

Parameters & Definitions

$\Delta Q$ is heat added, $\Delta U = n C_v \Delta T$ is internal energy change, and $W$ is work.

Energy conservation equation for thermodynamic systems.

Work in Isothermal & Adiabatic Processes

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Physics Isothermal & Adiabatic Processes

W_{iso} = nRT \ln\left(\frac{V_f}{V_i}\right)

W_{adi} = \frac{P_i V_i - P_f V_f}{\gamma - 1}

Parameters & Definitions

$W$ is work, $n$ is mole count, $R$ is gas constant, $T$ is temperature, $V_i, V_f$ are volumes, $P_i, P_f$ are pressures, and $\gamma$ is adiabatic index.

Work formulas for key thermodynamic paths.

Adiabatic State Equations (Poisson's Relations)

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Physics Isothermal & Adiabatic Processes

P V^\gamma = \text{constant}

T V^{\gamma-1} = \text{constant}

P^{1-\gamma} T^\gamma = \text{constant}

Parameters & Definitions

$P$ is pressure, $V$ is volume, $T$ is absolute temperature, and $\gamma = C_p/C_v$ is the adiabatic index (ratio of specific heats).

Governing state relations for a quasi-static adiabatic process of an ideal gas.

Refrigerator Coefficient of Performance (COP)

Physics Second Law of Thermodynamics

\beta = \frac{Q_C}{W} = \frac{T_C}{T_H - T_C}

Parameters & Definitions

$\beta$ is coefficient of performance, $Q_C$ is heat extracted from cold reservoir, $W$ is work input, $T_C$ is cold temperature, and $T_H$ is hot temperature.

Measures the efficiency (COP) of an ideal Carnot refrigerator.

Carnot Engine and Refrigerator performance

Physics Carnot Engine & Refrigerator

\eta = 1 - \frac{T_C}{T_H}

\beta_{COP} = \frac{T_C}{T_H - T_C}

Parameters & Definitions

$\eta$ is efficiency, $\beta_{COP}$ is coefficient of performance, $T_C$ is absolute cold reservoir temperature, and $T_H$ is absolute hot reservoir temperature.

Efficiency of a Carnot cycle engine and the coefficient of performance of a refrigerator.

Equation of State and Compression Work

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Physics State Equations & Work

PV = nRT

W = -\int_{V_i}^{V_f} P_{ext} dV

Parameters & Definitions

$P$ is pressure, $V$ is volume, $n$ is moles, $T$ is temperature, $R$ is gas constant, and $W$ is work done on the gas.

Relation linking pressure, volume, temperature, and moles, and the general work integral for compression.

Kinetic Model Pressure

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Physics Assumptions & Pressure Concept

P = \frac{1}{3} \rho v_{rms}^2

Parameters & Definitions

$P$ is pressure, $\rho$ is density, and $v_{rms}$ is RMS molecular speed.

Concept of pressure based on kinetic theory of gases.

Molecular Speeds and Specific Heats

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Physics Molecular Speeds & Degrees of Freedom

v_{rms} = \sqrt{\frac{3RT}{M}} = \sqrt{\frac{3k_B T}{m}}

C_v = \frac{f}{2}R \quad C_p = \left(\frac{f}{2} + 1\right)R

Parameters & Definitions

$v_{rms}$ is RMS speed, $M$ is molar mass, $m$ is single molecule mass, $k_B$ is Boltzmann constant, $C_v, C_p$ are specific heats, $f$ is degrees of freedom, and $R$ is gas constant.

Expressions for RMS velocity and molar heat capacities based on degrees of freedom.

Mean Free Path

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Physics Mean Free Path

\lambda = \frac{1}{\sqrt{2}\pi d^2 n}

Parameters & Definitions

$\lambda$ is mean free path, $d$ is collision diameter, and $n$ is number density.

The average distance traveled by a moving gas molecule between successive collisions.

Displacement, Velocity and Acceleration in SHM

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Physics Periodic Motion & SHM Basic Equation

x(t) = A \sin(\omega t + \phi)

v(x) = \omega \sqrt{A^2 - x^2}

a(x) = -\omega^2 x

Parameters & Definitions

$x$ is displacement, $A$ is amplitude, $\omega$ is angular frequency, $\phi$ is initial phase, $v$ is velocity, and $a$ is acceleration.

Kinematic equations describing standard simple harmonic motion.

Energy in SHM

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Physics Phase & Energy in SHM

E_{total} = \frac{1}{2} m \omega^2 A^2

Parameters & Definitions

$E_{total}$ is energy, $m$ is mass, $\omega$ is angular frequency, and $A$ is amplitude.

Total mechanical energy of SHM.

Periods of Standard Oscillators

NEET N

Physics Spring & Pendulum Periods

T_{spring} = 2\pi \sqrt{\frac{m}{k}}

T_{pend} = 2\pi \sqrt{\frac{L}{g}}

Parameters & Definitions

$T$ is time period, $k$ is spring constant, $m$ is mass, $L$ is pendulum length, and $g$ is acceleration due to gravity.

Time period formulas for springs and pendulums.

Amplitude Decay in Damped SHM

Physics Damped & Forced Oscillations

A(t) = A_0 e^{-\frac{b t}{2m}}

\omega' = \sqrt{\omega_0^2 - \left(\frac{b}{2m}\right)^2}

Parameters & Definitions

$A(t)$ is damped amplitude, $A_0$ is initial amplitude, $b$ is damping constant, $m$ is mass, and $\omega'$ is the damped angular frequency.

Expression showing exponential decay of amplitude over time in a weakly damped system.

Speed of Wave on String and in Gas

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Physics Longitudinal & Transverse Waves

v_{\text{string}} = \sqrt{\frac{T}{\mu}}

v_{\text{gas}} = \sqrt{\frac{\gamma R T}{M}}

Parameters & Definitions

$T$ is tension, $\mu$ is linear mass density, $\gamma$ is adiabatic index, $R$ is gas constant, $T$ is temperature, and $M$ is molar mass.

Determines the velocity of transverse waves on a stretched string, and longitudinal sound waves in a gas.

Progressive Wave Equation and String/Gas Wave Speeds

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Physics Progressive Waves & Speed

y(x,t) = A \sin(kx - \omega t)

v_{string} = \sqrt{\frac{T}{\mu}}

v_{gas} = \sqrt{\frac{\gamma R T}{M}}

Parameters & Definitions

$y$ is displacement, $A$ is amplitude, $k = 2\pi/\lambda$ is wave number, $\omega = 2\pi f$ is angular frequency, $v$ represents speed, $T$ is tension, $\mu$ is linear mass density, and $\gamma$ is adiabatic index of gas.

Equation of a harmonic progressive wave and formulas for transverse wave speed on a string and longitudinal wave in gases.

Equation of a Standing Wave

NEET N

Physics Superposition & Reflection

y = 2A \sin(kx) \cos(\omega t)

Parameters & Definitions

$y$ is the displacement at position $x$ and time $t$ , $A$ is the amplitude of individual waves, $k = 2\pi/\lambda$ is the wave number, and $\omega = 2\pi f$ is the angular frequency.

Mathematical representation of a stationary wave formed by the superposition of two identical travelling waves in opposite directions.

Harmonics in Organ Pipes

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Physics Standing Waves & Harmonics

f_{open} = \frac{v}{2L}

f_{closed} = \frac{v}{4L}

Parameters & Definitions

$f$ represents frequency, $v$ is sound velocity, and $L$ is length of pipe.

Fundamental frequencies of open and closed organ pipes.

Beat Frequency

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Physics Beats

f_{beat} = |f_1 - f_2|

Parameters & Definitions

$f_{beat}$ is beat frequency, and $f_1, f_2$ are source frequencies.

Formula to calculate the beat frequency from two close source frequencies.

General Doppler Shift Formula in Sound

Physics Doppler Effect in Sound

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

Parameters & Definitions

$f'$ is observed frequency, $f$ is source frequency, $v$ is speed of sound in medium, $v_o$ is observer speed, and $v_s$ is source speed.

Formula for observed frequency when observer and source are in relative motion along line of sight.

Quantization of Electric Charge

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Physics Electric Charges

q = n e

Parameters & Definitions

$q$ is the net charge, $n$ is any integer (positive or negative), and $e \approx 1.6 \times 10^{-19}$ C is the elementary charge of an electron.

Formula expressing that the total charge on a body is an integral multiple of the basic unit of charge.

Coulomb's Law of Electrostatic Force

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Physics Coulomb's Law & Superposition

\vec{F} = \frac{1}{4\pi\varepsilon_0} \frac{q_1 q_2}{r^2} \hat{r}

Parameters & Definitions

$\vec{F}$ is force, $q_1, q_2$ are point charges, $r$ is separation distance, $\hat{r}$ is unit vector along separation line, and $\varepsilon_0$ is vacuum permittivity.

Electrostatic force vector acting between two point charges separated in vacuum.

Electric Field of a Point Charge

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Physics Electric Fields

E = \frac{1}{4\pi\varepsilon_0} \frac{q}{r^2}

Parameters & Definitions

$E$ is electric field intensity, $q$ is charge magnitude, $r$ is distance, and $\varepsilon_0$ is permittivity of free space.

Calculates the magnitude of the electrostatic field produced by a point charge in vacuum.

Electric Dipole Fields and Torque

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Physics Electric Dipoles & Torque

E_{axial} \approx \frac{1}{4\pi\varepsilon_0} \frac{2p}{r^3}

E_{equatorial} \approx \frac{1}{4\pi\varepsilon_0} \frac{p}{r^3}

\vec{\tau} = \vec{p} \times \vec{E}

Parameters & Definitions

$p = q(2a)$ is electric dipole moment magnitude, $r$ is distance from dipole center ( $r \gg a$ ), $E$ is electric field, and $\vec{\tau}$ is torque vector in field $\vec{E}$ .

Electric fields at axial/equatorial positions and torque experienced in a uniform external field.

Gauss's Law and Electrostatic Field Applications

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Physics Electric Flux & Gauss Law

\Phi_E = \oint \vec{E} \cdot d\vec{A} = \frac{q_{en}}{\varepsilon_0}

E_{wire} = \frac{\lambda}{2\pi\varepsilon_0 r}

E_{sheet} = \frac{\sigma}{2\varepsilon_0}

Parameters & Definitions

$\Phi_E$ is electric flux, $q_{en}$ is enclosed net charge, $\lambda$ is linear charge density, $\sigma$ is surface charge density, and $r$ is radial distance.

Integral definition of flux and fields due to standard charge distributions.

Electric Potential

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Physics Electric Potential

V(r) = \frac{1}{4\pi\varepsilon_0} \frac{q}{r}

Parameters & Definitions

$V$ is electric potential, $q$ is charge, and $r$ is separation distance.

Potential of a point charge in electrostatic space.

Electric Potential Energy

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Physics Potential Energy of Charge Systems

U = \frac{1}{4\pi\varepsilon_0} \frac{q_1 q_2}{r}

Parameters & Definitions

$U$ is electrostatic potential energy, $q_1, q_2$ are charges, and $r$ is separation distance.

Potential energy of a two-charge configuration.

Induced Charge on a Dielectric Slab

NEET N

Physics Conductors & Dielectrics

q_p = q \left( 1 - \frac{1}{K} \right)

Parameters & Definitions

$q_p$ is the induced (polarization) charge, $q$ is the free charge on the capacitor plates, and $K$ is the dielectric constant of the slab.

Formula for the induced charge appearing on the faces of a dielectric slab placed in an external electric field.

Capacitance of Parallel Plate Capacitors

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Physics Capacitors & Parallel Plates

C = \frac{K \varepsilon_0 A}{d}

Parameters & Definitions

$C$ is capacitance, $K$ is dielectric constant ( $K=1$ in vacuum), $A$ is plate area, and $d$ is separation.

Parallel plate capacitance (with dielectric $K$ ).

Series/Parallel Capacitance Formulas

NEET N

Physics Series & Parallel Capacitor Combinations

C_{parallel} = \sum C_i \quad \frac{1}{C_{series}} = \sum \frac{1}{C_i}

Parameters & Definitions

$C_{parallel}$ is parallel equivalent capacitance, and $C_{series}$ is series equivalent.

Combinations equivalent formulas.

Stored Energy

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Physics Energy Stored in Capacitor

U_{stored} = \frac{1}{2} C V^2 = \frac{Q^2}{2C}

Parameters & Definitions

$V$ is voltage, $Q$ is charge, and $U_{stored}$ is stored potential energy.

Energy stored in a capacitor.

Drift Velocity and Current

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Physics Drift Velocity & Current

v_d = \frac{eE\tau}{m}

I = n e A v_d

Parameters & Definitions

$v_d$ is drift velocity, $e$ is electronic charge, $E$ is electric field, $\tau$ is relaxation time, $m$ is electron mass, $I$ is current, $n$ is free charge density, and $A$ is area.

Microscopic model of current carrying conductors.

Ohm's Law and Electrical Resistance

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Physics Ohm's Law & Resistance

V = I R

R = \rho \frac{L}{A}

Parameters & Definitions

$V$ is potential difference, $I$ is current, $R$ is resistance, $\rho$ is electrical resistivity, $L$ is length, and $A$ is cross-sectional area.

Formulas for voltage-current relationship and the dependence of resistance on geometry and resistivity.

Temperature effect on Resistance

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Physics Temperature Dependence of Resistance

R(T) = R_0 (1 + \alpha \Delta T)

Parameters & Definitions

$R(T)$ is final resistance, $R_0$ is initial resistance, $\alpha$ is temperature coefficient of resistance, and $\Delta T$ is temperature change.

Effect of temperature on resistance values.

EMF and Internal Resistance

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Physics Internal Resistance & EMF

V = E - I r

Parameters & Definitions

$V$ is terminal voltage, $E$ is cell electromotive force (EMF), $I$ is current, and $r$ is internal resistance.

Terminal potential difference of cells.

Equivalent EMF for Parallel Cells

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Physics Cell Combinations

E_{eq,parallel} = \frac{\sum E_i/r_i}{\sum 1/r_i}

Parameters & Definitions

$E_i$ and $r_i$ are the EMF and internal resistance values of individual cells, and $E_{eq,parallel}$ is equivalent EMF.

Equivalent values for parallel groups of cells.

Kirchhoff's Current and Voltage Laws

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Physics Kirchhoff's Laws

\sum I_{in} = \sum I_{out}

\sum \Delta V = 0

Parameters & Definitions

$I_{in}, I_{out}$ are currents entering/leaving junctions, and $\Delta V$ represents potential differences around a closed loop.

Conservation rules for charge (junction law) and energy (loop law) in circuits.

Balanced Wheatstone Bridge and Meter Bridge

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Physics Wheatstone & Metre Bridges

\frac{P}{Q} = \frac{R}{S} \quad \text{(Balanced Bridge)}

\frac{R}{S} = \frac{l}{100-l} \quad \text{(Meter Bridge)}

Parameters & Definitions

$P, Q, R, S$ are bridge resistances, and $l$ is the balance length in centimeters along the 1-meter wire.

Symmetry conditions for zero current in the central galvanometer of a Wheatstone bridge and its meter bridge application.

Galvanometer to Ammeter and Voltmeter Conversion

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Physics Wheatstone & Metre Bridges

S = \frac{I_g R_g}{I - I_g} \quad \text{(Ammeter Shunt)}

R = \frac{V}{I_g} - R_g \quad \text{(Voltmeter Series)}

Parameters & Definitions

$S$ is parallel shunt resistance, $R$ is series multiplier resistance, $R_g$ is galvanometer coil resistance, $I_g$ is full-scale deflection current, $I$ is ammeter range, and $V$ is voltmeter range.

Formulas to convert a basic galvanometer into a high-range ammeter or voltmeter.

Potentiometer Equations

Physics Potentiometer

\frac{E_1}{E_2} = \frac{l_1}{l_2}

r = R \left( \frac{l_1}{l_2} - 1 \right)

Parameters & Definitions

$E_1, E_2$ are EMFs of cells, $l_1, l_2$ are balancing lengths, $r$ is internal resistance, and $R$ is standard resistance box resistance.

Formulas to compare cell EMFs and measure internal resistance.

Carbon Resistor Value & Tolerance

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Physics Resistor Color Coding

R = (A \times 10 + B) \times 10^C \pm D\%

Parameters & Definitions

$A, B$ are the first two color bands representing significant figures; $C$ is the third band decimal multiplier (multiplier exponent); $D$ is the fourth band representing tolerance (Gold = 5%, Silver = 10%, No band = 20%). Color order (0-9): Black, Brown, Red, Orange, Yellow, Green, Blue, Violet, Grey, White.

Formula to determine the resistance and tolerance of a carbon resistor using color bands.

Biot-Savart Law and Circular Loop Field

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Physics Biot-Savart Law & Circular Loop

d\vec{B} = \frac{\mu_0}{4\pi} \frac{I (d\vec{l} \times \vec{r})}{r^3}

B_{axis} = \frac{\mu_0 I R^2}{2(R^2 + x^2)^{3/2}}

Parameters & Definitions

$d\vec{B}$ is differential magnetic field, $\mu_0$ is vacuum permeability, $I$ is current, $d\vec{l}$ is length vector, $\vec{r}$ is position vector, $R$ is circular loop radius, and $x$ is axial distance.

Magnetic field differential vector and field value on the axis of a circular loop.

Magnetic Field of Finite Wire and Circular Arc

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Physics Biot-Savart Law & Circular Loop

B_{\text{wire}} = \frac{\mu_0 I}{4\pi d}(\sin\phi_1 + \sin\phi_2)

B_{\text{arc}} = \frac{\mu_0 I}{4\pi R}\theta

Parameters & Definitions

$B$ is magnetic field, $I$ is current, $d$ is perpendicular distance, $\phi_1, \phi_2$ are angles subtended by wire ends, $R$ is circular arc radius, and $\theta$ is arc angle in radians.

Magnetic fields at a point due to a straight wire segment and at the center of a circular current arc.

Ampere's Circuital Law and Straight Wire Field

NEET N

Physics Ampere's Law & Solenoid Field

\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{en}

B_{wire} = \frac{\mu_0 I}{2\pi r}

Parameters & Definitions

$I_{en}$ is enclosed net current, $B_{wire}$ is magnetic field strength at distance $r$ from wire, and $d\vec{l}$ is differential length.

Line integral relation for magnetic fields and field due to a long straight current conductor.

Lorentz Force and Circular Orbit Radius

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Physics Lorentz Force & Orbit Radius

\vec{F} = q \left( \vec{E} + \vec{v} \times \vec{B} \right)

r_{orbit} = \frac{m v}{q B}

Parameters & Definitions

$\vec{F}$ is Lorentz force, $q$ is charge, $\vec{E}$ is electric field, $\vec{v}$ is velocity, $\vec{B}$ is magnetic field, $r_{orbit}$ is radius of orbit, and $m$ is mass of charge.

Force vector on moving charges and orbital parameters in uniform magnetic fields.

Magnetic Force on Current Wire

NEET N

Physics Forces on Current Wires

\vec{F} = I (\vec{L} \times \vec{B})

Parameters & Definitions

$I$ is current, $\vec{L}$ is wire length vector, and $\vec{B}$ is field vector.

Force vector on a current-carrying wire.

Force per Unit Length between Parallel Wires

NEET N

Physics Force between Parallel Current Wires

\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d}

Parameters & Definitions

$I_1, I_2$ are currents, $d$ is separation distance, and $F/L$ is force per unit length.

Force per unit length between two parallel wires.

Torque on Loop, Galvanometer sensitivities

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Physics Loop Torque & Galvanometer Sensitivities

\vec{\tau} = \vec{M} \times \vec{B}

I_{sens} = \frac{\theta}{I} = \frac{NBA}{C}

V_{sens} = \frac{\theta}{V} = \frac{NBA}{C R_g}

Parameters & Definitions

$\vec{\tau}$ is torque, $\vec{M}$ is magnetic dipole moment, $\vec{B}$ is field, $N$ is turn count, $A$ is area, $C$ is torsional restoring constant, and $R_g$ is galvanometer coil resistance.

Torque vector on current loop and equations for galvanometer sensitivities.

Magnetic Moment of a Revolving Electron

NEET N

Physics Dipole Moments & Revolving Electron

M_{electron} = \frac{e v r}{2} = \frac{e}{2m} L

Parameters & Definitions

$M_{electron}$ is magnetic moment, $e$ is electronic charge, $v$ is orbital speed, $r$ is orbital radius, $m$ is electron mass, and $L$ is orbital angular momentum.

Orbital magnetic dipole moment (Bohr Magneton) of a revolving hydrogenic electron.

Magnetic Field of a Bar Magnet

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Physics Bar Magnet & Field Lines

B_{\text{axial}} = \frac{\mu_0}{4\pi} \frac{2M}{r^3}

B_{\text{equatorial}} = \frac{\mu_0}{4\pi} \frac{M}{r^3}

Parameters & Definitions

$B$ is the magnetic field, $M$ is the magnetic dipole moment, $r$ is the distance from the magnet center ( $r \gg$ magnet length), and $\mu_0$ is the permeability of free space.

Magnetic field formulas at axial and equatorial points of a short bar magnet.

Magnetic Susceptibility and Curie's Law

NEET N

Physics Magnetic Materials

\mu_r = 1 + \chi_m

\chi_m = \frac{C}{T} \quad \text{(Curie's Law)}

Parameters & Definitions

$\mu_r$ is relative magnetic permeability, $\chi_m$ is magnetic susceptibility, $C$ is Curie's constant, and $T$ is temperature in Kelvin.

Formula for relative permeability and Curie's temperature dependence of paramagnetic susceptibility.

Faraday's and Lenz's Law of Induction

NEET N

Physics Faraday & Lenz Laws of Induction

\mathcal{E} = -\frac{d\Phi_B}{dt}

\Phi_B = \int \vec{B} \cdot d\vec{A}

Parameters & Definitions

$\mathcal{E}$ is induced EMF, $\Phi_B$ is magnetic flux, and $\vec{B}$ is magnetic field vector.

Mathematical expression relating induced EMF to time rate of change of magnetic flux.

Self and Mutual Inductance Definition

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Physics Self & Mutual Inductance

\Phi_B = L I \implies \mathcal{E}_s = -L \frac{dI}{dt}

\Phi_{12} = M I_2 \implies \mathcal{E}_1 = -M \frac{dI_2}{dt}

Parameters & Definitions

$L$ is self-inductance coefficient, $M$ is mutual inductance coefficient, $I, I_2$ are currents, and $\mathcal{E}_s, \mathcal{E}_1$ are induced EMFs.

Relationships linking magnetic flux linkage to current through coils.

Peak and RMS values of AC

NEET N

Physics AC RMS & Peak Values

I_{rms} = \frac{I_0}{\sqrt{2}}

V_{rms} = \frac{V_0}{\sqrt{2}}

Parameters & Definitions

$I_{rms}, V_{rms}$ are RMS current and voltage, and $I_0, V_0$ are peak values.

Formulas calculating Root Mean Square values for sinusoidal AC.

Impedance in LCR Series Circuits

NEET N

Physics Reactance & LCR Circuit Impedance

Z = \sqrt{R^2 + (X_L - X_C)^2}

Parameters & Definitions

$Z$ is impedance, $R$ is resistance, $X_L = \omega L$ is inductive reactance, and $X_C = 1/(\omega C)$ is capacitive reactance.

Impedance magnitude of LCR series circuits.

Resonant Frequency and Q-Factor

NEET N

Physics Resonance & Q-Factor

\omega_0 = \frac{1}{\sqrt{LC}}

Q = \frac{\omega_0 L}{R} = \frac{1}{R}\sqrt{\frac{L}{C}}

Parameters & Definitions

$\omega_0$ is resonant angular frequency, $Q$ is quality factor, $L$ is inductance, $C$ is capacitance, and $R$ is resistance.

Resonant frequency and Q-factor of LCR series circuits.

Average Power and Power Factor in AC

NEET N

Physics AC Power & Wattless Current

P_{avg} = V_{rms} I_{rms} \cos\phi

\cos\phi = \frac{R}{Z}

Parameters & Definitions

$P_{avg}$ is average power, $\cos\phi$ is power factor, and $\phi$ is the phase difference between current and voltage.

Expression for average active power dissipation in AC circuits.

Transformer Voltage and Current Relations

NEET N

Physics Transformers & AC Generators

\frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{I_p}{I_s}

Parameters & Definitions

$V_p, V_s$ are primary/secondary voltages, $N_p, N_s$ are primary/secondary turns, and $I_p, I_s$ are primary/secondary currents.

Voltage ratio and current ratio based on turns ratio in ideal transformers.

Maxwell's Displacement Current

NEET N

Physics Displacement Current

I_d = \varepsilon_0 \frac{d\Phi_E}{dt}

Parameters & Definitions

$I_d$ is displacement current, $\varepsilon_0$ is vacuum permittivity, and $\Phi_E$ is electric flux.

Current defined in terms of time rate of change of electric flux.

Velocity of Light and Fields Ratio

NEET N

Physics Electromagnetic Spectrum & Uses

c = \frac{E_0}{B_0} = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}

Parameters & Definitions

$c$ is speed of light, $E_0$ is electric field amplitude, $B_0$ is magnetic field amplitude, $\mu_0$ is permeability of free space, and $\varepsilon_0$ is permittivity of free space.

Relationship relating the speed of electromagnetic waves in a vacuum to the ratio of electric and magnetic field amplitudes, and vacuum constants.

Mirror Formula

NEET N

Physics Spherical Mirrors & Mirror Formula

\frac{1}{v} + \frac{1}{u} = \frac{1}{f}

Parameters & Definitions

$u, v$ are object/image distances, and $f$ is mirror focal length.

Fundamental equations describing reflection in spherical mirrors.

Snell's Law and Critical Angle

NEET N

Physics Refraction, Snell's Law & TIR

n_1 \sin\theta_1 = n_2 \sin\theta_2

\sin\theta_c = \frac{n_{rare}}{n_{dense}}

Parameters & Definitions

$\theta_1, \theta_2$ are angles, $n_1, n_2$ are refractive indices, and $\theta_c$ is critical angle.

Equations describing refraction and the limit of total internal reflection.

Refraction at Spherical Surfaces and Lens Maker's Formula

NEET N

Physics Refraction at Spherical Surfaces

\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}

\frac{1}{f} = \left(\frac{\mu_{\text{lens}}}{\mu_{\text{medium}}} - 1\right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)

Parameters & Definitions

$u$ is object distance, $v$ is image distance, $\mu_i$ are refractive indices, $R_i$ are curvature radii, and $f$ is focal length.

Refraction relation at a single curved boundary and the formula to determine the focal length of a thin lens.

Lens Equations

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Physics Thin Lenses & Lensmaker Formula

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

\frac{1}{f} = \left( \frac{n_{lens}}{n_{med}} - 1 \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)

Parameters & Definitions

$u, v$ are object/image distances, $f$ is focal length, $R_1, R_2$ are spherical radii, and $n$ represents refractive indices.

Thin lens formula and lensmaker's equation.

Prism Formula

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Physics Refraction through Prism

n_{prism} = \frac{\sin\left( \frac{A + \delta_m}{2} \right)}{\sin\left( \frac{A}{2} \right)}

Parameters & Definitions

$n_{prism}$ is the refractive index, $A$ is prism apex angle, and $\delta_m$ is minimum deviation angle.

Refractive index formula for a prism at minimum deviation.

Magnification of Microscope and Telescope

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Physics Optical Instruments

m_{\text{microscope}} = -\frac{L}{f_o} \left( 1 + \frac{D}{f_e} \right)

m_{\text{telescope}} = -\frac{f_o}{f_e}

Parameters & Definitions

$f_o$ and $f_e$ are focal lengths of objective and eyepiece respectively, $L$ is tube length, and $D = 25$ cm is the least distance of distinct vision.

Magnifying power formulas for compound microscope and astronomical telescope at normal adjustment.

Relation Between Phase and Path Difference

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Physics Wavefront & Huygens' Principle

\Delta \phi = \frac{2\pi}{\lambda} \Delta x

Parameters & Definitions

$\Delta \phi$ is phase difference, $\Delta x$ is path difference, and $\lambda$ is wavelength of light.

Converts spatial path difference of coherent waves into their temporal phase difference.

Interference Intensities and Fringe Width in YDSE

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Physics Interference & YDSE

I_{res} = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos\phi

\beta_{fringe} = \frac{\lambda D}{d}

Parameters & Definitions

$I_{res}$ is resulting intensity, $I_1, I_2$ are slit source intensities, $\phi$ is phase difference, $\beta_{fringe}$ is fringe width, $\lambda$ is wavelength, $D$ is slit-screen distance, and $d$ is slit separation distance.

Mathematical description of resulting intensity and bright/dark fringe width in Young's Double Slit Experiment.

Central Maximum Width

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Physics Single Slit Diffraction

w_{linear} = \frac{2\lambda D}{a}

Parameters & Definitions

$w_{linear}$ is linear width of central maximum, $a$ is slit width, and $D$ is distance to screen.

Formula for angular/linear width of central maximum in single slit diffraction.

Brewster's Law

NEET N

Physics Polarisation & Brewster Law

n = \tan i_p

Parameters & Definitions

$n$ is refractive index of medium, and $i_p$ is polarizing angle (Brewster's angle).

Brewster's polarization angle for reflecting surfaces.

Resolving Power of Microscope and Telescope

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Physics Resolving Power

\text{Resolving Power of Microscope} = \frac{2\mu \sin\theta}{1.22 \lambda}

\text{Resolving Power of Telescope} = \frac{D}{1.22\lambda}

Parameters & Definitions

$\mu$ is the refractive index of the medium between the object and the objective, $\theta$ is the semi-vertical angle of the cone of light, $\lambda$ is the wavelength, and $D$ is the diameter of the objective lens (aperture).

Formulas for the limit of resolution and resolving power of optical instruments.

Einstein's Photoelectric Equation

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Physics Einstein's Photoelectric Equation

K_{max} = h\nu - \phi = eV_0

Parameters & Definitions

$K_{max}$ is maximum kinetic energy of electrons, $h\nu$ is incident light energy, $\phi$ is material work function, $e$ is electronic charge, and $V_0$ is stopping potential.

Relation between incident photon energy, work function, and maximum kinetic energy of emitted photoelectrons.

de Broglie Wavelength of Matter Waves

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Physics de Broglie Wavelength

\lambda = \frac{h}{p} = \frac{h}{\sqrt{2mK}} = \frac{h}{\sqrt{2mqV}}

Parameters & Definitions

$\lambda$ is de Broglie wavelength, $h$ is Planck's constant, $p$ is momentum, $m$ is mass, $K$ is kinetic energy, $q$ is charge, and $V$ is accelerating potential.

Wavelength associated with a moving particle of momentum $p$ or kinetic energy $K$ .

Distance of Closest Approach

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Physics Rutherford Model

r_0 = \frac{1}{4\pi\epsilon_0} \frac{2 Z e^2}{K_\alpha}

Parameters & Definitions

$r_0$ is the distance of closest approach, $Z$ is the atomic number of the target nucleus, $e$ is elementary charge, $K_\alpha$ is kinetic energy of the incoming alpha particle.

Formula to find the minimum distance an alpha particle reaches before being repelled by a nucleus.

Bohr Model Radii and Energy Levels

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Physics Bohr Model & Energy Levels

r_n = a_0 \frac{n^2}{Z} \approx 0.529 \frac{n^2}{Z} \text{ \AA}

E_n = -E_0 \frac{Z^2}{n^2} \approx -13.6 \frac{Z^2}{n^2} \text{ eV}

\frac{1}{\lambda} = R Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)

Parameters & Definitions

$r_n$ is the $n$ -th orbit radius, $a_0$ is Bohr radius, $E_n$ is $n$ -th level energy, $Z$ is atomic number, $n, n_1, n_2$ are principal quantum numbers, and $R$ is Rydberg constant.

Quantized orbit radius and energy levels of hydrogen-like atoms.

Nuclear Radius and Mass Number Relation

NEET N

Physics Nuclear Size & Density

R = R_0 A^{1/3}

Parameters & Definitions

$R$ is nuclear radius, $R_0 \approx 1.2 \text{ fm}$ , and $A$ is mass number.

Empirical formula relating nuclear radius to mass number.

Mass Defect and Binding Energy

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Physics Mass Defect & Binding Energy

\Delta m = \left( Z m_p + (A-Z) m_n \right) - M_{nuc}

E_b = \Delta m c^2

Parameters & Definitions

$\Delta m$ is mass defect, $Z$ is proton count, $A$ is mass number, $m_p, m_n$ are proton/neutron masses, $M_{nuc}$ is nuclear mass, and $E_b$ is binding energy.

Difference in mass of components and energy binding the nucleus together.

Nuclear Reaction Q-Value

NEET N

Physics Nuclear Fission & Fusion

Q = (\sum M_{\text{reactants}} - \sum M_{\text{products}}) c^2

Parameters & Definitions

$Q$ is the reaction energy, $M_{\text{reactants}}$ is the total mass of the reactants, $M_{\text{products}}$ is the total mass of the products, and $c$ is the speed of light.

The amount of energy released or absorbed during a nuclear fission or fusion reaction.

Radioactive Decay Law and Half-Life

Physics Radioactive Decay Laws

N(t) = N_0 e^{-\lambda t}

T_{1/2} = \frac{\ln 2}{\lambda} \approx \frac{0.693}{\lambda}

\tau_{mean} = \frac{1}{\lambda}

Parameters & Definitions

$N(t)$ is remaining active nuclei at time $t$ , $N_0$ is initial count, $\lambda$ is decay constant, $T_{1/2}$ is half-life, and $\tau_{mean}$ is mean life.

Equations describing exponential decay rate and half-life duration of radioactive elements.

Bandgap Energy

NEET N

Physics Energy Bands in Solids

E_g = \frac{hc}{\lambda}

Parameters & Definitions

$E_g$ is the bandgap energy, $h$ is Planck's constant, $c$ is the speed of light, and $\lambda$ is the photon wavelength.

Energy difference between the valence band and conduction band, which determines the optical properties of semiconductors.

Law of Mass Action in Semiconductors

Physics Intrinsic & Extrinsic Carrier concentration

n_e n_h = n_i^2

Parameters & Definitions

$n_e$ is free electron density, $n_h$ is hole density, and $n_i$ is intrinsic carrier concentration.

Thermal equilibrium concentration product relation for electrons and holes.

Maximum Efficiency of Half-Wave and Full-Wave Rectifiers

Physics Semiconductor Diodes & Rectifiers

\eta_{\text{half}} = \frac{40.6\%}{1 + R_f/R_L}

\eta_{\text{full}} = \frac{81.2\%}{1 + R_f/R_L}

Parameters & Definitions

$\eta$ is rectifier efficiency, $R_f$ is forward diode resistance, and $R_L$ is load resistance.

Maximum theoretical conversion efficiency of AC power to DC power for half-wave and full-wave rectifiers.

Zener Diode as a Shunt Voltage Regulator

Physics Zener Diode as Voltage Regulator

I_S = I_Z + I_L

I_S = \frac{V_{\text{in}} - V_Z}{R_S} \quad I_L = \frac{V_Z}{R_L}

Parameters & Definitions

$I_S, I_Z, I_L$ are series, Zener, and load currents; $V_{\text{in}}$ is input voltage, $V_Z$ is Zener breakdown voltage, $R_S$ is series resistance, and $R_L$ is load resistance.

Circuit equations calculating series resistor and Zener currents to maintain constant load voltage.

Boolean Logic Gate Outputs

Physics Special Purpose Diodes & Logic Gates

Y_{\text{AND}} = A \cdot B \quad Y_{\text{OR}} = A + B

Y_{\text{NAND}} = \overline{A \cdot B} \quad Y_{\text{NOR}} = \overline{A + B}

Parameters & Definitions

$A, B$ are binary inputs (0 or 1), and $Y$ is the output.

Mathematical outputs for basic logic gates (AND, OR, NAND, NOR).

Least Count of Vernier Calliper and Screw Gauge

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Physics Vernier Calliper & Screw Gauge Least Count

LC_{Vernier} = 1\text{ MSD} - 1\text{ VSD}

LC_{Gauge} = \frac{\text{Pitch}}{\text{Number of Circular Scale Divisions}}

Parameters & Definitions

LC represents Least Count, MSD represents Main Scale Division, VSD represents Vernier Scale Division, and Pitch is the linear advancement per full rotation of the screw gauge thimble.

Expressions defining the limits of measurement resolution for callipers and gauges.

Mole Calculations

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Chemistry Mole Concept

n = \frac{w}{M}

n = \frac{N}{N_A}

n = \frac{V_{STP} \text{ (in L)}}{22.7}

Parameters & Definitions

$w$ is mass of substance, $M$ is molar mass, $N$ is count of particles, $N_A \approx 6.022 \times 10^{23}$ is Avogadro's number, and $V_{STP}$ is volume of gas at standard temperature and pressure.

Basic relationships to calculate the number of moles ( $n$ ) from mass, number of particles, or gas volume at STP.

Molarity, Molality and Mole Fraction

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Chemistry Molarity, Molality and Mole Fraction

M = \frac{n_{solute}}{V_{solution} \text{ (in L)}}

m = \frac{n_{solute}}{W_{solvent} \text{ (in kg)}}

x_A = \frac{n_A}{n_A + n_B}

Parameters & Definitions

$M$ is molarity, $m$ is molality, $x_A$ is mole fraction of component A, $n$ represents moles, $V$ represents volume, and $W$ represents solvent mass.

Formulas to express concentration of solute in a solution.

Rydberg Formula for Spectral Lines

NEET N

Chemistry Bohr Model & Spectral Lines

\bar{\nu} = \frac{1}{\lambda} = R_H Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)

Parameters & Definitions

$\bar{\nu}$ is wave number, $\lambda$ is wavelength, $R_H \approx 1.09677 \times 10^7 \text{ m}^{-1}$ is Rydberg constant, $Z$ is atomic number, and $n_1, n_2$ are principal quantum numbers ( $n_2 > n_1$ ).

Formula to calculate the wavelength or wave number of spectral lines emitted during electronic transitions in hydrogen-like atoms.

de Broglie Wavelength and Heisenberg Uncertainty Principle

NEET N

Chemistry de Broglie Wavelength & Uncertainty

\lambda = \frac{h}{mv} = \frac{h}{p}

\Delta x \cdot \Delta p \ge \frac{h}{4\pi}

Parameters & Definitions

$\lambda$ is de Broglie wavelength, $h$ is Planck's constant, $m$ is mass, $v$ is velocity, $p$ is momentum, $\Delta x$ is position uncertainty, and $\Delta p$ is momentum uncertainty.

Mathematical statements of wave-particle duality and the fundamental limit on simultaneous measurement precision.

Steric Number and Hybridization

NEET N

Chemistry VSEPR Shapes & Hybridization

SN = \frac{1}{2} [ V + M - C + A ]

Parameters & Definitions

$V$ is the number of valence electrons on the central atom, $M$ is the number of monovalent atoms bonded to it, $C$ is the charge of the cation, and $A$ is the charge of the anion.

Formula to calculate the steric number ( $SN$ ) of a central atom to determine its hybridization and geometry.

Bond Order (Molecular Orbital Theory)

NEET N

Chemistry Molecular Orbital Theory

\text{Bond Order} = \frac{N_b - N_a}{2}

Parameters & Definitions

$N_b$ is the number of electrons in bonding molecular orbitals, and $N_a$ is the number of electrons in antibonding molecular orbitals.

Formulas to calculate bond order, predicting stability and bond length comparison.

Dipole Moment

NEET N

Chemistry Dipole Moment

\mu = q \times d

Parameters & Definitions

$\mu$ is dipole moment, $q$ is magnitude of charge, and $d$ is separation distance.

Mathematical definition of molecular dipole moment for a charge separation.

Ideal Gas Equation

Chemistry Ideal Gas Equation

PV = nRT

Parameters & Definitions

$P$ is pressure, $V$ is volume, $n$ is moles, $T$ is temperature, and $R$ is gas constant.

Equation of state for an ideal gas.

van der Waals Equation

Chemistry van der Waals Equation

\left( P + \frac{an^2}{V^2} \right)(V - nb) = nRT

Parameters & Definitions

$P$ is pressure, $V$ is volume, $n$ is moles, $T$ is temperature, $R$ is gas constant, $a$ is molecular attraction factor, and $b$ is excluded volume factor.

Real gas equation incorporating molecular attraction and volume corrections.

Dalton's Law

Chemistry Dalton's Partial Pressures

P_i = x_i P_{total}

Parameters & Definitions

$P_i$ is partial pressure of gas $i$ , $x_i$ is its mole fraction, and $P_{total}$ is total pressure.

Partial pressures in gas mixtures.

Graham's Law of Diffusion

Chemistry Graham's Diffusion Law

\frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}} = \sqrt{\frac{d_2}{d_1}}

Parameters & Definitions

$r_1, r_2$ are diffusion rates, $M_1, M_2$ are molar masses, and $d_1, d_2$ are densities.

Relative rates of diffusion/effusion.

First Law and Expansion Work

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Chemistry First Law & Expansion Work

\Delta U = q + w

w_{rev} = -2.303 nRT \log_{10}\left(\frac{V_2}{V_1}\right)

Parameters & Definitions

$\Delta U$ is change in internal energy, $q$ is heat exchanged, $w$ is work, $n$ is moles, $R$ is gas constant, $T$ is temperature, and $V_1, V_2$ are volumes.

Energy conservation equation and reversible expansion work formulas for gas systems.

Enthalpy and Internal Energy Relation

NEET N

Chemistry Enthalpy & Hess's Law

\Delta H = \Delta U + \Delta n_g RT

Parameters & Definitions

$\Delta H$ is change in enthalpy, $\Delta U$ is change in internal energy, $\Delta n_g$ is change in gaseous moles, $R$ is gas constant, and $T$ is temperature.

Enthalpy change relation for gaseous reactions.

Entropy Change and Second Law of Thermodynamics

NEET N

Chemistry Entropy & Second Law

\Delta S = \frac{q_{\text{rev}}}{T}

\Delta S_{\text{total}} = \Delta S_{\text{system}} + \Delta S_{\text{surroundings}} \ge 0

Parameters & Definitions

$\Delta S$ is the change in entropy, $q_{\text{rev}}$ is the heat exchanged reversibly, and $T$ is the absolute temperature in Kelvin.

Definition of entropy change and the total entropy criterion for a spontaneous process.

Gibbs Free Energy and Spontaneity

NEET N

Chemistry Gibbs Energy & Equilibrium

\Delta G = \Delta H - T\Delta S

\Delta G^\circ = -2.303 RT \log_{10} K_{eq}

Parameters & Definitions

$\Delta G$ is Gibbs free energy change, $\Delta G^\circ$ is standard Gibbs energy change, $\Delta H$ is enthalpy change, $T$ is absolute temperature, $\Delta S$ is entropy change, and $K_{eq}$ is equilibrium constant.

Definition of Gibbs free energy change and standard Gibbs energy relation.

Relationship Between Kp and Kc

NEET N

Chemistry Kp and Kc Relations

K_p = K_c (RT)^{\Delta n_g}

Parameters & Definitions

$K_p, K_c$ are equilibrium constants, $R$ is gas constant, $T$ is temperature, and $\Delta n_g$ is change in moles of gaseous components.

Mathematical formula linking pressure-based and concentration-based equilibrium constants.

Reaction Quotient Shift Direction

NEET N

Chemistry Le Chatelier's Principle

Q_c < K_c \implies \text{shifts right (forward)}

Q_c > K_c \implies \text{shifts left (backward)}

Q_c = K_c \implies \text{at equilibrium}

Parameters & Definitions

$Q_c$ is the reaction quotient, and $K_c$ is the equilibrium constant.

Determines the shift direction of equilibrium by comparing the reaction quotient $Q_c$ and the equilibrium constant $K_c$ .

Van 't Hoff Reaction Isochore

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Chemistry Le Chatelier's Principle

\ln\left(\frac{K_2}{K_1}\right) = \frac{\Delta H^\circ}{R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right)

Parameters & Definitions

$K_1, K_2$ are equilibrium constants at temperatures $T_1, T_2$ , $\Delta H^\circ$ is standard enthalpy of reaction, and $R$ is gas constant.

Relates the equilibrium constants at two different temperatures to the standard enthalpy of reaction.

pH Definition

NEET N

Chemistry pH Scale

\text{pH} = -\log_{10}[H^+]

Parameters & Definitions

$[H^+]$ is the concentration of hydronium ions.

Mathematical definition of the pH scale.

Henderson-Hasselbalch Buffer Equations

NEET N

Chemistry Henderson Buffer Equation

\text{pH} = pK_a + \log_{10}\left( \frac{[\text{Conjugate Base}]}{[\text{Acid}]} \right)

\text{pOH} = pK_b + \log_{10}\left( \frac{[\text{Conjugate Acid}]}{[\text{Base}]} \right)

Parameters & Definitions

$pK_a = -\log K_a$ , $pK_b = -\log K_b$ , and brackets denote molar concentrations.

Formulas for calculating pH of acidic/basic buffer solutions.

Solubility Product Constant

NEET N

Chemistry Solubility Product (Ksp)

A_x B_y \rightleftharpoons xA^{y+} + yB^{x-} \implies K_{sp} = x^x y^y S^{x+y}

Parameters & Definitions

$K_{sp}$ is solubility product, $S$ is molar solubility of salt, and $x, y$ are stoichiometric coefficients of cations and anions.

Relationship between solubility ( $S$ ) and solubility product ( $K_{sp}$ ) for standard electrolyte salts.

Sum of Oxidation States

NEET N

Chemistry Oxidation States & Balancing

\sum_{i} n_i \cdot \text{O.S.}_i = \text{Net Charge}

Parameters & Definitions

$n_i$ is the number of atoms of species $i$ , $\text{O.S.}_i$ is their oxidation state, and $\text{Net Charge}$ is the overall charge.

Rule stating the sum of oxidation numbers of all atoms in a molecule/ion equals its total electrical charge.

Equivalent Weight of Redox Agent

NEET N

Chemistry Oxidation States & Balancing

E = \frac{\text{Molar Mass}}{\text{n-factor}}

Parameters & Definitions

$E$ is equivalent weight, $\text{Molar Mass}$ is the molecular weight, and $\text{n-factor}$ is the number of electrons gained or lost per mole of reactant.

Definition of equivalent mass of an oxidizing or reducing agent in a redox reaction.

Conductivity, Molar Conductivity and Kohlrausch's Law

NEET N

Chemistry Conductance & Kohlrausch Law

\Lambda_m = \frac{\kappa \times 1000}{C}

\Lambda_m^\circ = \nu_+ \lambda_+^\circ + \nu_- \lambda_-^\circ

Parameters & Definitions

$\Lambda_m$ is molar conductivity, $\kappa$ is specific conductivity, $C$ is molar concentration, $\Lambda_m^\circ$ is limiting molar conductivity, and $\nu_+, \nu_-$ are ion counts with limiting conductances $\lambda_+^\circ, \lambda_-^\circ$ .

Expressions for molar conductivity and its value at infinite dilution.

Debye-HÃ¼ckel-Onsager Equation

NEET N

Chemistry Conductance & Kohlrausch Law

\Lambda_m = \Lambda_m^\circ - A \sqrt{C}

Parameters & Definitions

$\Lambda_m$ is molar conductivity, $\Lambda_m^\circ$ is limiting molar conductivity at infinite dilution, $C$ is electrolyte concentration, and $A$ is a constant depending on solvent, charge type, and temperature.

Describes the concentration dependence of molar conductivity for strong electrolytes.

Nernst Equation

NEET N

Chemistry Galvanic Cells & Nernst Equation

E_{cell} = E^\circ_{cell} - \frac{0.0591}{n} \log_{10} Q \quad \text{at } 298\text{ K}

Parameters & Definitions

$E_{cell}$ is cell potential, $E^\circ_{cell}$ is standard potential, $n$ is number of electrons transferred, and $Q$ is reaction quotient.

Calculates cell potential under non-standard conditions.

Gibbs Free Energy and EMF

NEET N

Chemistry Gibbs Energy & Cell Potential

\Delta G = -n F E_{cell}

Parameters & Definitions

$\Delta G$ is Gibbs free energy change, $n$ is electrons transferred, $F \approx 96500 \text{ C mol}^{-1}$ is Faraday constant, and $E_{cell}$ is cell potential.

Links cell potential to Gibbs free energy change.

Faraday's Laws of Electrolysis

NEET N

Chemistry Electrolysis & Faraday's Laws

w = Z I t = \left( \frac{E_{eq}}{F} \right) I t

\text{Equivalent Moles} = \frac{I \times t}{96500}

Parameters & Definitions

$w$ is mass deposited, $Z$ is electrochemical equivalent, $I$ is current, $t$ is time, $E_{eq}$ is equivalent weight of substance, and $F$ is Faraday constant.

Quantitative mass yield of substances discharged at electrodes during electrolysis.

Henry's Law and Raoult's Law

NEET N

Chemistry Henry & Raoult Laws

p = K_H x

P_{total} = P_A^\circ x_A + P_B^\circ x_B

Parameters & Definitions

$p, P_{total}$ are vapor pressures, $K_H$ is Henry's constant, $x, x_A, x_B$ are mole fractions, and $P_A^\circ, P_B^\circ$ are pure component vapor pressures.

Equations showing vapor pressures of solute gases and volatile liquid solutions.

Vapor Pressure and Osmotic Pressure Equations

NEET N

Chemistry Vapor Pressure Lowering & Osmotic Pressure

\frac{P^\circ - P}{P^\circ} = i x_{solute}

\pi = i C R T

Parameters & Definitions

$P^\circ, P$ are vapor pressures, $i$ is van 't Hoff factor, $x_{solute}$ is mole fraction of solute, $\pi$ is osmotic pressure, $C$ is molarity, $R$ is gas constant, and $T$ is temperature.

Formulas to calculate vapor pressure lowering and osmotic pressure.

van 't Hoff Factor and Degree of Dissociation/Association

NEET N

Chemistry Vapor Pressure Lowering & Osmotic Pressure

\alpha = \frac{i - 1}{n - 1} \quad \text{(Dissociation)}

\beta = \frac{1 - i}{1 - 1/n} \quad \text{(Association)}

Parameters & Definitions

$i$ is the van 't Hoff factor, $\alpha$ is the degree of dissociation, $\beta$ is the degree of association, and $n$ is the number of ions/molecules formed or associated per reactant unit.

Relates the van 't Hoff factor ( $i$ ) to the degree of electrolyte dissociation ( $\alpha$ ) and association ( $\beta$ ).

Boiling and Freezing Point Shifts

NEET N

Chemistry Boiling Elevation & Freezing Depression

\Delta T_b = i K_b m

\Delta T_f = i K_f m

Parameters & Definitions

$\Delta T_b, \Delta T_f$ are temperature shifts, $i$ is van 't Hoff factor, $K_b, K_f$ are molal constants, and $m$ is molality of solution.

Formulas to calculate boiling point elevation and freezing point depression.

Integrated Rate Laws

NEET N

Chemistry Reaction Orders & Integrated Rate Laws

[A]_t = [A]_0 - kt \quad \text{(Zero-Order)}

k = \frac{2.303}{t} \log_{10}\left(\frac{[A]_0}{[A]_t}\right) \quad \text{(First-Order)}

Parameters & Definitions

$[A]_0$ is initial concentration, $[A]_t$ is concentration at time $t$ , and $k$ is rate constant.

Rate constant relations for zero-order and first-order chemical reactions.

Half-Lives

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Chemistry Half-life of Reaction

t_{1/2} = \frac{[A]_0}{2k} \quad \text{(Zero-Order)}

t_{1/2} = \frac{0.693}{k} \quad \text{(First-Order)}

Parameters & Definitions

$[A]_0$ is initial concentration, $k$ is rate constant, and $t_{1/2}$ is half-life.

Half-life relations for zero-order and first-order chemical reactions.

Arrhenius Equation for Temperature Dependence

NEET N

Chemistry Temperature Dependence & Arrhenius Equation

k = A e^{-\frac{E_a}{RT}} \implies \log_{10}\left(\frac{k_2}{k_1}\right) = \frac{E_a}{2.303 R} \left( \frac{T_2 - T_1}{T_1 T_2} \right)

Parameters & Definitions

$k, k_1, k_2$ are rate constants, $A$ is frequency factor, $E_a$ is activation energy, $R$ is gas constant, and $T, T_1, T_2$ are absolute temperatures.

Shows how chemical rate constant varies with temperature based on activation energy.

Crystal Density and Packing Efficiency

Chemistry Crystal Systems & Voids

\rho = \frac{Z \cdot M}{a^3 \cdot N_A}

\text{Packing Fraction} = \frac{Z \cdot \frac{4}{3}\pi r^3}{a^3} \quad \text{(FCC = 74\%, BCC = 68\%, Simple = 52.4\%)}

Parameters & Definitions

$\rho$ is the density, $Z$ is the number of atoms per unit cell, $M$ is the molar mass, $a$ is the edge length, $N_A$ is Avogadro's number, and $r$ is the atomic radius.

Formulas to calculate unit cell density and packing fraction in cubic crystal lattices.

Density of a Cubic Unit Cell

Chemistry Density of Unit Cell

\rho = \frac{z M}{N_A a^3}

Parameters & Definitions

$\rho$ is density, $z$ is number of atoms per unit cell, $M$ is molar mass, $N_A$ is Avogadro's number, and $a$ is edge length of the cubic cell.

Theoretical density of a crystalline solid based on lattice parameters.

Freundlich Adsorption Isotherm

Chemistry Adsorption & Freundlich Isotherm

\frac{x}{m} = k P^{1/n} \quad \left(\frac{1}{n} \le 1\right)

Parameters & Definitions

$x$ is mass of adsorbate, $m$ is mass of adsorbent, $P$ is pressure, and $k, n$ are temperature-dependent constants.

Empirical relationship for the adsorption of gas on solid adsorbent surfaces.

Coagulation Value

Chemistry Colloidal States & Properties

\text{Coagulation Value} = \frac{\text{Millimoles of electrolyte}}{\text{Volume of colloid in Litres}}

Parameters & Definitions

$\text{Coagulation Value}$ is expressed in millimoles per litre of colloid.

Minimum concentration of an electrolyte required to cause coagulation of a sol.

Gold Number

Chemistry Colloidal States & Properties

\text{Gold Number} = \text{mg of protective colloid for } 10\text{ mL gold sol against } 1\text{ mL of } 10\% \text{ NaCl}

Parameters & Definitions

$\text{Gold Number}$ is measured in milligrams.

Defines the protective power of a lyophilic colloid. A lower gold number indicates better protection.

Effective Nuclear Charge

NEET N

Chemistry Periodic Trends in Properties

Z_{\text{eff}} = Z - \sigma

Parameters & Definitions

$Z_{\text{eff}}$ is the effective nuclear charge, $Z$ is atomic number, and $\sigma$ is the shielding constant.

Slater's rule equation for calculating the effective nuclear charge felt by valence electrons.

Pauling Electronegativity Difference

NEET N

Chemistry Periodic Trends in Properties

\chi_A - \chi_B = 0.102 \sqrt{\Delta_E} \quad \text{where } \Delta_E = E_{d(A-B)} - \sqrt{E_{d(A-A)} \cdot E_{d(B-B)}}

Parameters & Definitions

$\chi_A, \chi_B$ are electronegativities, and $E_{d(A-B)}$ represents the bond dissociation energy of $A-B$ bond.

Estimates the electronegativity difference between two bonded atoms using bond dissociation energies in kJ/mol.

Volume Strength of Hydrogen Peroxide

Chemistry Properties & Compounds of Hydrogen

\text{Volume Strength} = 11.2 \times \text{Molarity}

\text{Volume Strength} = 5.6 \times \text{Normality}

Parameters & Definitions

Volume strength is the volume of $O_2$ (in L) released by 1 L of $H_2O_2$ at STP; Molarity and Normality represent solution concentrations.

Relations between volume strength, molarity, and normality of $H_2O_2$ solution.

Solvay Process Net Reaction

Chemistry Alkali & Alkaline Earth Metals

2\text{NaCl} + \text{CaCO}_3 \longrightarrow \text{Na}_2\text{CO}_3 + \text{CaCl}_2

Parameters & Definitions

Reactants are sodium chloride and calcium carbonate; products are sodium carbonate and calcium chloride.

Net overall reaction representing the manufacturing of sodium carbonate via the Solvay process.

Plaster of Paris Preparation

Chemistry Alkali & Alkaline Earth Metals

\text{CaSO}_4 \cdot 2\text{H}_2\text{O} \xrightarrow{120^\circ\text{C}} \text{CaSO}_4 \cdot \frac{1}{2}\text{H}_2\text{O} + \frac{3}{2}\text{H}_2\text{O}

Parameters & Definitions

Reactant is Gypsum, product is Plaster of Paris and steam.

Thermal decomposition of Gypsum to Plaster of Paris.

Borax Bead Thermal Decomposition

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Chemistry General Trends in Groups 13-18

\text{Na}_2\text{B}_4\text{O}_7 \cdot 10\text{H}_2\text{O} \xrightarrow{\Delta} \text{Na}_2\text{B}_4\text{O}_7 \xrightarrow{\Delta} 2\text{NaBO}_2 + \text{B}_2\text{O}_3

Parameters & Definitions

$\text{NaBO}_2$ is sodium metaborate and $\text{B}_2\text{O}_3$ is boric anhydride (boron trioxide).

Thermal swelling and decomposition of borax to form sodium metaborate and boric anhydride.

Xenon Tetrafluoride Hydrolysis

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Chemistry General Trends in Groups 13-18

6\text{XeF}_4 + 12\text{H}_2\text{O} \longrightarrow 4\text{Xe} + 2\text{XeO}_3 + 24\text{HF} + 3\text{O}_2

Parameters & Definitions

$\text{XeF}_4$ is xenon tetrafluoride, and $\text{XeO}_3$ is explosive xenon trioxide.

Complete hydrolysis reaction of xenon tetrafluoride producing xenon gas and xenon trioxide.

Chromate-Dichromate pH-Dependent Equilibrium

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Chemistry First-Row Transition Metals

2\text{CrO}_4^{2-} + 2\text{H}^+ \rightleftharpoons \text{Cr}_2\text{O}_7^{2-} + \text{H}_2\text{O}

Parameters & Definitions

$\text{CrO}_4^{2-}$ is yellow chromate ion (stable in alkaline solution), and $\text{Cr}_2\text{O}_7^{2-}$ is orange dichromate ion (stable in acidic solution).

Reversible pH-dependent equilibrium between yellow chromate and orange dichromate ions.

Dichromate Reduction in Acidic Medium

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Chemistry First-Row Transition Metals

\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6e^- \longrightarrow 2\text{Cr}^{3+} + 7\text{H}_2\text{O}

Parameters & Definitions

$\text{Cr}^{3+}$ is green chromic ion, and $n$ -factor of $\text{Cr}_2\text{O}_7^{2-}$ is 6.

Half-reaction for the reduction of dichromate ion in acidic solution, where chromium is reduced from +6 to +3.

Spin-Only Magnetic Moment Formula

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Chemistry Spin-Only Magnetic Moment

\mu_{spin} = \sqrt{n(n+2)} \text{ B.M.}

Parameters & Definitions

$\mu_{spin}$ is spin-only magnetic moment in Bohr Magnetons (B.M.), and $n$ is number of unpaired electrons.

Calculates magnetic moment of transition metal ions based on unpaired d-electrons.

Shielding Effectiveness Trend

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Chemistry Lanthanoids & Actinoids

\sigma(4f) < \sigma(5d) < \sigma(5p) < \sigma(5s)

Parameters & Definitions

$\sigma$ is shielding constant of respective subshells.

Shielding constant comparison showing the poor shielding power of f-orbitals, which leads to lanthanoid contraction.

General Lanthanoid Configuration

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Chemistry Lanthanoids & Actinoids

[\text{Xe}] \, 4f^{1-14} \, 5d^{0-1} \, 6s^2

Parameters & Definitions

$[\text{Xe}]$ is xenon noble gas core, $4f$ is filling inner f-orbital, $5d$ is transition d-orbital, and $6s$ is valence s-orbital.

General valence shell electronic configuration of the lanthanoid series elements.

Effective Atomic Number (EAN) Rule

NEET N

Chemistry Nomenclature & Isomerism

\text{EAN} = Z - \text{O.S.} + 2 \times \text{C.N.}

Parameters & Definitions

$Z$ is atomic number of metal, $\text{O.S.}$ is oxidation state of metal, and $\text{C.N.}$ is coordination number (number of coordinate bonds).

Calculates the effective atomic number of a central metal atom/ion in a coordination complex.

CFSE for Octahedral Complexes

NEET N

Chemistry Valence Bond & Crystal Field Theory

\text{CFSE} = \left( -0.4 n_{t_{2g}} + 0.6 n_{e_g} \right) \Delta_o + m P

Parameters & Definitions

CFSE is Crystal Field Stabilization Energy, $n_{t_{2g}}$ is number of electrons in $t_{2g}$ orbitals, $n_{e_g}$ is number of electrons in $e_g$ orbitals, $\Delta_o$ is octahedral splitting parameter, $P$ is pairing energy, and $m$ is number of paired electron configurations.

Stabilization energy calculation of d-electrons in octahedral crystal fields.

Ellingham Diagram Thermodynamic Condition

Chemistry Principles & Extraction Processes

\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ < 0

Parameters & Definitions

$\Delta G^\circ$ is standard Gibbs free energy change, $\Delta H^\circ$ is standard enthalpy change, $T$ is temperature, and $\Delta S^\circ$ is standard entropy change.

Thermodynamic spontaneity condition governing the reduction of metal oxides using carbon or other metals.

Mond Process for Nickel Refining

Chemistry Principles & Extraction Processes

\text{Ni} (\text{impure}) + 4\text{CO} \xrightarrow{330-350\text{ K}} \text{Ni(CO)}_4 \xrightarrow{450-470\text{ K}} \text{Ni} (\text{pure}) + 4\text{CO}

Parameters & Definitions

$\text{Ni(CO)}_4$ is volatile nickel tetracarbonyl complex.

Two-step gaseous carbonyl metallurgy process used for the purification of nickel metal.

Steam Distillation Mass Ratio

NEET N

Chemistry Purification Methods (Distillation, Chromatography)

\frac{w_1}{w_2} = \frac{p_1 M_1}{p_2 M_2}

Parameters & Definitions

$w_1, w_2$ are masses of organic compound and water, $p_1, p_2$ are vapor pressures at distillation temperature, and $M_1, M_2$ are molecular weights.

Formula relating the masses of the distilled organic liquid and water to their vapor pressures and molecular weights.

Chromatography Retention Factor

NEET N

Chemistry Purification Methods (Distillation, Chromatography)

R_f = \frac{\text{Distance traveled by substance from baseline}}{\text{Distance traveled by solvent front from baseline}}

Parameters & Definitions

$R_f$ is a dimensionless fraction, representing chromatographic mobility.

Defines the retardation factor ( $R_f$ ) of a compound in thin-layer or paper chromatography.

Nitrogen Percentage by Kjeldahl's Method

NEET N

Chemistry Qualitative & Quantitative Organic Analysis

\% \text{ N} = \frac{1.4 \times N \times V}{w}

Parameters & Definitions

$N$ is normality of acid, $V$ is volume of acid consumed by ammonia (in mL), and $w$ is mass of organic sample analyzed (in grams).

Quantitative estimation of nitrogen percentage in organic samples.

Nitrogen Percentage by Dumas' Method

NEET N

Chemistry Qualitative & Quantitative Organic Analysis

\% \text{ N} = \frac{28 \times V_{STP} \times 100}{22400 \times w}

Parameters & Definitions

$V_{STP}$ is volume of nitrogen collected at STP in mL, and $w$ is mass of organic compound in grams.

Quantitative estimation of nitrogen by measuring volume of nitrogen collected at STP.

Halogen Percentage by Carius Method

NEET N

Chemistry Qualitative & Quantitative Organic Analysis

\% \text{ Cl} = \frac{35.5}{143.5} \times \frac{m_{AgCl}}{w} \times 100

\% \text{ Br} = \frac{80}{188} \times \frac{m_{AgBr}}{w} \times 100

\% \text{ I} = \frac{127}{235} \times \frac{m_{AgI}}{w} \times 100

Parameters & Definitions

$m_{AgCl}, m_{AgBr}, m_{AgI}$ are the masses of the respective silver halide precipitates formed (in grams), and $w$ is the mass of the organic compound analyzed.

Quantitative estimation of halogens (Chlorine, Bromine, Iodine) from silver halide precipitates.

Sulfur Percentage by Carius Method

NEET N

Chemistry Qualitative & Quantitative Organic Analysis

\% \text{ S} = \frac{32}{233} \times \frac{m_{BaSO_4}}{w} \times 100

Parameters & Definitions

$m_{BaSO_4}$ is the mass of the barium sulfate precipitate formed (in grams), and $w$ is the mass of the organic compound analyzed.

Quantitative estimation of sulfur by converting it to barium sulfate precipitate.

Phosphorus Percentage Estimation

NEET N

Chemistry Qualitative & Quantitative Organic Analysis

\% \text{ P} = \frac{62}{222} \times \frac{m_{Mg_2P_2O_7}}{w} \times 100

Parameters & Definitions

$m_{Mg_2P_2O_7}$ is the mass of magnesium pyrophosphate precipitate formed (in grams), and $w$ is the mass of the organic compound analyzed.

Quantitative estimation of phosphorus by precipitating it as magnesium pyrophosphate.

Specific Optical Rotation

NEET N

Chemistry Nomenclature, Shapes & Isomerism

[\alpha]_\lambda^T = \frac{\alpha_{\text{observed}}}{l \cdot c}

Parameters & Definitions

$[\alpha]_\lambda^T$ is specific rotation, $\alpha_{\text{observed}}$ is observed rotation in degrees, $l$ is tube path length in decimeters, and $c$ is concentration in g/mL.

Calculates specific optical rotation of an optically active substance in solution.

Stereoisomer Count for Unsymmetrical Molecules

NEET N

Chemistry Nomenclature, Shapes & Isomerism

N = 2^n

Parameters & Definitions

$N$ is total number of stereoisomers, and $n$ is the number of chiral centers.

Calculates total number of stereoisomers (enantiomers + diastereomers) for an organic molecule with $n$ unsymmetric chiral centers.

Acid Dissociation Constant and pKa Relation

NEET N

Chemistry Electronic Displacements & Reaction Intermediates

pK_a = -\log_{10} K_a \implies \text{Acidic Strength} \propto K_a \propto \frac{1}{pK_a}

Parameters & Definitions

$K_a$ is acid dissociation constant, and $pK_a$ is the acid index (smaller $pK_a$ means stronger acid).

Relates the acid dissociation constant ( $K_a$ ) to its logarithmic index ( $pK_a$ ), indicating relative organic acidity.

Hyperconjugation Alpha-Hydrogen Stability

NEET N

Chemistry Electronic Displacements & Reaction Intermediates

\text{Carbocation/Radical Stability} \propto N_{\alpha\text{-H}}

Parameters & Definitions

$N_{\alpha\text{-H}}$ is the number of hydrogen atoms attached to carbons directly adjacent to the sp2 carbocation/radical center.

Relates the stability of carbocations and carbon free radicals to the number of hyperconjugable $\alpha$ -hydrogens.

Double Bond Equivalent (Degree of Unsaturation)

NEET N

Chemistry Alkanes, Alkenes, Alkynes & Aromatic Hydrocarbons

\text{DBE} = C + 1 - \frac{H + X - N}{2}

Parameters & Definitions

$C$ is number of carbon atoms, $H$ is hydrogen atoms, $X$ is halogen atoms, and $N$ is nitrogen atoms in the molecular formula.

Formula to calculate the number of rings or pi bonds in an organic molecule.

SN1 Reaction Kinetic Rate Law

NEET N

Chemistry Nucleophilic Substitution (SN1 & SN2) & Elimination

\text{Rate} = k [R\text{-}X]

Parameters & Definitions

$k$ is the rate constant, and $[R\text{-}X]$ is the concentration of the alkyl halide substrate.

First-order rate equation governing unimolecular nucleophilic substitution ( $S_N1$ ) reactions.

SN2 Reaction Kinetic Rate Law

NEET N

Chemistry Nucleophilic Substitution (SN1 & SN2) & Elimination

\text{Rate} = k [R\text{-}X][Nu^-]

Parameters & Definitions

$[R\text{-}X]$ is substrate concentration, and $[Nu^-]$ is nucleophile concentration.

Second-order rate equation governing bimolecular nucleophilic substitution ( $S_N2$ ) reactions.

Reimer-Tiemann Phenol Formylation

NEET N

Chemistry Preparations & Chemical Properties

\text{C}_6\text{H}_5\text{OH} + \text{CHCl}_3 + 3\text{NaOH} \longrightarrow o\text{-C}_6\text{H}_4(\text{OH})\text{CHO} + 3\text{NaCl} + 2\text{H}_2\text{O}

Parameters & Definitions

Reactants are phenol, chloroform, and sodium hydroxide; product is $o$ -salicylaldehyde.

Formylation of phenol to salicylaldehyde using chloroform and sodium hydroxide.

Hydroboration-Oxidation Net Reaction

NEET N

Chemistry Preparations & Chemical Properties

3R\text{-CH=CH}_2 + \text{BH}_3 \xrightarrow{\text{H}_2\text{O}_2 / \text{OH}^-} 3R\text{-CH}_2\text{-CH}_2\text{-OH} + \text{B(OH)}_3

Parameters & Definitions

Reactants are alkene and borane, giving a primary alcohol and boric acid.

Anti-Markovnikov hydration of an alkene to form a primary alcohol via hydroboration and oxidation.

Aldol Self-Condensation Reaction

NEET N

Chemistry Nucleophilic Addition & Carbonyl Condensations

2CH_3\text{-CHO} \xrightarrow{\text{dil. NaOH}} CH_3\text{-CH(OH)-CH}_2\text{-CHO} \xrightarrow{\Delta} CH_3\text{-CH=CH-CHO} + \text{H}_2\text{O}

Parameters & Definitions

Reactant is acetaldehyde; product is crotonaldehyde (but-2-enal).

Self-condensation of acetaldehyde in dilute base followed by dehydration to form crotonaldehyde (\alpha,\beta-unsaturated aldehyde).

Cannizzaro Reaction of Benzaldehyde

NEET N

Chemistry Nucleophilic Addition & Carbonyl Condensations

2\text{C}_6\text{H}_5\text{-CHO} + \text{NaOH} \longrightarrow \text{C}_6\text{H}_5\text{-COONa} + \text{C}_6\text{H}_5\text{-CH}_2\text{OH}

Parameters & Definitions

Reactant is benzaldehyde; products are sodium benzoate and benzyl alcohol.

Redox disproportional of non-enolizable aldehydes (e.g. benzaldehyde) in concentrated base.

Hoffmann Bromamide Degradation

NEET N

Chemistry Basicity & Synthetic Reactions of Amines

R\text{-CONH}_2 + \text{Br}_2 + 4\text{KOH} \longrightarrow R\text{-NH}_2 + \text{K}_2\text{CO}_3 + 2\text{KBr} + 2\text{H}_2\text{O}

Parameters & Definitions

$R\text{-CONH}_2$ is primary amide, and $R\text{-NH}_2$ is primary amine product.

Degradation of an amide to a primary amine with one fewer carbon atom using bromine and base.

Carbylamine Primary Amine Test

NEET N

Chemistry Basicity & Synthetic Reactions of Amines

R\text{-NH}_2 + \text{CHCl}_3 + 3\text{KOH} \longrightarrow R\text{-NC} + 3\text{KCl} + 3\text{H}_2\text{O}

Parameters & Definitions

$R\text{-NH}_2$ is primary amine, and $R\text{-NC}$ is alkyl/aryl isocyanide.

Diagnostic test for primary amines (both aliphatic and aromatic) forming an offensively smelling isocyanide.

Sucrose Acid Hydrolysis (Inversion of Cane Sugar)

NEET N

Chemistry Carbohydrates, Proteins & Nucleic Acids

\text{C}_{12}\text{H}_{22}\text{O}_{11} + \text{H}_2\text{O} \xrightarrow{\text{H}^+} \text{C}_6\text{H}_{12}\text{O}_6 \, (\text{D-glucose}) + \text{C}_6\text{H}_{12}\text{O}_6 \, (\text{D-fructose})

Parameters & Definitions

Specific rotation changes from $+66.5^\circ$ (sucrose) to a net laevorotatory mixture of products.

Hydrolysis of sucrose to form D-glucose and D-fructose, resulting in inversion of optical rotation.

Isoelectric Point of Simple Amino Acids

NEET N

Chemistry Carbohydrates, Proteins & Nucleic Acids

pI = \frac{pK_{a1} + pK_{a2}}{2}

Parameters & Definitions

$pI$ is isoelectric point, $pK_{a1}$ is logarithmic acid dissociation constant of carboxylic group, and $pK_{a2}$ is that of the ammonium group.

Calculates the isoelectric point ( $pI$ ) of an amino acid lacking an ionizable side chain.

Nylon-6,6 Preparation

Chemistry Polymers Structure & Polymerization

n\text{HOOC-(CH}_2)_4\text{-COOH} + n\text{H}_2\text{N-(CH}_2)_6\text{-NH}_2 \longrightarrow \text{[-CO-(CH}_2)_4\text{-CONH-(CH}_2)_6\text{-NH-]} _n + 2n\text{H}_2\text{O}

Parameters & Definitions

Reactants are adipic acid and hexamethylenediamine; product is the Nylon-6,6 repeat unit.

Condensation copolymerization of adipic acid and hexamethylenediamine to form Nylon-6,6 polyamide.

Buna-S Synthetic Rubber Synthesis

Chemistry Polymers Structure & Polymerization

n\text{CH}_2\text{=CH-CH=CH}_2 + n\text{C}_6\text{H}_5\text{-CH=CH}_2 \longrightarrow \text{[-CH}_2\text{-CH=CH-CH}_2\text{-CH(C}_6\text{H}_5)\text{-CH}_2\text{-]} _n

Parameters & Definitions

Reactants are butadiene and styrene; product is butadiene-styrene copolymer.

Addition copolymerization of buta-1,3-diene and styrene in 3:1 ratio to form Buna-S elastomer.

Saponification of Tristearin (Soap Formation)

Chemistry Medicines, Food Preservatives & Soaps

(\text{C}_{17}\text{H}_{35}\text{COO})_3\text{C}_3\text{H}_5 + 3\text{NaOH} \longrightarrow 3\text{C}_{17}\text{H}_{35}\text{COONa} + \text{C}_3\text{H}_5(\text{OH})_3

Parameters & Definitions

$\text{C}_{17}\text{H}_{35}\text{COONa}$ is sodium stearate (soap) and $\text{C}_3\text{H}_5(\text{OH})_3$ is glycerol.

Alkali hydrolysis of tristearin fat using sodium hydroxide to yield sodium stearate soap and glycerol.

Aspirin Preparation (Acetylation of Salicylic Acid)

Chemistry Medicines, Food Preservatives & Soaps

o\text{-HOC}_6\text{H}_4\text{COOH} + (\text{CH}_3\text{CO})_2\text{O} \longrightarrow o\text{-CH}_3\text{COOC}_6\text{H}_4\text{COOH} + \text{CH}_3\text{COOH}

Parameters & Definitions

Reactants are salicylic acid and acetic anhydride; products are aspirin and acetic acid.

Acetylation of salicylic acid's phenolic hydroxyl group using acetic anhydride to form acetylsalicylic acid (Aspirin).

Acid Rain Sulfuric Acid Formation

Chemistry Environmental Pollutants & Green Chemistry

2\text{SO}_2 + \text{O}_2 + 2\text{H}_2\text{O} \longrightarrow 2\text{H}_2\text{SO}_4

Parameters & Definitions

Reactants are sulfur dioxide gas, oxygen, and atmospheric water vapor; product is sulfuric acid.

Atmospheric oxidation of sulfur dioxide in water droplets leading to sulfuric acid formation in acid rain.

Biochemical Oxygen Demand (BOD)

Chemistry Environmental Pollutants & Green Chemistry

\text{BOD} = \text{Clean Water} \, (< 5 \text{ ppm}), \quad \text{Polluted Water} \, (\ge 17 \text{ ppm})

Parameters & Definitions

BOD is measured in parts per million (ppm) or mg/L.

Measure of water pollution denoting the amount of dissolved oxygen needed by aerobic biological organisms to break down organic material.

Prussian Blue Complex Formation (Lassaigne's Test)

NEET N

Chemistry Qualitative Tests & Salt Analysis

4\text{Fe}^{3+} + 3[\text{Fe(CN)}_6]^{4-} \longrightarrow \text{Fe}_4[\text{Fe(CN)}_6]_3

Parameters & Definitions

$\text{Fe}_4[\text{Fe(CN)}_6]_3$ is ferric ferrocyanide (Prussian blue precipitate).

Confirmatory test reaction for nitrogen in organic compounds, yielding a characteristic Prussian blue precipitate.

Halogen Percentage by Carius Method

NEET N

Chemistry Qualitative Tests & Salt Analysis

\% X = \frac{\text{Atomic Mass of } X}{\text{Molar Mass of } \text{Ag}X} \times \frac{\text{Mass of } \text{Ag}X \text{ formed}}{\text{Mass of Organic Compound}} \times 100\%

Parameters & Definitions

$X$ is halogen (Cl, Br, I), $\text{Ag}X$ is silver halide precipitate, and masses are measured in grams.

Quantitative formula for the estimation of halogens in organic compounds using the Carius method.

Taxonomic Categories (Obligate Hierarchy)

NEET N

Biology Taxonomic Hierarchy & Nomenclature

\text{Kingdom} \to \text{Phylum/Division} \to \text{Class} \to \text{Order} \to \text{Family} \to \text{Genus} \to \text{Species}

Parameters & Definitions

Each level is a taxon. Species is the basic unit of classification. Binomial nomenclature assigns a two-part Latin name: $\text{Genus + species epithet}$ (e.g., $\textit{Homo sapiens}$ ).

The mandatory sequence of taxonomic ranks used in biological classification from broadest to most specific.

Whittaker's Five Kingdoms

NEET N

Biology Five Kingdom Classification

\text{5 Kingdoms} = \{ \text{Monera, Protista, Fungi, Plantae, Animalia} \}

\text{Criteria} = \{ \text{Cell structure, Thallus org., Nutrition, Reproduction, Phylogeny} \}

Parameters & Definitions

Monera: prokaryotes (bacteria, cyanobacteria); Protista: unicellular eukaryotes; Fungi: heterotrophic, cell wall of chitin; Plantae: autotrophic, cell wall of cellulose; Animalia: heterotrophic, no cell wall.

R.H. Whittaker's classification scheme based on cell structure, body organisation, mode of nutrition, reproduction, and phylogenetic relationships.

Resolving Power of Microscopes

NEET N

Biology Cell Dimensions & Resolution

d = \frac{0.61 \lambda}{n \sin \theta}

\text{Human eye resolution} \approx 100 \, \mu\text{m}

\text{Light microscope} \approx 0.2 \, \mu\text{m}

\text{Electron microscope} \approx 0.2 \, \text{nm}

Parameters & Definitions

$d$ is the resolving power (limit of resolution), $\lambda$ is the wavelength of light/electron beam, $n$ is the refractive index, $\theta$ is the half-angle of the cone of light entering the objective.

The minimum distance between two points that can be distinguished as separate. Determines visibility of cellular structures.

Membrane Lipid-Protein Ratio

NEET N

Biology Fluid Mosaic Model of Membrane

\text{Protein : Lipid ratio} \approx 52\% : 40\%

\text{Carbohydrates} \approx 8\%

Parameters & Definitions

Human erythrocyte membrane. Lipids include phospholipids, cholesterol, and glycolipids. Integral proteins span the membrane; peripheral proteins are on the surface.

The composition of the plasma membrane varies between cell types — erythrocyte membranes are commonly used in NEET questions.

Michaelis-Menten Equation

NEET N

Biology Enzyme Kinetics

V = \frac{V_{\max} [S]}{K_m + [S]}

\text{At } [S] = K_m, \quad V = \frac{V_{\max}}{2}

Parameters & Definitions

$V$ is the reaction velocity; $V_{\max}$ is the maximum reaction velocity at substrate saturation; $[S]$ is the substrate concentration; $K_m$ is the Michaelis constant (substrate conc. at half $V_{\max}$ ). Lower $K_m$ means higher enzyme-substrate affinity.

Relates the velocity of an enzyme-catalyzed reaction to substrate concentration.

Enzyme Turnover Number

NEET N

Biology Enzyme Kinetics

k_{\text{cat}} = \frac{V_{\max}}{[E_T]}

\text{Carbonic anhydrase: } k_{\text{cat}} \approx 36 \times 10^6 \text{ s}^{-1}

Parameters & Definitions

$k_{\text{cat}}$ is the catalytic constant (turnover number); $V_{\max}$ is maximum velocity; $[E_T]$ is the total enzyme concentration. Carbonic anhydrase is one of the fastest known enzymes.

The number of substrate molecules converted to product per enzyme molecule per second at saturation.

Peptide Bond & Water Release

NEET N

Biology Amino Acids & Protein Structure

\text{Peptide bonds} = n - 1

\text{Water molecules released} = n - 1

Parameters & Definitions

$n$ is the number of amino acid residues in the polypeptide chain. Each peptide bond (–CO–NH–) is formed by a dehydration/condensation reaction releasing one water molecule.

The number of peptide bonds and water molecules released during polypeptide synthesis from amino acids.

Phosphodiester & Hydrogen Bonds in DNA

NEET N

Biology Nucleic Acid Calculations

\text{Total H-bonds} = 2(A) + 3(G) \quad \text{(or } 2T + 3C\text{)}

\text{Phosphodiester bonds (per strand)} = N - 1

\text{Total Phosphodiester bonds (dsDNA)} = 2(N - 1)

\text{Total nucleotides (dsDNA)} = 2N

Parameters & Definitions

$A$ , $T$ , $G$ , $C$ are the number of Adenine, Thymine, Guanine, Cytosine bases; $N$ is the number of base pairs; A–T pairs have 2 hydrogen bonds; G–C pairs have 3 hydrogen bonds.

Formulas to calculate total bonds in a double-stranded DNA molecule from its base pair composition.

Cell Cycle Phase Duration

NEET N

Biology Cell Cycle Phases & Duration

t_{\text{cell cycle}} = t_{G_1} + t_S + t_{G_2} + t_M

t_{G_1} \approx 11 \text{ hr}, \quad t_S \approx 8 \text{ hr}, \quad t_{G_2} \approx 4 \text{ hr}, \quad t_M \approx 1 \text{ hr}

\text{Interphase} = G_1 + S + G_2 \approx 95\% \text{ of cell cycle}

Parameters & Definitions

$G_1$ is the first gap phase (growth); $S$ is the synthesis phase (DNA replication); $G_2$ is the second gap phase; $M$ is mitosis. Interphase accounts for approximately 95% of the total cell cycle duration.

Approximate time distribution across cell cycle phases in a typical human cell (~24 hr cycle).

Cell Division Number Formulas

NEET N

Biology Mitotic & Meiotic Division Calculations

\text{Cells after } n \text{ mitotic divisions} = 2^n

\text{Mitotic divisions needed for } N \text{ cells} = N - 1

\text{Gametes from } n \text{ meiotic divisions} = 4n \text{ (spermatogenesis)}

\text{Ova from } n \text{ meiotic divisions} = n \text{ (oogenesis)}

Parameters & Definitions

$n$ is the number of divisions (mitotic) or the number of primary cells undergoing meiosis. In spermatogenesis, 1 primary spermatocyte yields 4 sperms. In oogenesis, 1 primary oocyte yields 1 ovum + 3 polar bodies.

Formulas to calculate daughter cells produced after multiple rounds of mitosis or meiosis.

DNA Content Changes During Division

NEET N

Biology Mitotic & Meiotic Division Calculations

\text{G}_1 \text{ phase}: 2n, 2C

\text{After S phase}: 2n, 4C

\text{After Mitosis}: 2n, 2C

\text{After Meiosis I}: n, 2C

\text{After Meiosis II}: n, C

Parameters & Definitions

$n$ represents the haploid chromosome number; $C$ represents the haploid DNA content. $2n$ = diploid, $2C$ = DNA amount in a diploid G1 cell, $4C$ = DNA amount after S phase replication.

Tracking chromosome number (n) and DNA content (C) across mitosis and meiosis stages.

Water Potential Components

NEET N

Biology Water Potential & Osmosis

\Psi_w = \Psi_s + \Psi_p

\Psi_s = -iCRT \quad \text{(Van't Hoff Equation for osmotic pressure)}

\text{DPD} = \text{OP} - \text{TP}

Parameters & Definitions

$\Psi_w$ is water potential; $\Psi_s$ is solute/osmotic potential (always negative); $\Psi_p$ is pressure/turgor potential; $i$ is ionization constant; $C$ is molar concentration; $R$ is gas constant; $T$ is absolute temperature. DPD = Diffusion Pressure Deficit; OP = Osmotic Pressure; TP = Turgor Pressure.

The water potential of a cell determines the direction of water movement between cells and from the soil into plant roots.

Plasmolysis Conditions

NEET N

Biology Water Potential & Osmosis

\text{Hypotonic: } \Psi_{\text{solution}} > \Psi_{\text{cell}} \implies \text{Endosmosis (cell swells)}

\text{Hypertonic: } \Psi_{\text{solution}} < \Psi_{\text{cell}} \implies \text{Exosmosis (plasmolysis)}

\text{Isotonic: } \Psi_{\text{solution}} = \Psi_{\text{cell}} \implies \text{Flaccid (no net movement)}

Parameters & Definitions

$\Psi_{\text{solution}}$ is the water potential of the external solution; $\Psi_{\text{cell}}$ is the water potential of the cell sap. Incipient plasmolysis occurs when turgor pressure ( $\Psi_p$ ) = 0.

Conditions for a plant cell in different solution types — determining water movement by comparing osmotic potentials.

Overall Equation of Photosynthesis

NEET N

Biology Photosynthesis

6\text{CO}_2 + 12\text{H}_2\text{O} \xrightarrow{h\nu} \text{C}_6\text{H}_{12}\text{O}_6 + 6\text{H}_2\text{O} + 6\text{O}_2

\text{Quantum yield} = \frac{\text{molecules of O}_2 \text{ evolved}}{\text{quanta of light absorbed}} = \frac{1}{8}

Parameters & Definitions

$h\nu$ represents light energy (photons); 12 water molecules are the source of oxygen ( $6\text{O}_2$ ); $\text{C}_6\text{H}_{12}\text{O}_6$ is glucose. Minimum 8 photons required to release 1 molecule of $\text{O}_2$ .

The balanced chemical equation for the overall process of photosynthesis in green plants.

ATP & NADPH Balance in Light Reactions

NEET N

Biology Photosynthesis

2\text{H}_2\text{O} \to 4\text{H}^+ + 4e^- + \text{O}_2 \quad \text{(Photolysis of Water)}

\text{Non-cyclic: } 12\text{H}_2\text{O} \to 12\text{NADPH} + 18\text{ATP (for fixing 6 CO}_2\text{)}

\text{Cyclic: only ATP produced, no NADPH, no O}_2 \text{ evolved}

Parameters & Definitions

Non-cyclic photophosphorylation involves both PS I and PS II. Cyclic photophosphorylation involves only PS I and produces ATP only. The Calvin cycle requires 18 ATP and 12 NADPH to fix 6 CO₂ into 1 glucose.

Products generated per molecule of water split and per O₂ evolved during the light-dependent reactions.

Calvin Cycle (C₃ Pathway) Requirements

NEET N

Biology Photosynthesis

\text{For 1 glucose (6 CO}_2 \text{ fixed):}

\text{ATP required} = 18

\text{NADPH required} = 12

\text{Per CO}_2 \text{ fixed: 3 ATP + 2 NADPH}

Parameters & Definitions

The Calvin cycle has 3 stages: Carbon fixation (RuBisCO), Reduction, and Regeneration of RuBP. For each CO₂ fixed, 3 ATP and 2 NADPH are consumed. Net product for 6 turns = 1 glucose (G3P).

The total ATP and NADPH consumed in the Calvin cycle for the synthesis of one molecule of glucose.

CO₂ Compensation Point

NEET N

Biology Photosynthesis

\text{At compensation point: Rate of photosynthesis} = \text{Rate of respiration}

\text{Net CO}_2 \text{ exchange} = 0

\text{C}_3 \text{ plants: compensation point} \approx 25\text{-}100 \text{ ppm CO}_2

\text{C}_4 \text{ plants: compensation point} \approx 0\text{-}10 \text{ ppm CO}_2

Parameters & Definitions

C₃ plants have higher compensation point due to photorespiration losses. C₄ plants have a CO₂-concentrating mechanism (Hatch-Slack pathway) that virtually eliminates photorespiration.

The CO₂ concentration at which the rate of photosynthesis exactly equals the rate of respiration.

Overall Equation of Aerobic Respiration

NEET N

Biology Cellular Respiration & ATP Yield

\text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2 \to 6\text{CO}_2 + 6\text{H}_2\text{O} + \text{Energy}

\text{Net ATP yield (theoretical max)} = 36 \text{ or } 38 \text{ ATP}

\text{Net ATP yield (revised estimate)} \approx 30 \text{ or } 32 \text{ ATP}

Parameters & Definitions

36 ATP if malate-aspartate shuttle is used (in heart/liver); 38 ATP is the older estimate. The revised estimate of 30–32 accounts for the actual H⁺/ATP ratio across the inner mitochondrial membrane.

The complete balanced equation and net ATP yield from oxidation of one glucose molecule.

Stage-wise ATP Balance Sheet

NEET N

Biology Cellular Respiration & ATP Yield

\text{Glycolysis: } 2 \text{ ATP} + 2 \text{ NADH} \quad (\text{net, in cytoplasm})

\text{Pyruvate} \to \text{Acetyl CoA: } 2 \text{ NADH}

\text{Krebs Cycle } (\times 2)\text{: } 2 \text{ ATP} + 6 \text{ NADH} + 2 \text{ FADH}_2

\text{ETC: } 1 \text{ NADH} \to 2.5 \text{ ATP}, \quad 1 \text{ FADH}_2 \to 1.5 \text{ ATP}

\text{Total NADH} = 10, \quad \text{Total FADH}_2 = 2

Parameters & Definitions

Glycolysis occurs in cytoplasm; Krebs cycle and ETC in mitochondria. 10 NADH × 2.5 = 25 ATP; 2 FADH₂ × 1.5 = 3 ATP; 4 substrate-level ATP. Total ≈ 32 ATP (revised).

ATP, NADH, and FADH₂ generated at each stage of aerobic respiration of one glucose.

Respiratory Quotient (RQ)

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Biology Cellular Respiration & ATP Yield

\text{RQ} = \frac{\text{Volume of CO}_2 \text{ released}}{\text{Volume of O}_2 \text{ consumed}}

\text{Carbohydrates: RQ} = 1.0

\text{Fats: RQ} \approx 0.7

\text{Proteins: RQ} \approx 0.8

\text{Organic acids: RQ} > 1.0

Parameters & Definitions

RQ indicates the type of substrate being respired. Carbohydrates give RQ = 1 (balanced exchange). Fats need more O₂ (RQ < 1). Organic acids like malic acid yield RQ > 1 (e.g., RQ for malic acid = 1.33).

The ratio of CO₂ released to O₂ consumed during cellular respiration, varies by substrate.

Anaerobic Respiration / Fermentation

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Biology Cellular Respiration & ATP Yield

\text{C}_6\text{H}_{12}\text{O}_6 \xrightarrow{\text{Yeast}} 2\text{C}_2\text{H}_5\text{OH} + 2\text{CO}_2 + 2\text{ATP}

\text{C}_6\text{H}_{12}\text{O}_6 \xrightarrow{\text{Muscle}} 2\text{C}_3\text{H}_6\text{O}_3 + 2\text{ATP}

Parameters & Definitions

Alcoholic fermentation occurs in yeast producing ethanol and CO₂. Lactic acid fermentation occurs in animal muscle cells under oxygen debt. Both produce only 2 ATP per glucose (substrate-level phosphorylation in glycolysis).

Equations for alcoholic and lactic acid fermentation under anaerobic conditions.

Essential Elements & Critical Concentration

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Biology Mineral Nutrition & Deficiency

\text{Macronutrients (> 10 mmol/kg DW): N, P, K, Ca, Mg, S}

\text{Micronutrients (< 10 mmol/kg DW): Fe, Mn, Zn, Cu, Mo, B, Cl, Ni}

\text{Total essential elements} = 17

Parameters & Definitions

DW = dry weight of plant tissue. 17 essential elements include C, H, O (from air/water) + 6 macronutrients + 8 micronutrients. Critical concentration is the concentration below which plant growth is retarded.

Criteria for element essentiality and the concept of critical concentration for plant nutrition.

Biological Nitrogen Fixation Equation

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Biology Mineral Nutrition & Deficiency

\text{N}_2 + 8e^- + 8\text{H}^+ + 16\text{ATP} \xrightarrow{\text{Nitrogenase}} 2\text{NH}_3 + \text{H}_2 + 16\text{ADP} + 16\text{P}_i

Parameters & Definitions

Nitrogenase is a Mo-Fe protein that requires anaerobic conditions. The reaction requires 16 ATP per N₂ fixed. Leghemoglobin in root nodules provides the microaerobic environment. H₂ is an obligatory byproduct.

The overall reaction catalyzed by the nitrogenase enzyme complex in nitrogen-fixing organisms.

Transpiration Pull & Root Pressure

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Biology Transport in Plants

\Psi_{\text{leaf}} < \Psi_{\text{stem}} < \Psi_{\text{root}} < \Psi_{\text{soil}}

\text{Transpiration Pull Magnitude} \approx -10 \text{ to } -30 \text{ bar}

\text{Root pressure} \approx 1\text{-}2 \text{ bar}

Parameters & Definitions

Water moves from higher water potential (soil) to lower water potential (leaf mesophyll → atmosphere). The transpiration pull (cohesion-tension theory) is the dominant mechanism. Root pressure is insufficient alone for tall trees.

Forces driving the ascent of sap in xylem and factors affecting transpiration rate.

Münch Mass Flow Hypothesis (Phloem Transport)

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Biology Transport in Plants

\text{Source (leaf): sucrose loading} \to \Psi_s \downarrow \to \Psi_w \downarrow \to \text{water enters} \to \text{pressure} \uparrow

\text{Sink (root): sucrose unloading} \to \Psi_s \uparrow \to \Psi_w \uparrow \to \text{water exits} \to \text{pressure} \downarrow

\text{Phloem velocity} \approx 1 \text{ cm/min}

Parameters & Definitions

Sucrose is actively loaded into sieve tube elements at source, lowering water potential and drawing water from xylem. At sink, sucrose is unloaded, increasing water potential. The resulting turgor pressure gradient drives bulk flow.

The pressure-driven bulk flow of phloem sap from source (leaves) to sink (roots, fruits, storage organs).

Absolute & Relative Growth Rates

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Biology Plant Growth & Development

\text{AGR} = \frac{W_2 - W_1}{t_2 - t_1} \quad \text{(Absolute Growth Rate)}

\text{RGR} = \frac{W_2 - W_1}{W_1 \cdot (t_2 - t_1)} \quad \text{(Relative Growth Rate)}

W_t = W_0 e^{rt} \quad \text{(Exponential Growth)}

Parameters & Definitions

$W_1$ and $W_2$ are initial and final size/mass at times $t_1$ and $t_2$ ; $r$ is the specific growth rate; $W_0$ and $W_t$ are sizes at time 0 and $t$ respectively.

Mathematical expressions for measuring plant growth over time.

Cross Ratios & Probability

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Biology Mendelian & Non-Mendelian Ratios

\text{Monohybrid Phenotypic Ratio} = 3 : 1

\text{Monohybrid Genotypic Ratio} = 1 : 2 : 1

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

\text{Monohybrid Test Cross} = 1 : 1

\text{Dihybrid Test Cross} = 1 : 1 : 1 : 1

Parameters & Definitions

Ratios are based on F₂ generation from true-breeding parents. Monohybrid cross involves 1 trait; Dihybrid cross involves 2 independent traits. Test cross involves crossing F₁ hybrid with homozygous recessive parent.

Standard phenotypic and genotypic ratios resulting from Monohybrid, Dihybrid, and Test crosses.

Modified Mendelian Ratios (Gene Interactions)

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Biology Mendelian & Non-Mendelian Ratios

\text{Incomplete Dominance: } 1 : 2 : 1 \text{ (Phenotypic = Genotypic)}

\text{Codominance: } 1 : 2 : 1 \quad (\text{e.g., } I^A I^A : I^A I^B : I^B I^B)

\text{Complementary genes: } 9 : 7

\text{Supplementary / Epistasis: } 9 : 3 : 4 \text{ (Recessive epistasis)}

\text{Duplicate genes: } 15 : 1

\text{Inhibitory genes: } 13 : 3

Parameters & Definitions

All are modifications of the standard 9:3:3:1 dihybrid ratio. Incomplete dominance shows blending (e.g., red × white → pink snapdragons). Codominance: both alleles express (e.g., ABO blood groups).

Non-Mendelian dihybrid ratios arising from epistasis and other gene interactions.

Hardy-Weinberg Equilibrium

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Biology Hardy-Weinberg Principle

p + q = 1 \quad \text{(Allele Frequencies)}

p^2 + 2pq + q^2 = 1 \quad \text{(Genotypic Frequencies)}

Parameters & Definitions

$p$ is the frequency of the dominant allele ( $A$ ); $q$ is the frequency of the recessive allele ( $a$ ); $p^2$ = freq. of $AA$ ; $2pq$ = freq. of $Aa$ ; $q^2$ = freq. of $aa$ . Five conditions: large population, random mating, no mutation, no migration, no selection.

Mathematical equations predicting allele and genotype frequencies in a non-evolving population.

Sex-Linked Trait Probabilities

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Biology Sex-Linked Inheritance & Probability

\text{Carrier female} \times \text{Normal male: } X^C X^c \times X^C Y

\text{Daughter: } \frac{1}{2} \text{ carrier, } \frac{1}{2} \text{ normal}

\text{Son: } \frac{1}{2} \text{ affected, } \frac{1}{2} \text{ normal}

P(\text{affected child}) = \frac{1}{4}

Parameters & Definitions

$X^C$ is the X-chromosome with the normal allele; $X^c$ is the X-chromosome with the recessive allele; $Y$ lacks the corresponding gene. X-linked recessive conditions predominantly affect males as they are hemizygous.

Probability calculations for X-linked recessive traits (e.g., colour blindness, haemophilia).

Recombination Frequency & Gene Mapping

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Biology Linkage & Recombination Frequency

\text{RF} = \frac{\text{Number of recombinant offspring}}{\text{Total offspring}} \times 100\%

1\% \text{ RF} = 1 \text{ centiMorgan (cM) map distance}

\text{RF} \leq 50\% \quad \text{(if } 50\%, \text{genes are unlinked/on different chromosomes)}

Parameters & Definitions

RF = recombination frequency; cM = centiMorgan (1 map unit). Linked genes show RF < 50%. Greater physical distance = higher RF. Genes on different chromosomes show 50% recombination (independent assortment).

Calculation of recombination frequency (RF) between linked genes and its use in chromosome mapping.

Probability Rules in Genetics

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Biology Pedigree Analysis & Probability

P(A \text{ and } B) = P(A) \times P(B) \quad \text{(Multiplication Rule)}

P(A \text{ or } B) = P(A) + P(B) \quad \text{(Addition Rule)}

P(\text{Aa from Aa} \times \text{Aa}) = \frac{1}{2}

P(\text{aa from Aa} \times \text{Aa}) = \frac{1}{4}

Parameters & Definitions

Multiplication rule applies for independent events occurring together. Addition rule applies for mutually exclusive outcomes. Used extensively in pedigree analysis to predict probability of affected offspring.

Fundamental probability rules applied to genetic crosses and pedigree analysis.

ABO Blood Group System

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Biology ABO & Rh Blood Group Genetics

\text{Alleles: } I^A, I^B \text{ (codominant)}, \; i \text{ (recessive)}

\text{Blood Group A: } I^A I^A \text{ or } I^A i

\text{Blood Group B: } I^B I^B \text{ or } I^B i

\text{Blood Group AB: } I^A I^B \quad \text{(Codominance)}

\text{Blood Group O: } ii

Parameters & Definitions

$I^A$ and $I^B$ are codominant alleles producing A and B antigens on RBC surface. $i$ is recessive producing no antigen. AB is universal recipient (no antibodies); O is universal donor (no antigens).

Multiple allele inheritance pattern for ABO blood groups showing codominance and dominance relationships.

DNA Double Helix Dimensions

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Biology DNA Structure & Chargaff's Rules

\text{Length} = N \times 0.34 \text{ nm}

\text{Distance per turn (pitch)} = 3.4 \text{ nm}

\text{Base pairs per turn} = 10

\text{Number of turns} = \frac{N}{10}

\text{Diameter of helix} = 2 \text{ nm (20 Å)}

Parameters & Definitions

$N$ is the total number of base pairs. Distance between adjacent base pairs = 0.34 nm. The right-handed B-DNA has a major groove and a minor groove. Sugar-phosphate backbone is on the outside.

Key dimensions of the B-form DNA double helix and calculation of total length from base pair count.

Chargaff's Rules of Base Pairing

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Biology DNA Structure & Chargaff's Rules

A = T \quad \text{and} \quad G = C \quad \text{(Chargaff's Rule)}

\frac{A + G}{T + C} = 1 \quad \text{(Purines = Pyrimidines)}

\frac{A + T}{G + C} \neq 1 \quad \text{(varies between species)}

\text{If } A = 30\%, \text{ then } T = 30\%, \; G = C = 20\%

Parameters & Definitions

$A$ = Adenine, $T$ = Thymine, $G$ = Guanine, $C$ = Cytosine. Chargaff's rule applies ONLY to double-stranded DNA. In single-stranded DNA or RNA, $A \neq T(U)$ and $G \neq C$ .

Quantitative relationships between purine and pyrimidine bases in double-stranded DNA.

DNA Replication & Strand Distribution

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Biology DNA Replication Calculations

\text{After } n \text{ rounds: Total DNA molecules} = 2^n

\text{Old (parental) strands} = 2 \quad \text{(always, in 2 molecules)}

\text{New strands} = 2^{n+1} - 2

\text{Molecules with at least one old strand} = 2

\text{Purely new molecules} = 2^n - 2

Parameters & Definitions

$n$ is the number of replication rounds. Semi-conservative replication means each daughter DNA retains one parental strand. Proved by Meselson-Stahl experiment using ¹⁵N (heavy) and ¹⁴N (light) isotopes.

Calculation of new and old strands after multiple rounds of semi-conservative DNA replication.

Codon & Amino Acid Calculations

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Biology Transcription & Translation Numerics

\text{Total codons} = 4^3 = 64

\text{Sense codons (amino acid coding)} = 61

\text{Stop codons (UAA, UAG, UGA)} = 3

\text{Start codon: AUG (Methionine)}

\text{Amino acids in polypeptide} = \frac{\text{mRNA codons} - 1}{1} = \frac{N/3 - 1}{1}

Parameters & Definitions

Each codon = 3 consecutive nucleotide bases on mRNA. $N$ = total nucleotides in the coding region of mRNA. The '-1' accounts for the stop codon which is not translated. The genetic code is degenerate (multiple codons for same amino acid) but non-ambiguous.

Numerical relationships between DNA bases, mRNA codons, and amino acids in the translated polypeptide.

Template vs Coding Strand Relations

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Biology Transcription & Translation Numerics

\text{Template (antisense) strand: } 3' \to 5'

\text{Coding (sense) strand: } 5' \to 3'

\text{mRNA} = \text{Coding strand sequence (with U replacing T)}

\text{RNA Polymerase reads: } 3' \to 5' \text{, synthesizes: } 5' \to 3'

Parameters & Definitions

Template strand is complementary and antiparallel to mRNA. Coding strand has the same sequence as mRNA (except T→U). In prokaryotes, RNA polymerase is a single enzyme; in eukaryotes: RNA Pol I (rRNA), Pol II (mRNA), Pol III (tRNA).

Relationship between the template strand, coding strand, and mRNA during transcription.

Human Genome Project Key Data

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Biology Human Genome Facts & Numbers

\text{Total base pairs} \approx 3.1 \times 10^9

\text{Average gene size} \approx 3000 \text{ base pairs}

\text{Total genes (estimated)} \approx 20,000 \text{-} 25,000

\text{Coding sequences} < 2\% \text{ of genome}

\text{Chromosome 1: most genes (2968)}

\text{Y chromosome: fewest genes (231)}

Parameters & Definitions

HGP used two key approaches: BAC (Bacterial Artificial Chromosome) and Shotgun sequencing. Less than 2% of the genome codes for proteins; the rest includes introns, repetitive sequences, and regulatory elements.

Important numerical facts about the human genome determined by the HGP (1990-2003).

Dental Formulas

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Biology Digestive System & Dental Formulas

\text{Permanent Dentition} = \frac{2.1.2.3}{2.1.2.3} \times 2 = 32

\text{Deciduous Dentition} = \frac{2.1.0.2}{2.1.0.2} \times 2 = 20

Parameters & Definitions

The digits represent: $\frac{\text{Incisors . Canines . Premolars . Molars}}{\text{Incisors . Canines . Premolars . Molars}}$ per half jaw. Heterodont (different types) and thecodont (embedded in sockets) dentition. Diphyodont = two sets in lifetime.

Represents the arrangement and type of teeth on one side of upper and lower jaws.

Caloric Value of Nutrients

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Biology Digestive System & Dental Formulas

\text{Carbohydrates: } 4.0 \text{ kcal/g} \; (17.16 \text{ kJ/g})

\text{Proteins: } 4.0 \text{ kcal/g} \; (17.16 \text{ kJ/g})

\text{Fats: } 9.0 \text{ kcal/g} \; (37.62 \text{ kJ/g})

Parameters & Definitions

Fats provide maximum energy per gram (2.25× more than carbohydrates). These values are used in calculating BMR (Basal Metabolic Rate) and dietary energy requirements.

Energy released per gram of each major nutrient class upon complete oxidation.

Cardiac Output

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Biology Cardiac Output & Volumes

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

\text{CO} = 70 \text{ mL} \times 72 \text{ beats/min} \approx 5040 \text{ mL/min} \approx 5 \text{ L/min}

Parameters & Definitions

Stroke Volume is the blood pumped per heartbeat ( $\approx 70$ mL). Heart Rate averages $\approx 72$ beats/min at rest. CO varies with exercise (can increase to 20–25 L/min).

Calculates the volume of blood pumped by each ventricle per minute.

Cardiac Cycle Duration

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Biology Cardiac Output & Volumes

\text{Total cardiac cycle} = \frac{60}{72} \approx 0.8 \text{ sec}

\text{Atrial systole} \approx 0.1 \text{ s}

\text{Ventricular systole} \approx 0.3 \text{ s}

\text{Joint diastole} \approx 0.4 \text{ s}

Parameters & Definitions

The cardiac cycle includes systole (contraction) and diastole (relaxation). SA node (pacemaker) generates 72 impulses/min. The conduction sequence: SA node → AV node → Bundle of His → Purkinje fibres.

Time intervals for different phases of the cardiac cycle at a normal heart rate of 72 bpm.

Lung Volumes

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Biology Respiratory Volumes & Capacities

\text{Tidal Volume (TV)} \approx 500 \text{ mL}

\text{Inspiratory Reserve Volume (IRV)} \approx 2500\text{-}3000 \text{ mL}

\text{Expiratory Reserve Volume (ERV)} \approx 1000\text{-}1100 \text{ mL}

\text{Residual Volume (RV)} \approx 1100\text{-}1200 \text{ mL}

Parameters & Definitions

TV is the air inhaled/exhaled in a normal breath. IRV is extra air that can be forcibly inhaled. ERV is extra air that can be forcibly exhaled. RV is air remaining after maximum exhalation.

Standard respiratory volumes measured by spirometry in a healthy adult.

Lung Capacity Relations

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Biology Respiratory Volumes & Capacities

\text{Vital Capacity (VC)} = \text{TV} + \text{IRV} + \text{ERV} \approx 3400\text{-}4600 \text{ mL}

\text{Inspiratory Capacity (IC)} = \text{TV} + \text{IRV}

\text{Expiratory Capacity (EC)} = \text{TV} + \text{ERV}

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

\text{Total Lung Capacity (TLC)} = \text{VC} + \text{RV} \approx 6000 \text{ mL}

Parameters & Definitions

VC is the maximum air that can be exhaled after maximum inhalation. TLC includes all four volumes. FRC is the air remaining after normal exhalation.

Summation formulas to calculate the four lung capacities from the four volumes.

Glomerular Filtration Rate & Net Filtration Pressure

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Biology Excretory System & Kidney Function

\text{GFR} \approx 125 \text{ mL/min} = 180 \text{ L/day}

\text{NFP} = P_{\text{GHP}} - (P_{\text{BCOP}} + P_{\text{CHP}})

\text{NFP} = 60 - (32 + 18) = 10 \text{ mmHg}

\text{Urine output} \approx 1.5 \text{ L/day}

\text{Reabsorption} \approx 99\%

Parameters & Definitions

$\text{GFR}$ = Glomerular Filtration Rate; $P_{\text{GHP}}$ = Glomerular Hydrostatic Pressure ( $\approx 60$ mmHg); $P_{\text{BCOP}}$ = Blood Colloid Osmotic Pressure ( $\approx 32$ mmHg); $P_{\text{CHP}}$ = Capsular Hydrostatic Pressure ( $\approx 18$ mmHg). About 99% of filtrate is reabsorbed.

Quantitative aspects of kidney filtration including GFR and the pressure driving filtration.

Countercurrent Multiplier Osmolarity

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Biology Excretory System & Kidney Function

\text{Cortex: } \approx 300 \text{ mOsm/L}

\text{Outer medulla: } \approx 600 \text{ mOsm/L}

\text{Inner medulla (tip): } \approx 1200 \text{ mOsm/L}

\text{Osmolarity gradient} = 300 \to 1200 \text{ mOsm/L}

Parameters & Definitions

The loop of Henle acts as a countercurrent multiplier creating an increasing osmolarity gradient from cortex to inner medulla. Vasa recta acts as a countercurrent exchanger maintaining this gradient. ADH controls water reabsorption from collecting duct.

Osmolarity gradient in the renal medulla maintained by the loop of Henle and vasa recta.

Blood Composition & Normal Values

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Biology Body Fluids & Blood Composition

\text{Total blood volume} \approx 5\text{-}5.5 \text{ L}

\text{Plasma} \approx 55\%, \quad \text{Formed elements} \approx 45\%

\text{RBC count: Male} \approx 5\text{-}5.5 \text{ million/mm}^3

\text{RBC count: Female} \approx 4.5\text{-}5 \text{ million/mm}^3

\text{WBC count} \approx 6000\text{-}8000 \text{ /mm}^3

\text{Platelet count} \approx 1.5\text{-}3.5 \text{ lakh/mm}^3

\text{Hb: Male} \approx 14\text{-}16 \text{ g/dL}, \; \text{Female} \approx 12\text{-}14 \text{ g/dL}

Parameters & Definitions

Plasma contains 90–92% water, 6–8% proteins (albumin, globulins, fibrinogen). Formed elements = RBCs + WBCs + Platelets. RBCs are enucleated and biconcave in mammals. Lifespan: RBC ≈ 120 days, WBC ≈ varies, Platelets ≈ 7–10 days.

Quantitative normal values for major blood components frequently tested in NEET.

Nerve Impulse & Resting Potential

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Biology Neural Control & Nervous System

\text{Resting Membrane Potential} \approx -70 \text{ mV}

\text{Action Potential (depolarization)} \approx +30 \text{ to } +40 \text{ mV}

\text{Speed of impulse: Myelinated} \approx 100 \text{ m/s}

\text{Speed of impulse: Non-myelinated} \approx 0.5\text{-}2 \text{ m/s}

\text{Synaptic delay} \approx 0.5 \text{ ms}

Parameters & Definitions

Resting potential maintained by Na⁺/K⁺ ATPase pump (3 Na⁺ out, 2 K⁺ in). Depolarization: Na⁺ influx via voltage-gated channels. Repolarization: K⁺ efflux. Saltatory conduction in myelinated neurons (node to node).

Electrical values associated with nerve impulse conduction across a neuron.

Key Hormonal Values & Conditions

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Biology Endocrine System & Hormonal Values

\text{Normal blood glucose: } 70\text{-}110 \text{ mg/dL (fasting)}

\text{Diabetes threshold: } > 126 \text{ mg/dL (fasting)}

\text{Normal blood Ca}^{2+}: 9\text{-}11 \text{ mg/dL}

\text{T}_3 \text{ and T}_4 \text{ require iodine; BMR regulation}

\text{Normal BMR} \approx 1600\text{-}1800 \text{ kcal/day (adults)}

Parameters & Definitions

Insulin lowers blood glucose (from β-cells of Langerhans); Glucagon raises it (from α-cells). PTH increases blood Ca²⁺; Calcitonin (TCT from thyroid C-cells) decreases it. T₃/T₄ from thyroid regulate BMR.

Normal physiological values regulated by hormones and associated disorders.

Human Skeletal System Counts

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Biology Locomotion & Movement

\text{Total bones in adult} = 206

\text{Axial skeleton} = 80 \quad (\text{skull: 22, vertebrae: 26, ribs: 24, sternum: 1, hyoid: 1})

\text{Appendicular skeleton} = 126

\text{Vertebral formula: C}_7 \text{T}_{12} \text{L}_5 \text{S}_1 \text{Co}_1 = 26

\text{Ribs: True (7 pairs), False (3 pairs), Floating (2 pairs)} = 24

Parameters & Definitions

C = Cervical, T = Thoracic, L = Lumbar, S = Sacrum (5 fused → 1), Co = Coccyx (4 fused → 1). Smallest bone: Stapes (middle ear). Longest bone: Femur. Total in newborn ≈ 300 (many fuse during growth).

Total number of bones in the human adult skeleton and key regional bone counts.

Sarcomere Structure & Contraction

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Biology Locomotion & Movement

\text{Sarcomere} = \text{Z-line to Z-line} \approx 2.0\text{-}2.5 \; \mu\text{m}

\text{During contraction:}

\text{A-band (dark): remains constant}

\text{I-band (light): decreases}

\text{H-zone: decreases or disappears}

\text{Sarcomere length: decreases}

Parameters & Definitions

A-band contains thick myosin filaments (constant length). I-band contains thin actin filaments. H-zone is the central part of A-band without actin overlap. Z-line anchors actin filaments. M-line is the center of the sarcomere.

Key measurements and band changes during muscle contraction based on the sliding filament theory.

Gametogenesis Cell Division Counts

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Biology Human Reproduction

\text{1 primary spermatocyte} \xrightarrow{\text{Meiosis}} 4 \text{ spermatozoa}

\text{1 primary oocyte} \xrightarrow{\text{Meiosis}} 1 \text{ ovum} + 3 \text{ polar bodies}

\text{Sperms from } n \text{ spermatocytes} = 4n

\text{Ova from } n \text{ oocytes} = n

Parameters & Definitions

Spermatogenesis produces 4 functional sperms per primary spermatocyte. Oogenesis produces 1 functional ovum per primary oocyte (3 polar bodies degenerate). Meiosis I reduces chromosome number; Meiosis II separates chromatids.

Number of gametes produced from a given number of primary cells undergoing meiosis.

Menstrual Cycle Phases & Duration

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Biology Human Reproduction

\text{Total cycle} \approx 28 \text{ days}

\text{Menstrual phase: Days } 1\text{-}5

\text{Follicular / Proliferative phase: Days } 6\text{-}13

\text{Ovulation: Day } 14

\text{Luteal / Secretory phase: Days } 15\text{-}28

Parameters & Definitions

FSH stimulates follicular growth; LH surge triggers ovulation on Day 14. Corpus luteum produces progesterone during luteal phase. If no fertilization, corpus luteum degenerates → drop in progesterone → menstruation.

Time durations of the phases of the human female menstrual cycle.

Human Embryonic Development Timeline

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Biology Human Reproduction

\text{Fertilization: Ampulla of fallopian tube}

\text{Cleavage begins: } \sim 24\text{-}30 \text{ hrs after fertilization}

\text{Morula (16 cells): Day } 3\text{-}4

\text{Blastocyst: Day } 5\text{-}6

\text{Implantation: Day } 6\text{-}7 \text{ (in endometrium)}

\text{Gestation period} = 9 \text{ months} \approx 266 \text{ days (from fertilization)}

Parameters & Definitions

Trophoblast forms placenta; inner cell mass forms embryo. Placenta is connected by umbilical cord. hCG (human chorionic gonadotropin) is produced by trophoblast — basis of pregnancy tests.

Key developmental events and their timing after fertilization.

Population Growth Equations

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Biology Population Ecology & Growth Models

\frac{dN}{dt} = rN \quad \text{(Exponential / J-shaped Growth)}

N_t = N_0 e^{rt} \quad \text{(Integral Form)}

\frac{dN}{dt} = rN \left( \frac{K - N}{K} \right) \quad \text{(Verhulst-Pearl Logistic / S-shaped Growth)}

Parameters & Definitions

$N$ = population size; $t$ = time; $r$ = intrinsic rate of natural increase (biotic potential); $N_0$ = initial population; $e$ = Euler's number ( $\approx 2.718$ ); $K$ = carrying capacity. When $N = K$ , growth rate = 0. When $N = K/2$ , growth rate is maximum.

Mathematical models representing population growth under unlimited (J-shaped) and limited (S-shaped) resource conditions.

Population Density Change Equation

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Biology Population Ecology & Growth Models

N_{t+1} = N_t + [(B + I) - (D + E)]

Parameters & Definitions

$N_t$ = population density at time $t$ ; $B$ = births; $I$ = immigration; $D$ = deaths; $E$ = emigration. $B$ and $I$ increase population; $D$ and $E$ decrease it.

Determines population size change by accounting for all gains and losses.

Age Distribution & Growth Status

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Biology Population Ecology & Growth Models

\text{Expanding (Growing):} \; \text{Pre-reproductive} > \text{Reproductive} > \text{Post-reproductive}

\text{Stable:} \; \text{Pre-reproductive} \approx \text{Reproductive} \approx \text{Post-reproductive}

\text{Declining:} \; \text{Pre-reproductive} < \text{Reproductive}

Parameters & Definitions

Expanding population: broad-based pyramid (high birth rate). Stable population: column-shaped. Declining population: inverted/urn-shaped (low birth rate, high proportion of elderly).

Relationship between age pyramid shape and population growth status.

Net Primary Productivity

NEET N

Biology Ecosystem Productivity & Energy Transfer

\text{NPP} = \text{GPP} - R_p

\text{Global NPP} \approx 170 \text{ billion tonnes/year}

\text{Ocean contribution} \approx 55 \text{ billion tonnes/year}

Parameters & Definitions

$\text{GPP}$ = Gross Primary Productivity (total photosynthesis); $\text{NPP}$ = Net Primary Productivity (biomass available to consumers); $R_p$ = respiratory losses by producers.

Relationship between total photosynthetic production and net energy stored as biomass.

Lindeman's 10% Law of Energy Transfer

NEET N

Biology Ecosystem Productivity & Energy Transfer

E_{n+1} = 0.10 \times E_n

\text{If producers} = 1000 \text{ kcal:}

\text{Primary consumers} = 100 \text{ kcal}

\text{Secondary consumers} = 10 \text{ kcal}

\text{Tertiary consumers} = 1 \text{ kcal}

Parameters & Definitions

$E_n$ = energy at trophic level $n$ . Only 10% is transferred; 90% is lost as heat (respiration), excretion, and decomposition. This limits food chains to typically 4–5 trophic levels.

Only 10% of energy at one trophic level is transferred to the next trophic level.

Ecosystem Nutrient Cycling

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Biology Ecosystem Productivity & Energy Transfer

\text{CO}_2 \text{ in atmosphere} \approx 0.04\% \; (\approx 400 \text{ ppm})

\text{CO}_2 \text{ fixation by photosynthesis} \approx 4 \times 10^{13} \text{ kg C/year}

\text{Turnover time for atmospheric CO}_2 \approx 4\text{-}5 \text{ years}

\text{Ocean dissolved CO}_2 = 71\% \text{ of global carbon}

Parameters & Definitions

Carbon cycles through atmosphere, biosphere, hydrosphere, and lithosphere. Photosynthesis and respiration are the major biological processes. Fossil fuel burning and deforestation increase atmospheric CO₂.

Key quantitative aspects of biogeochemical cycles and decomposition.

Species-Area Relationship

NEET N

Biology Biodiversity Patterns & Conservation

S = CA^Z \quad \text{(Power Law)}

\log S = \log C + Z \log A \quad \text{(Log-linearized form)}

Parameters & Definitions

$S$ = species richness; $A$ = area; $Z$ = regression slope (typically $0.1$ to $0.2$ for small areas within a continent; $0.6$ to $1.2$ for very large areas like continents); $C$ = Y-intercept (varies with taxonomic group).

Alexander von Humboldt's observation that species richness increases with area explored, following a power law.

Global Biodiversity Numbers

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Biology Biodiversity Patterns & Conservation

\text{Total known species} \approx 1.5 \text{ million}

\text{Estimated total species} \approx 5\text{-}50 \text{ million}

\text{India's share of global biodiversity} \approx 8.1\%

\text{IUCN Red List categories: } \text{LC, NT, VU, EN, CR, EW, EX}

\text{Insects dominate: } \approx 70\% \text{ of all species}

Parameters & Definitions

LC = Least Concern, NT = Near Threatened, VU = Vulnerable, EN = Endangered, CR = Critically Endangered, EW = Extinct in Wild, EX = Extinct. India is one of 17 mega-diversity countries (Paul Myers).

Key numerical facts about global species diversity and distribution.

Biochemical Oxygen Demand (BOD)

NEET N

Biology Environmental Issues & Pollution

\text{BOD} = \text{O}_2 \text{ consumed by microbes (mg/L) in 5 days at 20°C}

\text{Clean water BOD} < 3 \text{ mg/L}

\text{Moderately polluted: } 3\text{-}5 \text{ mg/L}

\text{Heavily polluted: } > 5 \text{ mg/L}

Parameters & Definitions

BOD is measured as mg of O₂ consumed per litre of water sample over 5 days at 20°C. Higher BOD = more organic pollutants = more microbial decomposition = more dissolved O₂ depletion.

A measure of the amount of organic matter in water — higher BOD indicates more pollution.

Greenhouse Effect & Global Warming

NEET N

Biology Environmental Issues & Pollution

\text{CO}_2 \text{ contribution:} \approx 60\% \text{ of greenhouse effect}

\text{CH}_4: \approx 20\%, \quad \text{N}_2\text{O}: \approx 6\%

\text{CFCs}: \approx 14\%

\text{Pre-industrial CO}_2 \approx 280 \text{ ppm}

\text{Current CO}_2 \approx 420 \text{ ppm}

Parameters & Definitions

Greenhouse gases trap infrared radiation reflected from Earth's surface. CFCs also deplete the ozone layer. Montreal Protocol (1987) banned CFCs. Kyoto Protocol (1997) set emission reduction targets.

Contribution of major greenhouse gases to global warming and key temperature data.

Restriction Enzyme Nomenclature & Fragments

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Biology Restriction Enzymes & PCR

\text{Naming: } \underbrace{E}_{\text{Genus}} \underbrace{co}_{\text{species}} \underbrace{R}_{\text{strain}} \underbrace{I}_{\text{order}}

\text{EcoRI cuts at: } 5'\text{-G}\downarrow\text{AATTC-3'} \quad (\text{palindrome})

\text{Fragments from } n \text{ cuts on linear DNA} = n + 1

\text{Fragments from } n \text{ cuts on circular DNA} = n

Parameters & Definitions

$E$ = genus $\textit{Escherichia}$ ; $co$ = species $\textit{coli}$ ; $R$ = strain RY13; $I$ = first enzyme isolated. Palindromic sequences read the same on both strands (5'→3'). Sticky ends have overhangs; blunt ends have no overhang.

Naming convention for restriction endonucleases and calculation of DNA fragments produced.

PCR Amplification Calculation

NEET N

Biology Restriction Enzymes & PCR

\text{Copies after } n \text{ cycles} = 2^n

\text{Starting from } N_0 \text{ molecules: } N_0 \times 2^n

\text{Cycle: Denaturation (94°C)} \to \text{Annealing (50-65°C)} \to \text{Extension (72°C)}

Parameters & Definitions

$n$ = number of PCR cycles (typically 25–35). Uses thermostable $\textit{Taq}$ polymerase (from $\textit{Thermus aquaticus}$ ). Each cycle doubles the DNA. 30 cycles produce $2^{30} \approx 10^9$ copies from a single molecule.

Polymerase Chain Reaction: number of DNA copies produced after multiple cycles.

Cloning Vector Insert Capacities

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Biology Cloning Vectors & Insert Size

\text{Plasmid: } < 10 \text{ kb}

\text{Phage (}\lambda\text{): } \sim 20 \text{ kb}

\text{Cosmid: } \sim 40 \text{ kb}

\text{BAC: } 100\text{-}300 \text{ kb}

\text{YAC: } 200\text{-}2000 \text{ kb}

Parameters & Definitions

kb = kilobase pairs. Plasmids are the most common vectors (e.g., pBR322, pUC). BAC = Bacterial Artificial Chromosome; YAC = Yeast Artificial Chromosome. Vectors must have origin of replication (ori), selectable marker, and cloning site.

Maximum DNA insert size for various cloning vectors used in recombinant DNA technology.

Bt Toxin Gene & Cry Proteins

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Biology Bt Crops & Transgenic Organisms

\text{cry1Ab, cry1Ac} \to \text{effective against cotton bollworms (Lepidoptera)}

\text{cry2Ab} \to \text{effective against cotton bollworms (Lepidoptera)}

\text{cry3} \to \text{effective against coleopteran pests (beetles)}

\text{Bt cotton: } cry1Ac + cry2Ab \text{ (stacked genes)}

Parameters & Definitions

$Bt$ = $\textit{Bacillus thuringiensis}$ . Cry proteins are inactive protoxins that become active (toxic) in alkaline insect gut (pH > 9.5). They create pores in the midgut epithelium, causing cell lysis and death of the insect.

Cry protein gene nomenclature and their target pest specificity in transgenic Bt crops.

ADA Deficiency Gene Therapy

NEET N

Biology Gene Therapy & Medical Applications

\text{ADA gene on Chromosome 20}

\text{ADA deficiency} \to \text{SCID (Severe Combined Immunodeficiency)}

\text{Treatment: Functional ADA cDNA} \to \text{retroviral vector} \to \text{patient's lymphocytes}

\text{Alternative: PEG-ADA enzyme replacement (not permanent)}

Parameters & Definitions

ADA = Adenosine Deaminase, essential for immune function. SCID patients lack functional T and B lymphocytes. Gene therapy introduces a functional copy of the ADA gene into the patient's own bone marrow cells or lymphocytes.

First approved gene therapy case: correcting Adenosine Deaminase deficiency.

Immunoglobulin Classes & Structure

NEET N

Biology Immunity & Immunoglobulins

\text{5 classes: IgG, IgA, IgM, IgE, IgD}

\text{Basic unit: 2 Heavy chains (H) + 2 Light chains (L)}

\text{IgG: most abundant in blood (}\approx 80\%\text{), crosses placenta}

\text{IgA: in secretions (saliva, tears, colostrum)}

\text{IgM: first response, pentamer}

\text{IgE: allergic reactions, binds mast cells}

Parameters & Definitions

H chain = Heavy chain (determines class: γ, α, μ, ε, δ). L chain = Light chain (κ or λ). Antigen-binding site = variable region of H + L chains. Each antibody has 2 antigen-binding sites (bivalent).

The five classes of antibodies and the basic structural unit of an immunoglobulin molecule.

Malaria Parasite Life Cycle Timing

NEET N

Biology Pathogen Incubation & Life Cycles

\text{P. vivax: fever every 48 hrs (Benign Tertian)}

\text{P. falciparum: fever every 36-48 hrs (Malignant Tertian)}

\text{P. malariae: fever every 72 hrs (Quartan)}

\text{Vector: Female } \textit{Anopheles} \text{ mosquito}

\text{Definitive host: Mosquito; Intermediate host: Human}

Parameters & Definitions

Sexual cycle (gametogony) occurs in mosquito (definitive host). Asexual cycle in human (intermediate host): liver stage (schizogony) → blood stage (erythrocytic schizogony). Merozoite release causes RBC lysis → fever.

Duration of key stages in the Plasmodium life cycle and fever periodicity.

Chromosome Number in Gametes & Zygote

NEET N

Biology Events in Sexual Reproduction

\text{Somatic cell (body)} = 2n \text{ (diploid)}

\text{Gamete (egg/sperm)} = n \text{ (haploid)}

\text{Zygote} = n + n = 2n \text{ (diploid restored)}

\text{Human: } 2n = 46, \; n = 23

\text{Meiocyte (2n)} \xrightarrow{\text{Meiosis}} \text{Gametes (n)}

Parameters & Definitions

$2n$ = diploid number (two copies of each chromosome); $n$ = haploid number (one copy). Meiosis halves the chromosome number. Fertilization restores the diploid number. Polyploidy = having more than 2n chromosomes.

Relationship between somatic cell and gametic chromosome numbers in sexually reproducing organisms.

Embryo Sac Development

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Biology Sexual Reproduction in Flowering Plants

\text{1 Megaspore Mother Cell (MMC, 2n)} \xrightarrow{\text{Meiosis}} 4 \text{ megaspores (n)}

\text{3 megaspores degenerate; 1 functional megaspore survives}

\text{Functional megaspore} \xrightarrow{3 \text{ mitotic divisions}} 8 \text{ nuclei}

\text{Mature embryo sac: 7 cells, 8 nuclei}

\text{3 Antipodals + 2 Synergids + 1 Egg cell + 1 Central cell (2 polar nuclei)}

Parameters & Definitions

The embryo sac = female gametophyte. Egg apparatus = egg cell + 2 synergids (at micropylar end). 3 antipodal cells at chalazal end. Central cell has 2 polar nuclei that fuse with one sperm → triploid endosperm (3n).

Numerical details of megasporogenesis and the 7-celled, 8-nucleate embryo sac (Polygonum type).

Double Fertilization & Endosperm Ploidy

NEET N

Biology Sexual Reproduction in Flowering Plants

\text{Sperm}_1 + \text{Egg cell (n)} \to \text{Zygote (2n)} \quad \text{(Syngamy)}

\text{Sperm}_2 + \text{Polar nuclei (n + n)} \to \text{Primary Endosperm Nucleus (3n)} \quad \text{(Triple Fusion)}

\text{Endosperm is triploid (3n)}

\text{Embryo develops from zygote (2n)}

Parameters & Definitions

Both events = double fertilization (unique to angiosperms, discovered by S.G. Nawaschin). Endosperm provides nutrition to the developing embryo. In some plants (e.g., orchids, Alisma), endosperm development is suppressed.

The unique double fertilization event in angiosperms producing diploid zygote and triploid endosperm.

Microsporogenesis & Pollen Development

NEET N

Biology Sexual Reproduction in Flowering Plants

\text{1 MMC (Microspore Mother Cell, 2n)} \xrightarrow{\text{Meiosis}} 4 \text{ microspores (n)}

\text{Each microspore} \to \text{1 pollen grain}

\text{Pollen grains from } n \text{ MMCs} = 4n

\text{Meiotic divisions for } P \text{ pollen grains} = \frac{P}{4}

Parameters & Definitions

Each microspore mother cell (2n) undergoes meiosis to produce a tetrad of 4 microspores. Each microspore develops into a pollen grain (male gametophyte) with 2 cells: vegetative (tube) cell and generative cell.

Calculation of pollen grains and meiotic divisions from microspore mother cells.

Seed & Fruit Numerical Relations

NEET N

Biology Sexual Reproduction in Flowering Plants

\text{Minimum pollen grains for } n \text{ seeds} = n

\text{Minimum meiotic divisions (pollen)} = \frac{n}{4}

\text{Minimum meiotic divisions (ovule)} = n

\text{1 ovule} \to \text{1 seed}

\text{Ovary} \to \text{Fruit; Ovule} \to \text{Seed}

Parameters & Definitions

Each ovule needs 1 pollen tube (with 2 sperms) for double fertilization. 1 anther typically has 4 pollen sacs (microsporangia). True fruit develops from ovary only; false fruit includes other floral parts (e.g., thalamus in apple).

Relationship between ovules, seeds, pollen grains, and fruits.

Contraceptive Methods Classification

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Biology Contraceptive Methods & Effectiveness

\text{Natural: Rhythm method, Coitus interruptus, Lactational amenorrhea}

\text{Barrier: Condoms, Diaphragm, Cervical cap}

\text{IUDs: Cu-T (Cu}^{2+} \text{ ions), LNG-20 (progesterone)}

\text{Hormonal: Pills (E + P), Implants, Injections}

\text{Surgical: Vasectomy (male), Tubectomy (female)}

Parameters & Definitions

Cu-T releases copper ions that are spermicidal. Hormonal methods inhibit ovulation and alter cervical mucus. Surgical methods are permanent. MTP (Medical Termination of Pregnancy) is legal in India up to 20 weeks (extended to 24 weeks for special categories under MTP Act 2021).

Classification of contraceptive methods based on mechanism and their typical use effectiveness.

ART Methods

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Biology Assisted Reproductive Technologies

\text{IVF: In Vitro Fertilization (test tube baby)}

\text{ZIFT: Zygote transferred to fallopian tube (8-cell stage)}

\text{IUT/GIFT: Transfer of gametes/embryo (> 8 cells) to uterus}

\text{ICSI: Intra-Cytoplasmic Sperm Injection (single sperm into ovum)}

\text{AI: Artificial Insemination (semen into vagina/uterus)}

Parameters & Definitions

IVF-ET = In Vitro Fertilization and Embryo Transfer. ZIFT transfers zygote/early embryo into fallopian tube. GIFT = Gamete Intra-Fallopian Transfer (gametes, not zygote). AI is simplest ART for cases of low sperm count.

Classification and key differences between major assisted reproductive technologies.

Floral Formula Notation System

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Biology Floral Formulas & Diagrams

\text{Solanaceae: } \oplus \, \bigcirc \, K_{(5)} \, C_{(5)} \, A_5 \, G_{(2)}

\text{Fabaceae (Papilionaceae): } \% \; \bigcirc \, K_{(5)} \, C_{1+2+(2)} \, A_{(9)+1} \, G_1

\text{Liliaceae: } \oplus \; Br \; P_{3+3} \, A_{3+3} \, G_{(3)}

Parameters & Definitions

$\oplus$ = actinomorphic; $\%$ = zygomorphic; $\bigcirc$ = bisexual; $K$ = calyx; $C$ = corolla; $P$ = perianth (tepals); $A$ = androecium; $G$ = gynoecium; $(\;)$ = fusion; $\overline{G}$ = superior ovary; $\underline{G}$ = inferior ovary.

Standard notation for representing the number and arrangement of floral parts in plant families.

Phyllotaxy & Leaf Arrangement Angles

NEET N

Biology Root, Stem & Leaf Numerics

\text{Alternate: } 1 \text{ leaf per node, } 180° \text{ divergence (e.g., Mustard)}

\text{Opposite: } 2 \text{ leaves per node, } 90° \text{ (decussate, e.g., Calotropis)}

\text{Whorled: } > 2 \text{ leaves per node (e.g., Alstonia)}

\text{Fibonacci angle} \approx 137.5° \text{ (optimizes light capture)}

Parameters & Definitions

Phyllotaxy determines the fraction of stem circumference between successive leaves. In alternate phyllotaxy, the fraction is typically 1/2, 1/3, 2/5, 3/8, etc. following the Fibonacci series.

Angular divergence between successive leaves in different phyllotaxy patterns.

Secondary Growth & Annual Rings

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Biology Vascular Bundle & Tissue System

\text{Age of tree (years)} = \text{Number of annual rings}

\text{Annual ring} = 1 \text{ spring wood} + 1 \text{ autumn wood}

\text{Heart wood (duramen): dark, dead, central}

\text{Sap wood (alburnum): light, functional, peripheral}

Parameters & Definitions

Dendrochronology = study of annual rings to determine tree age and past climate. Spring wood (early wood) has wider vessels; autumn wood (late wood) has narrower vessels. Vascular cambium produces secondary xylem (inward) and secondary phloem (outward).

Calculation of tree age from annual rings and key measurements in secondary growth.

Germ Layers & Body Symmetry Classification

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Biology Classification Basis & Body Plans

\text{Diploblastic: 2 layers (Ectoderm + Endoderm)} \to \text{Coelenterata}

\text{Triploblastic: 3 layers (Ecto + Meso + Endo)} \to \text{Platyhelminthes onward}

\text{Acoelomate: no body cavity} \to \text{Platyhelminthes}

\text{Pseudocoelomate: false coelom} \to \text{Aschelminthes}

\text{Eucoelomate (true coelom): Schizo-} \to \text{Annelida onward}

Parameters & Definitions

Coelom = body cavity lined by mesoderm on both sides. Schizocoelom develops from splitting of mesoderm (protostomes). Enterocoelom develops from archenteron pouches (deuterostomes: Echinodermata, Chordata).

Classification of animals based on number of germ layers, body symmetry, and coelom type.

Cockroach (Periplaneta americana) Key Counts

NEET N

Biology Cockroach Anatomy & Counts

\text{Body segments: Head (6) + Thorax (3) + Abdomen (10)} = 19

\text{Legs} = 3 \text{ pairs (one per thoracic segment)}

\text{Wings} = 2 \text{ pairs (mesothorax + metathorax)}

\text{Spiracles} = 10 \text{ pairs (2 thoracic + 8 abdominal)}

\text{Malpighian tubules} \approx 100\text{-}150

\text{Ovarioles per ovary} = 8

Parameters & Definitions

Head bears compound eyes (mosaic vision, ~2000 ommatidia each), antennae, and mouthparts (biting and chewing type). Blood (haemolymph) is colourless; open circulatory system with 13-chambered dorsal heart. Excretion by Malpighian tubules + uricotelic.

Important numerical facts about cockroach anatomy frequently tested in NEET.

Biogas Composition & Production

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Biology Biogas Production & Composition

\text{CH}_4 \text{ (Methane)} \approx 50\text{-}70\%

\text{CO}_2 \approx 30\text{-}40\%

\text{H}_2, \text{H}_2\text{S: trace amounts}

\text{Methanogen: } \textit{Methanobacterium} \text{ (anaerobic archaebacterium)}

Parameters & Definitions

Biogas is produced in anaerobic digesters (biogas plants). Cattle dung (gobar) is the substrate. Three stages: hydrolysis → acidogenesis → methanogenesis. Methanogens are obligate anaerobes found in rumen of cattle and sewage treatment sludge.

Composition of biogas produced by methanogenic bacteria from organic waste.

Sewage Treatment Stages & BOD Reduction

NEET N

Biology Sewage Treatment & BOD

\text{Primary treatment: physical (sedimentation, filtration)}

\text{Secondary treatment: biological (aeration, activated sludge)}

\text{BOD reduced by} \approx 90\text{-}95\% \text{ after secondary treatment}

\text{Flocs (activated sludge): } \textit{Zooglea} + \text{fungi + bacteria}

Parameters & Definitions

BOD = Biochemical Oxygen Demand. Primary effluent → aeration tanks (aerobic microbes reduce organic matter) → settling tanks → effluent released. Anaerobic digester processes sludge → biogas (CH₄). Clean effluent should have BOD < 30 mg/L.

The stages of sewage treatment and the role of microbes in reducing BOD of wastewater.

Key Microbial Products & Sources

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Biology Industrial Microbiology & Fermented Products

\text{Ethanol: } \textit{Saccharomyces cerevisiae} \text{ (yeast)}

\text{Citric acid: } \textit{Aspergillus niger}

\text{Penicillin: } \textit{Penicillium notatum/chrysogenum}

\text{Streptokinase: } \textit{Streptococcus} \text{ (clot buster)}

\text{Cyclosporin A: } \textit{Trichoderma polysporum} \text{ (immunosuppressant)}

\text{Statins: } \textit{Monascus purpureus} \text{ (cholesterol-lowering)}

Parameters & Definitions

Penicillin (Alexander Fleming, 1928) was the first antibiotic. Statins inhibit HMG-CoA reductase enzyme in cholesterol biosynthesis. Cyclosporin A is used in organ transplant patients. Streptokinase dissolves blood clots in myocardial infarction.

Important microbially-derived products, their source organisms, and applications.

Sporophyte vs Gametophyte Dominance

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Biology Alternation of Generations

\text{Bryophytes: Gametophyte (n) dominant, Sporophyte (2n) dependent}

\text{Pteridophytes: Sporophyte (2n) dominant, Gametophyte (n) = prothallus}

\text{Gymnosperms: Sporophyte (2n) dominant, seeds naked}

\text{Angiosperms: Sporophyte (2n) dominant, seeds enclosed in fruit}

\text{Trend: } n \text{ dominance} \xrightarrow{\text{evolution}} 2n \text{ dominance}

Parameters & Definitions

Gametophyte = haploid (n), produces gametes by mitosis. Sporophyte = diploid (2n), produces spores by meiosis. In bryophytes, the sporophyte is attached to and nutritionally dependent on the gametophyte. In higher plants, the reverse is true.

The relative dominance of haploid and diploid phases across plant groups.

No Formulas Found

SI and CGS Conversion Relations

General Dimensional Representation

Mean Absolute Error

Relative and Percentage Error

Propagation of Errors in Calculations

Average Speed and Velocity Inequality

Average and Instantaneous Velocity

Equations of Motion for Uniform Acceleration

Relative Velocity in One Dimension

Parallelogram Law of Vector Addition

Dot and Cross Products of Vectors

Formulas for Projectile Motion under Gravity

Centripetal Acceleration and Angular Velocity Relations

Newton's Second Law

Momentum and Impulse

Static and Kinetic Friction Limits

Critical Speeds on Level and Banked Circular Roads

Work Done by Forces

Work-Energy Theorem and Power

Relation Between Force and Potential Energy

Potential Energy of a Hookean Spring

Critical Speeds in Vertical Circular Motion

Coefficient of Restitution and Collision Speeds

Position of Centre of Mass

Centre of Mass for Continuous Media

Torque and Angular Acceleration Relation

Angular Momentum and Net Torque

Moment of Inertia and Radius of Gyration

Parallel and Perpendicular Axes Theorems

Universal Gravitational Force and Kepler's Third Law

Variation of g with Altitude, Depth, and Rotation

Gravitational Potential Energy and Potential

Escape Velocity and Satellite Orbital Velocity

Hooke's Law of Elasticity

Young's and Bulk Moduli

Poisson's Ratio and Elastic Constants Relations

Elastic Strain Energy Density

Hydrostatic Pressure variation

Buoyant Force (Archimedes' Principle)

Stokes' Law and Terminal Velocity

Reynolds Number Flow Regime

Equation of Continuity and Bernoulli's Theorem

Relation Between Surface Tension and Surface Energy

Excess Pressure in Drops/Bubbles

Height of Capillary Rise

Temperature Scale Conversions

Linear Expansion

Specific Heat Capacity and Latent Heat

Conduction Rate

Wien's Displacement Law

Stefan's Law and Wien's Law

Newton's Law of Cooling

Temperature Scale Conversions

First Law Equation

Work in Isothermal & Adiabatic Processes

Adiabatic State Equations (Poisson's Relations)

Refrigerator Coefficient of Performance (COP)

Carnot Engine and Refrigerator performance

Equation of State and Compression Work

Kinetic Model Pressure

Molecular Speeds and Specific Heats

Mean Free Path

Displacement, Velocity and Acceleration in SHM

Energy in SHM

Periods of Standard Oscillators

Amplitude Decay in Damped SHM

Speed of Wave on String and in Gas

Progressive Wave Equation and String/Gas Wave Speeds

Equation of a Standing Wave

Harmonics in Organ Pipes

Beat Frequency

General Doppler Shift Formula in Sound

Quantization of Electric Charge

Coulomb's Law of Electrostatic Force

Electric Field of a Point Charge

Electric Dipole Fields and Torque

Gauss's Law and Electrostatic Field Applications

Electric Potential