L-4/T-lICSE Date: 06/07/2013

L-4/T-lICSE Date: 06/07/2013

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKA

L-4/T -1 B. Sc. Engineering Examinations 2011-2012

Sub: CSE 401 (Artificial Intelligence)

Full Marks: 210 Time: 3 Hours

USE SEPARATE SCRIPTS FOR EACH SECTION

The figures in the margin indicate full marks.

SECTION -A

There are FOUR questions in this section. Answer any THREE.

1. (a) There are some predicates describe the block-world as follows.

on (A, B) - ,Block A is on block B.

on table (A) - Block A is on the table.

clear (A) . There is no block on top of block A.

holding (A) - The robot's arm is holding block A.

armempty - The robot's am: is holding n~u.meh<? ~

There are some actions: stack (x, y), €~x, y), pickup (x) and putdown (x)

Define the preconditions and effects for the actions using the predicates.

(b) What are the differences between "forward state-space-search" and the "backward

state-space-searcp"? Discuss using the following block-world problem. (Use actions and

(07)

predicates of 1.(a» (10)

(18)

A>- c5~) l~o~'6~)

h~~'(e.for"b, 1(10), (c) A flat tire problem is defined by the following predicates and actions.

initial state - at (flat, axle) A at (spare, trunk)

Goal state - at (spare, axle).

Actions:

(i) remove (spare, trunk) means spare tire is taken out from trunk and put on

ground.

(ii) remove (flat, axle) means flat tire is taken out from axle and put on ground.

(iii) puton (spare, axle) means spare tire is taken out from ground and put on axle.

(iv) leaveovernight'means neither flat por spare tire is on ground or on axle or in

trunk. How can a partial-order-planning he!p to achieve the goal state from the

initial state for t~e "flat-tire" problem?

eontd P/2

(t:).) 0', "1y. _:~':~i.:F,,! .j

\,,_ ~ ;'.' 1

'\

leo<.

. ..

=2=CSE 401

2. (a) (12) ,

\0Q-ll ~w') ~·J

PC H- t w) =-'-3It-

P (/dV)w).:-. 4'P( A-\ w)::,~ F~u "f'S2-. 10'(D ~ t.0-...)

For the above Bayesian Network compute (i) P(IA, W, H) and (ii) PnA I H) where

variables are W, A and H and these are all Boolean valued.

(b) What is "Markov blanket" in a Bayesian network? Explain with an example.

(c) For the given Bayesian Network find the correctness of the following query,

PCB I J = true, M = true) using variable elimination method. (Show the calculations).

(05)

(13)

~

~

~.r{y) 0.'~

FI~lA~ f:>~ 'Lce..)

(d) What is the role of clustering in "Bayesian Network'? (05)

3. (a)

Contd P/3

(12)

=3=CSE401-,Contd ... Q. No. 3(a)

For the above game tree using "a_p" pruning determine the value for the root node.

Find the branches to be pruned while children are visited from the left to right. (Show

the steps).

(b) Consider the problem of "wumpus world". Wumpus world is represented by a 4x4

grid. Initially the agent is at [1, 1]. There is one wumpus in one of the 16 squares except

[1, 1]. Three of the squares except [1;1] contain three pits. The positions of wumpus

and pits are randomly distributed, however wumpus does not live in a square where

there is a pit. Squares adjacent to wumpus are smelly and adjacent to pits are breezy. (18)

At [1, 1], the agent perceives neither stench nor breeze. Agent moves to [2, 1] where it

perceives both stench and breeze. When it returns to [1, 1] and thereafter moves to

[1,2], it perceives both stench and breeze.

From the initial knowledge base entail the following conclusions with the help of

propositional logic.

(i) whether [2, 2] lab~lled square contains the wumpus.

(ii) whether [1,3], [2, 2] and [3, 1] labeled squares contain pit.

(The grid of the problem is given as follows)

1,4 2,4 3,4 4,4

1,3 2,3 3,3 4,3

1,2 2,2 3,2 4,2

1, 1 2, I 3, I . 4, 1

IJ\-,,~

(c) What are the advantages of "a-p pruning" over "mini-max" search algorithm?

4. (a) Tony, Michael and Ellen belong to the Hoofers Club. Every member of the club is

either skier or a mountain climber or both. No mountain climber likes rain, and all skiers

like snow. Ellen dislikes whatever Tony likes and likes whatever Tony dislikes. Tony

likes rain and snow.

(i) Represent the problem using first-order logic.

(ii) Convert the sentences to CNF.

(iii) Find the member who is a mountain climber but not a skier.

(b) What are "unification" and "lifting lemma"?

(c) Explain "skolemization" with an example.

Contd P/4

(05)

(20)

(10)

(05)

=4=

CSE 401

SECTION-B

There are FOUR questions in this Section. Answer any THREE.

Assume if any missing value.

5. (a) Define in your own words: intelligence, artificial intelligence, and agent. (05)

(@urely animals, humans, and computers cannot be intelligent-they can do only what

their constituent atoms are told to do by the laws of physi~ the later statement true,

and does it imply the former? (15)

(c) Briefly describe the Turing Test. If the Turning Test is passed does this show that

computers exhibit intelligence? State your reasons.

6. (a) Consider the following map (not drawn to scale)

(15)

K 15 L 15 l\1FI'~UYtL ~'P 'Ca.)

Use the A* algorithm to work out a route from town A to town M. The straight line

distance between any town and town M is given in the following table.

Town Distance Town Distance

A 56 H 10B 22 I 8

C 30 J 5D 29 K 30E 29 L 15F 30 M 0G 14

(i) Provide the search tree for your solution, showing the order in which the nodes

were expanded and the cost at each node. You should not re-visit a town that

you have just come from.

Contd PIS

(10)

=5=CSE 401eouid ... Q. No. 6(a)

(ii) State the route you would take and the cost of that route.

(iii) Is your chosen route optimal? State your reasons.

(b) What are the differe~ces between informed search and uninformed search

algorithms?

(c) Briefly discuss the problems of greedy search algorithms.I

7. (a) Describe the idea behin~ simulated annealing and define the acceptance function

used by this algorithm.

(b) Outline the simulated annealing cooling schedule and describe its varIOUSI

components.

(c) How do evolutionary algorithms work? Explain the term self adaptation and its

necessity in the context of artificial intelligence.

(05)

(05)

(05)

(10)

(06)

(15)

(14)

8. (a) What is CSP? Is there a standard representation for CSP problems? Justify your

answer. (09)

(b) How do you apply CSP to the 8 queens problem? (06)

(c) Propose an approach to fuuilding an agent that plays chess. Within this approach,

what are some different strategies one can exploit? (20)

-----------------------------------,

A. S ./1' ?b l.....,..AA~. ~ C,, .

-,- .

'~

.... ;. ..~-

\, I.\.

(7).

! .

:3

). I

~~.- ~~::f!kiJ.

.~•...-

..~.'

(8)

(9)I

(9) _'

(9)

(18)'-

(5)

(10)

(6)J/

(14)

(

r ', I

._------------_._---_._._--SECTION-A

There are FOUR questions in this Section. Answer any THREE.

3. (a) Draw the SAP-I block diagram and derive its' control word. Show the timing diagram

of the fetch and execution cycle for the LDA instruction.

(b) "In SAP-I, instruction cycle equals machine cycle but in SAP-2 and SAP-3, the

Contd P/2

instruction cycle may equal to one or more machine cycles"-justify.

2. (a) Draw the circuit diagram to construct an 8 x 4 ROM using SSIIMSI chips.

(b) Implement an I-bit full adder circuit with your constructed ROM in question 2(a).

Show the circuit diagram after programming has been done on the ROM.

(c) Compute the number of programmable links for the following cases:

(i) 2" x m ROM

(ii) n x k x m PLA, where n denotes number of inputs, m denotes number of output"

k denotes number of programmable AND links.

(d) Write the use ISR, IRR, and IMR registers in the context of 8259.

1. (a) Explain the problems of the linear decoding approach.

(b) You are designing an 8086-based system that requires 16 K x 8 RAM. Consider the

address bus to be 16-bit wide. Your lab only has 4K x 8 RAM chips available. Draw the

block diagram of the memory system using the available RAM chip, clearly showing the

memory addresses you will use and the chip select signal you will produce for your

system. For the design, use the following approaches:

(i) Linear Decoding Approach

(ii) Partial Decoding Approach(c) You are designing a digital' system that has 25 interrupt signals designated by IRO-

IR24 where IRO has the highest priority. Assume that the micro-processor to be used in

the system has only one interrupt pin. Draw the circuit diagram to implement the

interrupt port\on of the system using the minimum number of8259 ICs.

(d) Explain the differences between SAP-2 stack and SAP-3 stack.

L-4/T-l/CSE Date: 23/07/2013BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKA

L-4/T-1 B. Sc. Engineering Examinations 2011-2012

Sub: CSE 403 (Digital System Design)

Full Marks: 210 Time: 3 HoursThe figures in the margin indicate full marks.


,; ,

/

=2=

.~

,.\

:.

(8)

(7)

(10)

(10+10)

MVI C, lOH

LOOPI: MVIB,OFH

LOOP2: DCR B

JNZ LOOP2

DCR C

NOP

JNZ LOOPI..

HLT

5. (a) Design a digital system that multiplies two fixed point numbers represented in 2's

complemented form (Assume each number to be k-bit). (6+8+5+6=25)

(i) Draw the flowchart of the system.

(ii) Draw the state diagram of the system and show the control outputs of each control

states.

(iii) Draw the block diagram of data processor part.

(iv) Design the control unit using one flip flop (J-K Flip Flop) per state method.

Contd P/3

4. (a) Discuss with example, the different ways of parallel data transfer between a digital

system and a physical I/O device.

(b) Design a microcontroller-based system that scans a 4 x 4 keyboard matrix and drives

four 7-segment displays. The system will identify each key pressed and scroll them from

right side of the displays and keep scrolling to left as each key is pressed. The system

continues indefinitely.

(i) Draw the block diagram showing inter-connections of the different components for

the system.

(ii) Draw the flowchart to develop the necessary software.

(c) What is a bidirectional register? Why is it necessary to use in SAP computers?

SECTION-BThere are FOUR questions in this Section. Answer any THREE.

Assume that memory involved instructions require 7 J.lS,pure register instructions require

4 J.ls, conditional jump instructions require 10 or 7J.ls and any other instruction require

10 J.ls. Now, determine the following considering the above instructions executed in

SAP-2 computer:

(i) How many bytes does the subroutine take to be stored in memory?

(ii) How long does in take to execute the subroutine?

Contd .;. Q. No.3

(c) Consider the following SAP-2 subroutine:

CSE 403

i

,t., ,,1 .!...:~...

(8+7+ 10=25)

. ~'.:

".

-,:,

(15) .'

(20)

(l

•::. t,•...

(5+5~10)

Contd P/4

(iii) USB

Bit No. Description

1-16 Micro operation select as shown in Figure 7(a)

17 MUX 1 Select

18-20 MUX 2 Select

21-26 Address Field

processor unit shown in figure 7(a)

SI So Cin= 0 Cin= 1

0 0 F=A+l F=A

0 1 F=B+l F=B

1 0 F=A-B F=A-B-l

1 1 F=B-A F= B-A-l

(b) Write short notes on any two of the following:

(i) AGP (ii) PCI

micro-operation:

pI :A+-AXORB--p2 : A +- A-I

p3: A+-A+B

(i) Draw a flowchart for the system.

(ii) Write the sequence of micro instructions to perform the function of the system. ,

(iii) Construct a table showing the ROM content for these microinstructions assuming

starting address 01100 1.

The micro-program control organization is shown in Figure 7(a). The ROM content

format is given below.

=3=

',',

Your design should be optimized. (minimum number of gates or ICs).

(b) Using J-K flip-flops, design one typical stage of a register that performs the following

7. (a) In an even parity checker, the output is set to 1 if the number of ones in a given set of

bits (not including the parity bit) is odd, making the number of ones in the entire set of

bit$ (including the parity bit) even; otherwise, the output is reset to O. Now you have to

design an even parity checker system for a number stored on register Rl using the

6. (a) Design an arithmetic unit using two selection variables, So and 81, that generates the

following arithmetic operations (use an adder and basic gates).

Contd ... Q. NO.5

(b) Design an arithmetic circuit with one selection variable s and two data inputs A and

B. When s = 0, the circuit performs the addition operation, F = A+B. When s = 1, the

circuit performs the increment operation F = A +1.

CSE 403

A.\,r-r'

'I,,,::,q~"rf\"~:,'ptr~...',

,~.:(~~l~"~-".

I.~:;',.'.:'~:t.:;~~.~~2.~/'?'ffi}:, :~.~~i' .

r:~::,:~"'I:P ~

j:,~t:i;~:'"I",,'";:,:j~~,; '.~i

r'~I',:,;'',.",[:",1~iJ 1, ~I,,,d,I;i!t"j:j} j:~':il'I"V\[::;If~,\\ e ,It.W~-~,I, 'IIA'"

1:1[1" ,, 14"

',' l{!;Ilt: ..;

:,:Jf",,t~;~'

...1:.'';" t. ,.,:.' ;;~.~

{o:' • ~!'>.~.i.:..

..•.

. '.~J

=4=

CSE 4038. (a) Design a comparator using only ALU and basic gates. The comparator takes two 4-bit

numbers A and B as inputs and provides three outputs for A<B, A>B and A = B.

(b) Illustrate the difference between Mode 0 (Interrupt on Terminal Count) and Mode 4

(Software - Triggered Strobe) of 8254 Programmable Interval Timer using suitable

timing diagrams.

(c) Briefly explain the effect on the output carryCout of ALU having the following.

specification:

SI So Cin Operation

0 0 0 F=A

0 0 1 F=A+l

0 1 0 F=A+B

0 1 1 F=A+B+l

1 0 0 F=A-B-l

1 0 1 F=A-B

1 1 0 F=A-l

1 1 1 F=A

-----------------------------------------

Contd PIS

,~ .

(13) ,.

(5) ,

'(17)

:~

~:".-,1.:',i'-,.

"

.,

_.~

';,;

L-4Tr-lICSE Date: 21/09/2013

BANGLADESH UNIVERSITYOF ENGINEERING AND TECHNOLOGY, DHAKA

L-4/T-l ]3. Sc. Engineering Examinations 2011-2012

Sub: CSE 411 (Simulation and Modeling)




SECTION-A


.. I,

1. (a) How does discrete event simulation differ from its continuous counterpart? Draw a

flow of control diagram Jor the Ilext-event time-advance approach for a discrete event

simulation.

(b) Using Monte Carlo simulation technique, compute the following integral:

(15)

(10)

You need to use following observation: for X ~ E~po(l), Var(X) = E[X2]- E[X]2 = 1.Use at least 10 random numbers to see how close the "simulated" result to the actual

result. For generating random numbers, i.e, U(O,l), pi~knumbers out of your mind or

use calculator's RAND button.

(c) Show a relationship among Normal, Gamma and Chi-Square distributions. (10)

2. (a) Discuss how lexis ratio helps in determining distribution families.

(b) Describe how MLE (Maximum Likelihood Estimation) is used to determine

parameters of a hypothesized distribution from a set of given data values.

(7)

(8)

(20)

I 1 2 3 4 5 6 '7 8, ,9 10

Values 2 5 6 7 8 12 15 18 19 20

.l..,

nA

F(X(;))i-I-n

I

, . (c)Compute the Kolmogorov-Smirnov (S-S) test statistic for the following ten (ordered)

data values against the hypothesized distribution, Discrete Uniform (0, 20). You may

find the following tabular representation h.elpful (where symbols have their usual

meaning).

Contd P/2

=2=CSE 411

3. (a) What are the general guidelines for choosing intervals in a Chi-Square test? (10)

(b) Using the composition method, derive a generator for a random variable having the

following density:

3

(15)

(c) Derive an acceptance-rejection method for generating beta (3,2) variates. Recall that

beta (3, 2) has the density function, j(x) = 12x2 (1- x), 0 < x <1. . (10)

4.. (a) Describe the Box-Muller method to generate standard normal variates. What is the

limitation of this technique? How can the technique be extended to generate normal

variates with arbitrary mean and variance?

(b) Let a random variable, X, be generated by the following acceptance-rejection

method:

(i) Generate Y - U(0,1).

(ii) Generate U - U(O,l).

(iii) If Y ~ U , then X = Y and return X, otherwise go back to step 1.

Show that X follows the density, j(x) = 2(1- x).Use, F(x) = p(X ~ x) = p(Y ~ x I A), where A refers to the event with statement 3 in the

above code.

SECTION -B

There are FOUR q!1estions in this section. Answer any THREE.

5. (a) A manufacturing system consists of five work stations and at present stations 1,2, ...,

5 consist of 3, 2, 4, 3, and 1 identical machines respectively. In effect, the system is a

network of five multi server queues. Assume that jobs arrive at the system with

interarrival times that are lID exponential random variables with mean 0.25 hour. There

are three types of jobs, and arriving jobs are of type 1, 2, and 3 with respective

probabilities 0.3, 0.5 and 0.2. Job types 1, 2, and 3 require 4, 3, and 5 tasks to be done,

respectively, and each task must be done at a specified station and in a prescrib~d order.

Contd P/3

(15)

(20)

=3=

CSE 411Contd •.•Q. No. 5(a)

!The routings for the different job types are: (15)

. Job type

1

2

3

Work stations in routing

3,1,2,5

4, 1,3

2,5, 1,4,3

Thus, type 2 jobs first have a task done at station 4, then have a task done at station 1,

and finally have a task done at station 3.

Ifa'j-oh arrives at a particular station and finds all machines in that station already busy,

'the job joins a single FIFO queue at the station. The time to perform a task at a

particular machine is an independent 2-Erlang random variable whose mean depends on

the job type and the station to which the machine belongs. The mean service times for

each job type and each task are:

Job type Mean service times for successive tasks (in hours)

1

2

3

0.50, 0.60, 0~85, 0.50

1.10,0.80,0.75

1.20,0.25,0.70,0.90, 1.00

Thus, a type 2 job requires a mean service time of 1.10 hours at station 4.

Suppose that all machines cost approximately the same and that the system has the

opportunity to purchase one new machine with an eye toward efficiency improvement.

~uggest a plan of action that can be used to identify bottlenecks. Explain your choice of

the output measures of system performance, and why a decision maker would be

interested in your findings ..

(b) Draw the event graph for the job-shop model. (6)

(c) Describe the arrival function, and the departure function for the job-shop model

using flowcharts. (14)

6. (a) Discuss how we can apply the central limit theorem to construct a confidence

interval for the mean. Explain the t confidence interval, and the t hypothesis test.

(b) Suppose that 7.3,6.1,3.8,8.4,6.9, 7.1, 5.3, 8.2,4.9 and 5.8 are 10 observations from

a distribution (not highly skewed) with unknown mean J.!. Compute X(IO), S2(1O), and

an approximate 90 percent confidence interval for J.!, assuming t9 095 = 1.83. Also, test

(20)

the null hypothesis Ho I.l = 6 at level a = 0.10, where symbols carry their usual

meanmg. (15)

Contd P/4

=4=

CSE 411

7. (a) Explain the need for random-number generators in a simulation of a system or a

process with the help of an illustrative example. (4)

(b) What are the desired properties of a good arithmetic random-number generator? (8)

(c) How can we generate a sequence of random numbers from linear congruential

generators (LCGs)? What are the two common objections against LCGs? What is a

quadratic congruential generator? How can we produce separate streams of random

numbers from a LCG? (4+4+3+3)

(d) Define the period of a random-number generator. What is a full-period LCG? What

are the necessary and sufficient conditions for full-period LCGs. (2+2+5)

-£,

9. (a) Distinguish betWeen empirical and theoretical tests for random-number generators.

What is the common idea behind the spectral test, and the lattice test? (6)

(b) What property is put under examination by the runs-up test? What is the test statistic

for this test? What is a runs-down test? What is the test statistics for the runs-down test? (8)

(c) Define Covariance, and Correlation between two random variables Xi and X} Show

that uncorrelated random variables are not necessarily independent. What is a

Covariance-stationary process? How can we assess whether a sequence of generated

random numbers exhibit discernible correlation? (4+4+4+9)

II.SM,~ r~\~ A 1,

2?~'? 'Lea)( ~

L-4/T -lICSE Date: 28/09/2013

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKA.L-4/T-l B. Sc. Engineering Examinations 2011-2012

Sub: HUM 411 (Business Law)




SECTION-A


1. (a) Define contract as per Contract Act, 1872 and classify the same. Briefly describe the

essential elements of a valid contract.

(b) What is offer? Explain the differences between "intention to make an offer" and

"invitation to make an offer" with the help of a decided can law.

(c) Distinguish between "Misrepresentation" and "Fraud".

2. (a) Define partnership as per Partnership Act, 1932 and elucidate its essential features.

(b) Give a brief outline; of the formalities to the observed for. the registration of a

partnership firm.

3. (a) Define "Wages" as per Payment of Wages Act, 1936 and explain how does it differ

from bonus.

(b) Briefly describe the provisions regarding (i) Employer's liability for payment of

wages; (ii) time for payment of wages and (iii) mode of payment of wages.I

4. (a) What do you understand by Negotiable Instrument? Name the various types of

Negotiable Instruments thl:ltare currently used is Bangladesh.

(b) What is a Bill of Exchange? Describe its essential features along with a specimen.

(c) What is a cheque? Hpw long it remains valid for use? Explain the circumstances

under which a cheque may be dishonored by a bank.

SECTION -B


5. (a) Define and classify c0rtpany as per the provisions of Companies Act 1994. Explain

with the help of a decided case law why a company is regarded as an artificial person in

the eye of law.

(b) What is memorandum 6fassociation? Discuss briefly its various contents.

Contd P/2•.

(10)

(7)

(6,X)

(15)

(15)

(8)

(8)

(13,X)

(10)

~.!

=2=

HUM 411

6. (a) Define Bailment and bring out its essential features. Explain the points of difference

between a Pledge and Mortgage.

(b) Explain in brief the various types of Bailment. Write a brief note on Hypothecation.

7. (a) Explain in brief how an agency may be created. How does an agent differ from a

servant? Explain who is legally empowered to act as an agent.

(b) Who is PrinCipal? What are the various rights and duties of agenttowards a principal?

8. Write short notes on: (any THREE)'

(a) Factory

(b) Intellectual Property Rights

(c) Safety measures for the workers

(d) Broker and Factor

(13X)(10)

(13X)(10)

(23 X)


L-4/T-l B. Sc. Engineering Examinations 2011-2012

Sub: CSE 421 (Basic Graph Theory)


USE SEPARATE SCRIPTS FOR EACH SECTIONThe figures in the margin indicate full marks.

SECTION-AThere are FOUR questions in this section. Answer any THREE.

1. (a) When do we call.two graphs G, and G2 isomorphic? Give an algorithm to check

whether two graphs are isomorphic or not. Does your algorithm take polynomial time? (8)(b) Wh~t is a self-complementary graph? Give two examples of self-complementary

graphs. (7)(c) Define (i) series-parallel graphs, (ii) interval graphs and (iii) chordal graphs with

illustrative examples.

(d) Briefly describe the idea of an algorithm to recognize an outerplanar graph.

(12)(8)

2. (a) Describe the following graph operations by illustrative examples: (i) subdividing an

edge and (ii) contraction of an edge. (6)(b) Let G be a simple graph of n vertices. If G has k connected components, then show

that the number m of edges of G satisfies m ~ (n - k) (n - k +1)/2. (7)(c) What do you mean by a perfect matching in a graph? Count the number of perfect

matchings in K3•3 and in Kn • (12)

(d) Define an M-altemating path and an M-augmenting path for a matching M in agraph G. Show that a matching M in a graph G is a maximum matching if and only if G

has no M-augmenting path. (10)

3. (a) Describe the structure of the Petersen graph. Show that the Petersen graph has

girth 5. (9)(b) Prove that Ks is non-planar. (7)

(c) Show that m ~ 2n - 4 for a planar bipartite graph of n vertices and m edges. (7)(d) Define the thickness ofa graph. Derive a lower bound on the thickness ofa graph. (7)(e) Construct a simple plane graph whose dual graph contains a loop and multiple edges.

Draw the dual of your graph. (5)

4. (a) Give an algorithm to recognize a triangle free graph using matrix multiplication. (7)(b) Define chromatic number and chromatic index of a graph. Find chromatic number of

W6and chromatic index of Ks. (8)

(c) Show that every simple planar graph is five colorable. (10)(d) Let G be a bipartite graph with maximum degree 11. ~hen show that z'(G) = 11,

where Z'(G) is the chromatic index ofG. (10)Contd P/2

[

=2=

CSE 421

SECTION-B


5. (a) If a tree T with m edge..shas a graceful labeling then prove that, K2m+l has a

decomposition into 2m + 1 copies of T.

(b) Show that, for n > 1, an integer list d of size n is graphic if and only if d' is graphic,

where d' is obtained from d by deleting its largest element I.i and subtracting 1 from its

I.i next largest element.

(c) Prove that, a graph is Eulerian if and only if it has at most one nontrivial component

and its vertices all have even degree.

(11)

(13)

(11)

6. (a) Let G be a simple graph of n vertices. Let u and v be ~ vertices in G such that

(u,v) EE(G) and dG(u)+dG(v)~n, then prove that G jHamiltonian if and only if

G + (u, v) is Hamiltonian. Using this lemma prove that, is G is a simple graph with

n ~ 3 vertices and if dG(v)~ n/2 for each vertex v, then G is Hamiltonian.

(b) For an n-vertex simple graph G (with n ~ 1), show that the following are equivalent

and characterize the trees with n-vertices:

(i) G is connected and has no cycles, (ii) G is connected and has n-l edges, (iii) G

has n-l edges and no cycles, (iv) G has no loops and has, for each u, v E V(G),

exactly one u, v-path.

(13+7)

(15)

7. (a) Prove that, the number of spanning trees of Kn is nn-2. (15)

(b) Prove that a graph G having three or more vertices is 2-connected if and only if for

each pair u, v E V(G) there exist internally disjoint u, v- paths in G. (13)

(c) If G is a 2-connected graph and G' is obtained from G by adding a new vertex y

with at least 2 neighbors in G, then G' is 2-connected. (7)

8. (a) If G is a simple graph, then prove that K(G) ~ K'(G) ~ o(G). Also prove that if G is a

3-regular graph then, K(G) = K'(G). (13+7)

(b) How many spanning trees does K2.r have? Explain with necessary figures.

(c) Prove that the center of a tree is a vertex or an edge.

(8)

(7)

(10)

/

,.

~\"L'"41T-1ICSE Date: 21109/2013

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKA


Sub: CSE 423 (Fault Tolerant Systems)

Full Marks: 210 Time : 3 Hours


The figures in the margin indicate full marks.----_._ ~-,-----_._ _-_ - _ _ _._ .._-

SECTION-AThere are FOUR questions in this section. Answer any THREE.

1. (a) Differentiate between the following temis: (5+5+5)(i) Fault and failure

(ii) Reliability and availability

(iii) Permanent and tran~ient faults(b) What is data dispersion? Derive availability in case of data dispersion over a fully-

connected 5-node network. (10)(c) A fail-soft system has 3 units as shown in Fig. 1. In the figure, 1 denotes the unit is

up, 0 denotes the unit is down, all solid lines denote arrival rate~d all dashed linesII

denote service rate, ~. Draw a simpler equivalent model for the system.

2. (a) Derive the memoryless property of exponential distribution.

(b) Deduce the relationship between reliability and instantaneous failure rate.

(c) What is MTTF? Does comparing reliabilities of two systems indicate in the same

way of comparing their MTTFs? Explain with an example.

(10)

(10)

(5+10)

3. (a) A system has two units. Failure rates of the units ae 0.00005/hr and 0.00002/hr.

Repair time of Unit 1 is 100 l)rs. The system fails if both of the units fail. In that case, an

immediate repair takes place. Besides, in case of Unit 2, a periodic check occurs in each

1000 hrs. In case of a failUre occurring in Unit 2, it becomes operational at the end of

the checking period. What is the overall average failure rate of the system? (25),

(b) You are given two independent computing systems. Let Xl and X2 be two random

variables that denote time lag between arrivals of two successive jobs in the two

systems respectively. Here, the job arrivals follow two different Poisson distributions

having arrival rates of Al and A2 respe'ctively. Determine the probability of XI being

less than X2. (10)

4. (a) What is "coverage" in modeling reliability of a system? (5)(b) Compare MTTFs of a single-component system and a TMR system. Which one is

the better system to use? (10+5)(c) Derive reliability of the system, in terms of the reliability of its component, ,as shown

in Fig. 2. Let Rx denote the reliability of the Xth component. Each component is shown

as a rectangle in the figure. (15)Contd P/2

{

=2=CSE 4i3

SECTION-B


5. (a) Differentiate between Extra-material and Pinhole defects.

(b) What is bum-in testing? Show its effectiveness through a graph having time in its X-

axis.

(c) How does the width of a wire exhibit impact on sensitivity of different types of

defects resulted during fabrication? .

(d) Should we use different types of redundancy schemes for defect circumvention in a

simultaneous manner? Illustrate with an example.

6. (a) Distinguish between defect removal and masking. How can we utilize these

techniques in case of memory arrays?

(b) Illustrate Moor and Shannon's work on building reliable relay circuit out of crummy

relays.

(c) What are the different types of radiation? Mention three negative impacts that may

be resulted from radiation.

(10)

(7)

(8)

(10)

(10)

(15)

(5+5=10)

7. (a) A square chip has an area of 1 cm x 1 cm. It has parallel and equally-spaced nodes

and separation having 0.5 ~m width. During manufacturing, such chips contain an

average of 10 random extra-material non-overlapping defects per cm2 area. These

defects are of two kinds: 80% are small having 0.25 ~m diameter and 20% are larger

having 0.75 ~m diameter. Calculate expected yield of such chips.

(b) A 6x6 memory array has 2 spare rows and 2 spare columns. The array experiences

defects at (1,3), (1,5), (2,3), (3,3), (4,1), (6,2), and (6,6) positions. Here, (x, y) denotes

x-th tow and y-th column. How can you circumvent all of these defects using available

spare rows and spare columns?

(c) How does the number of defects depend on defect size?,

(15)

(15)

(5)

8. (a) What is the benefit of using checkpoints? (5)(b) Can we apply bathtub curve in case of lifetime of a software? Briefly explain your

answer.

(c) Derive a time-variant model of a repairable Single-Component system. Hint: Use'

Laplace transform.

(5)

(25)

. '.' ',,',", -. ~". "~""~""""',~.~ -','~""" ..... , ._ ..•...'...•"..~."'..•..•..,~,....~.•.•.. ~""' ...•....", ..•.•....._.~,.~.,~'..,.". -..,. .._, ........••~...........•.•-~._-_....

CSE123 CA)

'5 .

h,% 2 ~ ~o~ ~ \.A..Q..6von 4 (c)

•" ,

L-4/T-1/CSE Date: 21/09/2013BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKA


Sub: CSE 433 (Digital Image Processing)




SECTION -A


2. (a) Briefly describe ideal low pass filter (ILPF), Gaussian low pass filter (GLPF) andt .

BU1frworth low pass filter (BLPF). Show that ILPF and GLPF are special cases of

BLPF. (15)

(b) What is an impulse train? Represent a continuous 1D function as a sampled function

using an impulse train and find its Fourier transform (FT) in terms of sampled function

itself. Use this result to derive the FT of an image.

3. (a) Explain the imaging procedure that is used in ultrasonography (USG).

(b) An image contains zero gray level everywhere except a constant rectangle of size

TxZ with gray level A. Find its Fourier transform in continuous domain. Draw the 1D

cross section of its spectrum. Can you explain from this why some filters produce

ringing effect?

(c) Explain the different types of redundancies that exist in image and/video data.

(20)

(10)

(18)

(7)

4. (a) Write down the expression for reconstruction of an image in terms of basis matrices

and transform coefficients. Make necessary changes in the expression to get a

compressed image. Derive the expression for expected mean square error between the

reconstructed image of this compressed image and the original image. Use this

expression to justify the structure of zonal coding mask. Why does lPEG use threshold

coding instead? (25)

(b) A linear scan of an image segment generates gray level sequence 128,40, 220, and

220 followed by an EOF marker. Compress this image segment using arithmetic coding. (10)Contd P/2

'.

=2=CSE 433

SECTION-B


5. (a) Give a formal definition of image segmentation. (3)

(b) Describe the "Region Splitting and Merging procedure for image segmentation.

Propose a suitable data structure for it and demonstrate how the split regions are stored

."

in that data structure.

(c) If the "Merging" step is left out, can "Region Splitting" be called an Image

segmentation process? Justify your answer.

(d) A car is moving at 72 kilometers per hour along a straight line path in the horizontal

direction. A high definition video camera was used to capture its motion in a sequence

of 25 frames. The frame rate of the camera is 20 frames per second. The physi~al

distance between successive pixels in each frame is 0.5 meters in the horizontal

direction. Calculate the horizontal displacement of the car in consecutive frames in

terms of pixels.

(e) Write an algorithm for finding a polygonal fit to closed curves.

(10)

(2)

(10)

(10)

6. (a) Derive the expression for first-order and second-order derivatives at a point x in the

horizontal intensity profile of a 2-d image. (4)

(b) Using the expressions obtained from 6(a), calculate the first-order and second-order

derivative values at each point in the horizontal intensity profile below of a 2-d image.

By analyzing these values, identify the following parts, with explanation: (12+4)

(i) Ramp

(ii) Isolated point

(iii) Line

(iv) Step._--._-._---_._--_. ~-.~...-.

"I,IIrI

I

/It, II ' :

, '.. I, I

"" .•..-.-•..'-,~

Figure fOr Question 202.)

Contd P/3

=3 =

CSE 433Contd ... Q. No. 6(b)

(c) What is meant by "double-edge" effect of second-order derivative? , (3)(d) Explain how you caq use the sign of the second-order derivative to determine

whether an edge is a transition from light to dark or from dark to light. (2)

(e) Describe the 3 fundament~l steps performed in edge detection. (5)

(f) Derive the expression for Laplacian of a Gaussian (LoG). (5)

7. (a) Assuming continuous intensity values, derive an intensity transformation function

that can make the intensity histogram uniform. Prove mathematically that the intensity -

histogram of the transformed image is uniform and independent of the intensity

histogram of the original image. (10), (b) For discrete intensity values, propose a transformation function for histogram

equalization. (3)

(c) A 3-bit image of size 64x64 pixels has the following histogram: (10)

Intensity levels Frequency

0 7901 10232 8503 6564 329

; 5 2456 1227 81

8.

Tabulate the histogram of the equalized image using the transform function that you

proposed.

(d) Explain Piecewise-Linear Transformation function. How is it related to a

thresholding function?

(e) Propose 2 smoothing filters of3x3 size. Which one of these is better and why?

(f) What is a median filter? What are its advantages?

(a) What is a gradient image? Provide a computationally suitable approximation of a

gradient image. Write down the Sobel gradient operators.

(b) Write down the ,steps for edge linking using Local processing approach.

(c) Explain the Hough transform approach for edge linking. How is an alternate

representation of lines used to mitigate the problem caused by infinite slope of lines?

How are the accumulator cells initialized and updated?

(5)

(4)

(3)

(3+2+3)

(10)

'(17)



Sub: HUM 211 (Sociology)




SECTION-AThere are FOUR, questions in this section. Answer any THREE.

1. (a) 'Sociology is a categoric~l and not a normative discipline' - Discuss.

(b) Evaluate the impact of industrial revolution for developing the distinct characteristics

or"sociology.

(c) Explain the main propert~es of functionalism.

2. (a) What do you understand by ethnocentrism? Critically explain the normative role of

culture in a society.

(b) How did Karl Marx respond against the functionalist view of culture? .

3. (a) What is social stratification? Explain different systems of social stratification in the

context of Bangladesh.

(b) 'The history of all hitherto existing societies is the history of class struggle' - explain

this statement highlighting Marx's view of class differences.

4. Write short notes on any three of the following:

(a) Agents of socialization

(b) Durkheim's view of anomie

(c) White collar crime

(d) Social mobility.

SECTION-BThere are FOUR questions in this section. Answer any THREE.

5. (a) What do you mean by Industrial Revolution? Describe the social effects of Industrial

Revolution.

(b) What is globalization? Describe the impacts of globalization on developing countries.

Contd P/2

t. ,,"

(7)

(8)

(8~)

(10)

(13 ~)

(10)

(13 ~)

(23 ~)

(13 ~)

(10)

(

J

=2=

HUM211

6. (a) Critically discuss the 'Robert Malthus Theory' of population.

(b) What is demography? Illustrate the elements of demography.

7. (a) Make a comparison between urban ecology and emergence of new urban sociology.

(b) Describe the social characteristics of pre-urban, urban and post-urban cities.

8. .Write short notes on any three o~the following:

(a) Population Pyramid

(b) Social change

(c) Types of environmental pollution

(d) Factory affecting over population in Bangladesh.

(8)

(15 ~)

(10)

(13 ~)

(23 ~)

.(15)

" ,1 .. 1

i .

. ;

n A B

0 - $ 1000 - $ 1000

1 $ 500 $ 800

2 $ 100 $ 600

3 $ 100 $ 500

4 $ 1000

Bomber type Description km/litre Number available

A Heavy 2 40

B Medium 2.5 30

Plant Distance from Probability of destruction bybase (km) A heavy bomber A medium bomber

1 400 0.10 0.08

2 450 0.20 0.16

3 500 0.15 0.12

4 600 0.25 0.20

Information about the location of the plants and their probability of being attacked by a

medium and a heavy bomber is given below:

or-Formulate the Linear Programming model in order to maximize the probability ,(uccess.

1. (a) What do you mean by validity and reliability of a selection tool? Discuss various

employee selection tools with their relative advantages and disadvantages. (15)(b) Differentiate consumer market and business market. Discuss the five patterns of target

market selection. (10)(c) The strategic bomber command receives instructions to interrupt the enemy tankproduction. The enemy has four key plants located in separate cities and destruction ofanyone plant will effectively halt the production of tanks. There is an acute shortage of

fuel, which limits the supply to 45,000 Htres for this particular mission. Any bomber sent

to any particular city must have at least' enough fuel for the round trip plus 100 litres. (10)The number of bombers available to the commander and their descriptions are as follows:

c~ ~ :2.YSN) (l;JC5S,to'l.>

SECTION-AThere are FOUR questions in this section. Answer anyTHREE.

L-,4ff-l/CSE Date: 05/10/2013BANGLADESH UNIVERSITY OF ENG1NEERING AND TECHNOLOGY, DHAKA


Sub: IPE 493 (Industrial Management)

Full Marks: 210 Time: 3 HoursThe figures in the margin indicate full marks.

USE SEPARATE SCRIPTS FOR EACH SECTION.H..__ .._ __ _.H .."_ _ ; ,.__ . _ .............................................• _ , - _ .._ __ __ _.- _ _ , _ _-_ .

'"' . (i) Find i* for each project(ii) Are the projects acceptable at MARR = 8%?

Contd P/2

.!

=2=.

.~ .:!....... . .~'-:.' ',J. ~r. ,.:"":,~

1.".I'I'! "~,

;, :1".:' •...

~.

(10)

(15)

(10)

(20)

Design

A B C

Cost of site $ 240 .$ 180 $ 200

Cost of building $ 2200 $ 700 $ 1400

Annual fee collection $ 830 $ 750 $ 600

Annual maintenance cost $ 410 $ 360 $ 310

Service life 30 yrs 30 yrs 30 yrs{-c n: V\ e d.-

At the end of the estimated service life, the selected facility would be turned down andC:

the land would be sold. It is estimated that, the proceeds from the resale of the land will

be equal to the cost of clearing the site. If the city's interest rate is known to be 10%,

which design alternative would be selected, based on benefit-cost criterion?

4Xl - 6X2- 5X3-AX4 ~ -20

-3XI-2xz+4x3+X4S 10

-8xl - 3X2+ 3X3+ 2X4S 20

Maximize

Subject to

(b) Describe the steps of human resource planning.

(c) A city that operates automobile parking facilities is evaluating a proposal to erect and

operate a structure for parking in its downtown area. Three designs for a facility to be

built on available sites have been identified as follows (all dollars are in thousands)

(b) Show that there is an unbounded solution to :the following Linear Programming

problem:

3. (a) What are the 4Ps of marketing? How do the psychological factors affect consumer's

buying behavior? Discuss.

Contd ... Q. No.2

IPE 493 (eSE)

~.,~...

4. (a) Define w&ste. What are the seven prominent types of waste defined by Fujiocho? And.

what are the seven elements to eliminate those wastes?

(b) Explain Maslow's hierarchy of needs.

(c) What are the advantages and disadvantages of matrix organization?

(d) Differentiate efficiency and effectiveness.

(10)

(15)

(5)

(5)

Contd P/3

=3=

;. ;

.. /,

:.

..(35)

So. \e.>

$ 2.00

0.80

$ 1.20

$ 12,000

3,000

30,00015,000

$ 60,000Total fixed expenses

Required:(a) How many pairs of stockings must be sold to breakeven? What does this represent

in total dollar sales?(b) Prepare a CVP graph for the store from a zero level of activity upto 70,000 pairs

, .of stockings sold each year. Indicate the breakeven point on the graph.(c) How many pairs of stockings must be sold to earn a $ 9000 target profit for the

first year?(d) Ms. Hall now has one full time and one part time salesperson working in the store.It will cost her an additional $ 8000 per year to convert the part time position to a full

time position. Ms. Hall believes that the change would bring in an additional $ 20,000in each year. Should she convert the position? Use incremental approach. (Do not

prepare an income statement).(e) Refer to original data. Actual operating results for the first year are as follows:

S~es $125~00

Less variable expense 50,000Contribution Margin Expenses 75,000Less Fixed Expenses 60,000

Net operating income $ 15,000

Contd P/4


(i) What is the store's degree of operating leverage?(ii) Ms. Hall is confident that with some effort she can increasesales by 20%next year. What would be the expected percentage increase in net operating

income? Use degree of operating leverage concept.

5. Teri Hall has recently opened Sheer Elegance, Inc., a store specializing in fashionablestockings. Ms. Hall has just completed a course in managerial accounting and shebelieves that she can apply certain aspects of the course to her business. She isparticularly interested in adopting the cost-volume-profit (CVP) approach to decision

making. Thus, she has prepared the following analysis:

Sales price per pair of stockingsVariable expense per pair of stockings

Contribution margin per pair of stockings

Fixed expenses per year:

Building rentalEquipment depreciation

SellingAdministrative

IPE 493 (CSE)

J"

" '

"

=4=

IPE 493 (eSE)

6. (a) Briefly explain three patterns of 'product/market organization'.

(b) What is additive seasonality and multiplicative seasonality? Define 'seasonal

relatives' .

(c) The maintenance department of a large hospital uses about 816 cases of liquid

cleanser annually. Ordering costs are $ 12, carrying costs are $ 4 per case a year, and the

new price schedule indicates that orders of less than 50 Cases will' cost $ 20 per case, 50

to 79 cases will cost $ 18 per case, 80 to 99 cases will cost $ 17 per case and larger orders

will cost $ 16 per case. Determine the optimal order quantity and total cost.

7. (a) Explain the four specific functions of a manager.

(b) Define five underlying patterns of time series data.

(c) What are the assumptions of 'human resource' model?

(d) What are the three zones of Juran Model? State with appropriate figure.

8. (a) Processing times (including setup times) and due dates for six jobs waiting to be

processed at a work center are given in the following table. Determine the sequence of

jobs, the average flow time, average tardiness and average number of jobs at the work

center, for each of these rules:

(i) FCFS

(ii) SPT

(iii) EDD

Job Processing Time (Days) Due Dates (Days)

A 2 7

B 8 16

C 4 4

D 10 17

E 5 15

F 12 18

Assume jobs arrived in the order shown.

(b) Classify 'cost of quality' with examples.

(c) Briefly explain Fiedler model of leadership.

->

1\:", ",',' ~'"

(15)

(5)

(15)

(15)'

(5)

(10)

(5)

(15)

(10)

(10)

."

j .:

"• !

~, i,, '



Sub: HUM 213 (Government)

Full Marks: 140 Time: 3 Hours~ The figures in the margin indicate full marks.

USE SEl>ARA TE SCRIPTS FOR EACH SECTION-_ _._ _-_ _ __ _ , --_ _ __ --_.__ __ _., _---_ _--_ _ __ _ _- _ .

SECTION -AThere are FOUR questions in this section. Answer any THREE.

1. (a) How do you define state? Identify the differences between society and state.

(b) Define constitution. E?,plain the characteristics of a good constitution.

2. (a) Who are citizens? Analyze the rights of a citizen in a state.

(b) Classify modem forms of government with examples.

3. (a) What is meant by independence of judiciary? How can it be secured?

(b) Make a comparative discussion on democracy and dictatorship.

4. (a) What is good governance? Examine the importance of civil society in ensuring good

governance.

(b) Critically examine the role of opposition party in parliamentary form of government.


5. (a) Explain the major characteristics of the constitution of Bangladesh.

(b) Write a note on the principal organs of United Nations Organization.

6. (a) Critically discuss the external and internal determinants of foreign relations of

Bangladesh.

(b) Discuss the importance of the Language Movement of 1952.

7. (a) What do you know about the functions of urban local government in Bangladesh?

(b) What is socialism? Explain the principles of Marxism.

8. (a) Make a note on the political system of United States of America (USA).

(b) Discuss the salient features of the constitution of United Kingdom (UK).

(11 ~)

(12)

(11 ~)

(12)

(11 ~)

(12)

(11 ~)

(12)

(11 ~)

(12)

(11~)

(12)

(11 ~)

(12)

(11 ~)

(12)

L-4/T-lICSE Date: 06/07/2013

Documents

Transcript of L-4/T-lICSE Date: 06/07/2013