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Monday, October 31, 2011

Fin622 Assignment No. 1 Fall 2011 solution

ABC corporation stock is selling for Rs. 150 per share according to Karachi stock exchange market summary. A rumor about the company has been heard that the firm will make an exciting new product announcement next week. By studying the industry, it is being concluded that this new product will support a growth rate of 20% in dividend for two years. After that it is expected that the growth rate in dividend will decline to 6% and remains same onwards. The firm currently pays an annual dividend of Rs. 4.

The rate of return on stocks like ABC Corporation is 10%.

Required:

I. Find out the values for D1, D2 and D3 (8 Marks)

II. What will be the price of stock (P2) at the end of year 2? (4 Marks)

III. What will be the present value (P0) of stock? (6 Marks)

IV. Should we buy stocks of ABC Corporation at Rs. 150? (2 Marks)

Solution

Find out the values for D1, D2 and D3

D1= 4 (1+0.2) =4.8

D2= 4.8 (1+0.2) =5.76

D3=5.76 (1+0.05) =6.11

What will be the price of stock (P2) at the end of year 2?

P2= 5.76 (1+0.2)/ .1-0.05

P2=138.24

What will be the present value (P0) of stock?

PO= 4.8/(1+.1)1 + 5.76/(1+.1)2 + 6.11/(1+.1)3 + 128.31/(1.1)3

= 110

Should we buy stocks of ABC Corporation at Rs. 150

As the present value of the stock is less then the current selling price so the stock should not be purchased.

Saturday, October 29, 2011

CS401 Assignment No. 1 Fall 2011 solution


Question No. 1:

a)

Suppose your computer has a processor with 24-bit address lines. What is maximum amount of memory that can be attached in your system? (Show the step(s) for calculation of maximum addressable memory) (2.5 marks)

Solution: -

Accessible memory addresses = 2number of address bits

224 = 16777216 bytes

16777216 / 1024 = 16384 KB

16384 / 1024 = 16 MB

b)

How many address bits are required for accessing 1GB RAM? (Show the step(s) for calculation of required address bits) (2.5 marks)

Solution: -

As you know 1GB means 1024MB so we can write it as

1GB = 1024 x 1MB

As you know that 1MB is 220

So we can write the expression as

1024 x 220

This can be further simplified as

210 x 220

=230

Hence, 30 address lines are required to access 1GB RAM.

Question No. 2:

What are the contents of memory locations 0151, 0152, 0153, ………….,0158 if 0151 is starting address for Label1. (1 mark for each location)

Label1: dw 8494

db 42

dw 54

dw 7500

db 01

Solution: -

Memory location Contents

0151 94

0152 84

0153 42

0154 54

0155 00

0156 00

0157 75

0158 01

Question No. 3:

a)

Calculate physical address using the following segment offset pairs. (1 mark each)

1. 00EA:02A4

2. 0100:AA23

3. D3B8:F222

4. 00A0:1234

5. 8FEf:0FFF

Solution: -

Memory Location

Contents

0151

94

0152

84

0153

42

0154

54

0155

00

0156

00

0157

75

0158

01

Question No. 3:

a)

Calculate physical address using the following segment offset pairs. (1 mark each)

1. 00EA:02A4

2. 0100:AA23

3. D3B8:F222

4. 00A0:1234

5. 8FEf:0FFF

Solution: -

1)

00EA0

002A4 +

_______

01144 = physical address

2)

01000

0AA23 +

_______

0BA23 = physical address

3)

D3B80

0F222 +

______

E2DA2 = physical address

4)

00A00

01234 +

________

01C34 = physical address

5)

8FEF0

00FFF +

_________

90EEF = physical address

b)

What is effective address generated by the following instructions? Every instruction is independent of others. vusolutions Initially bx = 0x0101, bp=0x0222, si=0x1234, var1=0x1771 (1 mark each)

1. mov ax, [bx+si]

2. mov ax, [bx+100] (100 is in decimal)

3. mov ax, [bp+si]

4. mov ax, [var1+bp]

5. mov ax, [si+var1]

Solution: -

1)

Effectice address = [bx+si]

= [0101 + 1234]

= [1335]

2)

Effectice address = [bx + 100]

After converting 100 into hexadecimal

Effectice address = [bx + 64]

= [0101 + 64]

= [0165]

3)

Effective address = [bp+si]

= [0222 + 1234]

= [1456]

4)

Effective address = [var1+bp]

= [1771 + 0222]

= [1993]

5)

Effective address = [si + var1]

= [1234 +

CS402 Assignment No. 1 Fall 2011 solution


Theory of Automata

CS402

ASSIGNMENT NO.1

Total Marks= 20 (4+4+4+4+4)

Assignment Submission Deadline

Your assignment must be uploaded before or on 31-10-2011 [upload your assignment well before due date to avoid any assignment uploading related issues]

Rules for Marking

It should be clear that your assignment will not get any credit if:

o The assignment is submitted after due date

o The assignment is copied

Objectives

Objectives of this assignment are to make students able to understand the following concepts,

o Basic concepts clarification

o Recursive Definition of a language

o Regular Expression

o Finite Automata

Question No.1 Basic Concepts [Sets, Letters, Valid Alphabet, Languages, Strings and Words]

a. Which of the following are strings generated from alphabet Σ = {a, b}

i. abba

ii. baa$a

iii. abc.

iv. ba?

v. b.bba

b. Which of the following are valid words for language of all strings ending with bab defined for alphabet Σ = {a, c , bab}

i. acccba

ii. cccbaa

iii. cccbab

iv. babbb

v. baaab

Question No.2 Defining Languages [Using Recursive Definition, Re’s, Fa’s]

Give recursive definitions of following languages defined over alphabet Σ = {a, b}

i. Having all strings starting with b and having length greater than 2

ii. NOT having ab at any place.

Question No.3 Regular Expressions

Give Regular Expression for each of the following language defined over alphabet Σ = {a, b}

i. Even Length strings ending with b

ii. Strings with b’s count multiple of three

Question No.4 Models To Recognize Languages (Fa’s)

Give Finite Automata (FA) for each of the following language defined over alphabet Σ = {a, b}

i. Language having all strings NOT containing aa at any place

ii. Language of all strings NOT STARTING with bb

Question No.5 Models To Recognize Languages (Nfa’s)

Give Non Deterministic Finite Automata (NFA) for each of the following language defined over alphabet Σ = {a, b}

i. Language of all strings STARTING WITH bba

ii. Language having all strings NOT having even no of a’s and b’s

You can view the demo video in file,http://vulms.vu.edu.pk/Courses/CS402/Downloads/Assignment1.00.zipto see how to make FA in MS Word.

Note:

Please keep in view the following points while attempting any question:

• Where OR is used in the description of a language it means that expressions on both sides of ‘OR’ are parts of the language.

• Where NOT is used in the description of the language it means that language includes all strings except described in the ‘NOT’ condition, for example

language NOT starting with a, means all strings not having a in the start (you have to evaluate yourself what kinds of strings are these).

Assignment Uploading Instructions:

o Upload single word file having solutions for all parts as well as chart images.

o You can crop and compress images in the word file by double clicking on an image and selecting compress all images option to decrease file size before

uploading it.

Appendix:

Definition of Set:

A set can be defined as follows:

“Non repeating collection of elements”

Example Sets:

i. {car, bus }

ii. {table, chair , stand}

iii. {basket ,eggs}

iv. { ^, #, *, / }

However {car, car, bus} is NOT a set according to its definition.

Solution:


Question No.1 Basic Concepts [Sets, Letters, Valid Alphabet, Languages, Strings and Words]
a. Which of the following are strings generated from alphabet Σ = {a, b}
i. abba
ii. baa$a
iii. abc.
iv. ba?
v. b.bba

b. Which of the following are valid words for language of all strings ending with bab defined for alphabet Σ = {a, c , bab}
i. acccba
ii. cccbaa
iii. cccbab
iv. babbb
v. baaab


Question No.2 Defining Languages [Using Recursive Definition, Re’s, Fa’s]
Give recursive definitions of following languages defined over alphabet Σ = {a, b}

i. Having all strings starting with b and having length greater than 2

Answer. { baa, bab, bba, bbb, bba, baab, ….. .. }

ii. NOT having ab at any place.


Answer. {^, a, b, ba, bab, bba, bbb, baa, bbba,…..}

Question No.3 Regular Expressions
Give Regular Expression for each of the following language defined over alphabet Σ = {a, b}

i. Even Length strings ending with b

Answer. { ^ ,ab, bb, aabb,abab, bbbb, aaaabb, aaabab, ……}

ii. Strings with b’s count multiple of three

Answer. {^, bbb, bbbbbb, bbbbbbbbb, bbbbbbbbbbbb, bbbbbbbbbbbbbbb,
bbbbbbbbbbbbbbbbbb, bbbbbbbbbbbbbbbbbbbbb,………}


Question No.4 Models To Recognize Languages (Fa’s)
Give Finite Automata (FA) for each of the following language defined over alphabet Σ = {a, b}

i. Language having all strings NOT containing aa at any place

Answer. { ^, a, b, ab, ba, abb, bab,bba, baba, abbb, ….}

ii. Language of all strings NOT STARTING with bb

Answer. { ^, a, b, aab, aaab, abab, aabab, …….}

Question No.5 Models To Recognize Languages (Nfa’s)
Give Non Deterministic Finite Automata (NFA) for each of the following language defined over alphabet Σ = {a, b}

i. Language of all strings STARTING WITH bba

Answer. { ^, bba, bbaa, bbaba, bbaab, bbab, bbabb, …}

ii. Language having all strings NOT having even no of a’s and b’s

Answer. {^, a, b, aaab, bbba, ababab, aaaaab, bbbbba, ……}

Friday, October 28, 2011

CS201 Assignment No. 1 Fall 2011 solution

Assignment No. 01

Semester: Fall 2011

CS201: Introduction to Programming Total Marks: 20

Due Date:02/11/2011

Problem Statement: Virtual Restaurant

You are required to write a program for BILLING SYSTEM of a virtual restaurant. The basic idea is that by entering the meal price, your billing system will calculate the Sales Tax, Total amount and Complement offer upon that meal. The program will process the billing of undetermined number for customers. At the end, program will show sum of total amount of all the customers.

Detailed Description:

Billing System should work as under:

> You are required to take meal price as input from user.

> After getting this input, program will calculate the sales tax on it as given below:

Meal Price Sales Tax applicable

Less than or equal to 1000 No sales Tax on it.

Greater than 1000 and less than or equal to 2000 1% of meal price.

Greater than 2000 2% of meal price.

> After calculating the sales tax, program will calculate and display the total amount of the meal according to given formula:

Total Amount = Meal_Price + Sales_Tax

> Now, program will prompt to serve the complement sweet dish to customer on the basis of total amount as given below:

Total Amount Sweet Dishes

Less than 1000 Candies

Greater than or equal to 1000 and less than 2000 Sweet Bread

Greater than or equal to 2000 and less than 3000 Pudding

Greater than or equal to 3000 and less than 4000 Cake

Other amounts Trifle

> After displaying the information of one customer, the program should ask the user if he/she again wants to process the bill of another customer. The user will be given two options. If user selects "Y or y", the program will start the processing of another customer. If user selects "N or n", the billing system exits.

> Before exiting from billing system, this program should display the total number of customers it processed, and sum of total amount of all the customers.

:::::::

You are required to write a program for BILLING SYSTEM of a virtual restaurant. The basic idea is that by entering the meal price, your billing system will calculate the Sales Tax, Total amount and Complement offer upon that meal.

#include

#include

int main()

{

int price;

cout << "Please enter meal price? ";

cin >> price;

float saleTax;

if(price<=100)

{

saleTax = 0.0 * price;

}

else if(price <= 200)

{

saleTax = 0.1 * price;

}

else

{

saleTax = 0.2 * price;

}

int totalAmount;

totalAmount = price + saleTax;

cout << "The total price of Meal is = " << totalAmount << endl;

getch();

}

Mgt411 Assignment No. 1 Fall 2011 solution


Semester “Fall 2010”

“Money & Banking (MGT411)”

Assignment No. 01 Marks: 20

Mr. Naeem is working as a finance manager at Superior Textile Mills Limited, after completing his MBA (Finance) from Virtual University of Pakistan.

Recently, he got married and shifted his family in a rented house near the office. Paying monthly rent is a painful experience and in this way he cannot save much for his future needs. Therefore, he is planning to purchase his own house for avoiding monthly rental expense. For this purpose he is expecting to sell share in his native house for Rs. 1,500,000/- which is not a sufficient amount to buy house in a big city. After considering various areas in Faisalabad city, he chose Model Town for his desired future residency. Based on the house prices data in that area, he learned that an average two bed room house currently costs Rs.2,400,000/-. So he has to set aside some funds for the next eight years so that he may be able to purchase his own house after having sufficient funds.

As Mr. Naeem is planning to purchase the house after eight years, so it is quite clear that the prices of the houses will not remain the same overtime. In order to estimate the rate at which the house price will increase he considered the historical price appreciation data in that area and resulted that house prices appreciated at the rate of 4% per annum.

Mr. Naeem is planning to invest the funds that will be devoted for purchasing the house, in a portfolio of investment. He feels that this investment portfolio containing stocks, bonds and govt. securities will give him the rate of return of 9% p.a.


SOLUTION


Please confirm this solution before submitting


Q#1: Considering the fact that the vu39.com house prices will grow at the rate of 4% per annum, what will be the future house price of the house Mr. Naeem intends to buy after 8 years


FV = PV (1+i )n
FV = 1,500,000 (1+0.04)8
FV = 1,500,000 (1.04)8
FV = 1,500,000 (1.3685)
FV = Rs. 2,052,853/-


Q#2: Based on the answer from Q#1(FV), how much amount Mr. Naeem should invest today (which earns 9% rate of return) so that he may be able to purchase his house after 8 years.


2,052,853 = PV (1+0.09)8
2,052,853 = PV (1.09)8
2,052,853 = PV (1.9925)
PV = 2,052,853 / 1.9925
PV = Rs. 1,030,290/-


Q#3: Assume the vusolutions house prices appreciate at the rate of 6% per annum instead of 4% then how much he should invest today in order to be able to purchase the house after 8 years.


FV = 1,500,000 (1.06)8
FV = 1,500,000 (1.5938)
FV = Rs. 2,390,772/-
2,390,772 = PV (1.09)8
2,390,772 = PV (1.9925)
PV = 2,390,772 / 1.9925
PV = Rs. 1,199,885/-


Q#4: If Mr. Naeem decides to deposit in less risky certificate of deposits earning vusolutions only 5% p.a. then how much funds he has to deposit in his bank to be able to purchase the house after 8 years.


2,052,853 = PV (1.05)8
2,052,853 = PV (1.4775)
PV = 2,052,853 / 1.4775
PV = Rs. 1,389,409/-


Q#5: If Mr. Naeem decides to invest in more risky growth stocks earning 12% rate of return then how much funds he has to invest to purchase his house after eight years.


2,052,853 = PV (1.12)8
2,052,853 = PV (2.4759)
PV = 2,052,853 / 2.4759
PV = Rs. 829,137/-