### Delhi CEE Syllabus:

### (a)Mathematics:

**Complex Numbers:**

Algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, cube roots of unity, triangle inequality.

**Matrices and Determinants:**

Determinants and Matrices of order two and three properties of determinants, evaluation of determinants, addition and multiplication of matrices, adjoint and inverse of a matrix. Solution of simultaneous linear equations using determinants.

**Quadratic Equations:**

Quadratic Equations and their solutions, relation between roots and coefficients, nature of roots, formation of quadratic equations with given roots.

**Permutations and Combinations:**

Fundamental principle of counting, permutation as an arrangement and combination as a selection, meaning of P(n,r) and C(n,r) simple applications.

**Sequences and Series:**

Arithmetic, Geometric and Harmonic progressions. Relation between A.M and H.M. Special series n, n2, n3, Arithmetico-Geometric series, exponential and logarithmic series.

**Vector Algebra:**

Vector and scalars, addition of two vector, components of a vector in two and three dimensional space, scalar and vector products, scalar and vector triple products. Application of vector to plane geometry.

**Trigonometry:**

Trigonometrical identities and equations. Inverse trigonometric functions and their properties. Properties of triangles including centroid, incentre, circumcentre and orthocenter. Solutions of triangles. Height and distances

**Measures of Central Tendency and Dispersion:**

Calculation of mean, median and mode, standard deviation, variance and mean deviation for grouped and ungrouped data.

**Probability:**

Probability of an event, addition and multiplication theorems of probability and their applications. Conditional probability; Baye’s theorem. Probability distribution of a random variate-Binomial and Poisson distributions and their properties.

**Differential Calculus:**

Polynomial, rational, trigonometric, logarithmic and exponential functions. Graphs of simple functions. Limits, continuity and differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order up to two. Applications of derivatives-maxima and minima of functions of one variable, tangents and normals, Rolle’s and Lagrange’s mean value theorems.

**Integral Calculus:**

Integral as an anti derivative, fundamental integral involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution by parts and by partial fractions. Integration using trigonometric identities. Integral as a limit of sum. Properties of definite integrals. Evaluation of definite integral, determining areas of the regions bounded by simple curves.

**Differential equations:**

Formation of differential equations. Solutions of first order differential equations-the method of separation of variable, homogeneous and linear differential equations.

**Two Dimensional Geometry:**

Review of Cartesian system of rectangular co-ordinates in a plane, distance formula, area of triangle, condition for the colinearity of three points, slope of a line, parallel and perpendicular lines, and intercepts of a line on the coordinate axes.

**The Straight line and Pair of Straight Lines:**

Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, distance of a point from a line. Equations of internal and external bisectors of angles between two lines, equation of a family of lines passing through the point of intersection of two lines, point of intersections and angles between two lines. Pair of straight lines-condition for the general second degree equation to represent a pair of lines, point of intersection and angle between pair of lines through the origin, combined equation of the bisector of the angles between a pair of lines

**Circles and Family of Circles:**

Equation of a circle-standard form, general form, parametric form, equation of a circle when the end points of a diameter are given. Radius and centre of a circle, points of intersection of a line and a circle. Condition for a line to be tangent, equation of a family of circles through the intersection of two circles, condition for two intersecting circles to be orthogonal.

**Conic Sections:**

Sections of Cones, equation of conic sections (parabola, ellipse and hyperbola) in standard forms, conditions for a line to be tangent and points(s) of tangency.

### (b)Chemistry:

**Basic Concepts:**

Atomic and molecular masses; Chemical Equation and Stoichiometry.

**States of Matter:**

Gaseous State: Gas laws, Avogadro’s hypothesis and gas equations; Kinetic Theory of Gases; Liquefaction, Critical Phenomena; Liquid State and Solid State.

**Atomic Structure:**

Bohr’s Model; de Broglie equation; Quantum Mechanical Model; Aufbau’s Principle, Pauli’s Exclusion Principles, Hund’s Rule, electronic configuration; Bonding:Lewis structure, SEPR theory, hybridization, ionic, covalent and coordinate covalent bonds, bonding in solid state, MO theory, bond order and magnetic properties of H2, O2, N2,F2.

**Solutions:**

Types, units of concentration, Raoult’s Law, colligative properties, abnormal molecular weights.

**Chemical Energetic and Thermodynamics:**

Internal Energy, Enthalpy, Hess’s law, First & Second laws of thermodynamics & applications; entropy, free energy; spontaneity of a chemical reaction.

**Chemical Kinetics & Chemical Equilibrium:**

Rate and orders of a reaction; activation energy; catalyst; rate law; physical & chemical equilibria; Le Chateliers’s principle; acid base equilibrium; acids and bases; pH; buffers; solubility product.

**Redox reactions, Electrochemistry & Surface Chemistry:**

Electron Transfer Concepts of Oxidation and Reduction; Electrochemical cells; emf; Nernst Equation; Molar conductivity; Kohlrausch’s Law; Fuel Cells; Corrosion. Physical & Chemical adsorbtion isotherms; Colloids: Preparation & Properties; Homogenous and Hetrogenous Catalysis; Enzymes.

**Periodic Properties, Chemical Families, Chemistry of Non Metals & Metals:**

Modern periodic law; ionization energy, electron affinity, atomic radii, valency, trends in groups and periods. Chemistry of s and p block elements; alkali metals, Alakaline earth metals, Boron, Carbon, nitrogen, oxygen halogen and noble gases families; hydrogen: position, Ortho para, isotopes, hybrids; Oxygen, water, Hydrogen peroxide, hard and soft water; Ammonia, Nitrogen oxides, nitric acid; Boron, Boric Acid, Borax; Carbides, Allotropy of Carbon; Sodium. Magnesium, Copper, Silver, Zinc, transition Metals, and Lanthanides: extraction, properties and uses.

**Co-Ordination Chemistry:**

Nomenclature, isomerism and bonding in coordination compounds; Werner’s Theory.

**Nuclear Chemistry:**

Radioactivity, Nuclear reactions, Radiocarbon dating, Radioactive series, Artificial Transmutation.

**Organic Chemistry Fundamentals:**

Purification; detection and estimation of elements; Empirical and Molecular formulae, Classification, Functional Groups, IUPAC Nomenclature, Hemolytic and Heterolytic Bond fissions, structural and Stereoisomerisms, Free radicals, Carbocations and carbonions; Substitution, addition, elimination and rearrangement reactions.

**Hydrocarbons & Halo Alkanes & Halo Alkenes:**

Alkanes, Alkenes and Alkynes, Halo alkanes & Halo alkenes: Preparation, properties and uses; Aromatic Hydrocarbons: Benzene, Structure, Resonance, Substitution in Benzene. Petroleum: Cracking, reforming, Octane Number.

**Organic Compounds containing Oxygen, Nitrogen:**

Preparation properties and uses of Aromatic and aliphatic alcohols, Polyhydric alcohols, ethers, aldehydes, ketones, carboxylilc acids and their derivatives; Cyanides, isocyanides, nitro compounds and amines.

**Synthetic and Natural polymers & Bi molecular:**

Natural and Synthetic polymers; Teflon, PVC, Polystyrene, Nylon 66 Terylene, and Bakelite, carbohydrates, amino acids and peptides, Nucleic Acids, lipids etc.

**Chemistry in Action & Environmental Chemistry:**

Dyes, Medicines (Antipyretics, Analgesics and Antibiotics), Rocket Propellants; Acid Rain, Ozone Hole, Green House Effect, Global Warming Industrial Pollution.

### (c)Physics:

**Physical World and Measurement :**

Need for measurement; Units of measurement; Systems of units; SI units, Fundamental and derived units, Length, mass and time measurements; Accuracy and precision of measuring instruments, Errors in measurement; Significant figures. Dimensions of physical quantities, dimensional analysis and its applications.

**Kinematics :**

Motion in a straight line, Position-time graph, speed and velocity, Uniform and non-uniform motion, average speed and instantaneous velocity.

Uniformly accelerated motion, velocity-time, position-time graphs, relations for uniformly accelerated motion (graphical treatment).

Elementary concepts of differentiation and integration for describing motion.

Scalar and vector quantities; Position and displacement vectors, general vectors and notation; Equality of vectors, multiplication of vectors by a real number; Addition and subtraction of vectors; Unit vector, Resolution of a vector in a plane-rectangular components, Multiplication of vectorscalar and vector products; vectors in three dimensions (elementary idea only). Motion in a plane, Cases of uniform velocity and uniform acceleration-Projectile motion. Uniform circular motion.

**Laws of Motion :**

Force and inertia, Newton’s first law of motion; Momentum, Newton’s second law of motion, Impulse; Newton’s third law of motion; Law of conservation of linear momentum and its applications; Equilibrium of concurrent forces; Static and Kinetic friction, Laws of friction, rolling friction, lubrication; Examples of variable-mass situation.

Dynamics of uniform circular motion; Centripetal force, examples of circular motion (vehicle on level circular road, vehicle on banked road); Inertial and non-inertial frames (elementary idea).

**Work, Energy and Power :**

Work done by a constant force and a variable force; Kinetic energy, Power; Work-energy theorem. Notion of Potential energy, potential energy of a spring, conservative forces; conservation of mechanical energy (Kinetic and potential energies), Non-conservative forces; elastic and inelastic collisions in one and two dimensions.

Different forms of energies in nature, Mass-energy equivalence (qualitative idea only).

**Motion of System of Particles and Rigid Body :**

Center of mass of a two-particle system, generalization to N particles, momentum conservation and center of mass motion, Application to some familiar systems; center of mass of a rigid body.

Moment of a force, Torque, angular momentum, physical meaning of angular momentum, conservation of angular momentum with some examples (Planetary motion).

Equilibrium of rigid bodies, rigid body rotation and equation of rotational motion, comparison of linear and rotational motions; Moment of inertia and its physical significance, radius of gyration, parallel and perpendicular axes theorems (statements without proofs); Moment of inertia of circular ring, disc, cylinder without slipping.

Examples of Binary system in nature (Binary Stars, Earth-moon system, diatomic molecules).

**Gravitation :**

The universal law of gravitation, Gravitational constant; acceleration due to gravity and its variation with the altitude, latitude, depth and rotation of the earth; Mass of the earth.

Gravitational potential energy near the surface of the earth, gravitational potential; Escape velocity, orbital velocity of satellite, Weightlessness, motion of satellite, geostationary and polar satellites; Statement of Kepler’s law of planetary motion; proof of second and third law (circular orbits); Inertial and Gravitational mass.

**Mechanics of Solids and Fluids :**

States of Matter, Inter-atomic and inter-molecular forces.

A. Solids: Elastic behaviour, Stress-Strain relationship, Hooke’s law, Young’s modulus, bulk modulus,

shear modulus, modulus of rigidity,some practical examples.

B. Fluids: Pressure due to fluid column. Pascal’s law and its applications (hydraulic lift and hydraulic

brakes), Effect of gravity on fluid pressure, Buoyancy, floatation and Archimedes’ principle; Viscosity,

Stokes’ law, Terminal velocity, Streamlined flow, Reynolds number, Bernoulli’s theorem and its applications. Surface energy and surface tension, angle of contact, applications of surface tension ideas in (i) formation of drops and bubbles, (ii) capillary rise.

**Heat and Thermodynamics :**

Kinetic theory of gases-assumptions, concept of pressure, Kinetic energy and temperature; mean, rms and most probable speed, degrees of freedom, li::Iw of equipartition of energy (statement only), concept of mean free path, Avogadro’s number.

Thermal equilibrium and temperature (zeroth law of thermodynamics), Heat, work and internal energy; Thermal expansion-thermometry; First law of thermodynamics, specific heat, specific heat of gases at constant volume and pressure (monoatomic, diatomic gases); specific heat of solids (Dulong and Petit’s law). Thermodynamical variables and equation of state, phase diagrams; ideal gas equation, isothermal and adiabatic processes;reversible and irreversible processes; Carnot engine and refrigerator or heat pump. Efficiency and coefficient of performance of heat engines; second law of theImodynamics (statement only) and some practical applications.

Transfer of heat-conduction, convection and radiation;Thermal conductivity of solids; Black body radiation- Kirchhoffs law, Wien’s displacement law, Stefan’s law (statements only); Newton’s law of cooling; solar constant and surface temperature of the sun.

**Oscillations :**

Periodic motion -period, frequency, displacement as a function of time and periodic functions. Simple harmonic motion (S.H.M.) and its equation; Phase, uniform circular motion and simple harmonic motion; oscillations of a spring-restoring force and force constant; Energy in S.H.M. Kinetic and potential energies; Simple pendulum -derivation of expression for its time period; Free, forced and damped oscillations (qualitative ideas only), resonance; coupled oscillations.

**Waves :**

Longitudinal and transverse waves, wave motion, speed of wave motion, Displacement relation for a progressive wave; principle of superposition of waves, Reflections of waves, standing waves in strings and pipes, fundamental mode and harmonics, Beats, Doppler effect.

**Electrostatics :**

Frictional electricity, charges and their conservation; Coulomb’s law-Forces between two point electric charges, Forces between multiple electric charges; Superposition principle and continuous charge distribution. Electric field and its physical significance, electric field due to a point charge, electric field lines; Electric dipole, electric field due to a dipole and behaviour of dipole in a uniform electric field.

Electric potential-physical meaning, potential difference, electric potential due to a point charge, a dipole and system of charges; Equipotential surfaces, Electrical potential energy of a system of two point charges and of electric dipoles in an electrostatic field.

Electric flux, Statement of Gauss’s theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell.

Conductors and insulators, presence of free charges and bound charges inside a conductor; Dielectrics and electric polarization, general concept of a capacitor and capacitance, combination of capacitors in series and in parallel, energy stored in a capacitor, capacitance of a parallel plate capacitor with and without dielectric medium between the plates; Van de Graff generator.

**Current Electricity :**

Electric current, flow of electric charges in a metallic conductor, drift velocity and mobility, and their relation with electric current; Ohm’s law, electrical resistance, V-I characteristics, Exceptions of Ohm’s law (Non-linear V-I characteristics), electrical resistivity and conductivity, classification of materials in terms of conductivity; Superconductivity (elementary idea); Carbon resistors, colour code for carbon resistors; combination of resistances -series and parallel. Temperature dependence of resistance.

Internal resistance of a cell, Potential difference and emf of a cell, combination of cells in series and in parallel.

Kirchoff’s laws -illustration by simple applications, Wheatstone bridge and its applications for temperature measurements, Meter bridge -special case of wheatstone bridge.

Potentiometer- principle and applications to measure potential difference and for comparing emfs of two cells. Electric power, thermal effects of current and Joule’s law; Chemical effects of current Faraday’s laws of electrolysis; Electro-chemical cells-Primary and secondary cells, solid state cells.

Thermoelectricity- Origin, elementary ideas of Seebeck effect, Thermocouple, Thermo emf, neutral and inversion temperatures. Measurement of temperature using a thermocouple.

**Magnetic Effect of Current and Magnetism :**

Concept of magnetic field, Oersted’s experiment, Biot-Savart’s law, magnetic field due to an infinitely long current carrying straight wire and a circular loop; Ampere’s circutallaw and its applications to straight and toroidal solenoids; Force on a moving charge in uniform magnetic and electric fields, Cyclotron; Force on current -carrying conductor in a uniform magnetic field. Forces between two parallel current-carrying conductors- definition of ampere. Torque experienced by a current loop in a uniform magnetic field, moving coil galvanometer -its current sensitivity and conversion to ammeter and voltmeter.

Current loop as a magnetic dipole and its magnetic dipole moment; Magnetic dipole moment of a revolving electron; Magnetic field intensity due to magnetic dipole (bar magnet) along the axis and perpendicular to the axis; Torque on a magnetic dipole (bar magnet) in a uniform magnetic field; Bar magnet as an equivalent solenoid, Magnetic field lines; Earth’s magnetic field and magnetic elements; Para, dia and ferro-magnetic substances with examples, Electro-magnets and permanent magnets.

**Electromagnetic Induction and Alternating Current :**

Electromagnetic induction, Faraday’s laws, Induced emf and current, Lenz’s law, Eddy currents, self and mutual inductances.

Alternating current, peak and rms values of alternating current/voltage, reactance and impedance.

LCR oscillations, LCR series circuit (Phasor diagram) – Resonant circuits and Q-factor; Power in AC circuits, wattless current. AC generator and Transformer.

**Electromagnetic Waves :**

Electromagnetic waves and their characteristics (qualitative ideas only); Transverse nature of electromagnetic waves.

Electromagnetic spectrum (Radio, microwaves, infra-red, optical, ultraviolet, X-rays, gamma rays including elementary facts about their uses; Propagation of electromagnetic waves in atmosphere

**Optics :**

Refraction of light, total internal reflection and its applications, spherical lenses, thin lens formula lens maker’s formula; Magnification, Power of a lens, combination of thin lenses in contact Refraction and dispersion of light due to a prism, Scattering of light – Blue colour of the sky and reddish appearance of the sun at sun-rise and sun-set.

Optical instruments -Compound microscope, astronomical telescope (refraction and reflection type) and their magnifying powers.

Wave front and Huygen’s principles; Reflection and refraction of plane wave at a plane surface using wave fronts (qualitative idea); Interference-Young’s double slit experiment and expression for fringe width, coherent sources and sustained interference of light; Diffraction-diffraction due to a single slit, width of central maximum, difference between interference and diffraction; Resolving power of microscope and telescope; Polarisation, Plane polarised light, Brewster’s law; Use of plane polarised light and polaroids.

**Dual Nature of Matter and Radiations :**

Photo-electric effect, Einstein Photo-electric equation -particle nature of light, photo-cell, Matte waves-wave nature of particles, de-Broglie relation, Davison and Germer experiment.

**Atomic Nucleus :**

Alpha-particle scattering experiment, size of the nucleus, composition of the nucleus-protons and neutrons. Nuclear instability -Radioactivity – Alpha, Beta and Gamma particles / rays and their properties, radioactive decay law, simple explanation of α – decay, β -decay and γ – decay. Mass. energy relation, mass defect, Binding Energy per nucleon, its variation with mass number, Nature of nuclear forces, nuclear reaction -Nuclear fission and Nuclear fusion.

**Solids and Semi-Conductor Devices :**

Energy bands in solids/(qualitative ideas only), difference between metals, insulators and semiconductors using band theory; Intrinsic and extrinsic semi-conductors, p-n junction, Semiconductor diode-characteristics under forward and reverse bias conditions, diode as a rectifier, solar cell, photodiode, LED, zener diode as a voltage regulator; Junction transistor, transistor action, characteristics of a transistor; Transistor as an amplifier (common emitter configuration) and oscillator; Logic gates (OR, AND, NOT, NAND and NOR); Elementary ideas about IC.

**Principles of Communication :**

Elementary idea of analog and digital communication; Need for modulation; Modulation-amplitude, frequency and pulse modulations; Elementary idea about demodulation, Data transmission and retrieval Fax and Modem. Space Communication: Propagation of E-M. waves in atmosphere. Sky and space wave propagation. Satellite communication. Applications in Remote Sensing.

**Line Communication :**

2-wire lines, cables, telephone links; optical communication (optical fiber, Lasers), elementary principle of light modulation.

**IMPORTANT NOTE: THE ABOVE ARTICLE WAS ONLY FOR INFORMATION, THE DELHI CEE HAS BEEN REPLACED BY THE JEE (MAINS).**

**Also See:**

Delhi CEE Eligibility Criteria