Computer based entrance test will be conducted in many cities across India. The entrance examination consists of the following two papers:

- General Aptitude paper - 90 Minutes
- Subject paper - 90 Minutes

**General Aptitude**

**Subject Paper**

Applicant should appear for one of the following relevant subject papers based on their graduation discipline.

- Mathematics
- Computer Science and Enginering
- Electronics and Communications Engineering
- Civil Engineering

**1. Mathematics**

- Finite Dimensional Linear Vector Space:

Linear Independence, Span, Basis, Orthonormal Set, Gram-Schmidt Orthogo- nalization Process, Inner Product, Dual Space, Eigen Space, Rank of a Matrix, Cayley-Hamiltonian Theorem, Similar Matrices, Linear Operator, Hermetian, Unitary and Normal Matrices, Spectral Decomposition.

- Group, Ring and Field:

Basic Concepts of Groups, Cyclic Group, Cosets, Elementary Concepts of Rings and Field

- Real Analysis:

Concepts of sets of Real numbers, Sequence of Real Numbers, Continuous and Diﬀerentiable Functions, Rolle’s Theorem, Mean Value Theorem and Taylor Se- ries, Reimann Integration

- Probability Theory:

Conditional Probability, Bayes Theorem, Random variable, PDF and CDF, Mo- ment Generating Function, Theoretical Distribution (Binomial, Poisson, Nor- mal, Uniform and Hyper geometric)

- Ordinary Diﬀerential Equation:

Equation of First order and First Degree, Second order Linear Equation with Constant coeﬃcients.

- Optimization:

Linear Programming Problem.

**2. Computer Science and Engineering**

Discrete Mathematics, Fundamental Programming Concepts, Control Flow, Functions, Recursion, Basic Data Structures, Basic algorithms, Boolean Algebra, Digital Building Blocks, Karnaugh's Maps, Computer Organisation, Number Systems. Capability to write programs in C or C++ is expected, Relational Databases (Functional dependencies, SQL), Computer Networks, Operating Systems.

**3. Electronics and Communications Engineering**

#### The paper will consist of two areas. Electronics and Signal Processing and Communication.

**Electronics:**

Networks: Nodal and mesh analysis, Wye-Delta transformation, steady state sinusoidal analysis, time and frequency domain analysis of RLC circuits, Laplace transformations, 2-port networks, Transfer functions.

Electronic Devices: Theory and Characteristics of Diodes such as Junction and Zener etc, Transistors such as BJT, JFET, and MOSFET etc, Photodiodes.

Analog Circuits: Small signal models and applications of diodes, BJTs, MOSFETs, Biasing of transistors, Types of Amplifiers, Op-amp circuits, Filters, Oscillators, Function generators and wave-shaping circuits.

Digital circuits: Boolean algebra, logic gates, Logic families, combinational, arithmetic, memory and sequential circuits, ADC, Microprocessors and Microcontrollers.

Control Systems: Components of control systems, Open and closed loop control systems, stability analysis, Routh-Hurwitz Criteria, Signal flow graphs, transient and steady state analysis of LTI control systems including frequency response, Root loci, Bode and Nyquist plots, lead and lag compensation, PID control.

**Signal Processing and Communications:**

Signals and Systems: Classification of signals, LTI system analysis, System properties, Fourier Series, Fourier Transform, discrete time Fourier series , Laplace Transform, Z-transform, System transfer function, Fourier analysis of LTI systems, Sampling theorem.

Probability theory and random processes: random variables, probability distribution function, probability density function, conditional probability, Bayes theorem, central limit theorem, functions of random variables, random processes, stationary random processes, auto-correlation and cross-correlation functions, power spectrum.

Communication Theory: Analog and Digital Modulation and demodulation, Superheterodyne Receivers, Quantization, Line Coding, Matched filters, Receiver structures in the presence of AWGN, Probability of error.

Digital Signal Processing: Discrete Fourier transform, FFT, Z-transform, Z-domain analysis of LTI systems, Circular convolution, Design of digital IIR and FIR filters.

**4. Civil Engineering**

**Engineering Mathematics:**

Determinants, matrices, limit, continuity and differentiability, mean value theorems, integral calculus, partial derivatives, maxima and minima, ordinary differential equations and applications, initial and boundary value problems, Laplace and Fourier transforms, test for convergence, sequences and series.

**Structural Engineering:**

Bending moments and shear Forces in statically determinate beams; Simple stress and strain relationships; Principal stresses, Mohr’s circle; Simple bending theory; Flexural and Shear stresses; Uniform torsion; Analysis of trusses and frames; Analysis of indeterminate structures by force/displacement methods; Influence lines; Matrix methods of structural analysis; Design of Reinforced Concrete Structures-Working stress and limit state design concepts, Design of structural members for flexure, shear and axial compression-Beams, Slabs, Columns, Footings, Staircases; Design of Steel Structures-tension and compression members, beam and beam-columns, column bases, beam-column connections, plastic analysis of beams

**Geotechnical Engineering:**

Design of Foundation Systems-Bearing Capacity, Shallow & Deep Foundations- Footings, Raft Foundations, Pile Foundations.

**Hydraulics and Water Resources Engineering: **

Properties of fluids, fluid statics, Continuity, momentum, energy and corresponding equations and applications, Laminar and turbulent flow, Flow in pipes, Flow measurement in channels and pipes, Kinematics of flow; Hydrologic cycle precipitation, evaporation, infiltration, hydrograph analysis, flood estimation and routing, reservoir capacity, reservoir and channel routing, surface run-off models.

Page last updated on *March, 2021*