Complete Syllabus

All topics covered in the ECETRIX entrance exam

📐 Mathematics (50 Questions) ▼

Algebra

Equations, inequalities, complex numbers

  • Quadratic and cubic equations
  • Arithmetic and Geometric Progressions (AP/GP)
  • Binomial theorem and permutations/combinations
  • De Moivre's theorem

Trigonometry

Functions, identities, equations

  • Inverse trigonometric functions
  • Properties of triangles
  • Heights and distances

Calculus

Limits, derivatives, integrals

  • Continuity and Differentiability
  • Mean Value Theorems (Rolle's, Lagrange's)
  • Applications of derivatives (Tangents, Normals, Maxima, Minima)
  • Definite and Indefinite Integration

Differential Equations

ODE, PDE, applications

  • First order linear and exact differential equations
  • Homogeneous and non-homogeneous equations
  • Formation of partial differential equations (PDE)

Matrices & Determinants

Properties, operations, inverses

  • Adjoint and inverse of a matrix
  • Rank of a matrix
  • Solving linear equations (Cramer's rule, Matrix inversion)

Probability

Events, distributions, statistics

  • Conditional Probability and Bayes' Theorem
  • Binomial, Poisson, and Normal distributions
  • Measures of central tendency and dispersion

Numerical Methods

Approximation techniques, algorithms

  • Bisection method and Newton-Raphson method
  • Interpolation (Lagrange, Newton's)
  • Numerical integration (Trapezoidal, Simpson's rules)

⚛️ Physics (25 Questions) ▼

Mechanics

Motion, forces, energy, momentum

  • Newton's Laws of Motion
  • Work-Energy Theorem and conservation laws
  • Rotational motion and moment of inertia
  • Simple Harmonic Motion (SHM)

Heat & Thermodynamics

Temperature, heat, laws

  • Zeroth, First, and Second Laws of Thermodynamics
  • Heat transfer mechanisms (Conduction, Convection, Radiation)
  • Specific heats of gases and phase transitions

Waves

Properties, interference, diffraction

  • Wave equation and wave motion types (Transverse, Longitudinal)
  • Doppler effect in sound
  • Huygens' Principle and Young's double-slit experiment

Electricity & Magnetism

Fields, circuits, induction

  • Coulomb's Law and Electric Field
  • Ohm's Law, Kirchhoff's Laws, and DC circuits
  • Faraday's Law of Induction and AC circuits (RLC)

Modern Physics

Quantum concepts, relativity, nuclear physics

  • Photoelectric effect and Bohr's model of the atom
  • Special theory of relativity (Time dilation, Length contraction)
  • Radioactivity, nuclear fission, and fusion

🧪 Chemistry (25 Questions) ▼

Physical Chemistry

Thermodynamics, kinetics, equilibrium

  • Chemical kinetics (Rate laws, reaction order)
  • Chemical and ionic equilibrium
  • Electrochemistry and Nernst equation
  • Colloids and surface chemistry

Organic Chemistry

Mechanisms, reactions, synthesis

  • Nomenclature (IUPAC) and isomerism
  • Reactions of alkanes, alkenes, and alkynes
  • Chemistry of functional groups (Alcohols, Aldehydes, Acids)
  • Polymers and Biomolecules (Carbohydrates, Proteins)

Inorganic Chemistry

Periodic table, bonding, compounds

  • Periodic properties and chemical bonding (VBT, MOT)
  • p-block, d-block, and f-block elements
  • Coordination compounds and isomerism

Environmental Chemistry

Pollution, sustainability, cycles

  • Atmospheric and water pollution (BOD, COD)
  • Green chemistry principles
  • Biogeochemical cycles (Carbon, Nitrogen)

💻 Computer Science & Engineering (100 Questions) ▼

Programming in C

Syntax, pointers, memory management

  • Control structures and functions
  • Arrays and strings handling
  • Dynamic memory allocation (malloc, calloc, realloc)
  • File handling in C

OOP in C++

Classes, inheritance, polymorphism

  • Constructors, destructors, and friend functions
  • Virtual functions and pure virtual functions
  • Operator overloading and exception handling

Data Structures

Arrays, linked lists, trees, graphs

  • Stack (push/pop) and Queue (enqueue/dequeue) operations
  • Tree traversals (Inorder, Preorder, Postorder)
  • Graph representations (Adjacency Matrix/List) and traversals (BFS, DFS)

Algorithms

Sorting, searching, dynamic programming

  • Time and space complexity analysis (Big O)
  • Sorting: Merge Sort, Quick Sort, Heap Sort
  • Searching: Binary Search, Hashing

DBMS

SQL, normalization, transactions

  • Relational Model and Relational Algebra
  • Functional Dependencies and Normal Forms (1NF, 2NF, 3NF, BCNF)
  • ACID properties and concurrency control

Operating Systems

Processes, memory, scheduling

  • Process states and Inter-Process Communication (IPC)
  • CPU Scheduling algorithms (FCFS, SJF, Priority, Round Robin)
  • Virtual memory and Paging
  • Deadlocks (Prevention, Avoidance, Detection)

Digital Electronics

Logic gates, circuits, design

  • Boolean Algebra and K-maps (Karnaugh Maps)
  • Combinational Circuits (Adders, Multiplexers, Decoders)
  • Sequential Circuits (Flip-Flops, Counters, Registers)

Computer Architecture

CPU, cache, instruction sets

  • Data representation (Floating point, Fixed point)
  • Pipelining and instruction level parallelism
  • Cache memory organization (Mapping techniques)
  • I/O organization (DMA, Interrupts)

Computer Networks

OSI model, protocols, TCP/IP

  • Networking devices (Hub, Switch, Router)
  • IP addressing (IPv4 and IPv6) and Subnetting
  • Transport layer protocols (TCP, UDP)
  • Application layer protocols (HTTP, DNS, FTP)

Web Technologies

HTML, CSS, JavaScript, HTTP

  • HTML5 semantic elements and forms
  • CSS layouts (Flexbox and Grid)
  • DOM manipulation and AJAX in JavaScript
  • Client-server architecture