DAYANANDA SAGAR ACADEMY OF TECHNOLOGY & MANAGEMENT(TC)
Udayapura, Kanakapura Road, Opp: Art of Living, Bengaluru-560082.
DEPARTMENT OF MATHEMATICS
Subject: Engineering Mathematics-IV (Common to CSE-1&2,ECE-1&2,ISE,ME-1&2)
NOTE: Last date for submission of Assignment is on 11/5/2015.
ASSIGNMENT-III
1. a) Define i) Random variable ii) Discrete probability distribution with an example.
(7M)(JUN-10, DEC-14,09)
b) The probability that a man aged 60 will live up to 70 is 0.65. What is the probability that
out of 10 men, now aged 60, i) exactly 9, ii) atmost 9 iii) atleast 7, will live up to the age of
70 years.
(7M)( JUN-09)
2. a) In a normal distribution, 31% of the items are under 45 and 8% are over 64. Find the mean
and standard deviation, given that A (0.5) =0.19 and A (1.4) =0.42 . (7M,JUN-09,DEC-12)
b) The probability that an individual suffers a bad reaction from an injection is 0.001.Find the
probability that out of 2000 individuals, more than 2will get a bad reaction
(6M,JUN-08)
3. The sale per day in a shop is exponentially distributed with average sale amounting to
Rs.100 and net profit is 8%. Find the probability that the net profit exceeds Rs.30 on a day.
(7M) (JUN-08)
b) Obtain mean and variance of binomial distribution function.
(7M)(JUN-10, DEC-14)
4. a) The life of an electric bulb is normally distributed with average life of 2000 hours and
standard deviation of 60hours. Out of 2500 such bulbs, find the number of bulbs that are
likely to last between 1900 and 2100 hours. Given [0  z  1.67]=0.4525. (7M,Jun08, Dec13)
b) Suppose a random variable X takes the values-3,-1, 2 and 5with respective probabilities
2k  3 k  2 k  1 k  1
. Find the value of k and i) find P [-3<X<4] and ii) P[X  2].
,
,
,
10
10 10 10.
(6M)(JUN-10)
5. a) Suppose that the student IQ scores form a normal distribution with mean 100 and standard
deviation 20. Find the percentage of students whose i) score is less than 80 ii) score falls
between 90 and 140, iii) score more than 120.
(7M)(JUN-10)
b) Derive mean and variance for the Poisson distribution.
(7M)(DEC-08, 13,JAN-10)
6.
a) The probability density function of a variate x is
X
0
1
2
3
4
5
6
P(x)
K 3K 5K 7K 9K 11K 13K
i) Find k. ii) Find P(x<4), P(x ≥ 5) and P(3<x  6 ).
(6M)(DEC-08, 10, JUN-11)
1.
b) Given that 2% of the fuses manufactured by a firm are defective, find by using Poisson
distribution, the probability that a box containing 200 fuses has i) No defective fuses
ii) 3 or more effective fuses iii) At least one defective fuse.
(7M)(DEC-10)
7. a) A die is tossed thrice. A success is getting 1 or 6 on a toss. Find the mean and variance of
the number of successes.
(7M)(DEC-11)
m
r
e m
b) For the Poisson distribution, prove that, P(r)=
, where m is the mean of distribution.
r!
Using binomial distribution
(6M)(DEC-11)
8. a) Fit a normal distribution to the following data:
(6M)(DEC-11)
X: 1 3 5 7 9
Y: 2 2 3 2 1
b) Alpha – particles are emitted by a radioactive source at an average of 5 emissions in 20
minutes. What is the probability that there will be i) exactly two emissions ii) at least two
emissions in 20 minutes?
(7M)(JUN-11)
2.
9) a) The probability that a pen manufactured by a company will be defective is 0.1 if 12 such
pens are selected, find the probability that i) exactly 2 will be defective, ii) at least 2 will
be defective,
iii) none will be defective.
(7M)(DEC-12)
b) A die is thrown 8 times. Find the probability that ‘3’ falls
(7M)(JUL-13)
i) Exactly 2 times
ii) At least once
iii) At the most 7 times
10) In a certain town the duration of shower has mean 5 minutes is distributed exponentially.
What is the probability that shower will last for i) 10 minutes or more; ii) less than 10
minutes; iii) between 10 and 12 minutes
(7M)(JUL-13)
b) The probability distribution of a finite random variable X is given by the following table:
x
0
1
2
3
4
5
6
7
P(x)
0
K
2k
2k
3k
Find k, p(x<6), p(x≥6), p(3<x≤6).
(6M)(DEC 13)
11) a) In a quiz contest of answering ‘YES’ or ‘NO’, what is the probability of guessing atleast 6
answers correctly out of 10 questions asked? Also find the probability of the same if there
are 4 options for a correct answer?
(7 M)(JUN-14)
b) Define exponential distribution and obtain the mean and S.D of the exponential
distribution.
(7 M)(JUN-14)
12) a) The probability density of a continuous random variable is given by
p(x)= y0 e  x ,  10  x   . Find y0. Also find the mean?
b) Obtain the mean and variance of the Normal probability distribution.
(6 M)(DEC-14)
DAYANANDA SAGAR ACADEMY OF TECHNOLOGY AND MANAGEMENT
UDAYAPURA, KANAKAPURA ROAD, BANGALORE- 82
Department of Information Science and Engineering
Subject: Graph Theory and Combinatorics
Class: IV Sem
Assignment –III
Subject code: 10CS42
1. A computer science professor has seven different programming books on a bookshelf.
Three of the books deal with C++, the other four with Java. In how many ways can the
professor arrange these books on the shelf
i.
If there are no restrictions.
ii. If the languages should alternate.
iii. If all the C++ books must be next to each other.
iv. If all the C++ books must be next to each other and all the Java books must be
next to each other.
(10 Marks, July 2006)
2. In a certain implementation of the programming language Pascal, an identifier consists of
a single letter or a letter followed by upto seven symbols, which may be letters or digits.
There are 36 reserved words. How many distinct identifiers are possible in this version of
Pascal?
(10 Marks, June 2010)
3. How many integers between 1 and 300 (inclusive) are
i.
divisible by at least one of 5, 6, 8?
ii. divisible by none of 5, 6, 8?
(10 Marks, June 2013)
4. How many non-negative integers solutions are there for the equationX1+X2+X3+X4=18,
where Xi≥7 for i=1,2,3,4.
(10 Marks, June 2008)
5. An apple, a banana, a mango and an orange are to be distributed to four boys B1, B2, B3
and B4. The boys B1 and B2 do not wish to have apple, the boy B3 does not want banana
or mango and B4 returns orange: In how many ways the distribution can be made so that
no boy is displeased?
(10 Marks, July 2007)
6. Define ordinary generating functions and exponential generating function. Give example
for each.
(10 Marks, June 2013)
7. Using generating function find the number of i)non negative and ii) positive integer
solutions of the equation x1+x2+x3+x4=25.
(10 Marks, Jan 2013)
8. Find the coefficient of x18 in the following products:
i.
ii.
(x+x2+x3+x4+x5)(x2+x3+x4+x5+…)5
(x+x3+x5+x7+x9)(x3+2x4+3x5+…)3
(10 Marks, Jan 2013)
DAYANANDA SAGAR ACADEMY OF TECHNOLOGY AND MANAGEMENT
UDAYAPURA, KANAKAPURA ROAD, BANGALORE- 82
Department of Information Science and Engineering
9. Find the exponential generating function of the sequence 1, 2, 22,23,24, ...
(10 Marks, July 2004)
10. The number of virus affected files in a system is 1,000 and this increases 250 % every
two hours. Use a recurrence relation to determine the number of virus affected files in the
system after one day.
(10 Marks, June 2013)
11. Solve the recurrence relation
an – 6an-1+9an-2=0, n≥2, given a0=5, a1=12
(10 Marks, Dec 2010)
12. Solve the Fibonacci relation
Fn+2=Fn+1+Fn for n>=0 given F0=0, F1=1.
(10 Marks, Jan 2013)
DAYANANDA SAGAR ACADEMY OF TECHNOLOGY AND MANAGEMENT
DEPARTMENT OF INFORMATION SCIENCE AND ENGG
Subject : Design & Analysis of Algorithms
Class : 4th sem
Assignment -3
Subject code : 10CS43
1. Write the formula to find the shortest path using floyd’s approach. Use floyd’s method to
solve the below all-pairs shortest paths problem.
(10 Marks,Dec 2007,July 2013)
2. Using Warshall’s algorithm, obtain the transitive closure of the matrix given below;
(10 Marks,June 2012)
3. Give the necessary recurrence relation used to solve 0/1 knapsack problem using
dynamic programming. Apply it to solve the following instance and show the results
n=4, m=5 values 12, 10, 20, 15 and weights are 2, 1, 3, 2 respectively.
(08 Marks, June 2014)
4. With pseudocode, explain how the searching for a patter BARBER in the given text
JIM_SAW_ME_IN_BARBER_SHOP is performed using Horspool’s algorithm.
(08 Marks, June 2014)
5. For the given graph, obtain optimal cost tour using dynamic programming.
(06 Marks, Dec 2014)
6. Show how comparison counting method sorts the list:
45, 2, 19, 10,33,22,1,23
(10 Marks) (Dec 2011)
7. What are Decision trees? Explain the concept of Decision trees for sorting algorithms
with an example.
(10 Marks)(Dec 2010)
8. Briefly explain the concepts of P, NP and NP complete problem.
(04 Marks,Dec 2010)
9. Define Decision trees. Write the Decision tree for the three element selection sort.
(06 Marks,Dec 2014)
10. Show how distribution counting method sorts the list:
12,13,10,12,10,12,11,10,13
(10 Marks) (Dec 2012)
11. Write Floyd’s algorithm to find the all pair shortest path problem and analyze with the
help of example
(10 Marks)(RS)
12. Brief Overflow and Underflow in numerical analysis algorithms. (02 Marks,July 2013)
***************************
DAYANANDA SAGAR ACADEMY OF TECHNOLOGY AND
MANAGEMENT
DEPARTMENT OF INFORMATION SCIENCE & ENGINEERING
Subject: UNIX and Shell Programming
Subject Code: 10CS44
ASSIGNMENT-3
1. What is shell programming? Explain with examples how expressions are evaluated in
shell programming.
2. Explain ‘for’ loop in shell programming in detail.
3. a) What is the ‘exit’ status of a command and where is it stores?
b) Explain Logical operator && and || conditional execution.
4. Write short notes on: a) read: Making scripts interactive b) Using command line
arguments.
5. Explain the use of test and [ ] to evaluate expressions in shell.
6. Write short notes on: a) File Tests b) Matching multiple patterns
7. Write a menu driven shell script to display list of files, process of user, todays date and
users of the system.
8. Explain while: looping statement in detail.
9. Explain with example, set and shift commands in UNIX to manipulate positional
parameters.
10. a) Explain trap in shell scripts with a suitable example.
b) Explain here document with an example. Also mention its use.
11. a) Special parameter used by the shell b) Numerical comparison operator used by test
12. a) String tests used by test b) file- related tests with test
Dayananda Sagar Academy of Technology & Management,
Bangalore – 82
Department of Information Science and Engineering
Assignment-III
Class: IV SEM ISE
Subject: Microprocessors (10CS45)
1.(a) Illustrate with a neat diagram , the working of 8086 in minimum mode .also give the timing
diagram of i/o read operation
(10 Marks, June 2010) (10 Marks, Dec 2013)
2. Explain the need of demultiplexing of buses in 8086. Also explain Describe demultiplexing
of multiplexed AD bus with neat diagram.
(10 Marks, July 2007)(10 Marks, Dec 2013)
3. (a)Explain the internal block diagram of 8288 bus controller with the explanation of each
pins?
(06 Marks, Dec 2013)
(b) Bring out the differences between 8086 and 8088 microprocessors?
(04 Marks, Jan 2013)
4.With the diagram explain the operation of 8284 clock generator? Also explain how clock
generator RESET and CLK pins are connected to 8088/8086 microprocessors?
(10 Marks, Jan 2013)
5. Explain memory devices that are used with 8086
(10 Marks, July 2012)
6. (a)Write and explain signal activities on 8086 buses, during a simple read operation.(timing
diagram during read bus cycle in 8086)
(06 Marks, Dec 2011)
(b) Write a program to interface a stepper motor to 8086 to rotate the motor in clockwise
direction
(05 Marks)
7. Describe the operation of 8086 in maximum mode. Give an example a typical maximum mode
configuration.
(10 Marks, Jan 2010)
8. (a)With internal block diagram, Explain 8254 PIT. Give any two applications of the 8254.
(06 Marks, June/July 2013, 05 Marks, Dec 2012)
(b) Explain the minimum mode pins of 8086?
(05 Marks, Dec 2013)
9. What are the sources of interrupts? Briefly explain the steps taken by a processor to execute
an interrupts instruction.
( 10 Marks, June/July 2013)
10. Briefly explain the structure of 8086 interrupt response and interrupt vector table with a neat
diagram.
(10 Marks, June /July 2009)(10 Marks, Dec 2013)
11. (a) Scan a 8 x 3 keypad for key closure and to store the code of the key pressed in a memory
location or display on screen. Also display row and column numbers of the key pressed.
(06 Marks)
(b) With a neat diagram explain the clock generator 8284?
(06 Marks, July 2012)
12. With a neat diagram explain the working of 8259 and also explain LCWs format
(10 Marks, June /July 2011)
DAYANANDA SAGAR ACADEMY OF TECHNOLOGY AND MANAGEMENT
DEPARTMENT OF INFORMATION SCIENCE AND ENGINEERING
Computer organisation (10CS46)
ASSIGNMENT-3
1. Explain direct mapping and associative mapping between cache memory and main
memory.
(10Marks, July2011, June2012)
2. (a) Briefly explain the 2 cache mapping functions?
(b) Define and explain following:
i.
Memory access time
ii.
Memory cycle time
iii. RAM
iv.
Static memories
(06 Marks, June2013)
(04 Marks, June2010)
3. With a neat diagram explain the translation of a virtual to physical address?
(10 Marks, June2013)
4. (a) Discuss in detail any one feature of memory design that leads to improves performance
of computer.
(06 Marks, June2013)
(b)Define: i) Memory latency
ii) Memory bandwidth iii) Hit –rate iv) Miss penalty.
(04 Marks, Dec2011)
5. Write note on i) Optical technology used in CD systems ii) RAID disk arrays
(10 Marks, Jan2009)
6. explain booths algorithm for
a) M= -13, Q= -09
b) M=14, Q= -5
(10Marks, July2011, June2012)
7. Perform the operation of division using (a) restoring (b) non-restoring method on the
following pairs of numbers X is the divisor and Y is dividend
(a) X=0101 Y=11111 (b) X=1001 Y=10010
8. Give the magnetic structure of magnetic disk and explain the working principle with
waveform?
(10 Marks, July09, June2012)
9. Multiple each of the following pairs of signed two’s complement number using bit pairing
of multipliers . A is multiplicand B is multiplier
(10 Marks,June2012)
(a) A=010111 B=110110 (b) A=111000 B= 011111 (c) A=001110 B=001110
(d) A=001101 B=010101
10. Write a program to evaluate the expression A2+2AB+C ina single accumulator processor .
and represent using one , two and three address formats
(10 Marks,June2013)
11. Registers R1,R2,R3 of aprocessor contain the decimal values 1250,5500,25. Determine the
values of the registers after each instruction is executed
(10 Marks,June2012)
(a) LOAD R3,(R2) (b) ADD (R2)+,R5 (c) MOVE #0250,R5 (d) ADD –(R2),R1
(e) STORE R5,20(R1,R2)
12. Perform the following operation
(10 Marks,June2011)
(a) (+5) – (-7) (b) (+2) + (+5) (c) (-7) – (-4) (d) (+6) – (-2) (e) (+2) – (-4)