This document contains questions from a fourth semester engineering examination on design and analysis of algorithms. It asks students to:
1) Define asymptotic notations and analyze the time complexity of a sample algorithm.
2) Solve recurrence relations for different algorithms.
3) Explain how bubble sort and quicksort work, including tracing quicksort on a sample data set and deriving its worst case complexity.
4) Write the recursive algorithm for merge sort.
The document contains questions assessing students' understanding of algorithm analysis, asymptotic notations, solving recurrence relations, and sorting algorithms like bubble sort, quicksort, and merge sort.
The document provides three questions from a past exam on Engineering Mathematics IV. Question 1a asks to find the third order Taylor approximation of the differential equation dy/dx = y + 1 with the initial condition y(0) = 0. Question 1b asks to solve a differential equation using the modified Euler's method at two points. Question 1c asks to find the value of y(0.4) using Milne's predictor-corrector method for a given differential equation.
This document contains the questions from an Engineering Mathematics examination from December 2012. It covers topics like:
- Using Taylor's series method and Runge-Kutta method to solve initial value problems
- Using Milne's method, Adams-Bashforth method, and Picard's method to solve differential equations
- Properties of analytic functions and bilinear transformations
- Evaluating integrals using Cauchy's integral formula and finding Laurent series
- Expressing polynomials in terms of Legendre polynomials
- Concepts related to probability distributions like binomial, exponential and normal distributions
- Hypothesis testing and confidence intervals
The questions test the students' understanding of numerical methods for solving differential equations, complex analysis topics, orthogonal
1. The document contains a 4 part engineering mathematics exam with multiple choice and numerical problems.
2. Problems involve differential equations, Taylor series approximations, numerical methods like Euler's method and Picard's method, complex analysis, probability, and statistics.
3. Questions range from deriving equations like the Cauchy-Riemann equations, to evaluating integrals using Cauchy's integral formula, to finding confidence intervals and performing hypothesis tests on statistical data.
This document contains a mock exam for the EE107 course with 5 multi-part questions covering topics such as eigenvalues and eigenvectors, partial derivatives, line and surface integrals using theorems like Green's theorem, Stokes' theorem, and Gauss's divergence theorem. The questions are followed by detailed solutions showing the steps and work to arrive at the answers.
This document contains mathematical formula tables including:
1. Greek alphabet, indices and logarithms, trigonometric identities, complex numbers, hyperbolic identities, and series.
2. Derivatives of common functions, product rule, quotient rule, chain rule, and Leibnitz's theorem.
3. Integrals of common functions, double integrals, and the substitution rule for integrals.
This document is a 3 page model question paper for the B.Tech degree examination in Engineering Mathematics - I. It contains 5 parts with a total of 100 marks. Part A contains 5 questions worth 15 marks total. Part B contains 5 questions worth 25 marks total. Part C contains 2 modules with 2 questions each, worth 60 marks total. The questions cover topics like eigenvalues and eigenvectors, homogeneous functions, integration, differential equations, and Laplace transforms.
1) The document discusses solving partial differential equations using variable separation. It presents the one-dimensional wave equation and solves it using variable separation.
2) It derives three cases for the solution based on whether k is positive, negative, or zero. It then presents the general solution as a summation involving sines and cosines.
3) It applies the general solution to two example problems of a vibrating string, finding the displacement as a function of position and time by satisfying the boundary conditions.
This document provides notes and formulae on additional mathematics for Form 5. It covers topics such as progressions, integration, vectors, trigonometric functions, and probability. For progressions, it defines arithmetic and geometric progressions and gives the formulas for calculating the nth term and sum of terms. For integration, it provides rules and formulas for integrating polynomials, trigonometric functions, and expressions with ax+b. It also defines vectors and their operations including vector addition and subtraction. Other sections cover trigonometric functions, their definitions, relationships and graphs, as well as probability topics such as calculating probabilities of events and distributions like the binomial.
The document provides three questions from a past exam on Engineering Mathematics IV. Question 1a asks to find the third order Taylor approximation of the differential equation dy/dx = y + 1 with the initial condition y(0) = 0. Question 1b asks to solve a differential equation using the modified Euler's method at two points. Question 1c asks to find the value of y(0.4) using Milne's predictor-corrector method for a given differential equation.
This document contains the questions from an Engineering Mathematics examination from December 2012. It covers topics like:
- Using Taylor's series method and Runge-Kutta method to solve initial value problems
- Using Milne's method, Adams-Bashforth method, and Picard's method to solve differential equations
- Properties of analytic functions and bilinear transformations
- Evaluating integrals using Cauchy's integral formula and finding Laurent series
- Expressing polynomials in terms of Legendre polynomials
- Concepts related to probability distributions like binomial, exponential and normal distributions
- Hypothesis testing and confidence intervals
The questions test the students' understanding of numerical methods for solving differential equations, complex analysis topics, orthogonal
1. The document contains a 4 part engineering mathematics exam with multiple choice and numerical problems.
2. Problems involve differential equations, Taylor series approximations, numerical methods like Euler's method and Picard's method, complex analysis, probability, and statistics.
3. Questions range from deriving equations like the Cauchy-Riemann equations, to evaluating integrals using Cauchy's integral formula, to finding confidence intervals and performing hypothesis tests on statistical data.
This document contains a mock exam for the EE107 course with 5 multi-part questions covering topics such as eigenvalues and eigenvectors, partial derivatives, line and surface integrals using theorems like Green's theorem, Stokes' theorem, and Gauss's divergence theorem. The questions are followed by detailed solutions showing the steps and work to arrive at the answers.
This document contains mathematical formula tables including:
1. Greek alphabet, indices and logarithms, trigonometric identities, complex numbers, hyperbolic identities, and series.
2. Derivatives of common functions, product rule, quotient rule, chain rule, and Leibnitz's theorem.
3. Integrals of common functions, double integrals, and the substitution rule for integrals.
This document is a 3 page model question paper for the B.Tech degree examination in Engineering Mathematics - I. It contains 5 parts with a total of 100 marks. Part A contains 5 questions worth 15 marks total. Part B contains 5 questions worth 25 marks total. Part C contains 2 modules with 2 questions each, worth 60 marks total. The questions cover topics like eigenvalues and eigenvectors, homogeneous functions, integration, differential equations, and Laplace transforms.
1) The document discusses solving partial differential equations using variable separation. It presents the one-dimensional wave equation and solves it using variable separation.
2) It derives three cases for the solution based on whether k is positive, negative, or zero. It then presents the general solution as a summation involving sines and cosines.
3) It applies the general solution to two example problems of a vibrating string, finding the displacement as a function of position and time by satisfying the boundary conditions.
This document provides notes and formulae on additional mathematics for Form 5. It covers topics such as progressions, integration, vectors, trigonometric functions, and probability. For progressions, it defines arithmetic and geometric progressions and gives the formulas for calculating the nth term and sum of terms. For integration, it provides rules and formulas for integrating polynomials, trigonometric functions, and expressions with ax+b. It also defines vectors and their operations including vector addition and subtraction. Other sections cover trigonometric functions, their definitions, relationships and graphs, as well as probability topics such as calculating probabilities of events and distributions like the binomial.
The document is a lecture on derivatives and the shapes of curves. It covers the mean value theorem, testing for monotonicity using the first derivative test, and finding intervals of monotonicity. It also discusses concavity and the second derivative test. Examples are provided to demonstrate how to find the intervals where a function is increasing or decreasing using the first derivative test.
We discuss the ideas of monotonicity (increasing or decreasing) and concavity (up or down) of a function. Because of the Mean Value Theorem, we can determine these characteristics using derivatives.
1. The document contains a past exam paper for an Advanced Mathematics exam with 10 questions across two parts (A and B).
2. The questions cover a range of advanced mathematics topics including Taylor series, differential equations, probability, statistics, and linear algebra.
3. Students must answer 5 questions total, with at least 2 questions from each part. Questions involve calculating values, proving statements, finding probabilities, and more.
1. This document contains notes and formulas for additional mathematics form 4. It covers topics such as quadratic equations, functions, indices and logarithms, coordinate geometry, and statistics.
2. Quadratic equations are discussed, including finding the roots of a quadratic equation and writing the equation from its roots. Quadratic functions are also covered, specifically the relationship between the sign of b^2 - 4ac and the nature of the roots.
3. Other topics include indices and logarithm laws, coordinate geometry concepts like distance and midpoints, statistics topics such as measures of central tendency (mean, median, mode), and measures of dispersion like standard deviation and interquartile range.
D. Ishii, K. Ueda, H. Hosobe, A. Goldsztejn: Interval-based Solving of Hybrid...dishii
An approach to reliable modeling, simulation and verification of hybrid systems is interval arithmetic, which guarantees that a set of intervals narrower than specified size encloses the solution. Interval-based computation of hybrid systems is often difficult, especially when the systems are described by nonlinear ordinary differential equations (ODEs) and nonlinear algebraic equations.We formulate the problem of detecting a discrete change in hybrid systems as a hybrid constraint system (HCS), consisting of a flow constraint on trajectories (i.e. continuous functions over time) and a guard constraint on states causing discrete changes. We also propose a technique for solving HCSs by coordinating (i) interval-based solving of nonlinear ODEs, and (ii) a constraint programming technique for reducing interval enclosures of solutions. The proposed technique reliably solves HCSs with nonlinear constraints. Our technique employs the interval Newton method to accelerate the reduction of interval enclosures, while guaranteeing that the enclosure contains a solution.
This document is from a Calculus I class at New York University. It provides an overview of functions, including the definition of a function, different ways functions can be represented (formulas, tables, graphs, verbal descriptions), properties of functions like monotonicity and symmetry, and examples of determining domains and ranges of functions. It aims to help students understand functions and their representations as a foundation for calculus.
MATHEON Center Days: Index determination and structural analysis using Algori...Dagmar Monett
This document discusses the work of research project D7 on numerical simulation of integrated circuits. The project uses algorithmic differentiation techniques to determine the tractability index of differential algebraic equations (DAEs) and compute consistent initial values. It provides examples of index determination for circuit simulation problems and discusses achievements, collaborations, and plans for future work extending the structural analysis methods to computational graphs.
An introduction to quantum stochastic calculusSpringer
The document discusses tensor products of Hilbert spaces. It defines positive definite kernels on sets and shows how they can be used to define tensor products. Given Hilbert spaces H1, ..., Hn, it constructs a kernel on the cartesian product of the spaces and shows that its Gelfand pair (H,φ) gives a tensor product of the Hilbert spaces. The map φ from the product space into H is multilinear and H is the completion of the algebraic tensor product of the vector spaces H1, ..., Hn.
This document contains lecture notes on derivatives from a Calculus I class at New York University. It discusses the derivative as a function, finding the derivative of other functions, and the relationship between a function and its derivative. The notes include examples of finding the derivative of the reciprocal function and state that if a function is decreasing on an interval, its derivative will be nonpositive on that interval, while if it is increasing the derivative will be nonnegative. It also contains proofs and graphs related to derivatives.
1. The document contains a math worksheet with fill-in-the-blank and multiple choice questions about integrals and areas bounded by curves.
2. The fill-in-the-blank questions involve evaluating definite integrals, finding values of integrals where functions are even or odd, and taking derivatives of integrals.
3. The multiple choice questions involve identifying the shape of a region bounded by an integral, evaluating definite integrals using geometry, and identifying which integral represents a particular bounded region.
The document discusses exponential growth and decay models in calculus. It covers modeling population growth, radioactive decay using carbon-14 dating, Newton's law of cooling, and continuously compounded interest. Examples are provided to illustrate exponential growth of bacteria populations using the differential equation y' = ky, and modeling radioactive decay where the relative rate of decay is constant and represented by the differential equation y' = -ky.
The document discusses solving the two-dimensional Laplace equation to model steady heat flow problems. It presents:
1) The general boundary value problem (BVP) for the Laplace equation in a semi-infinite and finite lamina.
2) The separation of variables method to obtain solutions as a sum of products of ordinary differential equations.
3) Applying boundary conditions to determine constants and obtain the general solution for temperature distribution.
4) Examples of applying the method to specific BVPs for steady heat flow, including plates with various boundary temperature profiles and geometries.
IJERD (www.ijerd.com) International Journal of Engineering Research and Devel...IJERD Editor
This document presents a theorem that establishes the existence of a fixed point for a mapping under a general contractive condition of integral type. The mapping considered generalizes various types of contractive mappings in an integral setting. The theorem proves that if a self-mapping on a complete metric space satisfies the given integral inequality involving the distance between images of points, where the integral involves a non-negative, summable function, then the mapping has a unique fixed point. Furthermore, the sequence of repeated applications of the mapping to any starting point will converge to this fixed point. The proof involves showing the distance between successive terms in the sequence decreases according to the integral inequality.
The document defines and provides examples of various types of functions, including:
- Polynomial functions including constant, linear, and general polynomial functions.
- Rational functions defined as the ratio of two polynomial functions.
- Trigonometric functions including sine, cosine, and their inverses.
- Other common functions like absolute value, square root, exponential, logarithmic, floor, and ceiling functions.
It also defines properties of functions like being one-to-one, even, or odd and provides examples of each.
[Vvedensky d.] group_theory,_problems_and_solution(book_fi.org)Dabe Milli
1) The document discusses problems related to group theory.
2) Problem 1 shows that the wave equation for light propagation is invariant under Lorentz transformations.
3) Problem 2 shows that the Schrodinger equation is invariant under a global phase change of the wavefunction, and uses Noether's theorem to show the conservation of probability.
This document discusses techniques for evaluating integrals involving exponential functions. It introduces the formulas for integrating exponentials and differentiating them. Several important definite integrals are evaluated, such as the integral from 0 to infinity of e^-ax dx = 1/a. Graphs are used to visualize these integrals. The document then evaluates the more complex integral from negative infinity to positive infinity of e^-ax^2 dx using a change of variables technique. Finally, it discusses how these integrals can be used in kinetic theory and derives an important ratio and normalization factor for Maxwell's velocity distribution.
This document contains the questions from an engineering mathematics exam with 8 questions divided into 2 parts (A and B). Part A contains 3 multi-part questions on topics related to differential equations, including using Taylor's series, Runge-Kutta method, and Milne's predictor-corrector method to solve initial value problems. Part B contains 5 multi-part questions covering additional topics such as Legendre polynomials, Bessel's differential equation, probability, hypothesis testing, and confidence intervals. The exam tests knowledge of numerical analysis techniques for solving differential equations as well as topics in advanced calculus, probability, and statistics.
The document contains questions from a past examination in Design and Analysis of Algorithms. It asks students to solve algorithmic problems related to recurrence relations, sorting algorithms like selection sort and merge sort, graph algorithms like minimum spanning trees and shortest paths, and divide-and-conquer algorithms. Students are required to analyze time complexities, provide pseudocode, and solve problems using algorithms like binary search, quicksort, Prim's algorithm, and shortest path algorithms on graphs.
This document contains exam questions related to Engineering Mathematics and Microcontrollers.
Part A of Engineering Mathematics asks students to: 1) Find an approximate value of y at x=0.1 and 0.2 using Taylor's series, 2) Solve a differential equation using Euler's modified method and carry out three modifications, 3) Determine the value of y(1.4) using Adams-Bashforth method given values of y at other points.
Part B asks students to: 1) Fit a least squares line to given data, 2) Prove and explain a trigonometric identity, 3) Find the probability of solving a problem given individual student probabilities, 4) Define terms related to probability distributions,
This document contains questions pertaining to signals and systems. It has two parts - Part A and Part B. Some key questions include:
1) Finding even and odd components of signals, determining if signals are energy or power signals, and plotting shifted versions of a signal.
2) Proving properties of LTI systems based on impulse response and input, determining output of LTI systems given various inputs and impulse responses.
3) Finding Fourier series coefficients and representations of signals, determining Fourier transforms and properties.
4) Determining difference/differential equation descriptions and impulse/frequency responses of systems based on given input-output relations or equations.
The document is a lecture on derivatives and the shapes of curves. It covers the mean value theorem, testing for monotonicity using the first derivative test, and finding intervals of monotonicity. It also discusses concavity and the second derivative test. Examples are provided to demonstrate how to find the intervals where a function is increasing or decreasing using the first derivative test.
We discuss the ideas of monotonicity (increasing or decreasing) and concavity (up or down) of a function. Because of the Mean Value Theorem, we can determine these characteristics using derivatives.
1. The document contains a past exam paper for an Advanced Mathematics exam with 10 questions across two parts (A and B).
2. The questions cover a range of advanced mathematics topics including Taylor series, differential equations, probability, statistics, and linear algebra.
3. Students must answer 5 questions total, with at least 2 questions from each part. Questions involve calculating values, proving statements, finding probabilities, and more.
1. This document contains notes and formulas for additional mathematics form 4. It covers topics such as quadratic equations, functions, indices and logarithms, coordinate geometry, and statistics.
2. Quadratic equations are discussed, including finding the roots of a quadratic equation and writing the equation from its roots. Quadratic functions are also covered, specifically the relationship between the sign of b^2 - 4ac and the nature of the roots.
3. Other topics include indices and logarithm laws, coordinate geometry concepts like distance and midpoints, statistics topics such as measures of central tendency (mean, median, mode), and measures of dispersion like standard deviation and interquartile range.
D. Ishii, K. Ueda, H. Hosobe, A. Goldsztejn: Interval-based Solving of Hybrid...dishii
An approach to reliable modeling, simulation and verification of hybrid systems is interval arithmetic, which guarantees that a set of intervals narrower than specified size encloses the solution. Interval-based computation of hybrid systems is often difficult, especially when the systems are described by nonlinear ordinary differential equations (ODEs) and nonlinear algebraic equations.We formulate the problem of detecting a discrete change in hybrid systems as a hybrid constraint system (HCS), consisting of a flow constraint on trajectories (i.e. continuous functions over time) and a guard constraint on states causing discrete changes. We also propose a technique for solving HCSs by coordinating (i) interval-based solving of nonlinear ODEs, and (ii) a constraint programming technique for reducing interval enclosures of solutions. The proposed technique reliably solves HCSs with nonlinear constraints. Our technique employs the interval Newton method to accelerate the reduction of interval enclosures, while guaranteeing that the enclosure contains a solution.
This document is from a Calculus I class at New York University. It provides an overview of functions, including the definition of a function, different ways functions can be represented (formulas, tables, graphs, verbal descriptions), properties of functions like monotonicity and symmetry, and examples of determining domains and ranges of functions. It aims to help students understand functions and their representations as a foundation for calculus.
MATHEON Center Days: Index determination and structural analysis using Algori...Dagmar Monett
This document discusses the work of research project D7 on numerical simulation of integrated circuits. The project uses algorithmic differentiation techniques to determine the tractability index of differential algebraic equations (DAEs) and compute consistent initial values. It provides examples of index determination for circuit simulation problems and discusses achievements, collaborations, and plans for future work extending the structural analysis methods to computational graphs.
An introduction to quantum stochastic calculusSpringer
The document discusses tensor products of Hilbert spaces. It defines positive definite kernels on sets and shows how they can be used to define tensor products. Given Hilbert spaces H1, ..., Hn, it constructs a kernel on the cartesian product of the spaces and shows that its Gelfand pair (H,φ) gives a tensor product of the Hilbert spaces. The map φ from the product space into H is multilinear and H is the completion of the algebraic tensor product of the vector spaces H1, ..., Hn.
This document contains lecture notes on derivatives from a Calculus I class at New York University. It discusses the derivative as a function, finding the derivative of other functions, and the relationship between a function and its derivative. The notes include examples of finding the derivative of the reciprocal function and state that if a function is decreasing on an interval, its derivative will be nonpositive on that interval, while if it is increasing the derivative will be nonnegative. It also contains proofs and graphs related to derivatives.
1. The document contains a math worksheet with fill-in-the-blank and multiple choice questions about integrals and areas bounded by curves.
2. The fill-in-the-blank questions involve evaluating definite integrals, finding values of integrals where functions are even or odd, and taking derivatives of integrals.
3. The multiple choice questions involve identifying the shape of a region bounded by an integral, evaluating definite integrals using geometry, and identifying which integral represents a particular bounded region.
The document discusses exponential growth and decay models in calculus. It covers modeling population growth, radioactive decay using carbon-14 dating, Newton's law of cooling, and continuously compounded interest. Examples are provided to illustrate exponential growth of bacteria populations using the differential equation y' = ky, and modeling radioactive decay where the relative rate of decay is constant and represented by the differential equation y' = -ky.
The document discusses solving the two-dimensional Laplace equation to model steady heat flow problems. It presents:
1) The general boundary value problem (BVP) for the Laplace equation in a semi-infinite and finite lamina.
2) The separation of variables method to obtain solutions as a sum of products of ordinary differential equations.
3) Applying boundary conditions to determine constants and obtain the general solution for temperature distribution.
4) Examples of applying the method to specific BVPs for steady heat flow, including plates with various boundary temperature profiles and geometries.
IJERD (www.ijerd.com) International Journal of Engineering Research and Devel...IJERD Editor
This document presents a theorem that establishes the existence of a fixed point for a mapping under a general contractive condition of integral type. The mapping considered generalizes various types of contractive mappings in an integral setting. The theorem proves that if a self-mapping on a complete metric space satisfies the given integral inequality involving the distance between images of points, where the integral involves a non-negative, summable function, then the mapping has a unique fixed point. Furthermore, the sequence of repeated applications of the mapping to any starting point will converge to this fixed point. The proof involves showing the distance between successive terms in the sequence decreases according to the integral inequality.
The document defines and provides examples of various types of functions, including:
- Polynomial functions including constant, linear, and general polynomial functions.
- Rational functions defined as the ratio of two polynomial functions.
- Trigonometric functions including sine, cosine, and their inverses.
- Other common functions like absolute value, square root, exponential, logarithmic, floor, and ceiling functions.
It also defines properties of functions like being one-to-one, even, or odd and provides examples of each.
[Vvedensky d.] group_theory,_problems_and_solution(book_fi.org)Dabe Milli
1) The document discusses problems related to group theory.
2) Problem 1 shows that the wave equation for light propagation is invariant under Lorentz transformations.
3) Problem 2 shows that the Schrodinger equation is invariant under a global phase change of the wavefunction, and uses Noether's theorem to show the conservation of probability.
This document discusses techniques for evaluating integrals involving exponential functions. It introduces the formulas for integrating exponentials and differentiating them. Several important definite integrals are evaluated, such as the integral from 0 to infinity of e^-ax dx = 1/a. Graphs are used to visualize these integrals. The document then evaluates the more complex integral from negative infinity to positive infinity of e^-ax^2 dx using a change of variables technique. Finally, it discusses how these integrals can be used in kinetic theory and derives an important ratio and normalization factor for Maxwell's velocity distribution.
This document contains the questions from an engineering mathematics exam with 8 questions divided into 2 parts (A and B). Part A contains 3 multi-part questions on topics related to differential equations, including using Taylor's series, Runge-Kutta method, and Milne's predictor-corrector method to solve initial value problems. Part B contains 5 multi-part questions covering additional topics such as Legendre polynomials, Bessel's differential equation, probability, hypothesis testing, and confidence intervals. The exam tests knowledge of numerical analysis techniques for solving differential equations as well as topics in advanced calculus, probability, and statistics.
The document contains questions from a past examination in Design and Analysis of Algorithms. It asks students to solve algorithmic problems related to recurrence relations, sorting algorithms like selection sort and merge sort, graph algorithms like minimum spanning trees and shortest paths, and divide-and-conquer algorithms. Students are required to analyze time complexities, provide pseudocode, and solve problems using algorithms like binary search, quicksort, Prim's algorithm, and shortest path algorithms on graphs.
This document contains exam questions related to Engineering Mathematics and Microcontrollers.
Part A of Engineering Mathematics asks students to: 1) Find an approximate value of y at x=0.1 and 0.2 using Taylor's series, 2) Solve a differential equation using Euler's modified method and carry out three modifications, 3) Determine the value of y(1.4) using Adams-Bashforth method given values of y at other points.
Part B asks students to: 1) Fit a least squares line to given data, 2) Prove and explain a trigonometric identity, 3) Find the probability of solving a problem given individual student probabilities, 4) Define terms related to probability distributions,
This document contains questions pertaining to signals and systems. It has two parts - Part A and Part B. Some key questions include:
1) Finding even and odd components of signals, determining if signals are energy or power signals, and plotting shifted versions of a signal.
2) Proving properties of LTI systems based on impulse response and input, determining output of LTI systems given various inputs and impulse responses.
3) Finding Fourier series coefficients and representations of signals, determining Fourier transforms and properties.
4) Determining difference/differential equation descriptions and impulse/frequency responses of systems based on given input-output relations or equations.
This document contains exam questions from an Advanced Mathematics exam. It includes questions on topics like:
1) Using Taylor's series and Runge-Kutta methods to approximate solutions to differential equations.
2) Finding analytic functions, bilinear transformations, and power series representations.
3) Evaluating integrals, reducing differential equations to standard forms, and expressing polynomials in terms of orthogonal polynomials.
4) Fitting curves to data using least squares, finding correlation coefficients and means of variables, and solving probability problems involving binomial, normal, and chi-square distributions.
5) Explaining statistical terms like null hypothesis, standard error, and tests of significance. Finding fixed probability vectors and probabilities in Markov chains.
This document contains the questions and solutions from the First Semester B.E. Degree Examination in Engineering Mathematics from January 2013. It includes 10 multiple choice questions testing concepts in calculus, differential equations, and linear algebra. It also contains 4 full problems to solve related to derivatives, integrals, differential equations, and vectors/matrices.
The document discusses solving various differential equations using different numerical methods. It contains 6 questions related to numerical methods for solving differential equations. Specifically, it involves:
1) Using Taylor's series, Euler's method, and Adams-Bashforth method to solve differential equations.
2) Employing Picard's method and Runge-Kutta method to obtain approximate solutions of differential equations.
3) Using Milne's method to obtain an approximate solution of a differential equation.
4) Defining an analytic function and obtaining Cauchy-Riemann equations in polar form.
The questions cover a wide range of numerical methods for solving differential equations including Taylor series, Euler's method, Picard
The document provides information about an engineering mathematics examination that will take place. It consists of 5 modules with multiple choice and long answer questions in each module. The exam will last 3 hours and students must answer 5 full questions by selecting at least 2 questions from each part. The document then lists the questions under each module.
(08 Marks)
(06 Marks)
Explain the working of a D-type flip-flop with truth table and timing diagram.
(08 Marks)
Design a 4-bit binary counter using D flip-flops. Obtain the state table and state diagram.
(08 Marks)
Explain the working of a JK flip-flop with truth table and timing diagram.
(08 Marks)
Design a 4-bit synchronous up/down counter using JK flip-flops. Obtain the state table and
state diagram.
(08 Marks)
c.
Explain the working of a shift register with block diagram.
This document contains instructions for 5 assignment questions involving numerical integration and solving differential equations. Question 1 involves using the quad function to evaluate several integrals. Question 2 involves using quad to evaluate Fresnel integrals and plot the results. Question 3 involves using Monte Carlo methods to estimate volumes and double integrals. Question 4 involves using Euler's method to solve an initial value problem and analyze errors. Question 5 involves using lsode to solve a system of differential equations modeling atmospheric circulation and experimenting with initial conditions.
This document contains questions from a Microcontrollers exam for a Fourth Semester B.E. degree. It is divided into two parts: Part A and Part B. Part A focuses on microcontroller fundamentals like architecture, instruction sets, and assembly language programming. Questions cover topics such as distinguishing microprocessors from microcontrollers, describing features of the 8051 microcontroller, interfacing memory, addressing modes, and writing assembly programs. Part B examines more advanced microcontroller concepts including timers, interrupts, serial communication, and peripheral interfacing. Questions explore differences between timers and counters, generating frequencies using timers, configuring external interrupts, sending messages via serial port, and operating modes of the 8255 peripheral.
b.
(08 Marks)
, 10, 12, 15)
(10 Marks)
Design a 4-bit binary adder using half adders and full adders.
(08 Marks)
c. Design a 4-bit binary subtractor using half subtractors and full subtractors.
(08 Marks)
3 a.
Design a 4-bit magnitude comparator using basic gates.
(10 Marks)
b.
Design a 4-bit binary comparator using basic gates.
(10 Marks)
4 a.
Design a 4-bit binary multiplier using AND gates and half adders.
(10
This document appears to contain questions from an examination in Basic Thermodynamics. It includes questions on various thermodynamics concepts like thermodynamic equilibrium, the zeroth law of thermodynamics, work, heat, and processes involving gases. Specifically, part A asks about the differences between thermal and thermodynamic equilibrium, the importance of the zeroth law, relationships between Celsius scales using ideal gases, and determining temperatures using two different thermometers. Part B asks about defining work and heat and distinguishing between them, calculating the temperature rise of brake shoes during braking of a vehicle, and finding the work done during compression of a gas using a given pressure-volume relationship.
This document contains a 9 question final exam for an applied ordinary differential equations engineering course. The questions cover a range of topics including: finding general and particular solutions to 1st and 2nd order differential equations using various methods; solving initial value problems; solving systems of differential equations; power series solutions; and modeling an LRC circuit with a differential equation. Students are given 3 hours to complete the exam worth a total of 100 points.
The document contains questions from a B.E. Degree Examination in Engineering Mathematics. It has two parts - Part A and Part B containing a total of 8 questions. The questions cover topics in graph theory, combinatorics, probability, differential equations and their solutions. Students are required to attempt 5 questions selecting at least 2 from each part.
This document appears to be an exam for the course Strength of Materials. It contains questions that ask students to:
- Define terms like "Bulk modulus"
- Derive expressions, like for the deformation of a member due to self weight
- Calculate things like the stress induced in a member due to an applied load
- Explain concepts such as principal stresses and maximum shear stress
- Solve problems involving things like eccentric loading on a beam and buckling of columns
The questions cover a wide range of topics in strength of materials including stress, strain, deformation, shear force and bending moment diagrams, principal stresses, and column buckling.
This document appears to be an exam paper for the subject Logic Design. It contains 10 questions divided into two parts - Part A and Part B. The questions cover various topics related to logic design including canonical forms, minimization of logic functions, multiplexers, decoders, adders and code converters. Students are instructed to answer any 5 full questions selecting at least 2 questions from each part. The exam is worth a total of 100 marks and is meant to evaluate students' understanding of fundamental concepts in logic design.
The document contains a midterm exam for an ODE class with 6 problems worth 10 points each. Problem 1 asks to find the general solution of a 7th order linear ODE using the method of undetermined coefficients. Problem 2 asks to solve a 2nd order linear ODE using either variation of parameters or undetermined coefficients. Problem 3 asks to solve a nonlinear 2nd order ODE using a substitution. Problem 4 asks to find the equation of motion for a mass attached to a spring with an external force applied. Problem 5 asks to solve an eigenvalue problem for a CE equation. Problem 6 asks to use variation of parameters to solve a 2nd order nonhomogeneous ODE.
The document contains a sixth semester examination question paper for the subject Modeling and Finite Element Analysis. It has two parts with a total of 8 questions. Some of the key questions asked are:
1) Derive an expression for maximum deflection of a simply supported beam with a point load at the center using Rayleigh-Ritz method and trigonometric functions.
2) Explain the basic steps involved in the finite element method.
3) Define a shape function and discuss the properties that shape functions should satisfy.
4) Derive the stiffness matrix for a 2D truss element and the strain-displacement matrix for a 1D linear element.
5) Discuss the various
This document contains exam questions for the subjects of Management and Entrepreneurship, Design of Machine Elements - I, Dynamics of Machines, and Manufacturing Process - III. It lists multiple choice and long answer questions covering topics such as characteristics of SSIs and WTO, stresses in shafts and bolts, flywheels, belt drives, balancing of rotating masses, cams, forging, and rolling processes. The questions are part of a fifth semester engineering exam and assess students' understanding of key concepts in these mechanical and production engineering subjects.
This document contains questions from a third semester Bachelor of Engineering degree examination in Mechanics of Materials. It includes two parts, Part A and Part B.
Part A contains three questions. Question 1 has sub-parts asking students to analyze data from a tensile test on mild steel and calculate properties like Young's modulus, proportional limit, true breaking stress and percentage elongation. Question 2 has sub-parts asking students to calculate total elongation of a brass bar under axial forces and find Poisson's ratio and elastic constants from tensile test data.
Part B likely contains similar analysis questions related to mechanics of materials, though the specific questions are not included in the document provided. The exam covers a range of topics testing students' understanding
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This document appears to be an exam paper containing 8 questions divided into 2 parts (A and B) related to the subject of Information Theory and Coding. It provides details of the questions asked, their point values, and asks examinees to answer 5 full questions total, selecting at least 2 from each part. The questions cover topics such as calculating information content, entropy, Huffman coding, channel capacity, and properties of mutual information. Examinees are given 3 hours to complete the exam with a maximum score of 100 points.
This document contains the questions from a third semester B.E. degree examination on Network Analysis. It has 8 questions divided into two parts - Part A and Part B.
The questions assess concepts related to network analysis including Fourier series expansion, Fourier transforms, Laplace transforms, solution of differential equations using separation of variables, curve fitting, eigen analysis, and more. Methods like Newton-Raphson, simplex method, relaxation method, and power method are also tested. Circuit analysis concepts involving RC circuits, transfer functions, and network theorems are covered.
The questions require deriving equations, solving problems numerically and graphically, explaining concepts, and designing circuits to assess the candidate's understanding of core topics in network analysis
This document contains questions for an examination in Object Oriented Modeling and Design. Part A includes questions about OO methodology stages, class modeling concepts like objects, classes and attributes, and creating a class model for an undirected graph. Part B focuses on UML concepts like associations, class diagrams, use case modeling and advanced sequence modeling. It asks students to design class models, write advanced use cases, and revise diagrams to eliminate ternary associations. The document tests students' understanding of core OO and UML modeling principles.
This document contains questions for an examination on Object Oriented Modeling and Design. It has two parts - Part A and Part B. Part A focuses on concepts related to UML, class modeling, associations, events, sequence diagrams and software development process. Part B focuses on use case modeling, class design, design patterns, and advanced OO concepts like templates and styles. The document provides guidelines for answering questions and allocates marks for each question.
This document contains questions from a Software Engineering exam, with multiple choice and descriptive answers across two sections. Key topics covered include:
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1. The document contains questions from a third semester B.E. degree examination in discrete mathematical structures.
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3. Several questions also involve topics like tautologies, propositional logic, and predicate logic.
This document contains information about an engineering mathematics examination, including questions on various topics like Fourier transforms, differential equations, interpolation, and numerical methods. It provides instructions to answer 5 full questions, with at least 2 questions from each part. The first part covers questions on Fourier series, transforms, differential equations, and interpolation. The second part includes questions on numerical methods, matrices, and integration.
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The document appears to be part of an engineering physics exam containing both multiple choice and written response questions.
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The written response sections ask students to derive expressions, explain concepts in more depth, and perform calculations. Examples include deriving an expression for group velocity based on wave superposition, discussing spontaneous and stimulated emission, and calculating de Broglie wavelength.
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The document is a past exam paper for an Engineering Chemistry exam. It contains 8 multiple choice questions and 4 free response questions on various topics in chemistry.
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The exam tests students' knowledge of key concepts in engineering chemistry including different fuel types and properties, electrochemical cells and applications, corrosion mechanisms, and characterization techniques important for materials.
This document appears to be an exam for an engineering chemistry course. It contains 8 multiple choice questions across two parts (Part A and Part B). The questions cover topics like fuels and combustion, electrochemistry, corrosion, polymers, water analysis, and more. The maximum marks for the exam is 100. Students are instructed to answer 5 full questions by choosing at least 2 from each part, and to answer all objective type questions on the OMR sheet provided.
This document contains the questions and answers from an engineering physics exam. It covers topics like:
- Blackbody radiation and Planck's law
- De Broglie wavelength and particle-wave duality
- Quantum mechanics including the particle in a box model
- Normalization constants and probability distributions in quantum mechanics
The exam contains multiple choice and short answer questions testing understanding of fundamental concepts in modern physics including wave-particle duality, quantum mechanics, and blackbody radiation. It requires calculations of quantities like de Broglie wavelength and energies of the particle in a box model.
This document is the first/second semester B.E. degree examination in engineering physics from June 2012. It contains 4 parts with multiple choice and short answer questions. Part A covers topics like the photoelectric effect, de Broglie wavelength, uncertainty principle, particle in a box, and more. Part B covers topics like lasers, spontaneous emission, holography, and more. Students are instructed to choose 5 questions to answer, with at least 2 from each part. They are also told which questions to answer on the OMR answer sheet.
This document contains a physics exam with multiple choice and short answer questions covering various topics in engineering physics. The exam is divided into three parts.
Part A contains questions on photoelectric effect, de Broglie hypothesis, phase and group velocity, kinetic energy, and the uncertainty principle. Part B focuses on topics like induced absorption, semiconductor lasers, population inversion, and holography. Part C asks about electrical conductivity, Fermi energy, dielectric properties, and magnetic materials. Students are asked to choose the best answer from options for multiple choice questions and provide explanations for short answer questions.
Computer Science and Information Science 3rd semester (2012-December) Question Papers
1. USN 1OMAT4l
Fourth Semester B.E. Degree Examination, December 2012
Engineering Mathematics - l/
Time: 3 hrs.
Note: Answer FIYE full questions, selecting
at least TWO questions from each part.
o
o
(f PART _ A /st
4,/.'.
$ = *')
g
la. Using the Taylor's series method, solve the initial value probf.-
dx
0)
the point x: 0.1 (06 Marks)
Ol : I
()
! b. Employ the fourth order Runge-Kutta method to solve '"'r,
=", +x' y(0) atthe points
(jX Y"
bo-
x: O.2and x : O.4.Take h :0.2. (07 Marks)
dy i_ :
a = xv + v-, y(0) :
d9
7n c. Given 1, y(0.1) :1.1169,y(0.2): 1.2773, y(0.3) 1.5049. Find y(0.4)
ool
troo dx
.= c.l using the Milne's predictor-corrector method. Apply the corrector formula twice. (07 Marks)
gil
oE
FO 2a. Employing the Picard's method, obtain the second order approximate solution of the
following problem at x : 0.2.
-P
dv
Z=x*yz, dz
11-y+zx) y(0):1, z(0):-1. (06 Marks)
AP dx dx
oc) b. Using the Runge-Kutta method, find the solution at x : 0.1 of the differential equation
GO
50i
d'v , dv
+- x'-' -2xy =1 underthe conditions y(0): 1, y'(0):0. Take step lengthh:0.1.
dx' dx
.G (07 Marks)
Using the Milne's method, obtain an approximate solution at the point x : 0.4 of the
problem q*:*9 y(0) : 1, y'(0) : 0.1. GiVen that y(0.1) : 1.03995,
LO
o-A ' dx' dx -6y=0,
y(0.2): 1.138036, y(0.3) : 1.29865, y'(0.1) : 0.6955, y'(0.2): 1.258, y'(0.3) : ,.tli*".u,
9.Y
otE
LO 3a. If (z) : u * iv is an anatyric tunction, then prove *" (* I r(r) l) -r | r(r) l) = ['1,;l' .
>.: [*
bo-
cao (06 Marks)
6=
oB b. Findananalyicfunctionwhoseimaginarypartis v=€*{(*'-y')cosy-2xysiny}.
tr> (07 Marks)
=o
o
t<
c. If (z) : u(r, 0) + iv(r, 0) is an analytic function, show that u and v satisfy the equation
a2rAta2
: c.i o(D-r to(D I oo
------..1-f ll (07 Marks)
=
o
o or -----l- -------.1-
tor r oo
Z
4a. Find the bilinear transformation that maps the points 1, i, -1 onto the points i, 0, -i
o
respectively. (06 Marks)
b. W: e'.
Discuss the transformation (07 Marks)
Evaluate lstn 'TZ' ]
cosgiz where c is the circle
c. , lzl:3. (07 Marks)
! tr-t')(z-2)
2. 1OMAT4l
PART _ B
5 a. Express the polynomial 2x3 -x' -3x+2 in terms of Legendre polynomials. (06 Marks)
b. Obtain the series solution ofBessel's differential equation r' (x' -r')y = 0 in
#*.t+
the form y: AJ,(x) + BJ-,(x). (07 Marks)
c. Derive Rodrique's formula P,(x) = j- *fx'' -1)'. (07 Marks)
' 2nnl dxn
6 a. State the axioms of probability. For any two events A and B, prove that
P(A u B) = P(A) + P(B) - P(A n B) . (06 Marks)
b. A bag contains 10 white balls and 3 red balls while another bag contains 3 white balls and
5 red balls. Two balls are drawn at ransom from the fust bag and put in the second bag and
then a ball is drawn at random from the second bag. What is the probability that it is a white
ball? (07 Marks)
c' In a bolt factory there are four machines ,A, B, C, D manufacturing respectlely 20o/o, 5oh,
25% 40% of the total production. Out of these 50 , 4yo, 3Yo and 2%o respectively are
defective. A bolt is drawn at random from the production and is found to be defective. Find
the probability that it was manufactured by A or D. (07 Marks)
7 a. The probabilit distributilon oI a finite random variable X is given by the following table:
.
f nnlte ra
a
Xi -1 0 1 2 J
p(xi) 0.1 k 0.2 2k 0.3 k
Determine the value of k and find the mean, variance and standard deviation. (06 Marks)
b. The probability that a pen manufactured by a company will be defective is 0.1. If i2 such
pens are selected, furd the probability that (i) exactly 2 will be defective, (ii) at least 2 will
be defective, (iii) none will be defective. (07 Marks)
c. In a normal distribution,3loh of the items are under 45 and 8o/o are over 64. Find the mean
and standard deviation, given that A(0.5):0.19 and A(1 .4):0.42, where A(z) is the area
under the standard normal curve from 0 to z>0. (07 Marks)
8 a. A biased coin is tossed 500 times and head turns up 120 times. Find the 95Yo confrdence
limits for the proportion of heads turning up in infinitely many tosses. (Given that z": 1.96)
(06 Marks)
b. A certain stimulus administered to each of 12 patients resulted in the following change in
blood pressure:
5, 2, 8, -1, 3, 0, 6, -2, l, 5, 0, 4 (in appropriate unit)
Can it be concluded that, on the whole, the stimulus will change the blood pressure. Use
to os(1 l):2.201. (07 Marks)
c. A die is thrown 60 times and the frequency distribution for the number appearing on the face
x is given the followine table:
a
x I 2 -) 4 5 6
Frequencv 15 6 4 7 11 t7
Test the hypothesis that the die is unbiased.
(Given that yf,o,(5) = 11.07 and X3o,(5) = 15.09) (07 Marks)
rl<{<{<xx
3. i
USN 10cs42
Fourth Semester B.E. Degree Examination, Decemb er 2Ol2
Graph Theory and Gombinatorics
Time: 3 hrs. Max. Marks:100
Note: Answer any FIVEfull questions selecting ut least two questionsfrom each part.
(J PART _ A
o
o
I a. Define connected graph. Prove that a connected graph with n vertices has at least (n - 1)
g edges. (06 Marks)
b. Define isomorphism of two graphs. Determine whether the two graphs (Fig.Q.1(b)(i)) and
(Fig. Q. 1 (b)(ii)) are isomorphic.
C)
o
L
a)X
d9
;,
troo Fie.Q.1(bxi)
.=N
cn <f,
c. Define a complete graph. In the complete graph with n vertices, where n
:1 0l)
Y() ) 3, showthat ur.
('-t)
.)tr
-.ca)
there edge disjoint Hamilton cycles. (07 Marks)
2
2 a. Design a regular graph with an example. Show that the Peterson graph is a non planar graph.
a= (07 Marks)
oO b. Prove that a graph is 2-chromatic if and only if it is a null bipartite graph. (06 Marks)
(d0 c. Define Hamiltonian and Eulerian graphs. Prove the complete graph K3,3 is Hamiltonian but
o0e
(nd not Eulerian. (07 Marks)
,6
E6 Define a tree. Prove that a connected graph is a tree if it is minimally connected. (06 Marks)
rao Define a spanning tree. Find all the spanning trees of the graph given below. (Fig.Q.3(b)).
oi=
(07 Marks)
:9
"c Fig.Q.3(b)
;o
6=
A,i,
c. Construct a optimal prefix code for the symbols a, o, g, u, y, zthat occur with frequencies
!o
5.v 20,28, 4, 17, 12,7 respectively. (07 Marks)
>' (ts
i50
o=
go
4a. Define matching edge connectivity and vertex connectivity. Give one example for each.
tr>
Xo
VL
o b. Using Prim's algorithm, find a minimal spanning tree for the weighted graph rn"ffiTlT]
U< following Fig.Q.a@). (07 Marks)
<N
o
'7
Vs
Fig.Q.a(b)
4. 10cs42
c. Three boys b1, bz, b: and four girls Et, Ez, Et, gt are such that
br is a cousin of gt, Ez and g+
bz is a cousin of gz and g+
b3 is a cousin of gz and g:.
If a boy must marry a cousin girl, find possible sets of such couples. (07 Marks)
PART - B
5A. Find the number of ways of giving 10 identical gift boxes to six pelsons A, B, C, D, E, F in
such a way that the total number of boxes given to A and B together does not exceed 4.
(06 Marks)
b. Define Catalan numbers. In how many ways can one travel in the xy plane from (0, 0) to
(3, 3) using the moves R: (x + 1, y) and U: (x, y + 1) if the path taken may touch but never
rise above the line y: x? Draw two such paths in the xy plane. (07 Marks)
c. Determine the coefficient of
i) xyz' inthe expansion of (2x - Y - z4
ii) a'bl.'dt in the expansion of (a + 2b - 3c + 2d + 5)'o. (07 Marks)
6a. How many integers between 1 and 300 (inclusive) are
i) divisible by 5, 6, 8?
ii) divisible by none of 5, 6, 8? (07 Marks)
b. In how many ways can the integer s 1,2,3 . . ... 10 be arranged in a line so that no even integer
is in it natural place? (06 Marks)
c. Find the rook polynomial for the followin ig.Q.6(c)). (07 Marks)
Fig.Q.6(c)
7a. Find the coefficient of xr8 in the following products:
i) (x*x2 +x3 +*o+*t) 1x2 +x3 +xa**',+....)t
iil (x * x3 + x5 + *' + *') 1x3 + 2xa + 3xs +.....;1. (07 Marks)
b. using the generating function find the number of i) non negative and positive integer
solutions of the equation x1 * x2 a x: + x4: 25. (06 Marks)
c. Find all the partitions of x7. (07 Marks)
8a. Solve the Fibonacci relation
Fn+z : Fn+r fFn for n 2 0 given Fo
: 0, Ft : 1. (07 Marks)
b. Solve the recurrence relation
An-2 dn- I * an . 2: 5n. (07 Marks)
c. Find a generating function for the recumence relation
iL * 5o.-r + 6ar-z:3r2,r) 2. (06 Marks)
*{<*{<+
a^f^
5. I
/
USN 10cs43
Fourth Semester B.E. Degree Examination, Decemb er 2012
Design and Analysis of Algorithm
Time: 3 hrs. Max. Marks:100
Note: Answer FIVE full questions, selecting atleast TWO questions from each part.
PART _ A
1a. Define asymptotic notations. (03 Marks)
d
o
b. Algorithm X(int N)
() {
a. intP;
E fori<-ltoN
{
o printf ("n % d t * tYo d: Yod", N, i, P);
I P:P+N;
3e lt
JI
i) What does this algorithm compute?
6v ii) What is the basic operation?
-.o
ool
trca
iii) How many times the basic operation is executed?
.= .-.1
(d+
iv) What is the efficiency class of this algorithm? Marks)
9il
c. Solve the following recurence relations.
otr n>0
-o
EP
t(n). = {[f(n-l)+n
o> 0
|. n=0
EE
x(n): 3x(n - 1) for n > 1, x(1):4
x(n): x(n l2)+n :
for n > 1, x(l) I n:2k. (08 Marks)
oO d. Sortthe list E XAM P L E bybubble sort, Isthere anypossibilitythat bubble sort canbe
stopped earlier? (05 Marks)
ooc
a. Discuss how quick sort works to sort an affay. Trace quick sort algorithm for the following
a6 data set 65,70,75,80,85,60, 55,50,45. Also derive the worst case complexity of quick
!d
sort. (09 Marks)
o; b. Write the recursive algorithm for merge sort. (04 Marks)
o- 5.
c. Consider the following set of 14 elements in anaffay list, -15, -6,0,7,9,23,54,82, 101,
o(e 112,I25, 13L,I42,151 when binary search is applied on these elements, find the elements
(.)
;6..
@=
which required maximum number of comparisons. Also determine average number of key
ao comparisons for successful search and unsuccessful search. (04 Marks)
6tE
!o
d. Derive the time complexity for defective chess board. (03 Marks
=-E
o.r
>'H 3 a. Solve the following instance of knapsack problem, algorithm
c50 Item 1 2 -) 4
o= Weight 4 7 J
AE
F>
5
VL
Profit 40 42 25 l2
o
U< Knapsack weight M: 10. (05 Marks)
-6t
o
o
z
L
o
o.
How Knapsack and Prim's algorithms guarantee the elimination of cycles? (07 Marks)
c. In the above graph Fig. Q3(C), determine the shortest distances from source vertex 5 to all
the remaining vertices, using Dijikstra's algorithm. (08 Marks)
6. 10cs42
c. Three boys b1, b2, b3 and four girls Er, Ez, gz, Eq are such that
br is a cousin of gr, gz and ga
bz is a cousin of gz and g+
b: is a cousin of gz and gl.
If a boy must marry a cousin girl, find possible sets of such couples. (07 Marks)
PART _ B
5a. Find the number of ways of giving 10 identical gift boxes to six persons A, B, C, D, E, F in
such a way that the total number of boxes given to A and B together does not exceed 4.
(06 Marks)
b. Define Catalan numbers. In how many ways can one travel in the xy plane from (0, 0) to
(3, 3) using the moves R: (x + 1, y) and U: (x, y + 1) if the path taken may touch but never
rise above the line y: x? Draw two such paths in the xy plane. (07 Marks)
c. Determine the coefficient of
i) xyzz inthe expansion of (2x - y - z)4
ii) ib3"'dt in the expansion of (a + 2b'- 3c + 2d + 5116. (07 Marks)
6a. How many integers between 1 and 300 (inclusive) are
D divisible by 5, 6, 8?
ii) divisible by none of 5, 6, 8? (07 Marks)
b. In how many ways canthe integers 1,2,3.....10 be arranged in a line so that no even integer
is in it natural place? (06 Marks)
c. Find the rook polynomial for the followin Fig.Q.6(c)). (07 Marks)
Fig.Q.6(c)
7a. Find the coefficient of xr8 in the following products:
i) (x+ x2 +x3 +xo + xs;1x2 + x3 + xa +rt +....)'
ii) (x + x3 + x5 + x7 + xe; 7x3 + 2x4 + 3x5 +.....13. (07 Marks)
b. Using the generating function find the number of i) non negative and ii) positive integer
solutions of the equation X1 -f x2 1 x: + x4: 25. (06 Marks)
c. Find all the partitions of x7. (07 Marks)
8a. Solve the Fibonacci relation
Fn+2 : Fn+r tFn for n > 0 given Fo : 0, Fr : 1. (07 Marks)
b. Solve the recurrence relation
dn-2 Zn-t-l &n' Z: 5n. (07 Marks)
c. Find a generating function for the recurrence relation
a, * 5ar-t 'l 6ar-z: 3r2, r ) 2. (06 Marks)
***rf*
a
7. /
USN l0cs43
Fourth Semester B.E. Degree Examination, December 2012
Design and Analysis of Algorithm
Time: 3 hrs. Max. Marks:100
Note: Answer FIVE full questions, selecting utleast TWO questions from each part.
PART _ A
la. Define asymptotic notations. (03 Marks)
ci
o
b. Algorithm X(int N)
o {
intP;
a fori<-ltoN
{
()
printf ("n % d t x t % d : o/od", N, i, P);
=
o! P:P+N;
C,X ll
iffi.
tt
J' D What does this algorithm compute?
=h
ii) What is the basic operation?
-*l
troo
iii) How many times the basic operation is executed?
.= .-.1
(B+
iv) What is the efficiency class of this algorithm? Marks)
c. Solve the following recwrence relations.
Yo
osl
aO
-! f(n) = {
[r(r-l)+n n>o
|. 0 n=0
x(n):3x(n - 1) for n > l, x(l):4
o= x(n) :
x(n | 2)+n for n > l, x(1) : I n:2k. (08 Marks)
o() d. Sort the list E X A M P L E by bubble sort, Is there anypossibilitythat bubble sort canbe
stopped earlier? (05 Marks)
o0i
(g(s
-o
a. Discuss how quick soft works to sort an affay. Trace quick sort algorithm for the following
-6 data set 65, 70, 75, 80, 85, 60, 55, 50, 45. Also derive the worst case complexity of quick
sort. (09 Marks)
]?o
oi= b. Write the recursive algorithm for merge sort. (04 Marks)
:e c. Consider the following set of 14 elements in anarray list, -15, -6,0,7,9,23,54,82, l0l,
o." 712,125,131, 142,151 when binary search is applied on these elements, find the elements
oj
which required maximum number of comparisons. Also determine average number of key
o=
}U comparisons for successful search and unsuccessful search. (04 Marks)
6tE
!o
d. Derive the time complexity for defective chess board. (03 Marks
JE
>. (! 3 a- Solve the following instance o sack problem, us algorithm
boo Item 4
tr50 2 J
o= Weight 4 7 5 J
o. ii
F>
:o Profit 40 42 25 t2
5L
^-
lr<
Knapsack weight M: 10. (05 Marks)
c.l
-
O
o
z
How Knapsack and Prim's algorithms guarantee the elimination of cycles? (07 Marks)
In the above graph Fig. Q3(C), determine the shortest distances from source vertex 5 to all
the remaining vertices, using Dijikstra's algorithm. (08 Marks)
8. 10cs43
4a. Solve the following tra veling sales person problem, using dynamic programming
[: TTill
lo 13 o r2t
(10 Marks)
L* 8 e ol starting city 1
(03 Marks)
b. Write Warshall- Floyd algorithm.
(07 Marks)
c. Generate the transitive closure of the graph given below.
o-#->o
rl
IJ
o<-e
I
Fig. Qa(c) Fig. Qs(c)
PART _ B
a. Match the pattern BAOBAB in the text BESS - KNEW - ABOUT - BAOBAS, using
i) Horspool's algorithm
ii) Boyer Moore algorithm. (08 Marks)
b. Write a BFS algorithm to check the connectivity of a given graph. (05 Marks)
c. Apply source elimination based algorithm to represent vertices in topological ordering for
(04 Marks)
the digraph given in Fig. Q5(c).
d. eppty aiitribution counting algorithm to sort the elements b, c, ,d c, b, a, a,b' (03 Marks)
6 a. What are decision trees? Explain with example, how decision trees are used in sorting
algorithms. (lo Marks)
b. Explain the concepts of P, NP, and NP - complete problems. (10 Marks)
Draw the state - space tree to generate solutions to 4 - Queen's problem. (04 Marks)
Apply backtracking method to solve subset sum problem for the instance n: 6, d : 30.
j
s {5, 10,12,13, 15, 18} (06 Marks)
c. What is branch - and - bound algorithm? How it is different from backtracking? (05 Marks)
d. Write the steps and apply nearest neighbour approximation algorithm on the TSP problem
with the starting vertex a, and calculate the accuracy ratio of approximation' (05 Marks)
Fig.7(d)
8 a. What are the different computation models? Discuss in detail. (10 Marks)
b. Let the input to the prefix computation problem be 5, 12,8,6,3,9,11, 12, 5, 6,7, 10, 4,3, 5
and let CI stand for addition. Solve the problem using work optimal algorithm. (10 Marks)
* :t ,.< *< {<
a .)
9. /
I
USN 10cs44
Fourth semester B.E. Degree Examination, Decemb er 2ol2
UNIX and Shell Programming
Time: 3 hrs. Max. Marks:100
Note: Answer FIVE full questions, selecting
o
o at least Tl,yO questionsfrom each part.
o
I
PART _ A
1 a. Explain salient features of TINIX operating system. (07 Marks)
o b. Compare internal and external commands in TINIX with suitable example. Explain why cd
() command cannot be an external command. (06 Marks)
Bq c. Illustrate with a diagram typical LINIX file system and explain different types of tiles
supported in IINIX. (07 Marks)
3
oo ll 2 a. Explain the basic file attributes displayed by ls - I command. (06 Marks)
troo
.=N
(B+
b' Discuss relative and absolute methods for changing file permissions. (06 Marks)
tuo c' Explain with a diagram the different modes of Vi editor and list the commands in each
Y(J
g
(.) mode. (08 Marks)
-O
EE
?,a 3a. Explain with an example use of single quote, double quote and back quote in a command
line. (06 Marks)
a:
b. Explain the following commands:
o()
-! i) cp?????progs ii) kill-s KILL 121 t22
aoc
d03
iii) wc -l < user.txt iv)ps-e I (06 Marks)
c. Explain the mechanism of process creation using system calls in UNIX. (04 Marks)
,6
d. Explain the following environment variables:
-?o
'Ca D PATH ii) HISTSIZE iii) PS2 iv) SHELL (04 Marks)
OE
o-A 4a. Discuss with example hard link and soft link applicable to UNIX files. (06 Marks)
o(v b. Explain the following commands:
a=
i) umask 022
4tE ii) find/ ! -name "*.C"-Print
!o iii) tr -d':l' < emp.txt
=E
Y,
-^o
iv) touch - m 0303 10 30 r,tu.txt (08 Marks)
coo c. Explain the following filters with options:
o=
so
E>
i) Paginate - Pr
^q
I
ii) Sort - Sort (06 Marks)
U<
*C..l PART _ B
O
o
5a. Explain with example basic regular expressions. (06 Marks)
Z b. Locate lines longer than 100 and smaller than 150 characters using (i) grep, (ii) sed.
(04 Marks)
o c. Discuss stream editor - sed with options. (06 Marks)
o.
d. How do these expressions differ:
i) [0-e]*and [0-9] [0-9]*
ii) ^[^ ^]and^^^ (04 Marks)
10. l0cs43
4 a. Solve the following traveling sales person problem, using dynamic programming
[o 10 15 2of
lr o e 1oI (10 Marks)
lu 13 o 0l
tt
L8 8 9 o -l starring city I
b. Write Warshall- Floyd algorithm. (03 Marks)
c. Generate the transitive closure of the graph given below. (07 Marks)
rrl-O
IJ
O----*->O
O+O Fig. Qa(c)
TYT
d.;o
Fig. Qs(c)
PART _ B
a. Matchthe pattern BAOBAB in the text BESS - KNEW - ABOUT - BAOBAS, using
i) Horspool'salgorithm
ii) Boyer Moore algorithm. (08 Marks)
b. Write a BFS algorithm to check the connectivity of a given graph. (05 Marks)
c. Apply source elimination based algorithm to represent vertices in topological ordering for
the digraph given in Fig. Q5(c). (04 Marks)
d. Apply distribution counting algorithm to sort the elements b, c, ,d c, b, a, a,b. (03 Marks)
6 a. What are decision trees? Explain with example, how decision trees are used in sorting
algorithms. (10 Marks)
b. Explain the concepts of P, NP, and NP - complete problems. (10 Marks)
7 a. Draw the state - space tree to generate solutions to 4 - Queen's problem. (04 Marks)
b. Apply backtracking method to solve subset sum problem for tho instance n : 6, d : 30.
:
S {5, 10,12,13, 15, 18} (06 Marks)
c. What is branch - and - bound algorithm? How it is different from backtracking? (05 Marks)
d. Write the steps and apply nearest neighbour approximation algorithm on the TSP problem
with the starting vertex a, and calculate the accuracy ratio of approximation. (05 Marks)
Fig. 7(d)
8 What are the different computation models? Discuss in detail. (10 Marks)
Let the input to the prefix computation problem be 5, 12,8, 6,3,9, ll, 12, 5, 6,7, 10, 4,3, 5
and let @ stand for addition. Solve the problem using work optimal algorithm. (10 Marks)
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a
11. /
USN l0cs44
Fourth Semester B.E. Degree Examination, December 2Ol2
UNIX and Shell Programming
Time: 3 hrs. Max. Marks:100
Note: Answer FIVEfull questions, selecting
(J
(.) at least TWO questionsfrom each part.
o
PART _ A
Explain salient features of UNIX operating system. (07 Marks)
() Compare internal and extemal commands in UNIX with suitable example. Explain why cd
command cannot be an external command.
E
C) (06 Marks)
!
oX c. Illustrate with a diagram typical TINIX file system and explain different types of files
supported in LINIX. (07 Marks)
:n
-oo ll 2a. Explain the basic file attributes displayed by ls - I command. (06 Marks)
troo
.= rl
b. Discuss relative and absolute methods for changing file permissions. (06 Marks)
cdt
c. Explain with a diagram the different modes of Vi editor and list the commands in each
9il
oE mode. (08 Marks)
aO
o>
3a. Explain with an example use of single quote, double quote and back quote in a command
line. (06 Marks)
#:! b. Explain the following commands:
oO
do i) cp ????? pross ii) kill-s KrLL 121 122
ooi iii) wc -l < user.txt iv)ps-e I (06 Marks)
c. Explain the mechanism of process creation using system calls in UNIX. (04 Marks)
-6
d. Explain the following environment variables:
E(n
,o i)PATH i0 HTSTSTZE iii) PS2 iv) SHELL (04 Marks)
OE
o6- 4a. Discuss with example hard link and soft link applicable to UNIX files. (06 Marks)
o."
oj b. Explain the following commands:
a=
i) umask 022
<o
i, tE ii) find/ ! -name "*.C"-Print
!o iii) -d':l' < emp.txt
tr
>'! iv) touch - m 0303 10 30 r,tu.txt (08 Marks)
co0 c. Explain the following filters with options: -rssT{q&L
o=
o- :j i) Paginate - Pr To*oo*
tr>
VL
9-
ii) Sort - Sort (06 Marks)
lr<
+ C.l PART _ B
0) 5a. Explain with example basic regular expressions. (06 Marks)
Z b. Locate lines longer than 100 and smaller than 150 characters using (i) grep, (ii) sed.
(04 Marks)
o c. Discuss stream editor - sed with options. (06 Marks)
d. How do these expressions differ:
i) [0-9]*and [0-9] [0-9]*
ii) ^[^ ^]and^^^ (04 Marks)
12. 10cs44
a. What is shell programming? Write a shell program to create a menu and execute a given
option based on users choice. Options include (i) list of users, (ii) list of processes,
(iii) list of files. (06 Marks)
b. Explain with example set and shift commands in UNIX to manipulate positional parameters.
(04 Marks)
c. Discuss use of trap statement for interrupting a program in UNIX. (04 Marks)
d. Explain with an example while and for loop in shell programming. (06 Marks)
7 a. Write a note on awk and explain built in variables in awk. (08 Marks)
b. Explain with example the following awk function:
o
i) split ii) Substr o o
iii) length iv) index o (08 Marks)
c. i) Write an awk statement to print odd numbered lines in a file.
ii) Write an awk statement to delete blank lines from a file. (04 Marks)
a. Explain string handling function in perl. (06 Marks)
b. Using command line arguments, write a perl program to find whether a given year is a leap
year. (07 Marks)
c. Write a perl program to convert a given decimal number to binary equivalent. (07 Marks)
,f****
a
13. /
USN 10cs4s
Fourth Semester B.E. Degree Examination, Decemb er 2Ol2
Microprocessors
Time: 3 hrs. Max. Marks:100
0.)
Note: Answer FIYEfull questions, selecting
o
C)
at least TWO questionsfrom eoch part.
!
a
PART _ A
(.)
2
(.)
I a. What is microprocessor? Explain how data, address and control buses interconnect various
()X
system components. (06 Marks)
b. Explain the program model visible register organization of 8086 pp. (07 Marks)
c. What is conventional memory? Explain segments and offsets. List default segment and
f^r
=h
offset register pairs. (07 Marks)
troo
.=N
gd 2a. Explain the descriptors of 80286 and 80386 microprocessors. Also explain prog invisible
ogl registers within 80286 pp.
-o (08 Marks)
b. Explain with examples the following addressing modes:
*,a
i) Scaled - indexed addressing mode
a=
ii) RIP relative addressing mode
o() iit) Relative prog memory addressing mode. (06 Marks)
c6O c. What is stack? What is the use of stack memory? Explain the execution of push and pop
botr instructions. (06 Marks)
-€ 3 a. Write bubble sort program using 8086 assembly instructing.
-od
'Ca b. Explain the following instructions with an example for each:
or= i) LEA &flit{Tfr'lc-
?o
so- ii) xcHG LB&i#"irii'd
o _:' iii) XLAT
o= ir) DIV
AE v) AAA.
LO c. What do you mean by segment override prefix? Explain the following assembler directives:
v,
^:
bo-
i) ASSUME
tro0
o=
ii) SMALL
90 iii) PRoc
5:
=o iv) EQU
rJ< v) LOCAL. (07 Marks)
-N
o
o
4 a. With format explain rotate instructions. Give examples to rotate right by 1-bit and rotate left
by 5-bits. (06 Marks)
b. Discuss with examples unconditional and conditional branching instructions. (04 Nlarks)
o
a c. What is a procedure? Explain the sequence of operation that takes place when a procedure is
called and returned. (04 Marks)
d. Explain m/c control instructions with examples. (06 Marks)
1 of2
14. 10cs4s
PART _ B
5a. Distinguish between the 16-bit and 32-bit versions of C/C ** when using the inline
assembler. (06 Marks)
b. Write a mixed language program that converts binary to ASCII. (07 Marks)
c. Write a mixed language module to realize macro to read a character from keyboard.
(07 Marks)
6a. Explain the functions of following pins of 8086 microprocessor.
i) RESET
ii) READY
iii) ALE
iv) LOCK. (04 Marks)
b. With diagram, explain RESET section of 8284 clock generator. Also indicate how clk and
RESET are connected to 8088 pp. (06 Marks)
c. Using timing diagram, explain the I/O write bus cycle in 8086 micro processor. (06 Marks)
d. Bring out the differences between 8086 and 8088 microprocessors. (04 Marks)
a. Explain how 74LS138 decodes 2732EPROMS for 32Kx 8 section of memory. Assume the
starting address is 40000H. Give the detailed memory map. (06 Marks)
b. What is flash memory? Explain how a flash memory is interfaced to 8086 pp. (06 Marks)
c. Explain 74138 decoder configurations to enable ports at address E 8 H to EFH. (08 Marks)
8a. Write an 8086 ALP to read a byte of data from port A and port B. Add the data and save the
result in a memory location. (05 Marks)
b. Explain command word format of 82C55 in mode-0. Write the control word format to
initialize to set PC3 and reset PC7. (07 Marks)
c. With internal block diagram, explain 8254 PIT. Give any two applications of the 8254.
(08 Marks)
{<***{<
2 of2
15. /
USN 10cs46
Fourth Semester B.E. Degree Examination, Decemb er 2Ol2
Gomputer Organization
Time: 3 hrs. Max. Marks:100
Note: Answer FIVEfull questions, selecting
atleast TWO questions from each part.
(J
o
o PART _ A
a. Explain the different functional units of a digital computer. (05 Marks)
b. Draw and explain the connection between memory and processor with the respective
(.)
(.)
registers. (05 Marks)
3q c. Explain clearly SPEC rating and its significance. Assuming that the reference computer is
ultra SPARCIO work station with 300 MHz ultra SPARC processor. A company has to
purchase 1000 new computers hence ordered testing of new computer with SPEC 2000.
:n Following observation were made.
bJl
troo
.= a.t
I
Runtime on reference co Runtime in new computer.;
Ioi
96' 50 minutes 5 Minutes
ogl
eO 75 Minutes 4 Minutes
E*
a:
o(.)
(d0
60 Minutes
30 Minutes
6 Minutes
3 Minutes
The company system manger will place the order for purchasing new computers only if
M/
overall SPEC rating is atleast 12. After the said test will the system manger place order for
ooi (10 Marks)
(B(3 purchase of new computer.
-o:
a6
<s 2a. What is little endian and big endian memory? Represent the number 64243848H in 32 bits
-? d)
'Ca big endian and little endian memory. (06 Marks)
or=
b. What is addressing mode? Explain immediate, direct and indiiect addressing mode by an
o-A example. (06 Marks)
c. Explain logical shift and rotate instructions, with examples. (08 Marks)
r.9
a=
t- ri,
Ntr
3a. Define memory mapped I/O and IO mapped I/O, with examples. (05 Marks)
!o b. Explain how interrupt requests flom several lO devices can be communicated to a processor
5.v
>'h
bo- through a single INTR line. (10 Marks)
coo c. What are the different methods of DMA? Explain them in brief. (05 Marks)
0)=
o;i
:o
o- 4a. With a block diagram, explain how the keyboard is connected to processor. (06 Marks)
J< b. Explain the serial port and serial interface. (06 Marks)
-..l c. Explain architecture and protocols, with respect to USB. (08 Marks)
o
z PART _ B
o
5a. Draw a diagram and explain the working of 16 Mega bits DRAM chip configured as
2M x 8. Also explain as at how it can be made to work in fast page mode. (10 Marks)
b. Briefly explain any four non-voltile memory concepts. (05 Marks)
c. With figure analyse the memory hierarchy interms of speed cost and size. (05 Marks)
16. -l
10cs46
6a. Explain the design of a four bits carry - look ahead adder circuit. (10 Marks)
b. Gives Booth's algorithm to multiply two binary numbers. Explain the working of algorithm
by taking an example. (10 Marks)
7 a. Write and explain the control sequence for execution of an unconditional branch instruction.
(10 Marks)
b. Draw and explain multiple bus organization. Explain its advantages. (10 Marks)
8 a. Write short note on power wall (06 Marks)
b. What you mean by shared memory multiprocessors. (06 Marks)
c. Explain the different approaches used in multithreading. (08 Marks)
{<**{<*