KRLMPCA CET Syllabus 2025: Download Physics, Chemistry & Mathematics Syllabus PDF

Chapters 

Topics 

Sets, relations and function 

Sets and their representation Union, intersection and complement of sets and their algebraic properties Power set; Relation, Types of relations, equivalence relations, functions; One-one, into and onto functions, the composition of functions. 

Complex numbers and quadratic equations 

Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions. Relation between roots and coefficients, nature of roots, formation of quadratic equations with given roots. 

Mathematical induction 

Principle of Mathematical Induction and its simple applications 

Matrices and determinants 

Matrices, algebra of matrices, types of matrices, determinants and matrices of order two and three. Properties of determinants, evaluation of determinants, area of triangles using determinants. Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices. 

Permutations and combinations 

The fundamental principle of counting, permutation as an arrangement and combination as selection, Meaning of P (n,r) and C (n,r), simple applications. Binomial theorem and its simple applications Binomial theorem for a positive integral index, general term and middle term, properties of Binomial coefficients simple applications 

Limit, continuity and differentiability 

Real–valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions Graphs of simple functions Limits, continuity and differentiability 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 upto two Rolle’s and Lagrange’s Mean Value Theorems Applications of derivatives: Rate of change of quantities, monotonic – increasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normal. 

Sequences and series 

Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers relation between A.M. and G.M. sum up to n terms of special series: S n, S n2, Sn3 Arithmetic – Geometric progression 

Differential equations 

Ordinary differential equations, their order and degree. Formation of differential equations. Solution of differential equations by the method of separation of variables, solution of homogeneous and linear differential equations of the type: dy/dx+p(x)y=q(x). 

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, Evaluation of simple integrals of the type Integral as limit of a sum. Fundamental Theorem of Calculus. Properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form. 

Coordinate geometry 

Cartesian system of rectangular coordinates 10 in a plane, distance formula, section formula, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes, Straight lines, Circles, conic sections. 

Vector algebra 

Vectors and scalars, addition of vectors, components of a vector in two dimensions and three-dimensional space, scalar and vector products, scalar and vector triple products. 

Statistics and probability 

Measures of Dispersion: Calculation of mean, median, mode of grouped and ungrouped data calculation of standard deviation, variance and mean deviation for grouped and ungrouped data. 

Probability: Probability of an event, addition and multiplication theorems of probability, Bayes’ theorem, probability distribution of a random variate, Bernoulli trials and Binomial distribution. 

Three-dimensional geometry 

Coordinates of a point in space, the distance between two points, section formula, direction ratios and direction cosines, the angle between two intersecting lines. Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in different forms, the intersection of a line and a plane, and coplanar lines. 

Trigonometry 

Trigonometric identities and equations, Trigonometric functions, Inverse trigonometric functions and their properties, Heights and Distances 

Mathematical reasoning, Statements, logical operations and, or, implies, implied by, if and only if Understanding of tautology, contradiction, converse and contrapositive. 

Chapters 

Topics 

Physics And Measurement 

Physics, technology and society, SI units, Fundamental and derived units Least count, accuracy and precision of measuring instruments, Errors in measurement, Dimensions of Physical quantities, dimensional analysis and its applications. 

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, Dynamics of uniform circular motion: Centripetal force and its applications. 

Kinematics 

Frame of reference 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, and relations for uniformly accelerated motion. Scalars and Vectors, Vector addition and Subtraction, Zero Vector, Scalar and Vector products, Unit Vector, Resolution of a Vector Relative Velocity, Motion in a plane, Projectile Motion, Uniform Circular Motion. 

Work, Energy And Power, Work done by a constant force and a variable force; kinetic and potential energies, work energy theorem, Power, Potential energy of a spring, conservation of mechanical energy, conservative and non-conservative forces; Elastic and inelastic collisions in one and two dimensions. 

Gravitation 

The universal law of gravitation, Acceleration due to gravity and its variation with altitude and depth, Kepler’s laws of planetary motion, Gravitational potential energy; gravitational potential, Escape velocity, Orbital velocity of a satellite, Geo-stationary satellites. 

Rotational Motion 

Centre of mass of a two-particle system, Centre of mass of a rigid body, Basic concepts of rotational motion, moment of a force, torque, angular momentum, conservation of angular momentum and its applications; moment of inertia, radius of gyration. Values of moments of inertia for simple geometrical objects, parallel and perpendicular axes theorems and their applications. Rigid body rotation, equations of rotational motion. 

Thermodynamics 

Thermal equilibrium, zeroth law of thermodynamics, concept of temperature. Heat, work and internal energy. The first law of thermodynamics. The second law of thermodynamics: reversible and irreversible processes. Carnot engine and its efficiency. 

Optics 

Reflection and refraction of light at plane and spherical surfaces, mirror formula, Total internal reflection and its applications, Deviation and Dispersion of light by a prism, Lens Formula, Magnification, Power of a Lens, Combination of thin lenses in contact, Microscope and Astronomical Telescope (reflecting and refracting) and their magnifying powers, Wave optics. 

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. Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number, nuclear fission and fusion. 

Communication Systems 

Propagation of electromagnetic waves in the atmosphere; Sky and space wave propagation, Need for modulation, Amplitude and Frequency Modulation, Bandwidth of signals, Bandwidth of Transmission medium, Basic Elements of a Communication System (Block Diagram only). 

Current Electricity 

Electric field, Electric current, Drift velocity, Ohm’s law, Electrical resistance, Resistances of different materials, V-I characteristics of Ohmic and non-ohmic conductors, Electrical energy and power, Electrical resistivity, Colour code for resistors; Series and parallel combinations of resistors; Temperature dependence of resistance. Electric Cell and its internal resistance, potential difference and emf of a cell, combination of cells in series and in parallel. Kirchhoff’s laws and their applications. Wheatstone bridge, Metre bridge. Potentiometer – principle and its applications. 

Oscillations And Waves 

Periodic motion: period, frequency, displacement as a function of time. Periodic functions. Simple harmonic motion (S.H.M.) and its equation; phase; 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, resonance. 

Wave motion: Longitudinal and transverse waves, speed of a wave. Displacement relation for a progressive wave. Principle of superposition of waves, reflection of waves, Standing waves in strings and organ pipes, fundamental mode and harmonics, Beats, Doppler Effect in sound. 

Kinetic Theory of Gases 

Equation of state of a perfect gas, work done on compressing a gas. Kinetic theory of gases – assumptions, concept of pressure. Kinetic energy and temperature: rms speed of gas molecules; Degrees of freedom, Law of equipartition of energy, applications to specific heat capacities of gases; Mean free path, Avogadro’s number. 

Properties of Solids and Liquids 

Elastic behaviour, Stress-strain relationship, Hooke’s Law, Young’s modulus, bulk modulus, modulus of rigidity. Pressure due to a fluid column; Pascal’s law and its applications. Viscosity, Stokes’ law, terminal velocity, streamline and turbulent flow, Reynolds number. Bernoulli’s principle and its applications. Surface energy and surface tension, angle of contact, application of surface tension – drops, bubbles and capillary rise. Heat, temperature, thermal expansion; specific heat capacity, calorimetry; change of state, latent heat. Heat transfer-conduction, convection and radiation, Newton’s law of cooling. 

Chapters 

Topics 

Some Basic Concepts in Chemistry 

Matter and its nature, Dalton’s atomic theory Concept of atom, molecule, element and compound Physical quantities and their measurements in Chemistry, precision and accuracy, significant figures, S.I. Units, dimensional analysis Laws of chemical combination Atomic and molecular masses, mole concept, molar mass, percentage composition, empirical and molecular formulae Chemical equations and stoichiometry. 

Chemical Bonding and Molecular Structure 

Ionic Bonding: Formation of ionic bonds, factors affecting the formation of ionic bonds; calculation of lattice enthalpy. Kossel–Lewis approach to chemical bond formation, the concept of ionic and covalent bonds. 

Covalent Bonding: Concept of electronegativity, Fajan’s rule, dipole moment Valence Shell Electron Pair Repulsion (VSEPR) theory and shapes of simple molecules. 

Quantum mechanical approach to covalent bonding: Valence bond theory – Its important features, the concept of hybridization involving s, p and d orbitals Resonance Molecular Orbital Theory – Its important features, LCAOs, types of molecular orbitals (bonding, antibonding), sigma and pi-bonds, molecular orbital electronic configurations of homonuclear diatomic molecules, concept of bond order, bond length and bond energy. 

States of Matter 

Gaseous State: Measurable properties of gases Gas laws – Boyle’s law, Charle’s law, Graham’s law of diffusion, Avogadro’s law, Dalton’s law of partial pressure Concept of Absolute scale of temperature; Ideal gas equation Kinetic theory of gases (only postulates) Concept of average, root mean square and most probable velocities Real gases, deviation from Ideal behaviour, compressibility factor and van der Waals equation. 

Liquid State: Properties of liquids – vapour pressure, viscosity surface tension and effect of temperature on them (qualitative treatment only). 

Solid State: Classification of solids: molecular, ionic, covalent and metallic solids, amorphous and crystalline solids (elementary idea) Bragg’s Law and its applications Unit cell and lattices, packing in solids (fcc, bcc and hcp lattices), voids, calculations involving unit cell parameters, imperfection in solids Electrical, magnetic and dielectric properties. 

Chemical Thermodynamics 

First law of thermodynamics – Concept of work, heat internal energy and enthalpy, heat capacity, molar heat capacity Hess’s law of constant heat summation Enthalpies of bond dissociation, combustion, formation, atomization, sublimation, phase transition, hydration, ionisation and solution Second law of thermodynamics Spontaneity of processes DS of the universe and DG of the system as criteria for spontaneity, Dgo (Standard Gibbs energy change) and equilibrium constant 

Atomic Structure 

Elementary ideas of quantum mechanics, the quantum mechanical model of the atom, its important features, the concept of atomic orbitals as one electron wave functions various quantum numbers (principal, angular momentum and magnetic quantum numbers) and their significant shapes of s, p and d – orbitals, electron spin and spin quantum number Rules for filling electrons in orbitals – Aufbau principle, Pauli’s exclusion principle and Hund’s rule, electronic configuration of elements, extra stability of half-filled and completely filled orbitals, Thomson and Rutherford atomic models and their limitations Nature of electromagnetic radiation, photoelectric effect Spectrum of the hydrogen atom, Bohr model of a hydrogen atom – its postulates, derivation of the relations for the energy of the electron and radii of the different orbits, limitations of Bohr’s model Dual nature of matter, de-Broglie’s relationship, Heisenberg uncertainty principle. 

Solutions 

Different methods for expressing the concentration of solution – molality, molarity, mole fraction, percentage (by volume and mass both), the vapour pressure of solutions and Raoult’s Law – Ideal and non-ideal solutions, vapour pressure – composition, plots for ideal and non-ideal solutions Colligative properties of dilute solutions – relative lowering of vapour pressure, depression of freezing point, elevation of boiling point and osmotic pressure Determination of molecular mass using colligative properties; Abnormal value of molar mass, van Hoff factor and its significance 

Redox Reactions and Electrochemistry 

Electrolytic and metallic conduction, conductance in electrolytic solutions, specific and molar conductivities and their variation with concentration: Kohlrausch’s law and its applications. Electronic concepts of oxidation and reduction, redox reactions, oxidation number, rules for assigning oxidation number, and balancing of redox reactions. 

Equilibrium 

Equilibria involving physical processes: Solid-liquid, liquid – gas and solid–gas equilibria, Henry’s law, a general characteristic of equilibrium involving physical processes. Equilibria involving chemical processes: Law of chemical equilibrium, equilibrium constants (Kp and Kc) and their significance, significance of DG and DGo in chemical equilibria, factors affecting equilibrium concentration, pressure, temperature, effect of catalyst; Le Chatelier’s principle. 

Ionic equilibrium: Weak and strong electrolytes, ionisation of electrolytes, various concepts of acids and bases (Arrhenius, Bronsted – Lowry and Lewis) and their ionisation, acid-base equilibria (including multistage ionisation) and ionisation constants, ionisation of water, pH scale, common ion effect, hydrolysis of salts and pH of their solutions, solubility of sparingly soluble salts and solubility products, buffer solutions. 

Surface Chemistry 

Colloidal state- distinction among true solutions, colloids and suspensions, classification of colloids – lyophilic, lyophobic multi molecular, macromolecular and associated colloids (micelles), preparation and properties of colloids – Tyndall effect, Brownian movement, electrophoresis, dialysis, coagulation and flocculation Emulsions and their characteristics. Adsorption- Physisorption and chemisorption and their characteristics, factors affecting adsorption of gases on solids – Freundlich and Langmuir adsorption isotherms, adsorption from solutions. 

Chemistry in Everyday Life 

Chemicals in food – Preservatives, artificial sweetening agents – common examples. Cleansing agents – Soaps and detergents, cleansing action. 

Chemicals in medicines – Analgesics, tranquillisers, antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihistamines – their meaning and common examples. 

Polymers 

General introduction and classification of polymers, general methods of polymerization-addition and condensation, copolymerization of Natural and synthetic rubber and vulcanization of some important polymers with emphasis on their monomers and uses – polythene, nylon, polyester and Bakelite. 

Organic Compounds Containing Nitrogen 

General methods of preparation, properties, reactions and uses. Amines: Nomenclature, classification, structure, basic character and identification of primary, secondary and tertiary amines and their basic character. Diazonium Salts: Importance in synthetic organic chemistry. 

Alcohols, Phenols and Ethers 

Alcohols: Identification of primary, secondary and tertiary alcohols; mechanism of dehydration. Phenols: Acidic nature, electrophilic substitution reactions: halogenation, nitration and sulphonation, Reimer – Tiemann reaction. Ethers: Structure. Aldehyde and Ketones: Nature of carbonyl group Nucleophilic addition to >C=O group, relative reactivities of aldehydes and ketones Important reactions such as – Nucleophilic addition reactions (addition of HCN, NH3 and its derivatives), Grignard reagent; oxidation; reduction (Wolff Kishner and Clemmensen); acidity of r – hydrogen, aldol condensation, Cannizzaro reaction, Haloform reaction; Chemical tests to distinguish between aldehydes and Ketones. 

S – Block Elements (Alkali and Alkaline Earth Metals) 

Group – 1 and 2 Elements: General introduction, electronic configuration and general trends in physical and chemical properties of elements, anomalous properties of the first element of each group, diagonal relationships. Preparation and properties of some important compounds – sodium carbonate and sodium hydroxide; Industrial uses of lime, limestone, Plaster of Paris and cement; Biological significance of Na, K, Mg and Ca. 

P – Block Elements 

Group – 13: Preparation, properties and uses of boron and aluminium; properties of boric acid, diborane, boron trifluoride, aluminium chloride and alums. Group – 14: Allotropes of carbon, tendency for catenation; Structure & properties of silicates, and zeolites. Group – 15: Properties and uses of nitrogen and phosphorus; Allotropic forms of phosphorus; Preparation, properties, structure and uses of ammonia, nitric acid, phosphine and phosphorus halides, (PCl3, PCl5); Structures of oxides and oxoacids of phosphorus. Group – 16: Preparation, properties, structures and uses of ozone; Allotropic forms of sulphur; Preparation, properties, structures and uses of sulphuric acid (including its industrial preparation); Structures of oxoacids of sulphur. Group – 17: Preparation, properties and uses of hydrochloric acid; Trends in the acidic nature of hydrogen halides; Structures of Interhalogen compounds and oxides and oxoacids of halogens. Group –18: Occurrence and uses of noble gases; Structures of fluorides and oxides of xenon. Group – 13 to Group 18 Elements General Introduction: Electronic configuration and general trends in physical and chemical properties of elements across the periods and down the groups; unique behaviour of the first element in each group. 

D – And F – Block Elements 

Transition Elements: General introduction, electronic configuration, occurrence and characteristics, general trends in properties of the first-row transition elements – physical properties, ionisation enthalpy, oxidation states, atomic radii, colour, catalytic behaviour, magnetic properties, complex formation, interstitial compounds, alloy formation; Preparation, properties and uses of K2 Cr2 O7 and KMnO4, Inner Transition Elements: Lanthanoids – Electronic configuration, oxidation states and lanthanide contraction. 

Hydrogen 

Position of hydrogen in the periodic table, isotopes, preparation, properties and uses of hydrogen Physical and chemical properties of water and heavy water Structure, preparation, reactions and uses of hydrogen peroxide Hydrogen as a fuel. 

Environmental Chemistry 

Environmental pollution – Atmospheric, water and soil. Atmospheric pollution – Tropospheric and Stratospheric Tropospheric pollution – Gaseous pollutants: Oxides of carbon, nitrogen and sulphur, hydrocarbons; their sources, harmful effects and prevention; Greenhouse effect and Global warming; Acid rain; Particulate pollutants: Smoke, dust, smog, fumes, mist; their sources, harmful effects and prevention. Stratospheric pollution- Formation and breakdown of ozone, depletion of the ozone layer – its mechanism and effects. Water Pollution – Major pollutants such as pathogens, organic wastes and chemical pollutants; their harmful effects and prevention. Soil pollution – Major pollutants such as Pesticides (insecticides, herbicides and fungicides), their harmful effects and prevention. Strategies to control environmental pollution.