KEAM 2025 Syllabus: Physics, Chemistry & Mathematics, Topics with Weightage

Particulars

Details

Exam Name

Kerala Engineering Architecture Medical (KEAM)

Conducting Body

Commissioner for Entrance Examinations (CEE), Kerala

Exam Mode

Computer-Based Test (CBT)

Duration

3 Hours (Engineering)

1.5 Hours (B.Pharm)

Type of Questions

Multiple-choice Questions (MCQs)

Total Questions

150 for Engineering

75 for B.Pharm

Total Marks

600 for Engineering

300 for B.Pharm

Subjects

Engineering: Mathematics (75), Physics (45), Chemistry (30)

B.Pharm: Physics (45), Chemistry (30)

Marking Scheme

• +4 for each correct answer
• -1 for incorrect answers
• No negative marking for unanswered questions

Medium

English

Subject

Unit

Topics

Mathematics

UNIT I: ALGEBRA

Sets, Relations and Functions

Sets and their representations: Finite and Infinite sets; Empty set; Equal sets; Subsets; Universal set; Venn Diagrams; Complement of a set; Operations on Sets (Union, Intersection and Difference of Set); Applications of sets: Ordered Pairs, Cartesian Product of Two sets; Relations, reflexive, symmetric, transitive and equivalence relations. Domain, Co-domain and Range: Functions: into, onto, one-one into, one-one onto Functions; Constant Function; Identity Function; composition of Functions; Invertible Functions.

Complex Numbers

Complex Numbers in the form a+ib; Real and Imaginary Parts of a Complex Number; Complex Conjugate, Argand Diagram, Representation of Complex Number as a point in the plane; Modulus of a Complex Number; Algebra of Complex Numbers.

Sequences and Series

Geometric Progression (G.P): first Term, Common Ratio and nth term, Sum to n Terms. Geometric Mean (G.M.); Insertion of Geometric Means, Relation between AM and GM. between any two given numbers.

Permutations, Combinations, Binomial Theorem

Fundamental Principle of Counting; The Factorial Notation; Permutation as an Arrangement; Meaning of P(n, r); Combination: Meaning of C(n,r); Applications of Permutations and Combinations. Statement of Binomial Theorem; Proof of Binomial Theorem for positive integral Exponent using Principle of Mathematical Induction and also by combinatorial Method; General and Middle Terms in Binomial Expansions; Properties of Binomial Coefficients.

Matrices and Determinants

Concept of a Matrix; Types of Matrices; Equality of Matrices (only real entries may be considered): Operations of Addition, Scalar Multiplication and Multiplication of Matrices; Statement of Important Results on operations of Matrices and their Verifications by Numerical Problem only; Determinant of a Square Matrix; Minors and Cofactors; singular and non-singular Matrices; Applications of Determinants in finding the Area of a Triangle. Transpose, Adjoint and Inverse of a Matrix; Consistency and Inconsistency of a system of Linear Equations; Solving a System of Linear Equations in Two or Three variables using the Inverse of a Matrix (only up to 3X3 Determinants and Matrices should be considered).

Linear Inequalities

Solutions of Linear Inequalities in one variable and its Graphical Representation; solution of a system of Linear Inequalities in one variable.

UNIT II: TRIGONOMETRY

Trigonometric functions and Inverse Trigonometric functions

Degree measures and Radian measure of positive and negative angles; relation between degree measure and radian measure, definition of trigonometric functions with the help of a unit circle, periodic functions, concept of periodicity of trigonometric functions, value of Trigonometric functions of x for x = 0, π/6, π/4, π/3, π/2, π, 3π/2, 2π; trigonometric functions of sum and difference of numbers.

Trigonometric functions of multiples and submultiples of numbers

Inverse Trigonometric Functions

Range, Domain, Principal Value, Branch, and Graphs of Inverse Trigonometric Functions.

UNIT III: GEOMETRY

Lines

Cartesian system of coordinates in a plane. Distance formula, Slope of a line, parallel and perpendicular lines. Various forms of equations of a line parallel to axes, slope-intercept form, the Slope point form, the Intercept form, the Normal form, the General form, Intersection of lines. Angles between two lines, condition for concurrency of three lines, Distance of a point from a line.

Conic sections

Sections of a cone. Circles, the standard form of the equation of a circle, its radius and centre. Equations of conic sections [Parabola, Ellipse and Hyperbola] in standard form and simple properties.

Vectors

Vectors and scalars, Magnitude and Direction of a vector, Types of vectors (Equal vectors, unit vector, Zero vector). Position vector of a point, localised and free vectors, parallel and collinear vectors, 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, Application of vectors in geometry. Scalar product of two vectors, projection of a vector on a line, and vector product of two vectors.

Three-Dimensional Geometry

Coordinate axes and coordinate planes in three dimensional space, coordinate of a point in space, distance between two points, section formula, direction cosines, and direction ratios of a line joining two points, projection of the join of two points on a given line, Angle between two lines whose direction ratios are given, Cartesian and vector equation of a line through (i) a point and parallel to a given vector (ii) through two points, coplanar and skew lines, Shortest distance between two lines, Condition for the intersection of two lines,

Unit IV: STATISTICS

Statistics and probability

Mean deviation, variance, and standard deviation for grouped and ungrouped data. Random experiments and sample space, Events as a subset of a sample space, occurrence of an event, sure and impossible events, Exhaustive events, Algebra of events, Meaning of equality, likely outcomes, mutually exclusive events. Probability of an event; Theorems on probability; Addition rule, Multiplication rule, Independent experiments and events. Finding P (A or B), P (A and B), and Bayes' theorem.

UNIT V: CALCULUS

Functions, Limits and Continuity

Concept of a real function; its domain and range; Modulus Function, Greatest integer function: Signum functions; Trigonometric functions and inverse trigonometric functions and their graphs; composite functions, Inverse of a function. Limit of a function; meaning and related notations; Left and right hand limits; Fundamental theorems on limits without proof (without proof); Continuity of a function at a point, Sum, Product and quotient of continuous functions; Continuity of special functions- Polynomial, Trigonometric, exponential, Logarithmic and Inverse trigonometric functions.

Differentiation

Derivative of a function; its geometrical and physical significance; Relationship between continuity and differentiability; Derivatives of polynomial, basic trigonometric, exponential, logarithmic and inverse trigonometric functions from first principles; derivatives of sum, difference, product and quotient of functions; derivatives of polynomial, trigonometric, exponential, logarithmic, inverse trigonometric and implicit functions; Logarithmic differentiation; derivatives of functions expressed in parametric form; chain rule and differentiation by substitution; Derivatives of Second order.

Application of Derivatives

Rate of change of quantities; increasing and decreasing functions and sign of the derivatives; maxima and minima; Greatest and least values;

Indefinite Integrals

Integration as inverse of differentiation; properties of integrals; Integrals involving algebraic, trigonometric, exponential and logarithmic functions; Integration by substitution; Integration by parts;

Integration of rational functions; Partial fractions and their use in integration

Definite Integrals

Fundamental theorems of integral calculus without proof; Evaluation of definite integrals by substitution

Application of definite integrals in finding areas bounded by a curve, circle, parabola and ellipse in standard form between two ordinates and x-axis; Area between two curves, line and circle; line and parabola; line and ellipse. Differential Equations Definition: order and degree; general and particular solutions of a differential equation; solution of differential equations by method of Separation of variables; Homogeneous differential equations of first order and their solutions; Solution of linear differential equations are functions of x or constants.

Linear Programming

Introduction, related terminology such as constraints, objective function, optimisation, different types of linear programming 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).

Physics

UNIT I: UNITS & MEASUREMENT

Need for measurement: Units of measurement; systems of units; SI units, fundamental and derived units. significant figures. Dimensions of physical quantities, dimensional analysis and its applications.

UNIT II: 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 and 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 vectors. Resolution of a vector in a plane – rectangular components. Scalar and Vector products of Vectors. Motion in a plane. Cases of uniform velocity and uniform acceleration – projectile motion. Uniform circular motion

UNIT III: LAWS OF MOTION

Intuitive concept of force. Inertia, Newton’s first law of motion; momentum and 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, and lubrication. Dynamics of uniform circular motion: Centripetal force, examples of circular motion (vehicle on level circular road, vehicle on banked road)

UNIT IV: WORK, ENERGY AND POWER

Work done by a constant force and a variable force; kinetic energy, work-energy theorem, and power. Notion of potential energy, potential energy of a spring, conservative forces; conservation of mechanical energy (kinetic and potential energies); non-conservative forces; motion in a vertical circle, elastic and inelastic collisions in one and two dimensions

UNIT V: MOTION OF SYSTEMS OF PARTICLES AND RIGID BODIES

Centre of mass of a two-particle system, momentum conservation and centre of mass motion. Centre of mass of a rigid body; centre of mass of uniform rod, circular ring, disc and sphere. Moment of a force, torque, angular momentum, and conservation of angular momentum with some examples. Equilibrium of rigid bodies, rigid body rotation and equation of rotational motion, comparison of linear and rotational motions; moment of inertia, radius of gyration. Values of M.I. for simple geometrical objects (no derivation).

UNIT VI: GRAVITATION

Kepler’s laws of planetary motion. The universal law of gravitation. Acceleration due to gravity and its variation with altitude and depth. Gravitational potential energy; gravitational potential. Escape velocity is the orbital velocity of a satellite.

UNIT VII: PROPERTIES OF BULK MATTER

Elastic behaviour, Stress-strain relationship, Hooke’s law, Young’s modulus, bulk modulus, shear modulus of rigidity, Poisson’s ratio, elastic energy. Pressure due to a fluid column; Pascal’s law and its applications (hydraulic lift and hydraulic brakes).Effect of gravity on fluid pressure. Viscosity, Stokes’ law, terminal velocity, Reynolds’ number, streamline and turbulent flow. Critical velocity, Bernoulli’s theorem and its applications. Surface energy and surface tension, angle of contact, excess of pressure, application of surface tension ideas to drops, bubbles and capillary rise. Heat, temperature, thermal expansion; thermal expansion of solids, liquids, and gases. Anomalous expansion. Specific heat capacity: C p, C v – calorimetry; change of state – latent heat. Heat transfer – conduction and thermal conductivity, convection and radiation. Qualitative ideas of Black Body Radiation, Wein’s displacement law, and Green greenhouse effect. Newton’s law of cooling and Stefan’s law.

UNIT VIII: THERMODYNAMICS

Thermal equilibrium and definition of temperature (zeroth law of Thermodynamics). Heat, work and internal energy. First law of thermodynamics. Isothermal and adiabatic processes. Second law of thermodynamics: Reversible and irreversible processes. Carnot Engine

UNIT IX: BEHAVIOUR OF PERFECT GAS AND KINETIC THEORY

Equation of state of a perfect gas, work done on compressing a gas. Kinetic theory of gases: Assumptions, concept of pressure. Avogadro’s number. Kinetic energy and temperature; rms speed of gas molecules; degrees of freedom, law of equipartition of energy (statement only) and application to specific heat capacities of gases; concept of mean free path.

UNIT X: OSCILLATIONS AND WAVES

Periodic motion – period, frequency, displacement as a function of time. Periodic functions. Simple harmonic motion (SHM) and its equation; phase, oscillations of a spring – restoring force and force constant, energy in SHM – kinetic and potential energies, simple pendulum – derivation of expression for its period, Wave motion. Longitudinal and transverse waves, speed of wave motion. 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.

UNIT XI: 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 the field due to an infinitely long uniformly charged straight wire, a uniformly charged infinite plane sheet, and a uniformly charged thin spherical shell (field inside and outside). Electric potential, potential difference, electric potential due to a point charge, a dipole and a system of charges; equipotential surfaces, 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 polarisation, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor.

UNIT XII: 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 (linear and non-linear), electrical energy and power, electrical resistivity and conductivity. Temperature dependence of resistance. 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

UNIT XIII: MAGNETIC EFFECTS OF CURRENT AND MAGNETISM

Concept of magnetic field, Oersted’s experiment. Biot-Savart law and its application to a current-carrying circular loop. Ampere’s law and its applications to infinitely long straight wires, straight solenoids. Force on a moving charge in uniform magnetic and electric fields. Cyclotron. Force on a current-carrying conductor in a uniform magnetic field. 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. 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, Para-, dia- and ferro-magnetic substances, with examples

UNIT XIV: ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS

Electromagnetic induction; Faraday’s law, induced emf and current; Lenz’s Law, Self and mutual inductance. Alternating currents, peak and rms value of alternating current/voltage; reactance and impedance; LCR series circuit, resonance; power in AC circuits, wattless current. AC generator and transformer.

UNIT XV: 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 XVI: 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, a combination of thin lenses in contact combination of a lens and a mirror. Refraction and dispersion of light through a prism, Optical instruments, Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers. Wave optics: Wavefront and Huygens’ principle, reflection and refraction of a 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, the width of the central maximum. Polarisation, plane polarised light; uses of plane polarised light and Polaroids

UNIT XVII: 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.

UNIT XVIII: ATOMS AND NUCLEI

Alpha-particle scattering experiment; Rutherford’s model of the 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.

UNIT XIX: 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.

Chemistry

UNIT 1: SOME BASIC CONCEPTS OF CHEMISTRY

General Introduction: Importance and scope of chemistry. Historical approach to particulate nature of matter, laws of chemical combination, Dalton’s atomic theory: concept of elements, atoms and molecules. Atomic and molecular masses. Mole concept and molar mass; percentage composition and empirical and molecular formula; chemical reactions, stoichiometry and calculations based on stoichiometry

UNIT 2: STRUCTURE OF ATOM

Discovery of electron, proton and neutron; atomic number, isotopes and isobars. Thompson’s model and its limitations, Rutherford’s model and its limitations, Bohr’s model and its limitations, concept of shells and subshells, dual nature of matter and light, de Broglie’s relationship, Heisenberg uncertainty principle, concept of orbitals, quantum numbers, shapes of s, p and d orbitals, rules for filling electrons in orbitals - Aufbau principle, Pauli exclusion principle and Hund’s rule, electronic configuration of atoms, stability of half filled and filled orbitals.

UNIT 3: CLASSIFICATION OF ELEMENTS AND PERIODICITY IN PROPERTIES

Significance of classification, brief history of the development of periodic table, modern periodic law and the present form of periodic table, periodic trends in properties of elements –atomic radii, ionic radii, inert gas radii, ionisation enthalpy, electron gain enthalpy, electronegativity, valence. Nomenclature of elements with atomic number greater than 100

UNIT 4: CHEMICAL BONDING AND MOLECULAR STRUCTURE

Valence electrons, ionic bond, covalent bond, bond parameters, Lewis structure, polar character of covalent bond, covalent character of ionic bond, valence bond theory, resonance, geometry of covalent molecules, VSEPR theory, concept of hybridization involving s, p and d orbitals and shapes of some simple molecules, molecular orbital theory of homonuclear diatomic molecules (qualitative idea only). Hydrogen bond.

UNIT 5: THERMODYNAMICS

Concepts of system, types of systems, surroundings, work, heat, energy, extensive and intensive properties, and state functions. First law of thermodynamics – internal energy and enthalpy, heat capacity and specific heat, measurement of ΔU and ΔH, Hess’s law of constant heat summation, enthalpy of: bond dissociation, combustion, formation, atomization, sublimation, phase transition, ionisation, solution and dilution. Introduction of entropy as a state function, Second law of thermodynamics, Gibbs energy change for spontaneous and non-spontaneous processes, criteria for equilibrium. Third law of thermodynamics –Brief introduction.

UNIT 6: EQUILIBRIUM

Equilibrium in physical and chemical processes, dynamic nature of equilibrium, law of mass action, equilibrium constant, factors affecting equilibrium – Le Chatelier’s principle; ionic equilibrium – ionization of acids and bases, strong and weak electrolytes, degree of ionization, ionization of polybasic acids, acid strength, concept of pH., Hydrolysis of salts (elementary idea), buffer solutions, Henderson equation, solubility product, common ion effect (with illustrative examples).

UNIT 7: REDOX REACTIONS AND ELECTROCHEMISTRY

Concept of oxidation and reduction, redox reactions, oxidation number, balancing redox reactions in terms of loss and gain of electrons and change in oxidation numbers, applications of 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 8 : SOLUTIONS

Types of solutions, expression of concentration of solutions of solids in liquids, solubility of gases in liquids, solid solutions, colligative properties – 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 9: 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 10: 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, ionisation 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 11: 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 12: ORGANIC CHEMISTRY – SOME BASIC PRINCIPLES AND TECHNIQUES

General introduction, methods of purification, qualitative and quantitative analysis, classification and IUPAC nomenclature of organic compounds. Electronic displacements in a covalent bond: inductive effect, electromeric effect, resonance and hyperconjugation. Homolytic and heterolytic fission of a covalent bond: free radicals, carbocations, carbanions; electrophiles and nucleophiles, types of organic reactions.

Subject

Number of Questions

Total Marks

Physics

45

180

Chemistry

30

120

Mathematics

75

300

Total

150

600