CUET Syllabus 2023 For Science Students (PCM)
CUET Syllabus 2023 For Science Students (PCM) – In this context, we are going to talk about the CUET syllabus 2023 for science students. In this context, we will provide you with the syllabus of all three subjects. It will serve as a helpful article for students who were in search of this kind of article. So, read it till the end.
CUET Maths Syllabus
| 1. Algebra | (i) Matrices and types of Matrices (ii) Equality of Matrices, transpose of a Matrix, Symmetric and Skew Symmetric Matrix (iii) Algebra of Matrices (iv) Determinants (v) Inverse of a Matrix (vi) Solving of simultaneous equations using Matrix Method |
| 2. Calculus | (i) Higher order derivatives (ii) Tangents and Normals (iii) Increasing and Decreasing Functions (iv). Maxima and Minima |
| 3. Integration and its Applications | (i) Indefinite integrals of simple functions (ii) Evaluation of indefinite integrals (iii) Definite Integrals (iv) Application of Integration as area under the curve |
| 4. Differential Equations | (i) Order and degree of differential equations (ii) Formulating and solving of differential equations with variable separable |
| 5. Probability Distributions | (i) Random variables and its probability distribution (ii) Expected value of a random variable (iii) Variance and Standard Deviation of a random variable (iv). Binomial Distribution |
| 6. Linear Programming | (i) Mathematical formulation of Linear Programming Problem (ii) Graphical method of solution for problems in two variables (iii) Feasible and infeasible regions (iv) Optimal feasible solution |
| Section B1: Mathematics | |
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| UNIT I: RELATIONS AND FUNCTIONS | 1. Relations and Functions: Types of relations: Reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations. 2. Inverse Trigonometric Functions: Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions. |
| UNIT II: ALGEBRA | 1. Matrices: Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and skew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, ifit exists; (Here all matrices will have real entries). 2. Determinants: Determinant of a square matrix (up to 3×3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix |
| UNIT III: CALCULUS | 1. Continuity and Differentiability: Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function. Concepts of exponential, logarithmic functions. Derivatives of log x and ex. Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second-order derivatives. Rolle’s and Lagrange’s Mean Value Theorems(without proof) and their geometric interpretations. 2. Applications of Derivatives: Applications of derivatives: Rate of change, increasing/ decreasing functions, tangents and normals, approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations). Tangent and Normal. 3. Integrals: Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, only simple integrals of the type to be evaluated. Definite integrals as a limit of a sum. Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals. 4. Applications of the Integrals: Applications in finding the area under simple curves, especially lines, arcs of circles/ parabolas/ ellipses (in standard form only), and area between the two above said curves (the region should be clearly identifiable). 5. Differential Equations: Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables, homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type – dy/dx + Py = Q, where P and Q are functions of x or constant dx/dy + Px = Q, where P and Q are functions of y or constant |
| UNIT IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY | 1. Vectors : Vectors and scalars, magnitude and direction of a vector. Direction cosines/ ratios of vectors. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Scalar (dot) product of vectors, projection of a vector on a line. Vector(cross) product of vectors, scalar triple product. 2. Three-dimensional Geometry : Direction cosines/ ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines.Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane. |
| Unit V : LinearProgramming | Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints). |
| Unit VI : Probability | Multiplications theorem on probability. Conditional probability, independent events, total probability, Baye’s theorem. Random variable and its probability distribution, mean and variance of haphazard variable. Repeated independent (Bernoulli) trials and Binomial distribution. |
| Section B2: Applied Mathematics | |
| Unit I: Numbers, Quantification and Numerical Applications | A. Modulo Arithmetic: Define modulus of an integer, Apply arithmetic operations using modular arithmetic rules B. Congruence Modulo: Define congruence modulo, Apply the definition in various problems C. Allegation and Mixture: Understand the rule of allegation to produce a mixture at a given price, Determine the mean price of a mixture, Apply rule of allegation D. Numerical Problems: Solve real-life problems mathematically E. Boats and Streams: Distinguish between upstream and downstream, Express the problem in the form of an equation F. Pipes and Cisterns: Determine the time taken by two or more pipes to fill or G. Races and Games: Compare the performance of two players w.r.t. time, distance taken/ distance covered/ Work done from the given data H. Partnership: Differentiate between active partner and sleeping partner, Determine the gain or loss to be divided among the partners in the ratio of their investment with due consideration of the time volume/ surface area for solid formed using two or more shapes I. Numerical Inequalities: Describe the basic concepts of numerical inequalities, Understand and write numerical inequalities |
| UNIT II: ALGEBRA | A. Matrices and types of matrices: Define matrix, Identify different kinds of matrices B. Equality of matrices, Transpose of a matrix, Symmetric and Skew symmetric matrix: Determine equality of two matrices, Write transpose of given matrix, Define symmetric and skew symmetric matrix |
| UNIT III: CALCULUS | A. Higher Order Derivatives: Determine second and higher order derivatives, Understand differentiation of parametric functions and implicit functions Identify dependent and independent variables B. Marginal Cost and Marginal Revenue using derivatives: Define marginal cost and marginal revenue, Find marginal cost and marginal revenue C. Maxima and Minima: Determine critical points of the function, Find the point(s) of local maxima and local minima and corresponding local maximum and local minimum values, and Find the absolute maximum and absolute minimum value of a function |
| UNIT IV: PROBABILITY DISTRIBUTIONS | A. Probability Distribution: Understand the concept of Random Variables and their Probability Distributions, Find the probability distribution of the discrete random variable B. Mathematical Expectation: Apply arithmetic mean of frequency distribution to find the expected value of a random variable C. Variance: Calculate the Variance and S.D. of a random variable |
| UNIT V: INDEX NUMBERS AND TIME BASED DATA | A. Index Numbers: Define Index numbers as a special type of average B. Construction of Index numbers: Construct different types of index numbers C. Test of Adequacy of Index Numbers: Apply time reversal test |
| UNIT VI: INDEX NUMBERS AND TIME BASED DATA | A. Population and Sample: Define Population and Sample, Differentiate between population and sample, and Define a representative sample from a population B. Parameter and Statistics and Statistical Interferences: Define Parameter with reference to Population, Define Statistics with reference to Sample, Explain the relation between Parameter and Statistic, Explain the limitation of Statistic to generalize the estimation for population, Interpret the concept of Statistical Significance and Statistical Inferences, State Central Limit Theorem, Explain the relation between Population-Sampling Distribution-Sample |
| UNIT VII: INDEX NUMBERS AND TIME BASED DATA | A. Time Series: Identify time series as chronological data B. Components of Time Series: Distinguish between different components of the time series C. Time Series analysis for univariate data: Solve practical problems based on statistical data and Interpret |
| UNIT VIII: FINANCIAL MATHEMATICS | A. Perpetuity, Sinking Funds: Explain the concept of perpetuity and sinking fund, Calculate perpetuity, and Differentiate between sinking fund and saving account B. Valuation of Bonds: Define the concept of valuation of bonds and related terms, Calculate the value of the bond using the present value approach C. Calculation of EMI: Explain the concept of EMI, Calculate EMI using various methods D. Linear method of Depreciation: Define the concept of the linear method of Depreciation, Interpret cost, residual value and useful life of an asset from the given information, Calculate depreciation |
| UNIT IX: LINEAR PROGRAMMING | A. Introduction and related terminology: Familiarize with terms related to Linear Programming Problem B. Mathematical formulation of Linear Programming Problem: Formulate Linear Programming Problem C. Different types of Linear Programming Problems: Identify and formulate different types of LPP D. Graphical Method of Solution for problems in two Variables: Draw the Graph for a system of linear inequalities involving two variables and to find its solution graphically E. Feasible and Infeasible Regions: Identify feasible, infeasible and bounded regions F. Feasible and infeasible solutions, optimal feasible solution: Understand feasible and infeasible solutions, Find the optimal feasible solution |
CUET Physics Syllabus
| Unit I: Electrostatics | Electric charges and their conservation. Coulomb’s law – force between two point charges, forces between multiple charges; superposition principle, and continuous charge distribution. Electric field, electric field due to a point charge, electric field lines; electric dipole, electric field due to a dipole; torque on a dipole in a uniform electric 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 (field inside and outside). Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges; equipotential surfaces, the electrical potential energy of a system of two point charges, and electric dipoles in an electrostatic field. Conductors and insulators, free charges, and bound charges inside a conductor. Dielectrics and electric polarization, capacitors and capacitance, the combination of capacitors in series and in parallel, the capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor, Van de Graaff generator. |
| Unit II: Current Electricity | Electric current, the 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 (linear and non-linear), electrical energy and power, electrical resistivity and conductivity. Carbon resistors, colour code for carbon resistors; series and parallel combinations of resistors; temperature dependence of resistance. The internal resistance of a cell, potential difference, and emf of a cell, combination of cells in series and in parallel. Kirchhoff ’s laws and simple applications. Wheatstone bridge, metre bridge Potentiometer – principle, and applications to measure potential difference, and for comparing emf of two cells; measurement of internal resistance of a cell. |
| Unit III: Magnetic Effects of Current and Magnetism | Concept of the magnetic field, Oersted’s experiment. Biot – Savart law and its application to current carrying circular loop. Ampere’s law and its applications to infinitely long straight wire, straight and toroidal solenoids. Force on a moving charge in uniform magnetic and electric fields. Cyclotron. Force on a current-carrying conductor in a uniform magnetic field. The force between two parallel current carrying conductors – definition of ampere. Torque experienced by a current loop in a 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. The magnetic dipole moment of a revolving electron. Magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and perpendicular to its 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 ferromagnetic substances, with examples. Electromagnets and factors affecting their strengths. Permanent magnets. |
| Unit IV: Electromagnetic Induction andAlternating Currents | Electromagnetic induction; Faraday’s law, induced emf and current; Lenz’s Law, Eddy currents. Self and mutual inductance. Alternating currents, peak and rms value of alternating current/voltage; reactance and impedance; LC oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits, wattless current. AC generator and transformer. |
| Unit V: Electromagnetic Waves | Need for displacement current. Electromagnetic waves and their characteristics (qualitative ideas only). Transverse nature of electromagnetic waves. Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, x-rays, gamma rays) including elementary facts about their uses. |
| Unit VI: Optics | Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal reflection, and its applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lens maker’s formula. Magnification, power of a lens, combination of thin lenses in contact combination of a lens and a mirror. Refraction and dispersion of light through a prism. Scattering of light–blue colour of the sky and reddish appearance of the sun at sunrise and sunset. Optical instruments: Human eye, image formation, and accommodation, correction of eye defects (myopia and hypermetropia) using lenses. Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers. Wave optics: Wavefront and Huygens’ principle, reflection, and refraction of plane wave at a plane surface using wavefronts. Proof of laws of reflection and refraction using Huygens’ principle. Interference, Young’s double hole experiment and expression for fringe width, coherent sources, and sustained interference of light. Diffraction due to a single slit, width of central maximum. Resolving the power of microscopes and astronomical telescopes. Polarisation, plane polarised light; Brewster’s law, uses of plane polarised light and Polaroids. |
| Unit VII: Dual Nature of Matter and Radiation | Photoelectric effect, Hertz and Lenard’s observations; Einstein’s photoelectric equation – particle nature of light. Matter waves – wave nature of particles, de Broglie relation. Davisson-Germer experiment (experimental details should be omitted; only the conclusion should be explained.) |
| Unit VIII: Atoms and Nuclei | Alpha-particle scattering experiment; Rutherford’s model of atom; Bohr model, energy levels, hydrogen spectrum. Composition and size of nucleus, atomic masses, isotopes, isobars; isotones. Radioactivity – alpha, beta, and gamma particles/rays, and their properties; radioactive decay law. Massenergy relation, mass defect; binding energy per nucleon and its variation with mass number; nuclear fission and fusion. |
| Unit IX: Electronic Devices | Energy bands in solids (qualitative ideas only), conductors, insulators, and semiconductors; semiconductor diode – I-V characteristics in forward and reverse bias, diode as a rectifier; I-V characteristics of LED, photodiode, solar cell, and Zener diode; 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). Transistor as a switch. |
| Unit X: Communication Systems | Elements of a communication system (block diagram only); bandwidth of signals (speech, TV, and digital data); bandwidth of transmission medium. Propagation of electromagnetic waves in the atmosphere, sky, and space wave propagation. Need for modulation. Production and detection of an amplitude-modulated wave. |
CUET Chemistry Syllabus
| Unit I: Solid State | Classification of solids based on different binding forces: molecular, ionic covalent, and metallic solids, amorphous and crystalline solids(elementary idea), unit cell in two dimensional and three-dimensional lattices, calculation of density of unit cell, packing in solids, packing efficiency, voids, number of atoms per unit cell in a cubic unit cell, point defects, electrical and magnetic properties, Band theory of metals, conductors, semiconductors and insulators and n and p-type semiconductors. |
| Unit II: Solutions | Types of solutions, expression of concentration of solutions of solids in liquids, the solubility of gases in liquids, solid solutions, colligative properties – the relative lowering of vapour pressure, Raoult’s law, elevation of B.P., depression of freezing point, osmotic pressure, determination of molecular masses using colligative properties, abnormal molecular mass, Vant Hoff factor. |
| Unit III: Electrochemistry | Redox reactions; conductance in electrolytic solutions, specific and molar conductivity variations of conductivity with concentration, Kohlrausch’s Law, electrolysis and laws of electrolysis (elementary idea), dry cell – electrolytic cells and Galvanic cells; lead accumulator, EMF of a cell, standard electrode potential, Nernst equation and its application to chemical cells. Relation between Gibbs energy change and EMF of a cell, fuel cells; corrosion. |
| Unit IV: Chemical Kinetics | Rate of a reaction (average and instantaneous), factors affecting rates of reaction: concentration, temperature, catalyst; order and molecularity of a reaction; rate law and specific rate constant, integrated rate equations, and half-life (only for zero and first-order reactions); concept of collision theory (elementary idea, no mathematical treatment). Activation energy, Arrhenius equation. |
| Unit V: Surface Chemistry | Adsorption – physisorption and chemisorption; factors affecting adsorption of gases on solids; catalysis: homogenous and heterogeneous, activity and selectivity: enzyme catalysis; colloidal state: the distinction between true solutions, colloids, and suspensions; lyophilic, lyophobic multimolecular and macromolecular colloids; properties of colloids; Tyndall effect, Brownian movement, electrophoresis, coagulation; emulsions – types of emulsions. |
| Unit VI: General Principles and Processes of Isolation of Elements | Principles and methods of extraction – concentration, oxidation, reduction electrolytic method, and refining; occurrence and principles of extraction of aluminum, copper, zinc, and iron. |
| Unit VII: p-Block Elements | Group 15 elements: General introduction, electronic configuration, occurrence, oxidation states, trends in physical and chemical properties; nitrogen – preparation, properties, and uses; compounds of nitrogen: preparation and properties of ammonia and nitric acid, oxides of nitrogen ( structure only); Phosphorous-allotropic forms; compounds of phosphorous: preparation and properties of phosphine ,halides (PCl3, PCl5) and oxoacids (elementary idea only). Group 16 elements: General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; dioxygen: preparation, properties, and uses; classification of oxides; ozone. Sulphur – allotropic forms; compounds of sulphur: preparation, properties, and uses of sulphur dioxide; sulphuric acid: industrial process of manufacture, properties and uses, oxoacids of sulphur (structures only). Group 17 elements: General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; compounds of halogens: preparation, properties and uses of chlorine and hydrochloric acid, interhalogen compounds, oxoacids of halogens(structures only). Group 18 elements: General introduction, electronic configuration, occurrence, trends in physical and chemical properties, uses. |
| Unit VIII: d and f Block Elements | General introduction, electronic configuration, occurrence and characteristics of transition metals, general trends in properties of the first-row transition metals – metallic character, ionization enthalpy, oxidation states, ionic radii, colour, catalytic property, magnetic properties, interstitial compounds, alloy formation. Preparation and properties of K2Cr2O7 and KMnO4. Lanthanoids – electronic configuration, oxidation states, chemical reactivity, and lanthanoid contraction and its consequences. Actinoids –Electronic configuration, oxidation states, and comparison with lanthanoids. |
| Unit IX: Coordination Compounds | Coordination compounds: Introduction, ligands, coordination number, colour, magnetic properties and shapes, IUPAC nomenclature of mononuclear coordination compounds, bonding, Werner’s theory VBT, CFT; isomerism (structural and stereo)importance of coordination compounds (in qualitative analysis, extraction of metals and biological systems). |
| Unit X: Haloalkanes and Haloarenes | Haloalkanes: Nomenclature, nature of C-X bond, physical and chemical properties, mechanis mof substitution reactions. Optical rotation. Haloarenes: Nature of C-X bond, substitution reactions (directive influence of halogen for monosubstituted compounds only). Uses and environmental effects of – dichloromethane, trichloromethane, tetrachloromethane, iodoform, freons, DDT. |
| Unit XI: Alcohols, Phenols, and Ethers | Alcohols: Nomenclature, methods of preparation, physical and chemical properties (of primary alcohols only); identification of primary, secondary, and tertiary alcohols; mechanism of dehydration, uses, with special reference to methanol and ethanol. Phenols: Nomenclature, methods of preparation, physical and chemical properties, acidic nature of phenol, electrophilic substitution reactions, uses of phenols. Ethers: Nomenclature, methods of preparation, physical and chemical properties, uses. |
| Unit XII: Aldehydes, Ketones, and Carboxylic Acids | Aldehydes and Ketones: Nomenclature, nature of carbonyl group, methods of preparation, physical and chemical properties, mechanism of nucleophilic addition, the reactivity of alpha hydrogen in aldehydes; uses. Carboxylic Acids: Nomenclature, acidic nature, methods of preparation, physical and chemical properties; uses. |
| Unit XIII: Organic Compounds Containing Nitrogen | Amines: Nomenclature, classification, structure, methods of preparation, physical and chemical properties, uses, identification of primary secondary, and tertiary amines. Cyanides and Isocyanides – will be mentioned at relevant places in context. Diazonium salts: Preparation, chemical reactions, and importance in synthetic organic chemistry. |
| Unit XIV: Biomolecules | Carbohydrates – Classification (aldoses and ketoses), monosaccharide (glucose and fructose), D-L configuration, oligosaccharides (sucrose, lactose, maltose), polysaccharides (starch, cellulose, glycogen): importance. Proteins – Elementary idea of a-amino acids, peptide bond, polypeptides, proteins, primary structure, secondary structure, tertiary structure and quaternary structure (qualitative idea only), denaturation of proteins; enzymes. Hormones –Elementary idea (excluding structure). Vitamins – Classification and functions. Nucleic Acids: DNA and RNA |
| Unit XV: Polymers | Classification – Natural and synthetic, methods of polymerization (addition and condensation), copolymerization. Some important polymers: natural and synthetic like polythene, nylon, polyesters, bakelite, rubber. Biodegradable and non-biodegradable polymers. |
| Unit XVI: Chemistry in Everyday Life | 1. Chemicals in medicines – analgesics, tranquilizers, antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, and antihistamines. 2. Chemicals in food– preservatives, artificial sweetening agents, elementary idea of antioxidants. 3. Cleansing agents – soaps and detergents, cleansing action. |
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