Engineering Mathematics :
Linear Algebra: Vector space, basis, linear dependence
and independence, matrix algebra, eigen values and eigen vectors, rank,
solution of linear equations –existence and uniqueness.
Calculus: Mean value theorems, theorems of integral
calculus, evaluation of definite and improper integrals, partial
derivatives, maxima and minima, multiple integrals, line, surface and
volume integrals, Taylor series.
Differential equations: First order equations (linear
and nonlinear), higher order linear differential equations, Cauchy's
and Euler's equations, methods of solution using variation of
parameters, complementary function and particular integral, partial
differential equations, variable separable method, initial and boundary
value problems
Vector Analysis: Vectors in plane and space, vector operations, gradient, divergence and curl, Gauss's, Green's and Stoke's theorems
Complex variables: Analytic functions, Cauchy's integral theorem, Cauchy's integral formula; Taylor's and Laurent's series, residue theorem.
Probability and Statistics: Mean, median, mode and
standard deviation; combinatorial probability, probability distribution
functions -binomial, Poisson, exponential and normal; Joint and
conditional probability; Correlation and regression analysis,
convergence criteria.
Numerical Methods: Solutions of non-linear algebraic equations, single and multi-step methods for differential equations.
GENERAL APTITUDE(GA):
Verbal Ability: English grammar, sentence completion, verbal analogies, word groups, instructions, critical reasoning and verbal deduction.
Electronics and Communication Engineering
Networks: Network solution methods: nodal and mesh
analysis; Network theorems: superposition, Thevenin and Norton’s,
maximum power transfer; Wye-Delta transformation; Steady state
sinusoidal analysis using phasors; Time domain analysis of simple linear
circuits; Solution of network equations using Laplace transform;
Frequency domain analysis of RLC circuits; Linear 2-port network
parameters: driving point and transfer functions; State equations for
networks
Continuous-time signals: Fourier series and Fourier transform
representations, sampling theorem and applications; Discrete-time
signals: discrete-time Fourier transform (DTFT),DFT, FFT, Z-transform,
interpolation of discrete-time signals;LTI systems: definition and
properties, causality, stability, impulse response, convolution, poles
and zeros, parallel and cascade structure, frequency response, group
delay, phase delay, digital filter design techniques
Electronic Devices: Energy bands in
intrinsic and extrinsic silicon; Carrier transport: diffusion current,
drift current, mobility and resistivity; Generation and recombination of
carriers; Poisson and continuity equations; P-N junction, Zener diode,
BJT, MOS capacitor, MOSFET, LED, photo diode and solar cell; Integrated
circuit fabrication process: oxidation, diffusion, ion implantation,
photolithography and twin-tub CMOS process
Analog Circuits: Small signal
equivalent circuits of diodes, BJTs and MOSFETs; Simple diode circuits:
clipping, clamping and rectifiers; Single-stage BJT and MOSFET
amplifiers: biasing, bias stability, mid-frequency small signal analysis
andfrequency response; BJT and MOSFET amplifiers: multi-stage,
differential, feedback, power and operational; Simple op-amp circuits;
Active filters; Sinusoidal oscillators: criterion for oscillation,
single-transistor and op-amp configurations; Function generators,
wave-shaping circuits and 555 timers; Voltage
reference circuits; Power supplies: ripple removal and regulation
Digital circuits: Number systems; Combinatorial circuits:
Boolean algebra, minimization of functions using Boolean identities and
Karnaugh map, logic gates and their static CMOS implementations,
arithmetic circuits, code converters, multiplexers, decoders and PLAs;
Sequentialcircuits:latches and flip-flops,counters,shift-registers and
finite state machines; Data converters: sample and hold circuits, ADCs
and DACs; Semiconductor memories: ROM, SRAM, DRAM; 8-bit microprocessor
(8085): architecture, programming, memory and I/O interfacing
Control Systems: Basic control system components;
Feedback principle; Transfer function; Block diagram representation;
Signal flow graph; Transient and steady
-state analysis of LTI systems; Frequency response; Routh-Hurwitz and
Nyquist stability criteria; Bode and root-locus plots; Lag, lead and
lag-lead compensation; State variable model and solution of state
equation of LTI systems.
Communications: Random processes: autocorrelation and
power spectral density, properties of white noise, filtering of random
signals through LTI systems; Analog communications: amplitude
modulation and demodulation, angle modulation and demodulation, spectra
of AM and FM, superheterodyne receivers, circuits for analog
communications; Information theory: entropy, mutual information and
channel capacity theorem; Digital communications: PCM, DPCM, digital
modulation schemes, amplitude, phase and frequency shift keying (ASK,
PSK, FSK), QAM, MAP and ML decoding, matched filter receiver,
calculation of bandwidth, SNR and BER for digital modulation;
Fundamentals of error correction, Hamming codes; Timing and frequency
synchronization, inter-
symbol interference and its mitigation; Basics of TDMA, FDMA and CDMA
Electromagnetics: Electrostatics; Maxwell’s equations:
differential and integral forms and their interpretation, boundary
conditions, wave equation, Poynting vector; Plane waves and properties:
reflection and refraction, polarization, phase and group velocity,
propagation through various media, skin depth; Transmission line
s: equations, characteristic impedance, impedance matching, impedance
transformation, S-
parameters, Smith chart; Waveguides: modes, boundary conditions, cut-off
frequencies, dispersion relations; Antennas: antenna types, radiation
pattern, gain and directi
vity, return loss, antenna arrays; Basics of radar; Light propagation in
optical fibers.
