Foundations: Linear Algebra/Matrices, Probability, Statistics and Combinatorics at the undergraduate engineering mathematics level, in addition to basic Calculus and Geometry.

Programming: Data Structures (arrays, matrices, etc.) and Basic Programming (choice of Java/C/C++/Python).

The online written test will contain multiple choice questions and programming questions. Total duration will be 60 mins.

Sample Test

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, Taylor series.
• Differential Equations: First order equations (linear and nonlinear), higher order linear differential 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
• 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 Random processes: autocorrelation and power spectral density, properties of white noise

Communications

• Information theory: entropy, mutual information and channel capacity theorem;
• Digital communications: digital modulation schemes, amplitude, phase and frequency shift keying (ASK, PSK, FSK), QAM, MAP and ML decoding, matched filter receiver, SNR and BER for digital modulation;

Signal Processing

• Continuous-time signals: Fourier series and Fourier transform representations, Laplace transform, 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, Transient and steady-state analysis
• Basic control system components; Feedback principle; Transfer function; Block diagram representation;

HFCS

• Devices: Energy bands in intrinsic and extrinsic silicon; Carrier transport: diffusion current, drift current, mobility and resistivity;
• 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 and frequency response; Simple op-amp circuits
• 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, multiplexers, Sequential circuits: latches and flip‐flops, counters, shift‐registers and finite state machines;
• Electromagnetic: Maxwell’s equations: differential and integral forms and their interpretation, boundary conditions, wave equation, Poynting vector; Transmission lines: equations, characteristic impedance, propagation constant, impedance matching, impedance transformation, S-parameters

Sample Test