CUET Science Preparation

Mathematical Methods (10 subtopics) Topic Select All

Calculus of single and multiple variables

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Partial derivatives, Jacobian

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Imperfect and perfect differentials

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Taylor expansion, Fourier series

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Vector algebra, Vector Calculus

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Multiple integrals

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Divergence theorem, green's theorem, Stokes' theorem

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First order equations and linear second order differential equations with constant coefficients

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Matrices and determinants

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Algebra of complex numbers

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Mechanics and General Properties of Matter (16 subtopics) Topic Select All

Newton's laws of motion and applications

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Velocity and acceleration in Cartesian, polar and cylindrical coordinate systems

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Uniformly rotating frame, centrifugal and Coriolis forces

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Motion under a central force, Kepler's laws

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Gravitational Law and field

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Conservative and non-conservative forces

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System of particles, Center of mass

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Conservation of linear and angular momentum, conservation of energy

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Variable mass systems

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Elastic and inelastic collisions

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Rigid body motion, fixed axis rotations

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Moments of Inertia and products of Inertia

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Parallel and perpendicular axes theorem

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Principal moments and axes

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Kinematics of moving fluids

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Equation of continuity, Euler's equation, Bernoulli's theorem

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Oscillations, Waves and Optics (17 subtopics) Topic Select All

Differential equation for simple harmonic oscillator

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Superposition of simple harmonic oscillators

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Lissajous figures

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Damped and forced oscillators, resonance

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Wave equation, traveling and standing waves

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Energy density and energy transmission in waves

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Group velocity and phase velocity

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Sound waves in media, Doppler Effect

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Fermat's Principle

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General theory of image formation

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Thick lens, thin lens and lens combinations

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Interference of light, optical path retardation

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Fraunhofer diffraction

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Rayleigh criterion and resolving power

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Diffraction gratings

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Polarization: linear, circular and elliptic polarization

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Double refraction and optical rotation

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Electricity and Magnetism (17 subtopics) Topic Select All

Coulomb's law, Gauss's law

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Electric field and potential

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Electrostatic boundary conditions

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Solution of Laplace's equation for simple cases

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Conductors, capacitors, dielectrics

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Dielectric polarization, volume and surface charges

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Electrostatic energy

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Biot-Savart law, Ampere's law

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Faraday's law of electromagnetic induction

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Self and mutual inductance

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Alternating currents

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Simple DC and AC circuits with R, L and C components

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Displacement current, Maxwell's equations

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Plane electromagnetic waves, Poynting's theorem

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Reflection and refraction at a dielectric interface

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Transmission and reflection coefficients

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Lorentz Force and motion of charged particles in electric and magnetic fields

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Kinetic theory, Thermodynamics (17 subtopics) Topic Select All

Elements of Kinetic theory of gases

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Velocity distribution and equipartition of energy

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Specific heat of Mono-, di- and tri-atomic gases

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Ideal gas, van-der-Waals gas and equation of state

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Mean free path

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Laws of thermodynamics

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Zeroth law and concept of thermal equilibrium

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First law and its consequences

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Isothermal and adiabatic processes

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Reversible, irreversible and quasi-static processes

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Second law and entropy

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Carnot cycle

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Maxwell's thermodynamic relations

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Thermodynamic potentials and their applications

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Phase transitions and Clausius-Clapeyron equation

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Ideas of ensembles

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Maxwell-Boltzmann, Fermi-Dirac and Bose Einstein distributions

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Modern Physics (17 subtopics) Topic Select All

Inertial frames and Galilean invariance

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Postulates of special relativity

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Lorentz transformations

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Length contraction, time dilation

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Relativistic velocity addition theorem

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Mass energy equivalence

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Blackbody radiation, photoelectric effect, Compton Effect

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Bohr's atomic model, X-rays

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Wave-particle duality, Uncertainty principle

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The superposition principle

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Calculation of expectation values

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Schrödinger equation and its solutions

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Reflection and transmission at a step potential

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Pauli Exclusion Principle

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Structure of atomic nucleus, mass and binding energy

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Radioactivity and its applications

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Laws of radioactive decay

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Solid State Physics, Devices and Electronics (19 subtopics) Topic Select All

Crystal structure, Bravais lattices and basis

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Miller indices

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X-ray diffraction and Bragg's law

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Intrinsic and extrinsic semiconductors

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Variation of resistivity with temperature

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Fermi level

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p-n junction diode, I-V characteristics

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Zener diode and its applications

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BJT: characteristics in CB, CE, CC modes

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Single stage amplifier, two stage R-C coupled amplifiers

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Simple Oscillators: Barkhausen condition, sinusoidal oscillators

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OPAMP and applications: Inverting and non-inverting amplifier

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Boolean algebra: Binary number systems

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Conversion from one system to another system

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Binary addition and subtraction

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Logic Gates AND, OR, NOT, NAND, NOR exclusive OR

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Truth tables

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Combination of gates

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de Morgan's theorem

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Algebra (15 subtopics) Topic Select All

Groups, subgroups, Abelian groups, non-abelian groups, cyclic groups, permutation groups

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Normal subgroups, Lagrange's Theorem for finite groups

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Group homomorphism and quotient groups

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Rings, Subrings, Ideal, Prime ideal, Maximal ideals

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Fields, quotient field

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Vector spaces

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Linear dependence and Independence of vectors

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Basis, dimension, linear transformations

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Matrix representation with respect to an ordered basis

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Range space and null space, rank-nullity theorem

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Rank and inverse of a matrix, determinant

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Solutions of systems of linear equations, consistency conditions

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Eigenvalues and eigenvectors

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Cayley-Hamilton theorem

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Symmetric, Skew symmetric, Hermitian, Skew-Hermitian, Orthogonal and Unitary matrices

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Real Analysis (13 subtopics) Topic Select All

Sequences and series of real numbers

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Convergent and divergent sequences, bounded and monotone sequences

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Convergence criteria for sequences of real numbers, Cauchy sequences

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Absolute and conditional convergence

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Tests of convergence for series of positive terms

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Functions of one variable: limit, continuity, differentiation

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Rolle's Theorem, Cauchy's Taylor's theorem

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Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets

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Completeness of R

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Power series (of real variable) including Taylor's and Maclaurin's

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Functions of two real variable: limit, continuity, partial derivatives, differentiability

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Maxima and minima, Method of Lagrange multipliers

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Homogeneous functions including Euler's theorem

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Complex Analysis (10 subtopics) Topic Select All

Functions of a complex Variable

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Differentiability and analyticity, Cauchy Riemann Equations

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Power series as an analytic function

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Properties of line integrals

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Goursat Theorem, Cauchy theorem

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Consequence of simply connectivity, index of a closed curves

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Cauchy's integral formula

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Morera's theorem, Liouville's theorem

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Fundamental theorem of Algebra

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Harmonic functions

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Integral Calculus (6 subtopics) Topic Select All

Integration as the inverse process of differentiation

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Definite integrals and their properties

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Fundamental theorem of integral calculus

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Double and triple integrals, change of order of integration

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Calculating surface areas and volumes using double integrals

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Calculating volumes using triple integrals

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Differential Equations (7 subtopics) Topic Select All

Ordinary differential equations of the first order of the form y'=f(x,y)

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Bernoulli's equation, exact differential equations, integrating factor

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Orthogonal trajectories

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Homogeneous differential equations-separable solutions

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Linear differential equations of second and higher order with constant coefficients

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Method of variation of parameters

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Cauchy-Euler equation

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Vector Calculus (4 subtopics) Topic Select All

Scalar and vector fields, gradient, divergence, curl and Laplacian

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Scalar line integrals and vector line integrals

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Scalar surface integrals and vector surface integrals

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Green's, Stokes and Gauss theorems and their applications

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Linear Programming (7 subtopics) Topic Select All

Convex sets, extreme points, convex hull

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Hyper plane & polyhedral Sets

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Convex function and concave functions

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Concept of basis, basic feasible solutions

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Formulation of Linear Programming Problem (LPP)

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Graphical Method of LPP

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Simplex Method

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Sequences and Series (2 subtopics) Topic Select All

Convergence of sequences of real numbers

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Comparison, root and ratio tests for convergence of series of real numbers

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Differential Calculus (4 subtopics) Topic Select All

Limits, continuity and differentiability of functions of one and two variables

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Rolle's Theorem, mean value theorems, Taylor's theorem

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Indeterminate forms

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Maxima and minima of functions of one and two variables

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Integral Calculus (4 subtopics) Topic Select All

Fundamental theorems of integral calculus

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Double and triple integrals

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Applications of definite integrals

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Arc lengths, areas and volumes

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Matrices (5 subtopics) Topic Select All

Rank, inverse of a matrix

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Systems of linear equations

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Linear transformations, eigenvalues and eigenvectors

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Cayley‐Hamilton theorem

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Symmetric, skew‐symmetric and orthogonal matrices

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Differential Equations (2 subtopics) Topic Select All

Ordinary differential equations of the first order of the form y' = f(x,y)

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Linear differential equations of the second order with constant coefficients

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Descriptive Statistics and Probability (7 subtopics) Topic Select All

Measure of Central tendency

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Measure of dispersion, skewness and Kurtosis

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Elementary analysis of data

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Axiomatic definition of probability and properties

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Conditional probability, multiplication rule

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Theorem of total probability

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Bayes' theorem and independence of events

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Random Variables (4 subtopics) Topic Select All

Probability mass function, probability density function and cumulative distribution functions

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Distribution of a function of a random variable

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Mathematical expectation, moments and moment generating function

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Chebyshev's inequality

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Standard Distributions (3 subtopics) Topic Select All

Binomial, negative binomial, geometric, Poisson, hyper-geometric, uniform, exponential, gamma, beta and normal distributions

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Poisson and normal approximations of a binomial distribution

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Chi-square distribution, t-distribution and F-distribution

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Joint Distributions (4 subtopics) Topic Select All

Joint, marginal and conditional distributions

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Distribution of functions of random variables

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Product moments, correlation, simple linear regression

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Independence of random variables

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Limit Theorems (2 subtopics) Topic Select All

Weak law of large numbers

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Central limit theorem (i.i.d. with finite variance case only)

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Estimation (7 subtopics) Topic Select All

Unbiasedness, consistency and efficiency of estimators

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Method of moments and method of maximum likelihood

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Sufficiency, factorization theorem

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Completeness, Rao‐Blackwell and Lehmann‐Scheffe theorems

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Uniformly minimum variance unbiased estimators

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Rao‐Cramer inequality

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Confidence intervals for the parameters of univariate normal, two independent normal, and one parameter exponential distributions

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Testing of Hypotheses (3 subtopics) Topic Select All

Basic concepts

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Applications of Neyman‐Pearson Lemma for testing simple and composite hypotheses

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Likelihood ratio tests

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Sampling and Designs of Experiments (3 subtopics) Topic Select All

Simple random sampling, stratified sampling and Cluster sampling

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One-way, two-way analysis of variance

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CRD, RBD, LSD and 2² and 2³ factorial experiments

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Gaseous State (4 subtopics) Topic Select All

Behavior of real gases

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van der Waals equation of state

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Kinetic molecular model of a gas

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Maxwell distribution

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Liquid State (4 subtopics) Topic Select All

Structure and physical properties of liquids

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Vapour pressure, surface tension, viscosity

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Effect of addition of various solutes

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Structure of water

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Ionic Equilibria (7 subtopics) Topic Select All

Strong, moderate and weak electrolytes

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Ionization of weak acids and bases

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Salt hydrolysis

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Buffer solutions

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Solubility and solubility product

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Brönsted-Lowry concept of acid-base reactions

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Lewis acid-base concept

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Solid State (4 subtopics) Topic Select All

Nature of the solid state

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X-ray diffraction

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Various types of defects in crystals

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Glasses and liquid crystals

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Thermodynamics (5 subtopics) Topic Select All

First law of thermodynamics

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Thermochemistry

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Second Law of thermodynamics

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Third law of thermodynamics

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Free Energy Functions

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Partial molar quantities (3 subtopics) Topic Select All

Partial molar quantities

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Gibbs-Duhem equation

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Chemical potential of ideal mixtures

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Dilute solutions or Colligative Properties (3 subtopics) Topic Select All

Dilute solutions

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Raoult's and Henry's Laws

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Colligative properties

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Molecular Spectroscopy & Photochemistry (6 subtopics) Topic Select All

Interaction of electromagnetic radiation with molecules

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Rotation spectroscopy

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Vibrational spectroscopy

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Raman spectroscopy

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Electronic spectroscopy

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Photophysical and photochemical processes

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Chemical Kinetics (4 subtopics) Topic Select All

Order and molecularity of a reaction

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Rate laws

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Temperature dependence of reaction rates

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Collision theory of reaction rates

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Catalysis (3 subtopics) Topic Select All

Types of catalyst

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Mechanisms of catalyzed reactions

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Enzyme catalysis

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Surface chemistry (4 subtopics) Topic Select All

Physical adsorption, chemisorption

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Adsorption isotherms

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BET theory

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Adsorption in solution

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Phase Equilibria (4 subtopics) Topic Select All

Gibbs Phase Rule

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Phase diagrams

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Binary solutions

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Nernst distribution law

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Introduction to Quantum Chemistry (5 subtopics) Topic Select All

Wave function and Schrödinger equation

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Simple harmonic oscillator model

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Rigid rotator model

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Hydrogen atom and hydrogen-like ions

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Valence bond and molecular orbital approaches

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Conductance (4 subtopics) Topic Select All

Arrhenius theory of electrolytic dissociation

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Conductivity and molar conductivity

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Kohlrausch law

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Applications of conductance measurement

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Electrochemistry (5 subtopics) Topic Select All

Faraday's laws of electrolysis

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Chemical cells

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Electromotive force

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Concentration cells

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Potentiometric titrations

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Atomic Structure (7 subtopics) Topic Select All

Bohr's theory

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Wave mechanics

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Quantum numbers

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Shapes of orbitals

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Pauli's Exclusion Principle

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Hund's rule

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Aufbau's principle

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Periodicity of Elements (2 subtopics) Topic Select All

s, p, d, f block elements

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Periodic properties

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Chemical Bonding (3 subtopics) Topic Select All

Ionic bond

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Covalent bond

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Molecular orbital theory

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Metallic bonding and Weak chemical forces (2 subtopics) Topic Select All

Metallic Bond

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Weak Chemical Forces

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Oxidation-Reduction and general principle of metallurgy (4 subtopics) Topic Select All

Redox equations

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Standard Electrode Potential

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Ellingham diagrams

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Methods of purification of metals

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Chemistry of s and p Block Elements (5 subtopics) Topic Select All

Inert pair effect

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Allotropy and catenation

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Hydrides

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Oxides and oxoacids

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Inter-halogen compounds

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Noble Gases (3 subtopics) Topic Select All

Occurrence and uses

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Preparation and properties of xenon compounds

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Bonding in noble gas compounds

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Inorganic Polymers (3 subtopics) Topic Select All

Types of inorganic polymers

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Silicones and siloxanes

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Borazines, silicates, phosphazenes, polysulphates

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Coordination Chemistry (5 subtopics) Topic Select All

Werner's theory

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Valence bond theory

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Crystal field theory

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IUPAC nomenclature

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Isomerism in coordination compounds

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Transition Elements (3 subtopics) Topic Select All

General group trends

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Stability of various oxidation states

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Chemistry of Ti, V, Cr Mn, Fe and Co

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Lanthanoids and Actinides (4 subtopics) Topic Select All

Electronic configuration

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Oxidation states

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Lanthanide contraction

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Separation of lanthanides

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Bioinorganic Chemistry (4 subtopics) Topic Select All

Metal ions in biological systems

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Geochemical effect on distribution of metals

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Toxicity of metal ions

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Iron and its application in biosystems

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Organometallic Compounds (4 subtopics) Topic Select All

Definition and classification

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Metal carbonyls

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General methods of preparation

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Structures of mononuclear and binuclear carbonyls

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Basics of Organic Chemistry (6 subtopics) Topic Select All

Classification and Nomenclature

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Hybridization

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Electronic Displacements

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Organic acids and bases

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Reaction intermediates

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Types of organic reactions

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Stereochemistry (4 subtopics) Topic Select All

Concept of asymmetry

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Geometrical isomerism

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Optical Isomerism

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Relative and absolute configuration

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Chemistry of Aliphatic Hydrocarbons (4 subtopics) Topic Select All

Chemistry of alkanes

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Chemistry of alkenes and alkynes

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Elimination reactions

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Addition reactions

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Cycloalkanes and Conformational Analysis (2 subtopics) Topic Select All

Cycloalkanes and stability

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Conformation analysis

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Aromatic Hydrocarbons (2 subtopics) Topic Select All

Aromaticity

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Electrophilic aromatic substitution

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Chemistry of Halogenated Hydrocarbons (3 subtopics) Topic Select All

Alkyl halides

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Aryl halides

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Organometallic compounds

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Alcohols, Phenols, Ethers and Epoxides (3 subtopics) Topic Select All

Alcohols: preparation and properties

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Phenols: preparation and properties

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Ethers and Epoxides: preparation and reactions

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Carbonyl Compounds (5 subtopics) Topic Select All

Structure, reactivity and preparation

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Nucleophilic additions

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Condensation reactions

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Oxidations and reductions

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Active methylene compounds

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Carboxylic Acids and their Derivatives (3 subtopics) Topic Select All

Preparation and reactions of carboxylic acids

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Reactions of acid derivatives

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Comparative study of nucleophilic substitution at acyl group

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Sulphur containing compounds (1 subtopics) Topic Select All

Preparation and reactions of thiols, thioethers and sulphonic acids

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Nitrogen Containing Functional Groups (3 subtopics) Topic Select All

Nitro compounds, nitriles and isonitriles

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Amines

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Diazonium salts

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Polynuclear Hydrocarbons (2 subtopics) Topic Select All

Reactions of naphthalene phenanthrene and anthracene

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Structure and derivatives of naphthalene and anthracene

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Heterocyclic Compounds (3 subtopics) Topic Select All

Classification and nomenclature

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Synthesis and reactions of various heterocycles

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Structure elucidation of indole, quinoline, and isoquinoline

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Alkaloids (3 subtopics) Topic Select All

Natural occurrence and general structural features

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Isolation and physiological action

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Structure elucidation and synthesis of specific alkaloids

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Terpenes (3 subtopics) Topic Select All

Occurrence and classification

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Isoprene rule

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Elucidation of structure and synthesis of specific terpenes

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Organic Spectroscopy (4 subtopics) Topic Select All

UV Spectroscopy

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IR Spectroscopy

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NMR Spectroscopy

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Mass Spectrometry

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