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Loyola College M.C.A. Computer Application April 2008 Mathematics For Computer Applications Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

XZ 30

M.C.A. DEGREE EXAMINATION – COMPUTER APPLICATION

FIRST SEMESTER – APRIL 2008

          MT 1902 / CA 1804 – MATHEMATICS FOR COMPUTER APPLICATIONS

 

 

 

Date : 05/05/2008            Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

SECTION A

Answer ALL the questions.                                                                         (10 x 2 = 20)

 

  1. Define least upper bound of a poset.
  2. Define a Lattice.
  3. What are the logic operators?
  4. Construct a phrase structure grammar for the language .
  5. Define context-sensitive language.
  6. For a DFA ,

show that the string 011011 is in L(M)

  1. State the Pigeon hole principle.
  2. Draw the Hasse diagram for the divisors of 32.
  3. Define a bipartite graph with an example.
  4. Prove that every cyclic group is abelian.

 

SECTION B

Answer ALL the questions.                                                                         (5 x 8 = 40)

 

  1. (a) Prove that the complement of any element ‘a’ of a Boolean algebra is uniquely determined.           Prove also that the map  is an anti – automorphism of period  2 and  satisfies                 (a Ú b)¢ = a¢ Ù b¢, (a Ù b)¢ = a¢ Ú b¢, a¢¢ = a.

(or)

(b) Discuss ‘negation’ and explain a method of constructing the truth table for P Ú ùQ and (P Ú Q) Ú ùP

 

  1. (a) Write a short note on principal conjunctive normal form and construct an equivalent formula             for ù.

(or)

(b) For a grammar  where P consists of the following production:

Then show that.

 

  1. (a) Let L be a set accepted by a non-deterministic finite automaton. Then prove that there exists a deterministic finite automaton that accepts L

(or)

(b) (i) Construct an equivalent deterministic automaton for a given non-deterministic automatonwhere .

(ii) If R and S are equivalence relations on the set X, prove that R Ç S is also an equivalence relation on X.

 

  1. (a) Prove that the equivalence relation ~ defined on the set A decomposes the set A into mutually disjoint equivalence classes.

(or)

(b) (i) A computer password consists of a letter of the alphabet followed by 3 or 4 digits. Find the total number of passwords that can be formed and the number of passwords in which no digit repeats.

(ii) Find the minimum number of students in a class to be sure that four out of them are born in the same month.

 

  1. (a) (i) Prove that a subgroup N of a group G is a normal subgroup of G iff the product of two left cosets of N in G is again a left coset N in G.

(ii) Define ring with an example.

(or)

(b) Prove that the following statements are equivalent for a connected graph G.

  • G is Eulerian
  • Every point of G has even degree
  • The set of edges of G can be partitioned into cycles.

 

SECTION C

Answer any TWO questions.                                                                       (2 x 20 = 40)

 

  1. (a) Explain conditional and bi-conditional connectives with an example.

(b) Define a Non – Deterministic Finite automata.

(c) For the non deterministic finite automaton,

 

give the transition table and show that 0100110 is in L (M).

 (10 + 2 + 8)

 

  1. (a) State and prove pumping lemma for regular sets.

(b) List any four applications of pumping lemma.

(c) Prove that if  and  be one-to-one onto functions, then  is also one-to-one onto and .

(10 + 4 + 6)

 

  1. (a) Show that in a graph G, any u – v walk contains a u – v path.

(b) Prove that a closed walk of odd length contains a cycle.

(c) State and prove Lagrange theorem.                                                            (4 + 4 + 12)

 

 

 

 

Loyola College M.C.A. Computer Application Nov 2008 Mathematics For Computer Applications Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

AB 31

M.C.A. DEGREE EXAMINATION – COMPUTER APPLICATION

FIRST SEMESTER – November 2008

    MT 1902 – MATHEMATICS FOR COMPUTER APPLICATIONS

 

 

 

Date : 11-11-08                 Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

Part A (Answer ALL questions)                                                                              2 x 10 = 20

  1. Define Lattice homomorphism between two lattices.
  2. With usual notations prove that (i)(ii) .
  3. Define context free grammar.
  4. What is the difference between deterministic finite automata and non-deterministic finite automata?
  5. Let G = (N, T, P, S), where N = {S}, T = {a}, P: {S → SS, S → a}. Check whether G is ambiguous or unambiguous.
  6. Give a deterministic finite automata accepting the set of all strings over {0, 1} containing 3 consecutive 0’s.
  7. If R and S be two relations defined by and , then find

RS, RR and R.

  1. Let and ,. Write the matrix of

of R and sketch its graph.

  1. Define ring with an example.
  2. State Kuratowski’s theorem.

Part B (Answer ALL questions)                                                                              5 x 8 = 40

  1. (a) Show that De Morgan’s laws given by and  hold in a

complemented, distributive lattice.

(OR)

(b) Let  be a lattice. For any  prove the following distributive inequalities:

) and .

  1. (a) Show that L(G) = is accepted by the grammar G = (N, T, P, S) where N = {S,A} T = {a, b}, P consists of the following productions: S → aSA, S → aZA, Z → bZB, Z → bB, BA → AB, AB → Ab, bB → bb, bA→ ba.

(OR)

(b) Let the grammar G = ({S,A}, {a, b}, P, S) where P consists of S →aAS, S → a,               A → SbA , A → SS, A → ba. For the string aabbaa find a

(i) leftmost derivation

(ii) rightmost derivation

(iii) derivation tree.

  1. (a) (i) Define deterministic finite state automata.

(ii) Draw the state diagram for the deterministic finite state automata,                            M =   where Q =, Σ ={a, b}, F =  and δ is defined as follows:

    δ     a     b

 

Check whether the string bbabab is accepted by M.                                            (3+5)

(OR)

(b) Given an non-deterministic finite automaton which accepts L. Prove that there exists a deterministic finite automaton that accepts L.

  1. (a) (i) Write short on Hasse diagram.

(ii) Let  and relation  be such that  if x divides y. Draw the

Hasse diagram of .                                                                                       (4+4)

(OR)

 

(b) (i) Show that n3+2n is divisible by 3 using principle of mathematical induction.

(ii) If the permutations of the elements of {1,2,3,4,5} be given by

, then find

α -1-1.                                                                                        (4+4)

 

 

  1. (a) Prove that there is a one- to-one correspondence between any two left cosets of H in G.

 

(OR)

 

(b) (i) If G is a graph in which the degree of every vertex is atlest two, then prove that G

contains a cycle.

(ii) Prove that the kernel of a homomorphism g from a group  to  is a subgroup

of  .                                                                                                                (4+4)

 

 

Part C (Answer ANY TWO questions)                                                                  2 x 20 = 40

16.(a)  Let G be (p,q)graph, then prove that the following statements are equivalent:

(i) G is a tree. (ii) Every two vertices of G are joined by a unique path (iii) G is connected

and  (iv) G is acyclic and p =  q+1.

(b) Let H be a subgroup of G. Then prove that any two left cosets of H in G are either

identical or have no element in common.                                                                  (14+6)

 

  1. (a) Let be a Boolean Algebra. Define the operations + and · on the elements of B by,

 

. Show that  is a boolean ring with identity 1.

(b) Prove that every chain is a distributive lattice.                                                           (15+5)

  1. (a) If G = (N, T, P, S) where N = {S, A,B}, T = {a,b}, and P consists of the following rules:

S → aB, S → bA, A → a, A → aS, A → bAA, B →b, B → bS, B → aBB. Then prove the following:

  • S w iff w consists of an equal number of a’s and b’s
  • A w iff w has one more a than it has b’s.
  • B w iff w has one more b than if has a’s

 

(b) State and prove pumping lemma.                                                                            (10+10) 

 

 

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Loyola College M.C.A. Computer Application Nov 2008 Accounting & Financial Management Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

QB 27

M.C.A. DEGREE EXAMINATION – COMPUTER APPLICATION

THIRD SEMESTER – November 2008

    CO 3901  – ACCOUNTING AND FINANCIAL MANAGEMENT

 

 

 

Date : 14-11-08                 Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION –A

 

ANSWER ALL THE QUESTIONS                                                                                   (10 X 2 =20)

1.What is meant by convention of conservatism ?

  1. Distinguish between capital expenditure and revenue expenditure ?
  2. What is meant by accounting ratio ?
  3. Define financial management ?

 

CHOOSE THE BEST ANSWER

  1. If 60 units of a product cost Rs.1800 and 40 units cost Rs 1200 the variable cost per

unit is ___________?

  1. a) Rs.40 b) Rs.10           c) Rs.30           d) Rs.20
  2. If 20 units of a product costs, Rs.2500 and 50 units costs Rs.3400 to produce, the

linear cost function is :

  1. a) 50x +3900 b)30x +1900    c) 20x +5000   d) 10x +900
  2. a) Which of the following is correct ?
  3. a) Assets = Liabilities – Capital          b) Assets = Capital – Liabilities
  4. c) Assets = Liability + Capital
  5. b) The ideal current ratio is :
  6. i) 4:1 ii) 3:1   iii) 2:1  iv) 1:1

 

STATE IF THE FOLLOWING  STATEMENTS  ARE True or False

8.a) The appropriate objective of an enterprise is the maximization of owner’s wealth.

  1. b) Withdrawal of money by the owner is an expenses for the business.
  2. a) P/E indicates the number of times the EPS is covered by its market price.
  3. b) The gain from sale of capital assets is an operating income.
  4. a) Sales budget is a functional budget.
  5. b) Low inventory turnover ratio indicates brisk sales.

 

SECTION – B

 

ANSWER ANY FIVE QUESTIONS                                                                                             (5 X 8 = 40)

 

  1. What is book – keeping ? Explain the fundamental accounting concepts and

conventions.

  1. Define the term Ratio. Explain the advantages and limitations of ratio analysis.
  2. Enumerate the objectives of financial management.

 

 

  1. Write up a Three – Column Cash Book

2004 Sep .  1 Cash in hand                                                                    3000

Cash at bank                                                                    200

4  Received a cheque  from Mr.Daniel                               185

Allowed him discount                                                     15

4 Deposit in to the bank                                                              500

5  Purchased furniture  for cash                                                1700

9 Given a cheque  to Mr.Knocks                                              1280

Received discount                                                                     40

18 Received a by cheque  from Mr.Bull                                   4000

19 Paid sundry expenses in cash                                                  30

23 Paid to Sri John in cash Rs.190, Received discount               10

24 Withdrew from bank for office cash                                     100

 

 

  1. The comparative Balance Sheet of M/s.RAGHU brothers for the two years

were as  follows :

Liabilities                  2004            2005      Assets                2004             2005

Rs.               Rs.                                   Rs.                 Rs.

Capital                       1,50,000  1,75,000    Building            1,10,000     1,50,000

Loan from Bank         1,60,000  1,00,000    Machinery         2,00,000    1,80,000

Creditors                        90,000  1,00,000    Stock                    50,000       45,000

Bills payable                 50,000     40,000    Debtors                70,000       80,000

Loan from S.B.I                __        65,000    Cash                     20,000      25,000

————————-                           ————————–                                                                             4,50,000    4,80,000                              4,50,000     4,80,000

————————–                           ————————-

Additional Information  :

1.Net profit for the year 2005 amounted to Rs .60,000.

2.During the year a machine whose book value  Rs.15,000  was sold for

Rs.13,000.

You are required to  Prepare a Cash Flow Statement.

 

  1. From the following information calculate the net present  value of the two

projects and suggest which of the two projects should be selected assuming a

discount rate of  10 %:

Project  X               Project  Y

Initial investment                    Rs.20,000                    Rs.30,000

Estimated life                             5 years                         5 years

Scrap value                              Rs.1000                       Rs.2000

The profit before depreciation and after tax is as follows:

Years               1                      2                      3                      4               5

Project  X        5,000        10,000               10,000            3,000           2,000

Project  Y        20,000      10,000                 5,000            3,000           2,000

P.V  factor  @ 10%  .909      .826               .751                .683            .621

 

  1. RIL ltd. Plans to sell 1,10,000 units of a certain product line in the first fiscal

quarter. 1,20,000 units in the second quarter,1,30,000 units in the third quarter,

1,50,000 units  in the fourth quarter and 1,40,000 units in the fifth quarter.

At the  beginning of the first quarter of the current year, there are 14,000

units of the product in stock. At the end of  each quarter, the company plans to

have an inventory equal to one- fifth of the sales  for the next fiscal quarter.

 

How many units must be manufactured in each quarter of  the current year.

 

18.Record the following transactions in the book of Journal .

Rs

April   2  commenced business with cash  Rs. 34,000 and

a bank balance of Rs.20,000

5   Withdrawn from bank for personal use                       6,000

12  Cash paid to Rahim

(in full  settlement of his a/c for Rs2300).                    2,000

14 Cash received from  Antony                                        6,000

15  Purchased machinery on credit from toy Traders       11,000

25   Paid salary                                                                     2,000

27   Sold goods to Ram Babu  on credit                                500

28    Purchased goods for cash by cheque                          12,000

 

 

 

 

 

 

 

 

 

 

 

SECTIION – C

 

ANSWER ANY TWO QUESTIONS                                                                                 (2 X 20 = 40)

 

19.A company expects to have Rs,37,500 cash in hand on 1st april and requires you to

prepare an estimate of cash position during three months ,April ,May and June.

The following information is supplied to you:

Sales                Purchases        wages              office expenses

February  75,000                45,000             16,500             10,500

March      84,000               48,000             18,000             10,500

April        90,000                52,500             19,500             11,250

May        1,20,000              60,000             24,750             12,570

June       1,35,000               60,000             28,250             14,000

Other information:

  1. Period of credit allowed by suppliers 2 month
  2. 20% sales is for cash and period of credit allowed to customers is 1month
  3. Delay in payment of all expenses 1 month.
  4. Income tax of Rs.57,500 is to be paid in June
  5. The company is to pay dividend to share holders in the month of April is

Rs.37,500 and a plant has been ordered to be received and paid in May  ,it

will cost Rs.1,20,000.

 

 

  1. Sale price Rs.20per unit

Variable manufacturing cost   Rs.11 per unit

Variable selling cost                Rs.3   per unit

Fixed factory overheads                     Rs.5,40,000

Fixed selling cost                                Rs.2,52,000

Calculate:

  1. BEP
  2. sales required to earn a profit of rs.60,000
  3. sales required to earn a profit of 10% on sales
  4. Profit when sales are Rs.20,00,000
  5. if company reduces  its selling price by 10%, how does the revised selling

price affect  the   break even point and the profit –volume ratio?

 

  1. The following figure relate to ITC ltd. for the year ended 31-03-06

Trading and profit /loss account

 

To  opening stock          75,000           By sales                       5,00,000

To purchases               3,25,000          By closing stock          1,00,000

,,Administration exp.      40,000         ,,dividend received          9,000

,,Selling exp.                  25,000          ,,profit on sale of shares 11,000

,,loss on sale of assets      5,000

,,Net profit                 1,50,000

———                                                 ———–

Calculate a. Gross Profit Ratio.         B. Net profit ratio

  1. operating ratio                 d. operating profit ratio

 

Following is the balance sheet of ITC ltd .as at 31st march 2006.

Liabilities                    Rs.                   Assets                          Rs.

Equity share capital            2,00,000 Cash at bank                           18,000

10%pref. share capital        2,00,000 Bills receivable            60,000

8% Debenture                     80,000  Short term investment 40,000

9%public debts                   40,000  Debtors                    1,40,000

Bank overdraft                    80,000  Stock                            80,000

Creditors                           1,34,000 Furniture                     60,000

Proposed dividend                20,000  Machinery               6,40,000

Reserves                             3,00,000  Goodwill                    76,000

Provision for tax                   40,000  Prepaid  expenses       20,000

Profit / loss a/c                      40,000

———-                                    ————

11,34,000                                11,34,000

————                                 ———–

Compute   :   Short Term  and  Long Term solvency ratios

 

 

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Loyola College M.C.A. Computer Application April 2009 Business Communication Question Paper PDF Download

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      LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.C.A DEGREE EXAMINATION – COMPUTER APPLICATION

NM 32

FIRST SEMESTER – April 2009

EL 1900 – BUSINESS COMMUNICATION

 

 

 

Date & Time: 04/05/2009 / 1:00 – 4:00  Dept. No.                                                  Max. : 100 Marks

 

 

SECTION – A                                   5 x 4 = 20 MARKS

  1. What is accent? How is it very import in speaking English?
  2. Place the stress marks ( ’ ) on the appropriate syllables of the following words.
  • re / mem / ber (2) Va / Ca / tion         (3) pe / cu / li / ar

(4) e / co / no / my       (5) Co/ llege                (6) Stu / pen / dous      (7) doc / tor

(8) pro /fess / or.

  1. How is dipththong different from Vowel?
  2. What is register in communication?
  3. What have you understood about neutral accent?

SECTION – B                                   5 x 6 = 30 MARKS

  1. What are the differences between Oral and Written communication?
  2. How does Writing play an important role in business?
  3. Write a short note on body language in communication?
  4. Describe the structure of formal letters with examples.
  5. Write short notes on agenda and minutes in meeting.

SECTION – C                                   5 x 10 = 50 MARKS

  1. Write a covering letter and CV in response to the following advertisement.

 

 

 

 

 

 

 

 

 

 

  1. Write short notes on the following.
  • Symposium 2) Conference             3) Convention             4) Panel – discussion.
  1. Write an essay on the principles of effective writing in business communication.
  2. Imagine that you are a sales manager of a company which manufactures furniture. Now the company’s sale is on the decrease. You are asked to submit a report about this trend. Prepare a report.
  3. What is the importance of memo in business?

Imagine that you are a manager of a Company, and prepare a memo suspending an employee for his misbehaviour with women staff.

 

 

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