ScholorShip Test Syllabus
Syllabus for APJ Scholarship Test
Time: 2hrs
Marks: 75M
ECE:
MATHS 1 Mark – 7Q; 2 Marks – 7Q
Network Theory  1 Mark – 6Q; 2 Marks – 6Q
Analog Circuits  1 Mark – 6Q; 2 Marks – 6Q
Digital Electronics  1 Mark – 6Q; 2 Marks – 6Q
EEE:
MATHS 1 Mark – 7Q; 2 Marks – 7Q
Network Theory  1 Mark – 6Q; 2 Marks – 6Q
Analog Circuits  1 Mark – 6Q; 2 Marks – 6Q
Digital Electronics  1 Mark – 6Q; 2 Marks – 6Q
EIE:
MATHS 1 Mark – 7Q; 2 Marks – 7Q
Network Theory  1 Mark – 6Q; 2 Marks – 6Q
Analog Circuits  1 Mark – 6Q; 2 Marks – 6Q
Digital Electronics  1 Mark – 6Q; 2 Marks – 6Q
MECHANICAL:
Maths 1 Mark – 7Q; 2 Marks – 7Q
Engineering Mechanics  1 Mark – 6Q; 2 Marks – 6Q
Fluid Mechanics  1 Mark – 6Q; 2 Marks – 6Q
Strength of Materials  1 Mark – 6Q; 2 Marks – 6Q
CIVIL:
Maths  1 Mark – 7Q; 2 Marks – 7Q
Engg. Mechanics  1 Mark – 6Q; 2 Marks – 6Q
Strength of Materials  1 Mark – 6Q; 2 Marks – 6Q
Fluid Mechanics  1 Mark – 6Q; 2 Marks – 6Q
CSE & IT:
Discrete Maths  1 Mark – 7Q; 2 Marks – 7Q
DBMS  1 Mark – 6Q; 2 Marks – 6Q
Programming and Data Structures  1 Mark – 6Q; 2 Marks – 6Q
Digital Logic  1 Mark – 6Q; 2 Marks – 6Q
ECE
1. MATHAETICS
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 Analysis:
Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula; Taylor’s and Laurent’s series, residue theorem.
Numerical Methods:
Solution of nonlinear equations, single and multistep methods for differential equations, convergence criteria.
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.
2. 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.
3. Analog Circuits:
Small signal equivalent circuits of diodes, BJTs and MOSFETs; Simple diode circuits: clipping, clamping and rectifiers; Singlestage BJT and MOSFET amplifiers: biasing, bias stability, midfrequency small signal analysis and frequency response; BJT and MOSFET amplifiers: multistage, differential, feedback, power and operational; Simple opamp circuits; Active filters; Sinusoidal oscillators: criterion for oscillation, singletransistor and opamp configurations; Function generators, waveshaping circuits and 555 timers; Voltage reference circuits; Power supplies: ripple removal and regulation.
4. 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; Sequential circuits: 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;
EEE
1. MATHMATICS
Linear Algebra:
Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.
Calculus:
Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives, 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, PartialDifferential Equations, Method of separation of variables
Complex variables:
Analytic functions, Cauchy’s integral theorem and integral formula, Taylor’s and Laurent’ series, Residue theorem, solution integrals.
Probability and Statistics:
Sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis.
Numerical Methods:
Solutions of nonlinear algebraic equations, single and multistep methods for differential equations.
Transform Theory:
Fourier transform, Laplace transform, Ztransform.
2. Analog and Digital Electronics:
Characteristics of diodes, BJT, MOSFET; Simple diode circuits: clipping, clamping, rectifiers; Amplifiers: Biasing, Equivalent circuit and Frequency response; Oscillators and Feedback, amplifiers; Operational amplifiers: Characteristics and applications; Simple active filters, VCOs and Timers, Combinational and Sequential logic circuits, Multiplexer, Demultiplexer, Schmitt trigger, Sample and hold circuits, A/D and D/A converters, 8085Microprocessor: Architecture, Programming and Interfacing.
3. Electric Circuits:
Network graph, KCL, KVL, Node and Mesh analysis, Transient response of dc and ac networks, Sinusoidal steady? state analysis, Resonance, Passive filters, Ideal current and voltage sources, Thevenin’s theorem, Norton’s theorem, Superposition theorem, Maximum power transfer theorem, Two?port networks, Three phase circuits, Power and power factor in ac circuits.
4. 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; Sequential circuits: 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;
MECHANICAL
1. Mathematics
Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.
Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives, 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, Partial Differential Equations and variable separable method.
Complex variables: Analytic functions, Cauchy's integral theorem and integral formula, Taylor's and Laurent' series, Residue theorem, solution integrals.
Probability and Statistics: Sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis.
Numerical Methods: Solutions of nonlinear algebraic equations, single and multistep methods for differential equations. Transform Theory: Fourier transform, Laplace transform, Ztransform
2. Engineering Mechanics: Free body diagrams and equilibrium; trusses and frames; virtual work; kinematics and dynamics of particles and of rigid bodies in plane motion, including impulse and momentum (linear and angular) and energy formulations; impact.
3. Strength of Materials: Stress and strain, stressstrain relationship and elastic constants, Mohr's circle for plane stress and plane strain, thin cylinders; shear force and bending moment diagrams; bending and shear stresses; deflection of beams; torsion of circular shafts; Euler's theory of columns; strain energy methods; thermal stresses.
4. Fluid Mechanics: Fluid properties; fluid statics, manometry, buoyancy; controlvolume analysis of mass, momentum and energy; fluid acceleration; differential equations of continuity and momentum; Bernoulli's equation; viscous flow of incompressible fluids; boundary layer; elementary turbulent flow; flow through pipes, head losses in pipes, bends etc.
CIVIL
1. MATHAMETICS
Linear Algebra
Matrix algebra, Systems of linear equations, Eigen values and Eigen Vectors.
Calculus:
Functions of single variable; Limit, continuity and differentiability; Mean value theorems, local maxima and minima, Taylor and Maclaurin series; Evaluation of definite and indefinite integrals, application of definite integral to obtain area and volume; Partial derivatives; Total derivative; Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.
Ordinary Differential Equation (ODE):
First order (linear and nonlinear) equations; higher order linear equations with constant coefficients; EulerCauchy equations; Laplace transform and its application in solving linear ODEs; initial and boundary value problems.
Partial Differential Equation (PDE):
Fourier series; separation of variables; solutions of onedimensional diffusion equation; first and second order onedimensional wave equation and twodimensional Laplace equation.
Complex variables:
Analytic functions, Cauchy’s integral theorem, Taylor and Laurent series. Probability and Statistics: Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Poisson, Normal and Binomial distributions.
Probability and Statistics:
Definitions of probability and sampling theorems; Conditional probability; Discrete Random variables: Poisson and Binomial distributions; Continuous random variables: normal and exponential distributions; Descriptive statistics – Mean, median, mode and standard deviation; Hypothesis testing.
Numerical Methods:
Accuracy and precision; error analysis. Numerical solutions of linear and nonlinear algebraic equations; Least square approximation, Newton’s and Lagrange polynomials, numerical differentiation, Integration by trapezoidal and Simpson’s rule, single and multistep methods for first order differential equations.
2. Engineering Mechanics:
System of forces, freebody diagrams, equilibrium equations; Internal forces in structures; Friction and its applications; Kinematics of point mass and rigid body; Centre of mass; Euler’s equations of motion; Impulsemomentum; Energy methods; Principles of virtual work.
3. Solid Mechanics:
Bending moment and shear force in statically determinate beams; Simple stress and strain relationships; Theories of failures; Simple bending theory, flexural and shear stresses, shear centre; Uniform torsion, buckling of column, combined and direct bending stresses.
4. Fluid Mechanics:
Properties of fluids, fluid statics; Continuity, momentum, energy and corresponding equations; Potential flow, applications of momentum and energy equations; Laminar and turbulent flow; Flow in pipes, pipe networks; Concept of boundary layer and its growth.
EIE
1. MATHAETICS
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 Analysis:
Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula; Taylor’s and Laurent’s series, residue theorem.
Numerical Methods:
Solution of nonlinear equations, single and multistep methods for differential equations, convergence criteria.
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.
2. 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.
3. Analog Circuits:
Small signal equivalent circuits of diodes, BJTs and MOSFETs; Simple diode circuits: clipping, clamping and rectifiers; Singlestage BJT and MOSFET amplifiers: biasing, bias stability, midfrequency small signal analysis and frequency response; BJT and MOSFET amplifiers: multistage, differential, feedback, power and operational; Simple opamp circuits; Active filters; Sinusoidal oscillators: criterion for oscillation, singletransistor and opamp configurations; Function generators, waveshaping circuits and 555 timers; Voltage reference circuits; Power supplies: ripple removal and regulation.
4. 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; Sequential circuits: 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;
CSE & IT
1. Engineering Mathematics:
Discrete Mathematics: Propositional and first order logic. Sets, relations, functions, partial
orders and lattices. Groups. Graphs: connectivity, matching, coloring. Combinatorics:
counting, recurrence relations, generating functions.
Linear Algebra: Matrices, determinants, system of linear equations, eigenvalues and
eigenvectors, LU decomposition.
Calculus: Limits, continuity and differentiability. Maxima and minima. Mean value
theorem. Integration.
Probability: Random variables. Uniform, normal, exponential, poisson and binomial
distributions. Mean, median, mode and standard deviation. Conditional probability and
Bayes theorem.
Section 2
DBMS
ER‐model. Relational model: relational algebra, tuple calculus, SQL. Integrity constraints,
normal forms. File organization, indexing (e.g., B and B+ trees). Transactions and
concurrency control.
Programming and Data Structures
Programming in C. Recursion. Arrays, stacks, queues, linked lists, trees, binary search
trees, binary heaps, graphs.
Digital Logic
Boolean algebra. Combinational and sequential circuits. Minimization. Number representations and computer arithmetic (fixed and floating point).
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