Linear Algebra

Matrix algebra, Systems of linear equations, Eigenvalues, and EigenVectors

Calculus

Functions of a single variable; Mean value theorems, local maxima, and minima, Taylor and Maclaurin series; Limit, continuity, and differentiability; Evaluation of definite and indefinite integrals, application of definite integral to obtain area and volume; Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface, and Volume integrals, Stokes, Gauss, and Green’s theorems; Partial derivatives; Total derivative;

Ordinary Differential Equation (ODE)

First order (linear and nonlinear) equations; higher order linear equations with constant coefficients; Laplace transform and its application in solving linear ODEs; Euler-Cauchy equations and boundary value problems.

Partial Differential Equation (PDE)

Fourier series; solutions of one-dimensional diffusion equation; separation of variables; first and second-order one-dimensional wave equation and two-dimensional Laplace equation.

Probability and Statistics

Definitions of probability and sampling theorems; Conditional probability; Descriptive statistics – Mean, median, mode, and standard deviation; Continuous random variables: normal and exponential distributions; Hypothesis testing; Continuous random variables, Discrete Random variables: Poisson and Binomial distributions: normal and exponential distributions.

Numerical Methods

Numerical solutions of linear and nonlinear algebraic equations, Integration by trapezoidal and Simpson’s rules, Single and multi-step methods for differential equations.

QUANTITATIVE APTITUDE

Data interpretation: data graphs (bar graphs, pie charts, and other graphs representing the data), 2- and 3-dimensional plots, maps, and tables Numerical computation and estimation: ratios, percentages, powers, exponents, and logarithms, permutations, and combinations, and series Mensuration and geometry Elementary statistics and probability.

ANALYTICAL APTITUDE

Logic: deduction and induction, Analogy, Numerical relations, and reasoning

VERBAL APTITUDE

Basic English grammar: tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech Basic vocabulary: words, idioms, and phrases in context Reading and comprehension Narrative sequencing

SPATIAL APTITUDE

Transformation of shapes: translation, rotation, scaling, mirroring, assembling, and grouping Paper folding, cutting, and patterns in 2 and 3 dimensions

Coulomb’s Law, Electric Field Intensity, Electric Flux Density, Gauss’s Law, Divergence, Electric field, and potential due to point, line, plane, and spherical charge distributions, Effect of the dielectric medium, Capacitance of simple configurations, Biot‐Savart’s law, Ampere’s law, Curl, Faraday’s law, Lorentz force, Inductance, Magnetomotive force, Reluctance, Magnetic circuits, Self and Mutual inductance of simple configurations.

Voltage and current sources

independent, dependent, ideal, and practical; v-i relationships of the resistor, inductor, mutual inductance, and capacitor; transient analysis of RLC circuits with dc excitation.
Kirchoff’s laws, mesh and nodal analysis, superposition, Thevenin, Norton, maximum power transfer, and reciprocity theorems.
Peak-, average- and RMS values of ac quantities; apparent-, active- and reactive powers; phasor analysis, impedance, and admittance; series and parallel resonance, locus diagrams, the realization of basic filters with R, L, and C elements. transient analysis of RLC circuits with ac excitation.
One-port and two-port networks, driving point impedance and admittance, open-, and short-circuit parameters.

Single phase transformer

equivalent circuit, phasor diagram, open circuit, and short circuit tests, regulation and efficiency; Three phase induction motors: the principle of operation, types, performance, torque-speed characteristics, no-load and blocked rotor tests, equivalent circuit, starting and speed control; Types of losses and efficiency calculations of electric machines.

Periodic, aperiodic, and impulse signals; Laplace, Fourier, and z-transforms; transfer function, a frequency response of first and second-order linear time-invariant systems, the impulse response of systems; convolution, correlation. Discrete-time system: impulse response, frequency response, pulse transfer function; DFT and FFT; basics of IIR and FIR filters.

Feedback principles, signal flow graphs, transient response, steady-state-errors, Bode plot, phase and gain margins, Routh and Nyquist criteria, root loci, design of lead, lag, and lead-lag compensators, state-space representation of systems; time-delay systems; mechanical, hydraulic and pneumatic system components, synchro pair, servo, and stepper motors, servo valves; on-off, P, PI, PID, cascade, feedforward, and ratio controllers, tuning of PID controllers and sizing of control valves.

Characteristics and applications of the diode, Zener diode, BJT, and MOSFET; small signal analysis of transistor circuits, feedback amplifiers. Characteristics of ideal and practical operational amplifiers; applications of opamps: adder, subtractor, integrator, differentiator, difference amplifier, instrumentation amplifier, precision rectifier, active filters, oscillators, signal generators, voltage controlled oscillators, and phase locked loop, sources, and effects of noise and interference in electronic circuits

Combinational logic circuits, minimization of Boolean functions. IC families: TTL and CMOS. Arithmetic circuits, comparators, Schmitt trigger, multi-vibrators, sequential circuits, flipflops, shift registers, timers, and counters; sample-and-hold circuit, multiplexer, analog-to-digital (successive approximation, integrating, flash and sigma-delta) and digital-to-analog converters (weighted R, R2R ladder and current steering logic). Characteristics of ADC and DAC (resolution, quantization, significant bits, conversion/settling time); basics of number systems, Embedded Systems: Microprocessor and microcontroller applications, memory and input-output interfacing; basics of data acquisition systems, basics of distributed control systems (DCS) and programmable logic controllers.

SI units, standards (R, L, C, voltage, current, and frequency), systematic and random errors in measurement, expression of uncertainty – accuracy and precision, propagation of errors, linear and weighted regression. Bridges: Wheatstone, Kelvin, Megohm, Maxwell, Anderson, Schering, and Wien for measurement of R, L, C and frequency, Q-meter. Measurement of voltage, current, and power in single and three-phase circuits; ac and dc current probes; true rms meters, voltage and current scaling, instrument transformers, timer/counter, time, phase, and frequency measurements, digital voltmeter, digital multimeter; oscilloscope, shielding and grounding.

Resistive-, capacitive-, inductive-, piezoelectric-, Hall effect sensors and associated signal conditioning circuits; transducers for industrial instrumentation: displacement (linear and angular), velocity, acceleration, force, torque, vibration, shock, pressure (including low pressure), flow (variable head, variable area, electromagnetic, ultrasonic, turbine, and open channel flow meters) temperature (thermocouple, bolometer, RTD (3/4 wire), thermistor, pyrometer, and semiconductor); liquid level, pH, conductivity and viscosity measurement. 4-20 mA two-wire transmitter.

Amplitude- and frequency modulation and demodulation; Shannon’s sampling theorem, pulse code modulation; frequency and time division multiplexing, amplitude-, phase-, frequency-, quadrature amplitude, pulse shift keying for digital modulation; optical sources and detectors: LED, laser, photo-diode, light dependent resistor, square law detectors and their characteristics; interferometer: applications in metrology; basics of fiber optic sensing. UV-VIS Spectrophotometers, Mass spectrometer.