Tribhuvan University • IOE Entrance Examination
IOE Syllabus — Official Entrance Examination Blueprint
The official 140-mark IOE syllabus for engineering entrance in Nepal. Chapter-wise curriculum across Mathematics (50), Physics (45), Chemistry (25), and English (20).
29 Units•287 Topics•140 Marks
Mathematics
(गणित)50 Marks • 36 Questions
Set, Relations & Functions
8 topicsTypes of Sets & Set OperationsVenn Diagrams & ApplicationsCartesian Product of SetsBinary Relations & TypesEquivalence Relations & Equivalence ClassesDomain, Co-domain & Range of FunctionsInjective, Surjective & Bijective FunctionsComposite Functions & Inverse Functions
Algebra: Complex Numbers
7 topicsImaginary Unit & Integral Powers of iAlgebra of Complex Numbers (Addition, Subtraction, Multiplication, Division)Conjugate, Modulus & Principal ArgumentPolar & Euler FormsDe Moivre's Theorem & ApplicationsCube Roots of Unity & Their Algebraic PropertiesSquare Roots of Complex Numbers
Algebra: Quadratic Equations
7 topicsQuadratic Equations & Roots FormulaNature of Roots & DiscriminantRelations Between Roots and CoefficientsSymmetric Functions of RootsFormation of Quadratic EquationsCondition for Common RootsSign & Extremum Values of Quadratic Expressions
Algebra: Sequences & Series
8 topicsArithmetic Progression (AP)Geometric Progression (GP)Harmonic Progression (HP)Arithmetic, Geometric & Harmonic Means (AM, GM, HM)Inequality of Means (AM ≥ GM ≥ HM)Sum to Infinity of Geometric Series (|r| < 1)Sum of First n Natural Numbers, Squares & CubesArithmetico-Geometric Progression (AGP)
Permutations, Combinations & Binomial Theorem
9 topicsFundamental Principles of CountingPermutations of Distinct & Repeated Objects (ⁿP_r)Circular PermutationsCombinations & Selection Rules (ⁿC_r)Restricted Permutations & CombinationsBinomial Theorem for Positive Integral IndexGeneral Term (T_r+1), Middle Term & Independent TermProperties of Binomial CoefficientsExponential & Logarithmic Series
Matrices & Determinants
7 topicsTypes of Matrices & Matrix OperationsTranspose, Symmetric & Skew-Symmetric MatricesDeterminants of Order 2 and 3 & PropertiesMinors, Cofactors & Adjoint of a MatrixSingular & Non-Singular MatricesInverse of a Square MatrixCramer's Rule & System of Linear Equations
Trigonometry
8 topicsCompound, Multiple & Sub-multiple AnglesTransformation of Sums and ProductsConditional Trigonometric IdentitiesGeneral Solutions of Trigonometric EquationsInverse Circular Functions & Principal ValuesProperties of Triangles: Sine, Cosine & Projection RulesArea of Triangle, In-radius, Circum-radius & Ex-radiiHeights & Distances
Coordinate Geometry (2D)
11 topicsDistance & Section FormulasSlopes & Forms of Straight LinesAngle Between Two LinesPerpendicular Distance & Parallel Line SeparationPair of Straight Lines Through Origin (ax² + 2hxy + by² = 0)Condition for Orthogonal & Coincident Pair of LinesCircles: Standard & General Equations, Center & RadiusTangents, Normals & Length of TangentParabola: Standard Equation, Focus, Directrix & Latus RectumEllipse: Standard Equation, Eccentricity, Foci & DirectricesHyperbola: Standard Equation, Eccentricity, Foci & Asymptotes
Vectors & 3D Geometry
9 topics3D Coordinate System, Distance & Section FormulasDirection Cosines & Direction Ratios of a LineAngle Between Two Lines in SpaceEquations of a Plane (General, Intercept, Normal Forms)Distance of a Point from a PlaneVector Algebra: Addition, Subtraction & Scalar MultiplicationDot (Scalar) Product & Geometric ProjectionCross (Vector) Product & Areas of Triangles/ParallelogramsScalar Triple Product & Coplanarity of Vectors
Calculus: Limits & Differential Calculus
12 topicsLimits of Algebraic, Trigonometric, Exponential & Logarithmic FunctionsIndeterminate Forms & L'Hôpital's RuleContinuity of Functions at a Point & in an IntervalDerivatives from First PrincipleProduct, Quotient & Chain Rules of DifferentiationDerivatives of Inverse Trigonometric, Implicit & Parametric FunctionsHigher-Order Derivatives (Second Derivative)Tangents & Normals to CurvesRate of Change, Velocity & AccelerationMonotonicity (Increasing & Decreasing Functions)Local Maxima & Minima (First & Second Derivative Tests)Rolle's Theorem & Lagrange's Mean Value Theorem
Calculus: Integral Calculus & Differential Equations
11 topicsIndefinite Integrals & Standard FormulasIntegration by SubstitutionIntegration by PartsIntegration by Partial FractionsDefinite Integrals & Fundamental Theorem of CalculusProperties of Definite Integrals (King's Property, Symmetry)Area Bounded by CurvesDifferential Equations: Order & DegreeSeparable Variable Differential EquationsHomogeneous First-Order Differential EquationsLinear Differential Equations (Integrating Factor Method)
Institute of Engineering (IOE), Tribhuvan University entrance examination curriculum.