# Details for PhD(CSE/ ECE) Admissions

**Written Test (for CSE)**

**Written test:** The written test will have two sections (Part A and B) as described below. The questions will be on standard B.Tech. level concepts (MSc for non CSE/IT areas). Syllabus for the test is given below. The questions may be a mixture of multiple choice, fill in the blanks, one-two line answers, and similar short answers. They will not require long descriptive answers. Use of calculators and similar computing devices will not be permitted.

- Part-A is compulsory. This section will have questions from discrete maths, data structures, algorithms and programming concepts.

**Syllabus:**

Sets, Relations, Boolean Algebra, Combinatorics, Summation, Asymptotic notation, Recurrences, Basic data structures (arrays, linked-list, stacks, queues), Trees, Graphs, Sorting, Graph algorithms, Dynamic programming, Divide and conquer, Heaps, Hash tables, Basic programming concepts.

- In Part-B, candidates need to choose ANY ONE from the following 5 subsections. The candidate will have to specify their choice during registration ON THE MORNING of the test.

- Linear algebra, probability, statistics, logic.
- § Syllabus:

Mathematical Logic: Propositional Logic; First Order Logic.

Probability: Conditional Probability; Mean, Median, Mode and Standard Deviation; Bayes Theorem, Random Variables; Distributions; uniform, normal, exponential, Poisson, Binomial.

Probability & Statistics: Probability space, conditional probability, Bayes theorem, independence, Random variables, joint and conditional distributions, standard probability distributions and their properties, expectation, conditional expectation, moments; Weak and strong law of large numbers, central limit theorem; Mean, Median, Mode and Variance, Testing of hypotheses, Distributions; uniform, normal, exponential, Poisson, Binomial.

Linear Algebra: Algebra of matrices, determinants, systems of linear equations, Eigen values and Eigen vectors.

- § Syllabus:
- Computer networks, operating systems
- § Syllabus:

Computer Networks: ISO/OSI stack, LAN technologies (Ethernet, Token ring), Flow and error control techniques, Routing algorithms, Congestion control, TCP/UDP and sockets, IP(v4), Application layer protocols (icmp, dns, smtp, pop, ftp, http); Basic concepts of hubs, switches, gateways, and routers. Network security basic concepts of public key and private key cryptography, digital signature, firewalls.

Operating System: Processes, Threads, Inter-process communication, Concurrency, Synchronization, Deadlock, CPU scheduling, Memory management and virtual memory, File systems, I/O systems, Protection and security.

- § Syllabus:
- Databases and software engineering
- § Syllabus:

Databases: ER-model, Relational model (relational algebra, tuple calculus), Database design (integrity constraints, normal forms), Query languages (SQL), File structures (sequential files, indexing, B and B+ trees), Transactions and concurrency control.

Information Systems and Software Engineering: information gathering, requirement and feasibility analysis, data flow diagrams, process specifications, input/output design, process life cycle, planning and managing the project, design, coding, testing, implementation, maintenance.

- § Syllabus:
- Computer hardware
- § Syllabus:

Digital Logic: Logic functions, Minimization, Design and synthesis of combinational and sequential circuits; Number representation and computer arithmetic (fixed and floating point).

Computer Organization and Architecture: Machine instructions and addressing modes, ALU and data-path, CPU control design, Memory interface, I/O interface (Interrupt and DMA mode), Instruction pipelining, Cache and main memory, Secondary storage.

- § Syllabus:
- Artificial intelligence, machine learning and image processing
- § Syllabus:

Image understanding and representation, Image transformations, Filtering, noise removal, Edge detection, Color image processing, and transformations, Decision tree, and Bayes classification.

- § Syllabus:

**Written Test (for ECE)****Written test:**The written test will have two sections (Part A and B) as described below. The questions will be on standard B.Tech. level concepts. Syllabus for the test is given below. The questions may be a mixture of multiple choice, fill in the blanks, one-two line answers, and similar short answers. They will not require long descriptive answers. Use of calculators and similar computing devices will not be permitted.- Part-A is compulsory. This section will have questions from circuit theory, calculus and probability.
- Syllabus:

Calculus: Mean value theorems, Theorems of integral calculus, Maxima and minima, First order differential equation (linear and nonlinear), Initial and boundary value problems

Probability: Conditional probability, Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Circuits: Thevenin and Norton's maximum power transfer, Wye-Delta transformation. Time domain analysis of simple RLC circuits, Solution of network equations using Laplace transform: frequency domain analysis of RLC circuits.

- Syllabus:
- In Part-B, candidates need to choose ANY ONE from the following 4 subsections. The candidate will have to specify their choice during registration on the morning of the test.
- Digital Circuits
- § Syllabus:

Boolean algebra, minimization of Boolean functions; logic gates; digital IC families (DTL, TTL, ECL, MOS, CMOS).

Combinatorial circuits: arithmetic circuits, multiplexers, decoders, PROMs and PLAs.

Sequential circuits: latches and flip-flops, counters and shift-registers. Sample and hold circuits, ADCs, DACs. Semiconductor memories.

Microprocessor: architecture, programming, memory and I/O interfacing.

- § Syllabus:
- Signals and Systems
- § Syllabus:

Definitions and properties of Laplace transform, continuous-time and discrete-time Fourier series, continuous-time and discrete-time Fourier Transform, DFT and FFT, z-transform. Sampling theorem.

Linear Time-Invariant (LTI) Systems: definitions and properties; causality, stability, impulse response, convolution, poles and zeros, parallel and cascade structure, frequency response, group delay, phase delay. Signal transmission through LTI systems.

- § Syllabus:
- Analog Circuits
- § Syllabus:

Analog Circuits: Small Signal Equivalent circuits of diodes, BJTs, MOSFETs and analog CMOS. Simple diode circuits, clipping, clamping, rectifier. Biasing and bias stability of transistor and FET amplifiers.

Amplifiers: single-and multi-stage, differential and operational, feedback, and power. Frequency response of amplifiers. Simple op-amp circuits. Filters. Sinusoidal oscillators; criterion for oscillation; single-transistor and op-amp configurations. Function generators and wave-shaping circuits, 555 Timers. Power supplies.

- § Syllabus:
- Communication Systems
- § Syllabus:

Random signals and noise: probability, random variables, probability density function, autocorrelation, power spectral density.

Analog communication systems: amplitude and angle modulation and demodulation systems, spectral analysis of these operations, signal-to-noise ratio (SNR) calculations for amplitude modulation (AM) and frequency modulation (FM) for low noise conditions.

Digital communication systems: pulse code modulation (PCM), differential pulse code modulation (DPCM), digital modulation schemes: amplitude, phase and frequency shift keying schemes (ASK, PSK, FSK), matched filter receivers, bandwidth consideration and probability of error calculations for these schemes. Basics of TDMA, FDMA and CDMA and GSM.

- § Syllabus:

Additional requirements for candidates apply in ECE:

- MTech candidates applying in ECE must mention 3 courses in the application out of the courses listed below. Candidate shall be interviewed in the courses mentioned in application.
- BTech candidates applying in ECE must mention 4 courses in the application out of the courses listed below. Candidate shall be interviewed in the courses mentioned in application.

Advanced Signal Processing Statistical Signal Processing Digital VLSI Design Analog CMOS design Digital Communications Communication Networks Linear systems Introduction to Robotics RF Circuit design Antennas and Propagation Embedded systems *For syllabus, Click Here

- Digital Circuits

- Linear algebra, probability, statistics, logic.