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Section 1: Engineering Mathematics

**Linear Algebra:** Matrix algebra, systems of linear equations, Eigen values and Eigen
vectors.

**Calculus:** Mean value theorems, theorems of integral calculus, partial derivatives, maxima
and minima, multiple integrals, Fourier series, vector identities, line, surface and volume
integrals, Stokes, Gauss and Green’s theorems.

**Differential equations: **First order equation (linear and nonlinear), higher order linear
differential equations with constant coefficients, method of variation of parameters,
Cauchy’s and Euler’s equations, initial and boundary value problems, solution of partial
differential equations: variable separable method.

**Analysis of complex variables:** Analytic functions, Cauchy’s integral theorem and integral
formula, Taylor’s and Laurent’s series, residue theorem, solution of integrals.

**Probability and Statistics:** Sampling theorems, conditional probability, mean, median,
mode and standard deviation, random variables, discrete and continuous distributions:
normal, Poisson and binomial distributions.

**Numerical Methods: **Matrix inversion, solutions of non-linear algebraic equations, iterative
methods for solving differential equations, numerical integration, regression and
correlation analysis.

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Instrumentation Engineering

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Section 2: Electrical Circuits

**Voltage and current sources:** independent, dependent, ideal and practical; v-i
relationships of resistor, inductor, mutual inductor 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, realization of basic filters with R, L and C elements.
One-port and two-port networks, driving point impedance and admittance, open-, and
short circuit parameters.

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Section 3: Signals and Systems

Periodic, aperiodic and impulse signals; Laplace, Fourier and z-transforms; transfer
function, frequency response of first and second order linear time invariant systems,
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.

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Section 4: Control Systems

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, P-I, P-I-D, cascade, feedforward, and ratio
controllers.

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Section 5: Analog Electronics

Characteristics and applications of diode, Zener diode, BJT and MOSFET; small signal
analysis of transistor circuits, feedback amplifiers. Characteristics of operational amplifiers;
applications of opamps: difference amplifier, adder, subtractor, integrator, differentiator,
instrumentation amplifier, precision rectifier, active filters and other circuits. Oscillators,
signal generators, voltage controlled oscillators and phase locked loop.

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Section 6: Digital Electronics

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-todigital
(successive approximation, integrating, flash and sigma-delta) and digital-toanalog
converters (weighted R, R-2R ladder and current steering logic). Characteristics of
ADC and DAC (resolution, quantization, significant bits, conversion/settling time); basics of
number systems, 8-bit microprocessor and microcontroller: applications, memory and
input-output interfacing; basics of data acquisition systems.

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Section 7: Measurements

SI units, systematic and random errors in measurement, expression of uncertainty -
accuracy and precision index, propagation of errors. PMMC, MI and dynamometer type
instruments; dc potentiometer; bridges for measurement of R, L and C, 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.

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Section 8: Sensors and Industrial Instrumentation

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 (differential pressure, 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.

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Section 9: Communication and Optical Instrumentation

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