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Delhi-CEE is conducted by the University of Delhi for admission to First Semester of Bachelor of Engineering Courses for DELHI REGION candidates.

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## Delhi University Combined Entrance Examination (Delhi-CEE) Syllabus

### 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., G.M. and H.M. Special series’ n, n2, n3, Arithmetico-Geometric series, exponential and logarithmic series.**Vector Algebra:**Vectors and scalars, addition of two vectors, components of a vector in two and three dimensional space, scalar and vector products, scalar and vector triple products. Application of vectors to plane geometry.**Trigonometry:**Trigonometrical identities and equations. Inverse trigonometric functions and their properties. Properties of triangles including centroid, incentre, circumcentre and orthocentre. Solution of triangles. Heights 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; Bayes’ 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 integrals 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 variables, homogeneous and linear differential equations.**Two Dimensional Geometry:**Review of Cartesian system of rectangular co-ordinates in a plane, distance formula, area of a triangle, condition for the co linearity 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 bisectors 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, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, conditions for a line to be a tangent and point(s) of tangency.

### 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 & 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.**x**.**Nuclear Chemistry**

Radioactivity, Nuclear reactions, Radiocarbon dating, Radioactive series, Artificial Transmutation.**xi. 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 carbanions; Substitution, addition, elimination and rearrangement reactions.**xii.****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.**xiii.****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.**xiv.****Synthetic and Natural Polymers & Bimolecular**

Natural and Synthetic polymers; Teflon, PVC, Polystyrene, Nylon 66 Terylene, and Bakelite; carbohydrates, amino acids and peptides, Nucleic Acids, lipids etc.**xv**.**Chemistry in Action & Environmental Chemistry**

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

### Physics

- Physical World & Measurement
- Kinematics
- Laws of Motion
- Work, energy and Power
- Motion of System of Particles and Rigid Body
- Gravitation
- Mechanics of solids and fluids
- Heat and thermodynamics
- Oscillations
- Waves
- Electrostatics
- Current electricity
- Magnetic effect of current and magnetism
- Electromagnetic induction and altering current
- Electromagnetic waves
- Optics
- Dual nature of matter and radiations
- Atomic nucleus
- Solids and semi conductor devices
- Principles of communication
- Line communication