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West Bengal State University

B.A/B.SC/B.Com ( Hon., Major, General ) Examination

2010 Question Paper

Part-I (Major)

COMPUTER APPLICATION

PAPER-I

Duration : 4 Hours Maximum Marks : 100

Candidates are required to give their answers in their own words as far as practicable.

The figure in the margin indicate full marks.

1. Answer any nine questions : [9*2=18]

a) Define countable with example.

b) What do you mean by multiset ? Site an example.

C) How many vertices are there in a graph with 20 edges if each vertex is of degree 5 ?

d) How many three digit numbers can be formed using the digits 0, 4, 5, 7, 9 ?

e) What is data ?

f) What do you mean by linked list ?

g) Write outputs of X-OR and X-NOR gates.

h) Convert (EA20)16 = (?)2 .

i) What is contradiction ?

j) What is an array ?

k) What is encoder ?

l) What is multiplexer ?

GROUP-A

Answer any four [4*6=24]

2.

a) Prove or disprove : (P->(QvR)=((P->Q)v(Q->R))

Where P, Q, R are all proportional variables. [3]

b) Prove by Mathematical Induction :

6.7^n -2.3^n is divisible by 4 for all n in N [3]

3.

a) State the pigeon hole principle. Let X= {X1,X2,….X40} be a se of natural numbers.

Prove that if they are divided by 35 then at least of the remainders will be same. [3]

b) How many positive numbers less than 1000 are there which are divisible by 3, 5, 7 respectively ? [3]

4.

a) Solve the recurrence relationship using substitution method :

an-an-1-n = 0, a0 = 1. [3]

b) In a class of 80 students 60% play Football, 30% play Cricket and 30 % do not play any game. How many students play both the game? [3]

5.

a) Show that the number of edges in a complete graph with n vertices is n(n-1)/2. [3]

b) Let T is a graph with n vertices. T has no cycle and has (n-1) edges. Then show that T is a tree. [3]

6.

a) Define time complexity. Find the time complexity in terms of O for the following algorithms. [3]

i) for (i=0; i<10; i++)

{

…………………

…………………..

}

ii) for (i=2; i<=n+1; i++)

{

for (j=0;j<=n+1;j++)

{

………

………..

}

}

b) Let f : R? R is a function such that f(x) = 3x + 5. Show that f(x) is "bijective" function.[3]

GROUP – B

Answer any two questions. [2*12=24]

7.

a) Write an algorithm / program in C to insert a new node in the linked list. [6]

b) Traverse the linked list till last node is reached by an algorithm or a program.[6]

8.

a) Write Prim's algorithm to find minimum cost spanning tree. Give an example of your own.

[6+6=12]

9.

a) Write a program or algorithm to quick sort. [12]

GROUP-C

Answer any three question. [3*8=24]

10.

a) What do you mean by direct memory access(DMA) data transfer ? [4]

b) Convert decimal number 62 into binary, Hexadecimal, gray and 6 base number.[4]

11. Given that A= B'.C +B.C'. Show that

a) A' = B.C + B'.C' [2]

b) B = A'.C + A.C' [6]

using Boolean algebra.

12.

a) Show that the function F = A.B + C.D + E.F can be expressed using all NAND operators and also draw the circuit. [4]

b) Find out minimal SOP and POS using 3-variable k-map. [4]

F(X,Y,Z) = Sum(m(0,1,5,7)) + Sum(n(2,4))

13. Describe half-adder with the help of schematic diagram, circuit realization and truth table. [8]

GROUP-D

14. Write short notes on any two of the following : [2*5=10]

a) Salient features of s/w project management.

b) Coding standards and programming style.

c) Industrial standards : ISO 9002

d) Waterfall model.

West Bengal State University

B.A/B.SC/B.Com ( Hon., Major, General ) Examination

2010 Question Paper

Part-I (Major)

COMPUTER APPLICATION

PAPER-I

Duration : 4 Hours Maximum Marks : 100

Candidates are required to give their answers in their own words as far as practicable.

The figure in the margin indicate full marks.

1. Answer any nine questions : [9*2=18]

a) Define countable with example.

b) What do you mean by multiset ? Site an example.

C) How many vertices are there in a graph with 20 edges if each vertex is of degree 5 ?

d) How many three digit numbers can be formed using the digits 0, 4, 5, 7, 9 ?

e) What is data ?

f) What do you mean by linked list ?

g) Write outputs of X-OR and X-NOR gates.

h) Convert (EA20)16 = (?)2 .

i) What is contradiction ?

j) What is an array ?

k) What is encoder ?

l) What is multiplexer ?

GROUP-A

Answer any four [4*6=24]

2.

a) Prove or disprove : (P->(QvR)=((P->Q)v(Q->R))

Where P, Q, R are all proportional variables. [3]

b) Prove by Mathematical Induction :

6.7^n -2.3^n is divisible by 4 for all n in N [3]

3.

a) State the pigeon hole principle. Let X= {X1,X2,….X40} be a se of natural numbers.

Prove that if they are divided by 35 then at least of the remainders will be same. [3]

b) How many positive numbers less than 1000 are there which are divisible by 3, 5, 7 respectively ? [3]

4.

a) Solve the recurrence relationship using substitution method :

an-an-1-n = 0, a0 = 1. [3]

b) In a class of 80 students 60% play Football, 30% play Cricket and 30 % do not play any game. How many students play both the game? [3]

5.

a) Show that the number of edges in a complete graph with n vertices is n(n-1)/2. [3]

b) Let T is a graph with n vertices. T has no cycle and has (n-1) edges. Then show that T is a tree. [3]

6.

a) Define time complexity. Find the time complexity in terms of O for the following algorithms. [3]

i) for (i=0; i<10; i++)

{

…………………

…………………..

}

ii) for (i=2; i<=n+1; i++)

{

for (j=0;j<=n+1;j++)

{

………

………..

}

}

b) Let f : R? R is a function such that f(x) = 3x + 5. Show that f(x) is "bijective" function.[3]

GROUP – B

Answer any two questions. [2*12=24]

7.

a) Write an algorithm / program in C to insert a new node in the linked list. [6]

b) Traverse the linked list till last node is reached by an algorithm or a program.[6]

8.

a) Write Prim's algorithm to find minimum cost spanning tree. Give an example of your own.

[6+6=12]

9.

a) Write a program or algorithm to quick sort. [12]

GROUP-C

Answer any three question. [3*8=24]

10.

a) What do you mean by direct memory access(DMA) data transfer ? [4]

b) Convert decimal number 62 into binary, Hexadecimal, gray and 6 base number.[4]

11. Given that A= B'.C +B.C'. Show that

a) A' = B.C + B'.C' [2]

b) B = A'.C + A.C' [6]

using Boolean algebra.

12.

a) Show that the function F = A.B + C.D + E.F can be expressed using all NAND operators and also draw the circuit. [4]

b) Find out minimal SOP and POS using 3-variable k-map. [4]

F(X,Y,Z) = Sum(m(0,1,5,7)) + Sum(n(2,4))

13. Describe half-adder with the help of schematic diagram, circuit realization and truth table. [8]

GROUP-D

14. Write short notes on any two of the following : [2*5=10]

a) Salient features of s/w project management.

b) Coding standards and programming style.

c) Industrial standards : ISO 9002

d) Waterfall model.

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