IOE Entrance Exam Syllabus
Akancha Chhetri
Content Writer | Updated: June 16, 2025 21:05 NST
The Institute of Engineering (IOE) B.E./B.Arch. Entrance Exam is a national-level test conducted by Tribhuvan University for students seeking admission to undergraduate engineering (B.E.) and architecture (B.Arch.) programs in Nepal. The exam evaluates candidates in four subjects: Mathematics (50 marks), Physics (40 marks), Chemistry (30 marks), and English (20 marks).
| Subjects | Marks |
|---|---|
| Mathematics | 50 |
| Physics | 40 |
| Chemistry | 30 |
| English | 20 |
| Total | 140 |
Download IOE entrance exam syllabus here
Mathematics Course Structure
| Chapter Title | Topics Covered |
|---|---|
| Set, Logic and Functions | 1.1 Set, real number system, intervals, absolute value, logic, connectives, laws of logic |
| 1.2 Function, types of functions – injective, surjective, bijective, algebraic, trigonometric, exponential and logarithmic; Inverse of function, composite functions | |
| Algebra | 2.1 Matrices and determinants, types and properties, inverse of a matrix |
| 2.2 Complex numbers and Polynomial equations | |
| 2.3 Sequence and series, Permutation and Combination | |
| 2.4 Binomial theorem, exponential and logarithmic series | |
| Trigonometry | 3.1 Trigonometric equations and general values |
| 3.2 Inverse trigonometric functions, principal value | |
| 3.3 Properties of triangles, in-centre, ortho-centre and circum-centre, solution of triangles | |
| Coordinate Geometry | 4.1 Straight lines, pair of lines |
| 4.2 Circles, equations of circle in different forms, tangent and normal | |
| 4.3 Conic sections: Parabola, Ellipse and Hyperbola, standard equations and simple properties | |
| 4.4 Coordinates in space, Plane and its equation | |
| Calculus | 5.1 Limit and continuity of functions, indeterminate forms, L’Hospital’s rule |
| 5.2 Derivatives, rules of derivatives, geometrical & physical meanings, higher order derivatives, Applications of derivative: tangent and normal, rate of change, maxima and minima | |
| 5.3 Integration, linear properties, rules of integration, standard integrals, definite integral, Applications of definite integral: area under a curve and area between two curves | |
| 5.4 Differential equations: definition, order and degree, differential equation of first order and first degree: variable separable method, homogeneous, linear and exact differential equations, integrating factor | |
| Vectors and their Products | 6.1 Vectors in plane and space, algebra of vectors, linear combination of vectors, linearly dependent and independent set of vectors |
| 6.2 Product of two vectors, scalar and vector product of two vectors, scalar triple product | |
| Statistics and Probability | 7.1 Measures of location and measures of dispersion |
| 7.2 Correlation and regression | |
| 7.3 Basic terms of probability, conditional and compound probability, additive and multiplicative rules, Bayes’ theorem, binomial distribution |
Physics Course Structure
| Chapter Title | Topics Covered |
|---|---|
| Mechanics | 1.1 Physical Quantities, Vector and Kinematics: Dimensions, Vector laws, Vector Algebra, Equations of Motion, Projectile & Relative Motion |
| 1.2 Newton’s Laws of Motion and Friction: Conservation of linear momentum, Applications of Newton’s Laws in Equilibrium and Non-equilibrium, laws of Solid Friction and verification | |
| 1.3 Work, Energy and Power: Work-Energy theorem, Kinetic and Potential energy, Conservation of Energy, Conservative and non-conservative forces, Elastic and inelastic collisions | |
| 1.4 Circular motion, Gravitation and SHM: Centripetal force, Conical Pendulum, Banking of Track, Gravitational Potential, variation of g, Motion of satellite, Rocket launch technology, Energy in SHM, Spring -Mass system, simple Pendulum, Damped and Forced oscillation, resonance | |
| 1.5 Rotational Dynamics: Moment of Inertia, Radius of Gyration, Rotational KE, Center of gravity and center of mass, Torque, Conservation of Angular momentum | |
| 1.6 Elasticity: Hook’s law, Young modulus, Bulk modulus, modulus of rigidity, Poissons’ ratio, elastic energy | |
| 1.7 Fluid Mechanics: buoyancy, flotation, Archimedes’ principle, surface tension, capillarity and applications, viscosity, Newton, Stoke and Poiseuille’s formula, Reynold number, continuity equation, Bernoulli’s equation | |
| Heat and Thermodynamics | 2.1 Temperature and Quantity of Heat: Thermal Equilibrium, Specific heat, latent heat Method of Mixture, Measurement of specific heat and latent heat, Newton’s law of cooling, triple point |
| 2.2 Thermal expansion: Expansion of Solid & Liquid, Measurement and Applications of expansions | |
| 2.3 Transfer of Heat: Conduction, Convection, Radiation, Thermal Conductivity, Black body radiation, Stefan- Boltzmann law | |
| 2.4 Thermal properties of Matter: Molecular Properties of matter, Kinetic Theory of gases, heat capacities of gases and solids | |
| 2.5 Laws of Thermodynamics: First law, Heat and Work, relation of specific heat of gas, thermodynamics processes, Second law, Heat engine, efficiency, Carnot Cycle, Otto Cycle, Diesel cycle, Refrigerator, Entropy. | |
| Geometric and Physical Optics | 3.1 Reflection: Plane & Curved mirrors, Mirror formula |
| 3.2 Refraction: Plane Surface, Critical Angle, Total Internal Reflection, Lateral shift, Prism, Minimum Deviation, Lenses, Lens Formula, Lens maker’s formula, Combination of lenses in contact, Optical Fiber | |
| 3.3 Dispersion: Spectrum, Dispersive Power, Chromatic Aberration, Achromatism, Spherical Aberration, Scattering of light | |
| 3.4 Nature and Propagation of Light: Huygen’s principle, Velocity of light | |
| 3.5 Interference: Coherent sources, Young’s double slit experiment | |
| 3.6 Diffraction: Fraunhoffer diffraction, Diffraction grating, Resolving power | |
| 3.7 Polarization: Brewster’s law, Transverse nature of light, Polaroid | |
| Waves and Sound | 4.1 Wave Motion: Travelling and Stationary wave |
| 4.2 Mechanical Waves: velocity of sound in solid, gas and liquid, effect of temperature, pressure, humidity | |
| 4.3 Waves in Pipes and String: closed and Open pipes, Resonance, Resonance Tube, string, laws of vibration of fixed string | |
| 4.4 Acoustic Phenomena: Pressure amplitude, intensity level, quality and pitch, Ultrasonic and Infrasonic, Doppler’s effect | |
| Electricity & Magnetism | 5.1 Electrostatics: Coulomb’s law, Electric field and Gauss law, Potential and potential gradient, Capacitors, combination of capacitors, types of capacitors, effect of dielectrics, Energy stored by capacitors, polarization and displacement |
| 5.2 DC Circuits: Ohm’s law, resistivity and conductivity, work and power, Galvanometer and Ohm meter, internal resistance, Joule’s law, Kirchhoff’s law and applications | |
| 5.3 Thermoelectric Effect: Seebeck effect, Thermocouples, Peltier effect, Thermopile, Thomson effect | |
| 5.4 Magnetic effect: Force on a conductor and charge, Torque, Hall’s effect, Biot-Savart’s law, Ampere’s law, Force between parallel conductors | |
| 5.5 Magnetic properties of matter: Earth magnetism, magnetic materials, permeability, susceptibility, hysteresis | |
| 5.6 Electromagnetic Induction: Faraday’s law, Induced emf, AC Generators, Self and mutual induction, energy stored by inductor, transformer | |
| 5.7 Alternating Currents: RMS value, Phasor diagram of capacitance, inductance and resistance, Quality factor, Power factor | |
| Modern Physics | 6.1 Electrons: Millikons’s experiment, Cathode rays, specific charge |
| 6.2 Photons & Quantization of Energy: Photoelectric effect, Plank’s constant, Bohr’s theory, spectral series, De Broglie theory, Uncertainty principle, X-ray and Bragg’s law, Laser | |
| 6.3 Solids & Semiconductor Devices: Intrinsic and extrinsic semiconductors, P-N junction, Rectification, Zener diode, Transistor, Logic gates | |
| 6.4 Radioactivity & Nuclear Reaction: Atomic mass, Isotopes, Nuclear density, Einstein’s mass energy relation, mass defect, fission & fusion, law of radioactive disintegration, carbon dating, health hazard | |
|
6.5. Recent Trends in Physics 6.5.1 Particle Physics: Particle and anti-particle, Quarks, Lepton, Baryon, Mesons, Higgs |
Chemistry Course Structure
| Chapter Title | Topics Covered |
|---|---|
| Physical Chemistry | 1.1 Chemical Arithmetic: Dalton’s atomic theory and Laws of Stoichiometry, Atomic mass and Molecular mass, Empirical molecular formula and limiting Reactants, Avogadro are Hypothesis and its applications and Equivalent masses. |
| 1.2 State of Matter: Gaseous state, liquid and solid states. | |
| 1.3 Atomic Structure and Periodic Classification of Elements: | |
| 1.4 Oxidation, Reduction and Equilibrium | |
| 1.5 Volumetric Analysis, | |
| 1.6 Ionic Equilibrium, Acid, Base and Salt | |
| 1.7 Electrochemistry | |
| 1.8 Energetic of Chemical Reaction, Chemical Kinetics, Chemical Bonding and Shape of Molecules | |
| Inorganic Chemistry | 2.1 Non-metal: Hydrogen, Oxygen, Ozone, Water, Nitrogen and its compounds, Halogen, Carbon, Phosphorous, sulphur, Noble gas and Environment pollution. |
| 2.2 Metals: Metallurgical Principle, Alkali metal, Alkaline Earth metals, Coinage metals: Copper, Silver, Gold | |
| 2.3 Extraction of Metal: Zinc and Mercury, Iron Compound | |
| Organic Chemistry | 3.1 Introduction: Fundamental principles, Purification of organic compounds, Nomenclature of Organic compounds, Structure isomerism and idea of reaction mechanism |
| 3.2 Hydrocarbons: Alkanes, Alkenes and Alkynes, Aromatic hydrocarbons | |
| 3.3 Haloalkanes and Haloarenes | |
| 3.4 Alcohols, Phenols and Ethers | |
| 3.5 Aldehydes, Ketones , Carboxylic Acid and Derivatives, Aliphatic and Aromatic | |
| 3.6 Nitro Compounds and Amines: Aromatic and Aliphatic |
English Course Structure
| Chapter Title | Topics Covered |
|---|---|
| Grammar I | 1.1 Sequence of Tense, Concord /Agreement |
| 1.2 Direct and Indirect Speech | |
| 1.3 Kinds of Sentences and Transformation of Sentences | |
| Grammar II | 2.1 Basic Grammatical Patterns/Structures, Conditional Sentences |
| 2.2 Parts of Speech, Active and Passive Voice | |
| 2.3 Verbal: Infinitives, Gerund and Participles | |
| 2.4 Punctuation and Use of Prepositions | |
| 2.5 Vocabulary | |
| 2.6 Idiomatic Expressions | |
| Phonetics | 3.2 Phonemes (Vowels/Consonants) |
| 3.3 Syllables and Stress (Word/Sentence) | |
| Comprehension | 4.1 Comprehensions of reading passages on a variety of topics and style with special references to General English and Technical English |