BCECE LE Engineering Official Syllabus
Complete chapter and topic breakdown for Bihar B.Tech Lateral Entry entrance examination as notified by BCECEB.
Section 1: Mathematics (50 Questions • 200 Marks)
Mathematics carries one-third of total exam marks and is rank-determining. Questions test diploma-level calculus, matrices, geometry, and differential equations.
Unit 1: Solid Geometry
Cartesian co-ordinates in three dimensions; Direction cosines and direction ratios; Equations of planes and straight lines in symmetric and unsymmetric forms; Shortest distance between two skew lines; Sphere: equations, tangent plane, and intersection with a plane.
Unit 2: Differential Calculus
Successive differentiation; Leibnitz's theorem and its applications; Partial differentiation; Euler’s theorem on homogeneous functions; Jacobians; Tangents and normals; Curvature, radius of curvature in Cartesian and polar coordinates; Asymptotes; Envelopes and evolutes; Maxima and minima of functions of two independent variables; Lagrange’s method of undetermined multipliers.
Unit 3: Integral Calculus
Integration of rational, irrational, and trigonometric functions; Reduction formulae; Definite integrals and their properties; Beta and Gamma functions and relation between them; Double and triple integrals; Applications to evaluation of areas and volumes of revolutions.
Unit 4: Differential Equations
First order differential equations: Exact equations, linear equations, Bernoulli’s form; Orthogonal trajectories; Second order linear differential equations with constant coefficients; Complementary function and Particular Integrals; Method of variation of parameters; Cauchy-Euler homogeneous linear equations.
Unit 5: Vector Calculus
Scalar and vector point functions; Gradient of a scalar field; Divergence and Curl of a vector field; Physical interpretations; Directional derivatives; Line integrals, Surface integrals, and Volume integrals; Green’s theorem in a plane, Gauss’s divergence theorem, and Stokes’ theorem (statements and verification).
Unit 6: Matrices
Algebra of matrices; Elementary row and column operations; Rank of a matrix; Consistency and solution of system of linear equations using matrix methods (Gauss elimination); Eigenvalues and Eigenvectors; Cayley-Hamilton theorem and its application to find the inverse of a matrix; Diagonalization of matrices.
Solve 500+ topic-wise calculus, matrix, and vector practice questions.
Section 2: Engineering Mechanics (50 Questions • 200 Marks)
Engineering Mechanics tests foundational principles of statics, dynamics, friction, and kinematics applicable across all engineering branches.
Unit 1: Vector Methods & Basic Concepts
Representation of vectors, scalar and vector products; System of coplanar forces: Resultant and equilibrant of concurrent, parallel, and non-concurrent force systems; Free body diagrams; Varignon’s theorem of moments.
Unit 2: Equilibrium of Rigid Bodies
Conditions of equilibrium in two dimensions; Lami’s theorem; Types of supports and support reactions; Analysis of simple plane trusses by method of joints and method of sections.
Unit 3: Friction
Laws of dry (Coulomb) friction; Angle of friction, angle of repose, cone of friction; Equilibrium of bodies on rough horizontal and inclined planes; Ladder friction, wedge friction, screw jack, and belt friction.
Unit 4: Centroid, Center of Gravity & Moment of Inertia
Centroid of simple lines, plane figures, and composite areas; Center of gravity of solid bodies; Area moment of inertia: Parallel axis theorem, perpendicular axis theorem; Polar moment of inertia; Radius of gyration; Moment of inertia of standard composite sections (I, T, L, channel sections).
Unit 5: Kinematics of Particles
Rectilinear motion with constant and variable acceleration; Curvilinear motion in rectangular and normal-tangential coordinates; Projectile motion; Relative velocity.
Unit 6: Kinetics of Particles & Rigid Bodies
Newton’s second law of motion; D’Alembert’s principle; Work, Energy, and Power; Principle of work-energy; Conservative forces and conservation of energy; Principle of impulse and momentum; Direct central impact of elastic bodies.
Master force diagrams, friction numericals, and equilibrium questions.
Section 3: Technical English (50 Questions • Mandatory Qualifying)
Technical English is qualifying in nature: You must score at least 35 marks out of 200 (minimum 9 net correct questions) for your Mathematics and Mechanics papers to be evaluated.
Grammar & Sentence Construction
Parts of speech; Subject-verb agreement; Tenses and aspect; Active and passive voice; Direct and indirect speech; Modals and conditionals; Transformation of sentences.
Vocabulary & Terminology
Synonyms and Antonyms; Homophones and Homonyms; One-word substitutions; Idioms and Phrasal verbs; Commonly confused words; Technical suffixes and prefixes.
Error Detection & Syntax
Identifying grammatical errors in sentences; Correction of incorrect prepositions, articles, and modifiers; Punctuation rules and conventions.
Comprehension & Technical Communication
Reading comprehension passages; Drawing inferences; Technical report terminology; Formal letter and memo conventions; Precise writing essentials.
Clear the mandatory 35-mark qualifying cutoff with confidence.