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Monday, 14 November 2011

Web Supporting Technologies (New) pattern |Mca |pune university

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Web Supporting Technologies (New) pattern |Mca |pune university
Web Supporting Technologies (New) pattern |Mca |pune university question papers with marks.

3. a) Design HTML form lo reserve a 'Air Ticket'. Take suitable fields. Using
Java script check validations for:
i) From and To city are 2 different cities
ii) Age of passengers should not be greater than 90
iii) Name should have 25 characters and doesn't have any special character or
number.
b) What is CSS ? Describe the types to create CSS.

4. a) Write a VB Script code for accepting numeric value. If first button is active
convert number to Binary and If second click convert number to Octal.
Enter No       : Converted No:
Binary Octal

b) Write the difference between DTD and Schema.

5. a) Write a code for creating following external stylesheet.
i) Color of text should be 'Navy'
ii) Text having 13 font-size. Times New Roman font, and Italic
iii) Three types of hyperlinks with mentioned color
visited-red, active-blue, current-maroon
iv) Set border for paragraph in 'Magenta' color.
b) What is WWW ? Explain Three Tier Architecture of web based application.
6. Write short notes on following (any 3):
1) Features of XML.
2) Error Handling in VB Script.
3) Types of lists in HTML.
4) String object in Java Script.


2) Solve any four from remaining.
3) Figures to the right indicate full marks.

Explain following tags with basic attributes :

10

a) <body>
b) <marquee>
c) <frame>
d) <img>
e) <form>
2. a) Write a Javascript code to calculate Sales Commission as per the total sales
value is entered. Accept total sales in Rs. in a text box, after clicking on a 'Find Commission' button, display the commission value in a new text box. No one should be able to change the value of commission, directly in a text box. Criteria : Sales <50 then comm = 0 Sales >50 and sales <=500 then comm = 10% of sales.
Sales >500 then comm = 50 + 8% of sales. 8
b) What is XML ? Write the difference between XML-DTD and XMl^schema.       7
3. a) What is a style-sheet ? Explain font, background and text style options in
detail. 8
b) Explain Window and Navigator objects in Javascript. 7

4. a) Write a VBscript code to validate customers entry form. Validation
criterias are: 8
i) Name should have 25 characters and doesn't have any special Characters/
Numbers.
ii) Address should have 200 characters.
iii) Credit card number must be a 16-digit number.
b) What is Image mapping ? Explain the types of Image mapping with examples.       7
P.T.O.

a) Design XML file lo store the details of a bill with elements like billNo, billdate,
PONO, billamt, billdue date. Using XMLDSO display the details in HTML
with proper formatting. 8
b) How to create array in VB script ? Explain any 5 array functions. 7
Write short notes on any 3 :                                                                  15
a) W3C
b) XSLT
c) Web Hosting
d) <script> tag.





1. What is XML-DSO ? Display the contents of any XML document using XMLDSO object. 10
2. a) Write a Javascript code which will display Patient Master Form, having
following fields Patient Id, Patient name, address, city, contact no.. Date of
Birth. Validate above fields with different criterias. 8

b) What is www ? Explain 3-tier architecture. 7

3. a) Write an External CSS for including following styles.
Apply styles on any HTML page 8
i) Paragraph with Background Image
ii) Align hi text in center of web page
iii) h2 with right indent lOpx
iv) Table with blue border at Top and Bottom
b) Explain string object and date object in VB script. 7
4. a) Write a VB script code to design a arithmetic calculator.
8 b) Explain Document object model in Java script. 7
5. a) What is Image Mapping ? Explain client side Image map.
8 b) Explain simple sheet using XSLT with example. 7
6. Write short notes on any 3 : (5x3=15)

a) < frameset > lag
b) Classes in CSS
c) Error Handling in VB script
d) Web Publishing.

Explain Client and Server side Image mapping with example.
a) Explain Document Object Model (DOM).
b) Consider given XML document.

< ? rem I version = "l.0"> <info> <stud>
<name> Nila </name>
<Address> Tilak Road, Mumbai </Address>
<phone> 12345 </phone>
<age> 20 </age>
<email-id> nita@yahoo.com </cmail-id> </stud> <stud>
<name> Rahul </namc>
<Address> M.G. Road, Pune </Address>
<phone> 67890 </phone>
<age> 21 </age>
<email-id> rauLg@hotmail.com </email-id> </stud> </info>
Display the content of above document in Table format using XMLDSO
object.

OOAD tricks with tips with practical example

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OOAD tricks with tips with practical example
OOAD tricks with tips
 Mention the assumptions made for solving case study.
1. a) Draw the use case diagram and class diagram for a placement agency site who
provides the facility for candidates to register with their academic details,
personal details and skill set. Site also gives provision to update their profiles.
Organizations can also register with their requirements. Search facility is
provided to search job and suitable candidates.
b) Explain the Association with Objects.

2. Compare 'Structured System Analysis and Design 1 and 'Object Oriented Analysis
and Design'.
3. Describe the steps involved in constructing the object modeling and functional modeling using OMT.
4. a) Explain the multi-tiered architecture. 6 b) Draw the sequence diagram for sending an e-mail.
5. Draw the Activity Diagram for the following bank transactions :

a) Money Deposit
b) Amount Withdrawal
c) Request for Debit/Credit Card
d) Checking the Balance.

6. Draw the state transition diagram for the fully automated washing machine.      
7. Write short notes on any two:

a) Patterns.
b) Guidelines for developing test cases.
c) Guidelines for designing the user interface.

How to learn OOAD with questions

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How to learn OOAD with questions
How to learn OOAD with questions , the question will come in your mind when you will think about ooad so here i  have given some important question about OOAD try to implement it as soon as possible.

a)Draw the use case diagram and class diagram for a Customer order from a retail catalog. The payment can be done by either cash, cheque or credit card. The order contains order details with its associated items. Pending order reports arc generated periodically. Rejected or damaged goods are returned with GRN.      
b)Compare Objects and Classes.
, Discuss the structure of Class Responsibility Collaborator approach with an
example.
Explain the steps of Grady Booch notations of OO methodology with example.    
Discuss the categories of patterns with example.
a) Explain the four phases of Rational Unified Process.
b) Draw the sequence diagram for contacting a person using a Mobile Phone.      
MCA admission procedure is as follows:
a) DTE Advertises the date of MCA Entrance examinations.
b) Student has to apply for the entrance examination.
c) Results announced by DTE
d) Student has to fill up the option form to select the college of his/her choice.
e) DTE displays allotment list in the web site and intimation to all colleges.
0 Students should visit the allotted colleges and complete the admission procedure.
Draw the Activity Diagram for the above process.
Draw the state transition diagram for Online shopping of Books.
a) Narrate the guidelines for developing the test plans.
b) Discuss the framework of Persistent Objects.

Sunday, 13 November 2011

Object Oriented Analysis And Design(ooad) (2005 Pattern ) | Mca | pune university

23:57:00 Leave a Reply
Object Oriented Analysis And Design(ooad) (2005 Pattern ) | Mca | pune university
Object Oriented Analysis And Design(ooad) (2005 Pattern ) | Mca | pune university question papers with marks.

I. a) A Premier Institute has well-stocked Library providing services to various members viz., students, research scholars, faculty members, visiting staff, staff. The Library has books, journals, periodicals, magazines, newspapers and CDs. A member can borrow a book for a period of one week, journals and periodicals for two days and CD for one day. A fine of Rs. 5A per day will be charged for not reluming on time. The rules for issuing number of books are as follows :
Students - 2 books
Research scholars - 3 books
Faculty members - 5 books
Visiting staff      - 3 books


To avail the additional books every member has to obtain a special permission from their respective MOD. Draw the use case diagram and class diagram for
the above case. 15

b) Explain polymorphism and Encapsulation with examples. 5
2. Describe the four phases of RUP in detail. 10
3. Compare Grady Booch Methodology with OMT. 10
4. a) Draw a sequence diagram for sending an SMS to your friend through your
mobile phone. 5
b) Compare object oriented versus relational database. 5
5. Draw an activity diagram for different operations in ATM. 10

6. A temperature controller has been interfaced with a manufacturing unit in a factory which maintains the moderate temperature of 50°C. If the temperature goes beyond/below the moderate temperature the unit activates cooling/heating units respectively and indicates through different signals. Draw a state diagram for the above ease. 10
7. Write short notes on any two : (5x2=10)
i) CRC
ii) Any two patterns
iii) Test cases.

c++(cpp) cplusplus examples with questions

23:47:00 Leave a Reply
c++(cpp) cplusplus examples with questions
Learn  object oriented programming language with given questions and develop the logic.
a) What will be the output of following program
class a {
a()
{ cout«" 1" ; ) ~a( ) I cout « M 2 "; ( class b : a
i
b( )
{ cout « " 3"; ) ~b( )
{ coul « " 4    )
)
void main ( ) I
b obj ; I
b) Is new better than malloc ( ) ? Justify your answer.



c) Explain Ihe output of the following :
class mca
(
public : int a; private : int b; protected : int c ;
};
void main( ) I
mca obj 1;
cout « obj I.a «obj l.b « obj l.c;
}

d) Explain output :
main ( ) {
char s [ ] = "man" ; inl t ;
for(i = 0;s[i];i++)
cout «\ n« s[i] «* (s + i) «* (i + s) « i[s] ; )

e) # include < iostream.h>
void main ( )
{
inl n = 5. fact = 1 ; while (n >1) fact * = n - -;
cout « \ n « factorial value < < \ n « fact ; 1
0 Explain bool dala type in C++.



2.a) What is Object Oriented Programming ? Explain features of OOP in detail. , b) What is Class Templates 7 Explain its uses in detail.

3. a) Write a program to design a class for addition of two objects using friend
function.
b) Write a C++ program to design a class 'String' and overload operator + for concatenation of two strings.
4. What constructor and Destructor ? Write a program to demonstrate invocation of
Constructor and Destructor in multiple inheritance.
| 5.a) What is Run Time Type Information (RTTI) 7 Explain with suitable example, b) Write a C++ program illustrating NAMESPACE for addition of 2x2 matrix.
6. Define a class date with suitable constructor method. Write a member function to swap two dale objects. Write a function to validate the date.

7.a) What is library function < cmath > ? Explain with a C++ program for sqrt.
b) What is relational operator 7 Write a C++ program illustrating equal to (= =) operator.
5. Write a program in C++ that consist of two classes time 12 and time 24. The first
one maintains lime on 12-hour basis whereas the other one maintains it on 24-
hour basis. Provide conversion functions to carry out the conversions from object
of one type to another.
OR
There are UK) records present in a file. Each record containing 6-character Ilem_Codi\ 20-character ltvm_Namc and an Integer Quantity. Write a program in C++ to read these records arrange them in the ascending order and write them in the same file overwriting the earlier records.

c++(cpp) interview questions with example

23:43:00 Leave a Reply
c++(cpp) interview questions with example
c++ interview questions with example
b) What are user defined manipulators ? Illustrate with sample program.
3. a) Write a program to display the number of objects created using static data
member.
b) What is Namespace ? Explain the nested namespaces with an example.
4. What is a Constructor ? Explain its uses. Write a program to demonstrate dynamic constructor and parameterized constructor.
5. What are the rules for operator overloading ? Write a program to overload '*' operator to perform matrix multiplication.

6 Explain all types of inheritance with suitable example for each type."

7. An ABC company has the following details of their employees in the file
"emp. dat".
1) Empld
2) Emp Name
3) Emp Address
4) Emp Dept (Admin /Sales /Production / IT)
5) Emp phone
6) Emp Age.
Write a program to read the above file. Create new files such as adm.dat, Sal.dat, Pro. dat, IT.dat respectively, to store the employee details according to their department.
8. Write short notes on the following :
a) New Style Cast.
b) Standard Template Library.
c) Exception Handling.

Object Oriented Programming Using C++ | Mca Pune university

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Object Oriented Programming Using C++ | Mca Pune university
Object Oriented Programming Using C++ (New) pattern question papers with marks.


Explain what will be the output of following program
| A)
#include <iostrcam.h>
void main(void)
{ char str[] = "the boring stuff";
char *p = "that's interesting";
cout«endl«str;
cout«endl«p;
cout«endl«(void*)str;
cout«end 1 «(void')p;

B)
#include <iostream.h> #include <iomanip.h>
void main(void)
 int i = 650;
float a = 425.123;
cout«setiosflags(ios::showbase/ios::uppcrcase); cout«i«endl; cout.precision(4);
cout«setiosflags(ios::showpoint)«a;

C) #include <math.h>
 #include <sidio.h>
 main(void)
{
double number = 123.54;
 double down, up;
down = floor(number);
 up = ceil(number);
printf("originaJ number %5.21f\n", number);
printf("number rounded down %5.21An", down);
printf("number rounded up %5.21f\n", up);
 return 0;
)

D)
#include <stdio.h>
 #include <string.h>
 #include <conio.h>
main(void)
 (
char string! 101;
char *strl = "computer";
clrscr();
slrncpy(string, str 1, 5);
string[3] = W;
 printf("%s\n", string);
 return 0;
}

B) public class A
 {
int x = 4;
)
private class B :: class A
 {
int x = 20;
 cout « "x =" «x;
}
F;)
 Explain scope resolution operator:: in C++ with suitable example.


i. A) Explain difference between public, private and protected class with C++ code.   5
B) What are the types of Inheritance ? Explain with suitable example. 5
3. A) Write a program to design a class for addition of two objects using friend
Function. 5
B) Write a C++ program to overload the operator '+', which will be used to
concat the two strings. 5

4. A) Write a program to demonstrate invocation of Constructor and Destructor.      5
B) Write a C++ program to swap two integer number and two real numbers.
Use templates. 5

5. A) Explain Runtime Type Information (RTTI) with suitable example. 5
B) Write a program to accept two numbers and perform basic mathematical operation on it.
Handle the exception like zero_divide_error. 5

6. Write a C++ program that reads the data from FILE1 .txt and copy every alternate
character to FILE2.txt. 10
B. A) Write a function powcr() to raise a number x to a power y. The function takes
a double value for x and int value for y, and returns result. Use default value 2
for y to make the function to calculate squares when this argument is omitted.
Write a main that gets the values of x and y from the user. 5
B) Write a C++ program illustrating static member function. 5

8. Define a class to represent a Bank Account. Include the following
Data Members: 10
a) Name of the Depositor. c) Type of Account
b) Account No. d) Balance Amount. Member Functions: l) To Assign initial value

b) To Deposit an amount
c) To Withdraw an amount
d) To Display Name of Depositor & Balance. Define all member functions and mainQ. Generate the saving account report slip as an output.

Management Support System with marks

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Management Support System with marks
IT - 33 : MANAGEMENT SUPPORT SYSTEM
(2005 Pattern)

time : 3 Hours Max. Marks : 70

Instructions : I) Q. 1 & Q. 6 are compulsory.
2) Attempt any three from Q. 2 to Q. 5.
3) Figures to the right indicate marks,


1. a) Explain in delaiI the information requirements for personnel function using
systems approach, 15
b) Explain the application for negative feedback with an example. 5
2. "The information requirements varies according to the level of management". Comment. 10
3. Explain various software and hardware requirements towards implementation of EIS. Differentiate between EIS and DSS. 10
4. Explain conceptual and physical view of MIS. 10
5. "Simulation is not strictly a type of model". Comment. 10
6. Write short notes on (any four) : 20

a) Law of requisite Variety.
b) Sensitivity Analysis.
c) Newell Simon Model.
d) Expert Systems.
e) Value of Information.



! a) The GBD company has had a computer for several years and has added applications based on the power or persuasion of executives of different functions. They now wish to examine their status relative to the concept of management information system. The following is the list (portfolio) of applications currently on the system for sales and marketing accounting, production and information system.
Payroll
Account payables
Daily cash report
Weekly production schedule
Competitive Position Analysis (yearly)
Weekly payroll report
Monthly cash flow projection
Sales order accounting
Weekly data processing error report.
Classify these applications according to the management information system
conceptual model. 10
b) Explain the application of negative feedback in the following:
- A management reporting system using budgets. 10
I "The uncertainty and risk is high at strategic level of management." Comment      10
I Explain characteristics and limitations of human information processing. 10

4. Explain needs and characteristics of EIS. 10
5. "The determination of optional solutions can be provided through heuristic programming" Justify. 10
6. Explain about all phases of Herbert Simon model. 10
7. Write short notes on any four of the following: (4x5=20)

a) Law of requisity variety.
b) MIS and other academics disciplines.
c) Quality of information, dj Expert system, e) Operations research techniques.

Management Support System | Mss important questions

23:21:00 Leave a Reply
Management Support System | Mss important questions
Management Support System | Mss important questions
1. a) Explain in detail the information requirements for marketing functions using
systems approach.
b) Explain the application of law of requisite variety with an example.
2. Explain how quality of information improves the decision making capability of people in an organization ?
3. Explain Newell Simon model with diagrammatic representation.
4. a) How Expert system is different from conventional system ?
b) How DSS differs from MIS ?
5. "Sensitivity analysis helps in identifying value of additional information to support decision making". Comment.
6. Write short notes on any four :

a) Types of systems
b) MIS Vs.DP (Data Processing)
c) Simulation
d) Static Models
e) Herbert Simon Model.

Management Support System interview questions

23:18:00 Leave a Reply
Management Support System interview questions
Management Support System Model papers
1. a) Explain in delaiI the information requirements for personnel function using
systems approach,
b) Explain the application for negative feedback with an example.
2. "The information requirements varies according to the level of management". Comment.
3. Explain various software and hardware requirements towards implementation of EIS. Differentiate between EIS and DSS.
4. Explain conceptual and physical view of MIS.
5. "Simulation is not strictly a type of model". Comment.
6. Write short notes on (any four) :

a) Law of requisite Variety.
b) Sensitivity Analysis.
c) Newell Simon Model.
d) Expert Systems.
e) Value of Information.

: Management Support System(mss) (New Course) | Mca pune University

23:10:00 Leave a Reply
: Management Support System(mss) (New Course) | Mca pune University
 Management Support System(New Course)
Management Support System (New Course) | Mca pune University

Time : 3 Hours Max. Marks : 70

Instructions : I) Q.I and Q. 6 are compulsory.
2) Solve any 3 from Q. 2~Q. 5.
I. Explain in detail the information required in designing IT-based MIS for handling
personnel function. 20
2 Explain needs of information at different managerial levels. 10
3. Explain Newell Simon model with diagram. 10
4. Differentiate between HIS and DSS. 10
|5. Define MIS and explain structure of MIS based on management activities and
functions. 10
[ 6. Write short notes (any 4) : 20
a) Types of systems
b| Negative feedback
c) MIS Vs. Data processing
(I) F.xpert system
e) Herbert Simon Model
0 Modelling process.

How to learn computer network with Questions

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How to learn computer network with Questions
Learn computer nework by solving questions.
By solving given questions you can learn computer networks in easy way.
2) Draw neat diagram wherever necessary.
1. A) Explain in detail E-mail Protocols. 10 B) What is DNS ? Explain DNS resolving process in detail. 10
2. What is firewall ? Explain different types of firewalls and also rules and policies
on firewall. 10
3. Explain LAN accessing techniques - CSMA/CD and polling in detail.             10
4. Explain in detail DHCP & scope resolution. 10
5. Explain in detail sliding window and TCP connection. 10
6. Explain HTTP Communication in detail. 10
7. Write short notes (any four): (4x5=20)
i) Packet switching
ii) Bridge
iii) Ethernet Network
iv) Brodband ISDN
v) Problems with SNMP
vi) IPV4 Vs IPV6.

Computer Networks interview important questions

22:59:00 Leave a Reply
Computer Networks interview important questions
Computer Networks  interview  important questions 

a) Explain DHCP in detail. Explain scope resolution in DHCP with example.    
Explain various components used in building LAN.
xplain E-mail procedure using message structure, addressing, sending and
cciving.
Explain various IP addressing scheme with example.
Explain SNMP organisation and problems with SNMP.
What is firewall ? Explain firewall policies and rules.
Compare 1PV4 and 1PV6 datagram structure.
a) Circuit switching
b) Connection-Oriented networks
c) Cable transmission media
d) ISDN
e) X.25 network
f) Datalink layer in OS I model.

Computer Networks Question papers Mca Pune university

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Computer Networks Question papers Mca Pune university
 Computer Networks (New Course) (2005 Pattern).
Computer Networks(CN) Question papers Mca Pune university
l.a) What is DNS and DNS protocols ? How delegation of-authority is executed in
DNS ? 10
b) Explain TCP as a reliable protocol. 10
2. Explain REQUEST and RESPONSE in HTTP communication. 10
3. What is VPN ? Explain IP Sec Protocol's role in VPN communication. 10
4. Explain various components used in building a local area network. 10
5. Explain DHLP scope resolution with example. 10
y MB •
6. Write short notes (any four) : " (4x5=20)
i) ATM traffic management
ii) IP routing
iii) Firewall
iv) Topologies
v) Gigabyte Network
vi) Data-Link Layer in OSI model.

Probability And Combinatorics (p & c) (New) (2005 Pattern)

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Probability And Combinatorics (p & c) | Mca | Pune university









1. Solve any four :
a) Slate different approaches to probability. State axioms of probability. 5
b) State and prove binomial theorem. 5
c) Suppose a license plate contain 3 letters followed by 4 digits. How many different license plates can be printed if:

a) Only the letters are repeated ?
b) Only the digits can be repeated ? 5
d) In how many ways 6 rings be worn on 4 fingers when
i) There can be only one ring on each finger.
ii) There can be any number of rings on each finger. 5
e) Solve the recurrence relation an - "-a^, + 2()an_2 = 0 to the initial conditions
a( = 2. 5

2. a) Find how many numbers between I and 500 both inclusive are divisible by
either 2 or 3 or 7 or 11. 7
b) Prove that
C(n, 1) + C(n, 3) + .... = C(n, 0) + C(n, 2) + ... = 2"'1. 8
3. a) Determine the discrete numeric function corresponding to generating function      8
I
A(z)=
5-6z + z2
b) hind the number of non negative integer solutions of the equation X, +X2+ X3 = 28
such that 4 < X, < 21, 5 <, ^ < 22, 6 £ X3 < 23. 7
4. a) Explain the following terms with examples. 6
i) Random Variable ii) Sample Space       iii) Events


b) The following table represents the joint probability distribution of the discrete
random variable (X, Y). 8

1 2 3
1 k 5k 3k
2 2k 6k 7k
3 9k 10k Ilk


Find
i) k
ii) Conditional probability distribution of X given Y = 1
iii) Conditional probability distribution of Y given X = 2 and
iv) P(X + Y = 4)
c) Find mean and variance of Poisson distribution. 6

5. a) State Baye's theorem and solve the following. There arc 5 boys and 3 girls in
room No. 1 and there are 7 boys and 3 girls in room No. 2. A girl from one of
the two rooms laughed loudly. What is the probability the girl who laughed
loudly was from room No. 2 ? 7
b) A random variable X has following : N1 (t) = 2/(2 -1).
Find i) E(X) and ii) Var (X). 8
6. a) Find mean and variance of continuous uniform distribution. 7
b) The joint probability density function of (X, Y) is given by :
f(X,Y) =2e"xe"2y,0< x <oo,0<y <oo
■ 0 otherwise Compute :
i) P(X > I. Y < 1)
ii) P (X < Y) 8

lt/H/07/1545

[3180]-205


MT-21: PROBABILITY AND COMBINATORICS (New) (2005 Pattern)
ime: 3 Hours Max. Marks: 70



N.B.: I) Question No. I and Question No. 4 are compulsory.
2) Solve any one from Question No. 2 and 3 and any one question from Question No. 5 and Question No. 6.
3) Figures to the right indicate full marks.

a) State and prove the Principle of Inclusion and Exclusion (PIE). 7
b) How many seven-place secret codes are possible when three of the entries are letters and four are digits. Repetition of digits and letters are allowed. 7
c) Solve the following Recurrence Relation 6
I «.-Vi + 2°v2 = 2 (5)n r —,—p fipa
a) If six people attended a party, where before joining the party they deposit
their hats in a check room. After the party the hats gel mixed up and the six
gentlemen picked their hats at random manner. What is the probability that
none of them receives their own hat 7
f2n" 2
+ 2
+ +
n 0 1 n
,   J 1 J
b) Show the following by using combinatoric arguments: 8
(2n)  (nf   (n)2             (n^2
; n>r
ii)
i)

+ + fr + 2] + +
r r
V            « r r
- r + 1

) Determine the discrete numeric function for which the generating function is 4-4z + z*i
) Find the number of positive integer solutions of the equation:
X! + x2 + x3 = 21; Xj > 2, x-, > 4, x3 > 5 ) Find the coefficient of x6 y8 z'° in the expansion of (2x3 - 3y2 - 5z)16.






4. a) State moment generating function and find moment generating function of I
Gamma distribution.
b) Show that Poisson distribution is a limiting case of Binomial distribution.
c) Solve the following problem using Baye's theorem.
Of the eggs supplied to a co-operative 30%, 20%, 35% and 15% come from the poultry farms A, B, C and D respectively. Rotten eggs account for 2%M 1%, 2.5%, and 1% of the supplies by A, B, C, D respectively. An egg \m taken at random and found to be defective. What is the probability that
i) It was supplied by A     ii) It was supplied by C

5. a) State and prove mcmoryless/forgetfullness property of Exponential
Dislri bulion.
b) The joint probability function for the random variables X and Y is given below:

\ Y X \ 0 1 2


0 1/
/8 i/
/9 1/
/6
1 1/ /9 1/ /IK 1/
/v
2 1/ 1/
/6 i/
/I8

Find:
i) The marginal probability distribution of X and Y
ii) P [X> 1/ Y > 1]
iii) Are X and Y independent ?

6. a) The joint density function of (X, Y) is given by
f (x, y) = 2e~* e-2y ; 0 < x < oo
0 0 < y < oo
otherwise
compute:
i) P(X> 1, Y< 1) ii) P(X<Y)
b) Calculate mean and variance of Geometric distribution.
MT21 : PROBABILITY AND COMBINATORICS (New) (2005 Pattern)
Time : 3 Hours Max. Marks : 70

N.B.:   i) Question No. 1 and question No. 4 are compulsory.
ii) Solve any one question from question nos. 2 and 3.
iii) Solve any one question from question nos. 5 and 6.
iv) Figures to the right indicate full marks.

1. a) Stale and prove Derangement theorem.
b) A shop sells six different flavours of ice-creams. In how many ways a customer
choose 4 ice-cream cones if :
i) they are not necessarily of different flavours.
ii) they contain only 3 different flavours.
c) Solve the recurrence relation a      5a , + 6a =5".
d) In how many ways we can arrange the alphabets of the word 'ARRANGE' so that
i) Two A's arc always together.
ii) Two A's are together and two R are not together. (5 Marks each)
2. a) Find number of non-negative integer solutions of the equation
x, + x2 + x3 = 17 if 2 < x, <8, 3 <     <8f 4<x3<8. 7
b) How many ways are there to distribute eight balls into six boxes with the first two boxes collectively having atmost four balls if:
i) the balls are identical
ii) the balls are distinct. 8

3. a) Determine the discrete numeric function corresponding to generating function.        7

A(z)=-^T 4-4z + z2
b) Find coefficient of x4yV' in the expansion of (2x2 - y - 3z2)8. 4
c) If 4 Americans, 3 Frenchmen and 3 Englishmen are to be seated for dinner. How many ways they can sit on circular table if :
i) there is no restriction
ii) same nationality must sit next to each other ? 4
P.T.O.

4. a) Define the following events with illustration.
i) Exhaustive events ii) Mutually exclusive events
iii) Equally likely events iv) Independent events. 8
b) In a basket there are 12 mangoes of which 7 are good. A sample of 3 mangoes is drawn from it.- Find the expected no. of bad mangoes drawn. 6
c) Find Mean and Variance of Geometric distribution. 6
5. a) Given the following bivariate probability distribution obtain :
i) Marginal distributions of X and V
ii) Conditional distribution of X given Y = 2
iii) Condition distribution of Y given X = 0
iv) Expectation of X. 8

0

I

X5
x, x5 x5 X, x5
X,
x,
X,


b) Obtain Mean and Variance of Binomial distribution using cumulant generating
function. 7

x2 + -^  for 0<x<l,0£y £2
0 elsewhere
6. a) If a joint pdf of two dimensional random variable (X.Y) is given by f(x) =

Find : i) P (Y < X)     ii) P(Y< % / X<

S

b) Obtain moment generating function of exponential distribution. Hence find
Mean and Variance of the distribution. 7






MT 21: PROBABILITY AND COMBINATORICS (New) (2005 Pattern)

3 Hours

Max. Marks: 70



Instructions: i) Question No, I and Question No. 4 are compulsory, ii) Solve any one from Question Nos. 2 and 3. Hi) Solve any one jmm Question Nos. 5 and 6. iv) Figures to the right indicate full marks.

Solve any four:
a) State and prove the formula for Derangement of n objects.
b) A palindrome is a word thai reads the same from front and backwards, for e.g. LIRIL. How many 7-letter palindromes can be made out of English alphabets ?
In how many ways 5 cakes be given to 7 children, if
i) no child can possess more than one cake.
ii) a child can have any number of cakes.
In how many ways the 6 letters are kept in 6 envelops if two of the letters are too large for one of the envelopes.
Solve the recurrence relation an(? - oa^ + 9an = 0 given that a0 = 5, a. = 9.
b) Show that rC
l) Find how many numbers between 1 and 350 both inclusive are divisible by either 2 or 3 or 5 or 7 ?
-«C + "2c + + nc = n-'cr(l
A(z) =
5-6z + z-
b) There are eight persons. In how many different ways can they be seated around a Round table ?

a) Explain the following terms with examples.
i) Random Variable
ii) Sample Space
iii) Events





r.i <>.

13080] - 205
s/

b) The following table represents the joint probability distribution of the discrete random variable (X, Y). Find all marginal probability distributions and conditional probability distributions of X given Y.

\Y x\ 1 2 — 3
1 1/12 0 1/18
2 1/6 1/9 1/4
3 0 1/5 2/15



c) If a r.v. X is Exponentially distributed then show that
P[X > s + t/X > s] = P[X > t], for any s, t > 0 1

5. a) State Baye's theorem and solve the following. There are 4 boys and 2 girls in
room No. 1 and there are 5 boys and 3 girls in room No. 2. A girl from one of the two rooms laughed loudly. What is the probability the girl who laughed loudly was from room No. 2 ?
b) A random variable X has following: Mx(t) = 2/(2 - t) Find i) E(X) and
ii) Var(X). 8
6. a) Find mean and variance of Hypergeometric distribution. 8
k/v'x ; 0<x<4 0;       otherwise

b) The probability density function of continuous r.v. X is given as!
c
f(x) =

Find i) k
ii) Pd < X <2)
iii) Distribution function of X.