COMPUTER SCIENCE PAPER 1 THEORY YEAR 2008

Transcription

1 COMPUTER SCIENCE PAPER 1 THEORY YEAR 2008 PART I Answer all questions in this part Question 1. a) State the two complement properties of Boolean Algebra. Verify any one of them using the truth table. b) Simplify the following Boolean expression stating clearly the laws used for simplification at each step. XY + XZ + XYZ c) Find the complement of: X.(Y Z + YZ) d) Convert the following Product of Sum form into its corresponding Sum of Product form:- F(X,Y,Z)= π(2,4,6,7) e) Draw the truth table of the propositional logic expressions p q and p q. [2 x 5 = 10] Question 2. a) Mention two points which distinguish a static data member from an ordinary data member in a class. b) Convert the following infix expression to its postfix form:- A / (B+C) +D * (E-F) c) What do LIFO and FIFO stand for? Name a data structure that follows LIFO principle and one that follows FIFO principle? d) A two dimensional array defined as x[3 6, -2 2] requires 2 bytes of storage space for each element. If the array is stored in row major order, determine the address of X[5,1], given the base address as e) List the nodes in the tree given below in : i) Preorder ii) Postorder [ 2 x 5 = 10] Question 3. (a) The following is a function of some class. It returns 1 if the number is a perfect number otherwise it returns 0. /* A perfect number is a number which is equal to the sum of its factors other than the number itself. */ intperfectno(int n) int?1?; for(int j=1;?2?;j++) if(?3?) sum?4?;

2 if(?5?) return 1; else return 0; i) What is the expression at?1? ii) What is the expression at?2? iii) What is the expression at?3? iv) What is the expression at?4? v) What is the expression at?5? [1 x 5 = 5] (b) The following functions show() and calling() are a part of some class. Assume that the parameter n is greater than 1 when the function is invoked. It returns the value 1when true otherwise it returns 0. Show the dry run/working. void calling() int f=2; show(n,f); int show(int n, int f) if(n==f) return 1; if(n%f==0 n==1) return 0; else return(show(n,f+1)); i) What will the function show() return when the value of n is 11? [2] ii) What will the function show() return when the value of n is 27? [2] iii) In one line state what function show() is doing? [1] PartII Answer any seven questions in this part, choosing three questions from Section A and four questions from Section B. Section A Answer any three questions. Question 4. (a) Given F(A,B,C,D)= Σ(5,6,7,8,9,10,14) Use Karnaugh map to reduce the given function F using the SOP form. Draw a logic gate diagram for the reduced SOP form. You may use gates with more than two inputs. Assume that the variables and their complements are available as inputs. (b) X(A,B,C,D)= π(0,2,6,8,10,14) Use Karnaugh map to reduce the given function X using the POS form. Draw a logic gate diagram for the reduced POS form. You may use gates with more than two inputs. Assume that the variables and their complements are available as inputs. [ 5 x 2 = 10]

3 Question 5. The immigration rules of a country allow the issue of work cum stay permits to an applicant only if the applicant satisfies any one of the following conditions:- The spouse of the applicant is a permanent resident of that country, having lived there for at least five years. OR The applicant possesses certain special skills as specified in the skill requirement list of that country and is sponsored by a permanent resident of that country. The inputs are:- A : The spouse or sponsor has permanent residence status. B : The spouse has lived in the country for 5 or more years. C : The applicant possesses the required special skills. D : Sponsorship by a permanent resident. Output:- X : Denotes eligible for permit issue. [ 1 indicates Yes and 0 indicates No in all cases] a) Draw the truth tables for the inputs and outputs given above and write the SOP expression for X(A,B,C,D). [5] b) Reduce X(A,B,C,D) using Karnaugh s map. Draw the logic gate diagram for the reduced SOP expression for X(A,B,C,D) using AND & OR gates. You may use gates with more than 2 inputs. Assume that variables and their complements are available as inputs. [5] Question 6. (a) How is an XOR gate different from an OR gate? Draw a truth table representing a 3 input XOR operation. Derive its SOP expression and draw the logic gate diagram for the SOP expression. [4] (b) What is the purpose of a multiplexer? Mention any two applications of a multiplexer. [3] (c) Draw the logic gate diagram for the following three input function F(X,Y,Z) using NOR gates only. F(X,Y,Z)= Σ(0,1,3,4,7) [3] Question 7. (a) Reduce the following expression using the laws of Boolean Algebra. Draw the logic gate diagram for the simplified expression:- F=A.(A +B). C. (A+C) [4] (b) State the principles of duality. Give an example. [3] (c) Convert AB + BC to its canonical SOP form using Boolean Algebra. [3] Question 8. (a) Draw the truth table and logic circuit diagram for a 3 x 8 decoder. State the difference between a multiplexer and a decoder. [5] (b) Reduce the following Boolean expression to the simplest form:- A.[B+C(AB+AC) ] [3] (c) Given F(X,Y,Z)= Σ(1,3,7) Prove F(X,Y,Z)= π ( 0,2,4,5,6) [2]

4 Section B Answer any 4 questions. Each program should be written in such a way that it clearly depicts the logic of the problem. This can be achieved by using mnemonic names and comments in the program. (Flowcharts and algorithms are not required) The programs must be written in C++/Java Question 9. NIC institute s resource manager has decided to network the computer resources like printer, storage media, etc. so that minimum resources and maximum sharing could be availed. Accordingly printers are linked to a centralized system and the printing jobs are done on a first come first served basis, only. This is like the first person s printing job will get done first and the next person s job will be done as the next job in the list and so on. In order to avoid collision, the restriction is that no more than 20 printing jobs can be added. Define the class Printjob with the following details: Class name : Printjob job[] : array of integers to hold the printing jobs. Newjob : to add a new printing job into the array. Capacity : the maximum capacity of the integer array. Front : to point out to the index of the front. Rear : to point out to the index of the last. Member functions Printjob() : constructor to initialize data members. Capacity=20, Front = Rear=-1 and call the function createjob(). void createjob() : to create an array to hold the printing jobs. void addjob() : adds the new printing job to the end of the last printing job, if possible, otherwise displays the message Printjob is full, cannot add any more. void removejob() : Removes the printing job from the front if the printing job is not empty, otherwise displays the message Printjob is empty. (a) Specify the class Printjob giving details of the constructor and the function void addjob(), void createjob() and void removejob() only. You do not need to write the main function. [8] (b) What is the common name of the entity described above? [1] (c) State one of its applications [1] Question 10. A special number is a number in which the sum of the factorial of each digit is equal to the number itself. For example:- 145 = 1! + 4! + 5! = Design a class Special to check if a given number is a special number. Some of the members of the class are given below:

5 Class name : Special N : Integer Member functions Special() : constructor to assign 0 to n Special(int) : Parameterized constructor to assign a value to n void sum() : calculate and display the sum of the first and last digit of n. void isspecial() : check and display if the number n is a special number. Specify the class Special giving details of the constructor, void sum() and void isspecial(). You need not write the main function. [10] Question 11. A class Collection contains an array of 100 integers. Using the following class description create an array with common elements from two integer arrays. Some of the members of the class are given below: Class name : Collection arr[] : integer array len : length of the array Member functions Collection() : default constructor Collection(int) : parameterized constructor to assign the length of the array. void inparr() : to accept the array elements. Collection common(collection) : returns a Collection containing the common elements of current Collection object and the Collection object passed as a parameter. void arrange() : sort the array elements of the object containing common elements in ascending order using any sorting technique. void display() : displays the array elements. Specify the class Collection giving the details of the constructors, void inparr() and void arrange(). Collection common(collection). You need not write the main Function. [10] Question 12. A class Employee contains employee details and another class Salary calculates the employee s net salary. The details of the two classes are given below: Class name : Employee empno : stores the employee number. empname : stores the employee name empdesig : stores the employee s designation. Member functions: Employee() : default constructor. Employee( ) : parameterized constructor to assign values to data members. void display() : display the employee details. Class name : Salary

6 basic : float variable to store the basic pay. Member functions Salary( ) : parameterized constructor to assign values to data members. void calculate() : calculates the employee s net salary according to the following rules: DA = 10% of basic HRA = 15% of basic Salary = basic + DA +H RA PF= 8 % of Salary Net Salary = Salary PF Display the employee details and the Net salary. Specify the class Employee giving details of the constructors and member function void display(). Using the concept of inheritance specify the class Salary giving details of the constructor and the member function void calculate(). The main function need not be written. [10] Question 13. A class Revstr defines a recursive function to reverse a string and check whether it is a palindrome. The details of the class are given below: Class name : Revstr Str : stores the string. Revst : stores the reverse of the string. Member functions void getstr() : to accept the string. void recreverse(int) : to reverse the string using recursive technique. void check() : to display the original string, its reverse and whether the string is a palindrome or not. Specify the class Revstr giving details of the functions void getstr(), void recreverse(int) and void check(). The main function need not be written. [10] Question 14. A class Modify has been defined with the following details: Class name : Modify St : stores a string len : to store the length of the string. Member functions void read() : to accept the string inuppercase alphabets. void putin(int, char) : to insert a character at the specified position in the string and display the changed string. void takeout(int) : to remove character from the specified position in the string and display the changed string. void change() : to replace each character in the original string by the character which is a t a distance of 2 moves ahead. For example:- ABCD becomes CDEF, XYZ becomes ZAB. Specify the class Modify giving details of the functions vod read(), void putin(int,char), void takeout(int) and void change(). The main function need not be written. [10]

7 COMPUTER SCIENCE PAPER 1 THEORY YEAR 2009 PART I Answer all questions in this part Question 1. (a) Obtain the truth table to verify the following expression: X(Y+Z) = XY + XZ. Also name the law stated above. (b) Answer the following questions related to the gate given below: i) What is the output of the above gate if input A=0, B=1 ii) What are the values of the inputs if output is 1? (c) Given F= A +(B=C).( D +E). Find F and show the relevant working in steps. (d) State the dual for the following expression and also draw the logic gate diagram for the dual expression obtained using NOR gate only. P= A.B + C.D (e) For the given truth table where A,B,C are inputs and X is the output, A B C D Write i) Canonical Sum of Product expression ii) Canonical Product of Sum expression [2 x 5 = 10] Question 2. (a) State a difference between linear and non linear data structure. Give one example of each. (b) Convert the following infix expression to its postfix form:- ((P*Q) / (R/S +T)) + U (c) Simplify the following expression by using the Boolean laws. Show the working in steps and also mention the laws used.: X Y Z + X Y Z+ X YZ+X YZ + XY Z+ XY Z (d) Each element of an array A[20][10] requires 2 bytes of storage. If the address of A[6][8] is 4000, find the base address at A[0][0] when the array is stored row major wise. (e) Define inheritance. How is it useful in programming? [2 x 5 = 10]

8 Question 3. (a) The following function trial() and perform() are a part of some class. Answer the following parts given below. Show the dry run/working. int trial() if(n==1) return 2; else if(n==2) return 3; else return trial(n-2) + trial(n-1); void perform(int p) int x; for(int i=1;i<=p;i++) x=trial(i); System.out.print(x+ ); i) What will the function trial() return when the value of n is 4? [2] ii) What will be the output of the function perform() when the value of p is 5? [2] iii) In one line state what the function trial() is doing, apart from recursion? [1] (b) Answer the following from the diagram of a binary tree given below: i) Root of the tree. ii) External nodes of the tree. iii) List the nodes in the tree using inorder traversal. iv) Left subtree v) Height of the tree [1 X 5 = 5]

9 Part II Section A Answer any three questions Question 4. (a) F(P,Q,R,S)= P Q RS + P QRS + PQ R S+PQ RS +PQ RS+PQR S+PQRS +PQRS Use Karnaugh map to reduce the given function F using the SOP form. Draw a logic gate diagram for the reduced SOP form. You may use gates with more than two inputs. Assume that the variables and their complements are available as inputs. (b) F(A,B,C,D)= π(0,1,2,3,5,7,9,13) Use Karnaugh map to reduce the given function F using the POS form. Draw a logic gate diagram for the reduced POS form. You may use gates with more than two inputs. Assume that the variables and their complements are available as inputs. [5 x 2 = 10] Question 5. A provisional store announces a special discount on all its products as a festival offer only to those who satisfy any one of the following conditions: If he/she is an employee of the store and has a service of more than ten years OR If he/she is a regular customer of the store whose age is less than 65 years and is not an employee of the store OR If he/she is a senior citizen but not a regular customer of the store The inputs are: E : Employee of the store R : Regular customer of the store S : Service of the employee is more than 10 years C : Senior citizen of 65 years or above Output X : Denotes eligible for discount[ 1 indicates YES and 0 indicates NO in all cases] (a) Draw the truth table for the inputs and outputs given above an write the SOP expression for X(E,R,S,C) (b) Reduce X(E,R,S,C) using Karnaugh s map. Draw the logic gate diagram for the reduced SOP expression for X(E,R,S,C) using AND, OR gates. You may use gates with more than 2 inputs. Assume that the variables and their complements are available as inputs. [5 x 2= 10] Question 6. (a) Draw a truth table representing a 2 input XNOR gate and derive its SOP expression along with its logic gate diagram. [3] (b) Simplify the following expression and convert it to its canonical POS form: (X.Y+Z)(Y+Z.X) [3] (c) From the logic circuit diagram given below, name the parts (1), (2), (3) and finally derive the Boolean expression and simplify it: [4]

10 Question 7. (a) Prove that the complement of A(A+B).B(B+C ) is a universal gate. [2] (b) Minimise the following expression. At each step state clearly the law used. [3] Y=(A+B ).(B+CD) (c) Draw the truth table and logic circuit diagram for a decimal to binary encoder. [5] Question 8. (a) State a difference between multiplexers and decoders. Also state a use of each. [2] (b) Verify the following Boolean expression with the help of truth table. [3] (c) Write the SOP expression, truth table and the logic circuit of full adder. [5] Section B Answer any 4 questions. Each program should be written in such a way that it clearly depicts the logic of the problem. This can be achieved by using mnemonic names and comments in the program. (Flowcharts and algorithms are not required) The programs must be written in C++/Java Question 9. A magic number is a number in which the eventual sum of digits of the number is equal to 1. For example, 172 = = = = 1 Then 172 is a magic number. Design a class Magic to check if a given number is a magic number. Some of the members of the class are given below: Class name : Magic n : stores the number Member functions Magic() : constructor to assign 0 to n void getnum(intnn) : to assign the parameter value to the number, n=nn int Sum_of_digits(int) : return the sum of the digits of number void ismagic() : checks if the given number is a magic number by calling the function Sum_of_digits(int) and displays appropriate message. Specify the class Magic by giving details of the constructor, void getnum(int), intsum_of_digits(int) and void ismagic(). You need not write the main function. [10] Question 10. A transpose of an array is obtained by interchanging the elements of rows and columns. A class Transarray contains a two dimensional integer array of order [ m x n]. The maximum value possible for both m and n is 20. Design a class Transarray to find the transpose of a given matrix. The details of the members of the class are given below: Class name : Trasarray arr[][] : stores the matrix elements m : integer to store the number of rows. n : integer to store the number of columns.

11 Member functions Transarray() : default constructor. Transarray(intmm,intnn) : to inititalize the size of the matrix, m=mm,n=nn. voidfillarray() : to enter elements into the matrix. void transpose(transarray A) : to find the transpose of a given matrix. voiddisaparray() : displays the array in a matrix form. Specify the class Transarray giving details of the constructors, void fillarray(), void transpose(transarray) and void disparray(). You need not write the main function. [10] Question 11. A library issues books on a rental basis at a 2% charge on the cost price of the book per day. As per the rules of the library, a book can be retained for 7 days without any fine. If the book is returned after 7 days, a fine will also be charged for the excess days as per the chart given below: Number of excess days Fine per day 1 to to Above 10 days 5.00 Design a class Library and another class Compute to perform the task. The details of the 2 classes are given below: Class name : Library name : name of the book author : author of the book p : price of the book in decimals Member functions Library( ) : parameterized constructor to assign values to data members. void show() : display the book details class name : Compute d : number of days taken in returning the book. f : to store the fine. Member functions Compute( ) : parameterized constructor to assign values to data Members of both classes. void fine() : calculate the fine for excess days. void display() : displays the book details along with the number of days, fine and total amount to be paid. Total amount is calculated as: (2% of price of book * total no. of days) + fine Specify the class Library giving details of the constructors and void show(). Using the concept of inheritance, specify the class Compute giving details of the constructor, void fine() and the void display() function. You need not write the main function. [10]

12 Question 12. A class PrimeFac contains an array of 50 integers. Some of the members of the class are given below: Class name : PrimeFac num[] : array to store integers. freq[] : array to store the frequency of prime factors of numbers. Member functions PrimeFac() : constructor to inititalize array elements to 0. void enter() : to enter values into array num[] voidfrefac() : to determine the frequency of prime factors of the numbers stored in num[] and assign it to freq[]. voiddisp() : to display both the arrays. Specify the classprimefac giving details of the constructor, void enter(), void frefac() and void disp(). You need not write the main function. [10] Question 13. Class Binary contains an array of n integers (n<=100) that are already arranged in ascending order. The subscripts of the array elements vary from 0 to n-1. The data members and member functions of class Binary are given below: Class name : Binary A[] : integer array of 100 elements n : size of array l : location of the lower bound u : location of the upper bound Member functions: Binary(intnn) : constructor to initialize the size n to nn and the other instance variables. voidreaddata() : to fill the elements of the array in ascending order. intbinary_search(int v) : returns the location of the value(v) to be searched in the list by binary search method using the recursive technique. The function returns -1 if the number is not present in the given list. (a) Specify the class Binary giving details of the constructor, void readdata() and intbinary_search(int). younedd not write the main function. [8] (b) State the base case in the recursive technique binary_search(). [1] (c) What are the drawbacks of using the recursive technique? [1]

13 Question 14. A class SortWord has been defined with the following details: Class name : SortWord txt : stores the word. len : stores the length of the word. Member functions SortWord() : default constructor voidreadtxt() : to accept the word in lower case. voidsorttxt() : to sort the word in alphabetical order of characters using bubble sort technique and display it. voidchangetxt() : to change the case of vowels in the word to upper case. For example :- school becomes school. voiddisp() : to display the changed string. Specify the class SortWord giving the details of the functions constructor, void readtxt(), void sorttxt(), void changetxt() and void disp(). You need not write the main function. [10]

14 COMPUTER SCIENCE PAPER 1 THEORY YEAR 2010 Question 1. (a) If X=A BC + AB C + ABC + A BC then find the value of X when A=1; B=0; C=1 (b) Verify if, P.(~P+Q )=(P Q) using truth table. (c) Draw the logic circuit of NOR using NAND gate only. (d) Convert the following function into its Canonical Sum-Of_products form: F(X,Y,Z)= Σ(0,1,5,7) (e) Show that the dual of P QR + PQ R + P Q R is equal to the complement of PQ R + Q(P R + PR ) [2 x 5 = 10] Question 2. (a) State the difference between an interface and a class. (b) Convert the following infix notation to postfix notation. ( A+B) / C * (D +E) (c) A character array B[7][6] has a base address 1046 at 0,0. Calculate the address at B[2][3] if the array is stored Column Major wise. Each character requires 2 bytes of storage. (d) State the use of exception handling. Name the two types of exceptions. (e) i) What is the worst-case complexity of the following code segment : for(int i=0;i<n;i++) Sequence of statements for(int j=0;j<m;j++) Sequence of statements ii) How would the complexity change if the second loop went to N instead of M? [2 x 5 = 10] Question 3. (a) The following function numbers(int) and numbers1(int) are a part of some class. Answer the questions given below showing the dry run/working: public void numbers(int n) if(n>0) System.out.print(n+ ); numbers(n-2); System.out.print(n+ ); public String numbers1(int n) If(n<=0) return ; return(numbers(n-1)+n+ ; i) What will be the output of the function numbers(int n) when n=5? [2] ii) What will the function numbers1(int n) return when n=6? [2] iii) State in one line what is the function numbers1(int) doing apart from recursion? [1]

15 (b) The following function is a part of some class. It sorts the array a[] in ascending order using insertion sort technique. There are some places in the code marked by?1?,?2?,?3?,?4?,?5? which must be replaced by expression/ statement so that the function works correctly. void insertsort(int a[]) int m=?1?; int b,i,t; for(i=?2?;i<m;i++) t=a[i]; b=i-1; while(?3?>=0 && t<a[b]) a[b+1]= a[b];?4?;?5?=t; i) What is the expression or statement at?1? [1] ii) What is the expression or statement at?2? [1] iii) What is the expression or statement at?3? [1] iv) What is the expression or statement at?4? [1] v) What is the expression or statement at?5? [1] Part II Section A Answer any three questions Question 4. (a) Given F(P,Q,R,S)= Σ(0,2,5,7,8,10,11,13,14,15) (i) Reduce the above expression by using 4- variable K-Map, showing the various groups (i.e. octals, quads and pairs). (ii) Draw the logic gate diagram of the reduced expression using NAND gate only. (b) Given F(A,B,C,D)= (A + B + C + D). (A + B + C + D ). (A + B + C + D ). (A + B + C + D). (A + B + C + D ). (A + B + C + D ). (A + B + C + D). (A + B + C + D) (i) Reduce the above expression by using 4- variable K-Map, showing the various groups (i.e. octals, quads and pairs). (ii) Draw the logic gate diagram of the reduced expression using NOR gate only. [5 x 2 =10] Question 5. A government institution intends to award a medal to a person who qualifies any one of the following criteria: The person should have been an Indian citizen and had lost his/her life in a war but has not completed 25 years of service. OR The person must be an Indian citizen and has served the nation for a continuous period of 25 years or more but has not lost his/her life in a war. OR

16 The person is not an Indian citizen but has taken active part in activities for the upliftment of the nation. The inputs are: INPUTS A The person is/was an Indian citizen B Has a continuous service of more than 25 years C Lost his/her life in a war D Taken part in activities for upliftment of the nation Output X Denotes eligible for medal [ 1 indicates YES ad 0 indicates NO in all cases] (a) Draw the truth table for the inputs and outputs given above and write the POS expression for X(A,B,C,D).. (b) Reduce X(A,B,C,D) using Karnaugh s map. Draw the logic gate diagram for the reduced POS expression for X(A,B,C,D) using AND and OR gate. You may use gates with two or more inputs. Assume that the variable and their complements are available as inputs. [5 x 2 = 10] Question 6. (a) What are Maxterms? Convert the following function as a Product of Maxterms: F(P,Q,R)= (P+Q).(P +R ) (b) State whether the following expression is a Tautology or Contradiction with the help of a truth table: (X Z). [(X Y).(Y Z)] (c) What is a Multiplexer? Draw the truth table and logic diagram of a 8:1 multiplexer. [2+3+5=10] Question 7. (a) Draw the circuit diagram for a 3 to 8 decoder. (b) Draw the truth table for a half adder. Also derive a POS expression for the half adder and draw its logic circuit. (c) Simplify the following expression and also draw the circuit for the reduced expression. [Show the step wise working along with the laws used.] F= X. (Y+Z.(X.Y +X.Z) ) [3+3+4=10] Section B Answer any 2 questions. Each program should be written in such a way that it clearly depicts the logic of the problem. This can be achieved by using mnemonic names and comments in the program. Question 8. The co-ordinates of a point P on a two-dimensional plane can be represented by P(x,y) with x as the x co-ordinate and y as the y co-ordinate. The co-ordinates of midpoint of two points P1(x1,y1) and P2(x2,y2) can be calculated as P(x,y) where: x=x1+x2/2, y=y1+y2/2 Design a class Point with the following details: Class name : Point x : stores the x co-ordinate y : stores the y co-ordinate

17 Member functions: Point() : constructor to initialize x=0 and y=0 void readpoint() : accepts the co-ordinates x and y of a point Point midpoint(point A, Point B) : calculates and returns the midpoint of the two points A and B. void displaypoint() : displays the co-ordinates of a point Specify the class Point giving details of the constructor( ), member functions void readpoint(), Point midpoint(point, Point) and void displaypoint() along with the main function to create an object and call the functions accordingly to calculate the midpoint between any two given points. [10] Question 9. Input a word in uppercase and check for the position of the first occurring vowel and perform the following operation. (i) Words that begin with a vowel are concatenated with Y. For example, EUROPE becomes EUROPEY. (ii) Words that contain a vowel in between should have the first part from the position of the vowel till end, followed by the part of the string from beginning till position of the vowel and is concatenated by C. For example PROJECT becomes OJECTPRC. (iii) Words which do not contain a vowel are concatenated with N. For example, SKY becomes SKYN. Design a class Rearrange using the description of the data members and member functions given below: Class name : Rearrange Txt : to store a word Cxt : to store the rearranged word len : to store the length of the word Member functions Rearrange() : constructor to initialize the instance variables void readword() : to accept the word input in UPPERCASE void convert() : converts the word into its changed form and stores it in string Txt void display() : displays the original and the changed word Specify the class Rearrange giving the details of the constructor(), void readword(), void convert() and void display(). Define a main function to create an object and call the function accordingly to enable the task. [10] Question 10. Design a class Change to perform string related operations. The details of the class are given below: Class name : Change str : stores the word newstr : stores the changed word len : stores the length of the word Member functions Change() : default constructor void inputword() : to accept a word char caseconvert(char ch) : converts the case of the character and returns it void recchange(int) : extracts characters using recursive technique and changes its case using caseconvert() and forms a new word void display() : displays both the words

18 (a) Specify the class Change, giving details of the constructor(), member functions void inputword(), char caseconvert(char ch), void recchange(int) and void display(). Define the main function to create an object and call the functions accordingly to enable the above change in the given word. [8] (b) Differentiate between finite and infinite recursion. [2] Section C Answer any 2 questions. Each program/algorithm should be written in such a way that it clearly depicts the logic of the problem step wise. This can also be achieved by using pseudo codes. (Flowcharts are not required) The programs must be written in Java. The algorithm must be written in general standard form wherever required. Question 11. A super class Worker has been defined to store the details of a worker. Define a sub class Wages to compute the monthly wages for the worker. The details of both the classes are given below: Class name : Worker : Name : to store the name of the worker Basic : to store the basic pay in decimal Member functions Worker(.) : parameterized constructor to assign values to the instance variables void display() : display worker details class name : Wages hrs : stores the hours worked rate : stores rate per hour wage : stores the overall wage of the worker Member functions Wages(.) : parameterized constructor to assign values to the instance variables of both classes double overtime( ) : calculates and returns the overtime amount as (hours * rate ) void display() : calculates the wage using the formula wage=overtime amount +basic pay and displays it along with other details Specify the class Worker giving details of the constructor() and void display(). Using the concept of inheritance, specify the class Wages giving details of the constructor(), double overtime() and void display(). The main function need not be written. [10] Question 12. Define a class Repeat which allows the user to add elements from one end (rear) and remove elements from one end (rear) and remove elements from the other end (front) only. The following details of the class Repeat are given below: Class name : Repeat st[] : an array to hold a maximum of 100 integer elements cap : stores the capacity of the array

19 f r Member functions Repeat(int m) void pushvalue(int v) int popvalue() void disp() : to point to the index of the front : to point to the index of the rear : constructor to initialize the data members cap=m, f=0, r=0 and to create the integer array : to add integers from the rear index if possible else display the message overflow : to remove and return element from the front, if array is empty then return : displays the elements present in the list (a) Specify the class Repeat giving details of the constructor(int), member function void pushvalue(int), int popvalue() and void disp(). The main function need not be written. [8] (b) What is the common name of the entity described above? [1] (c) On what principle does this entity work? [1] Question 13. (a) A linked list is formed from the objects of the class, class ListNodes int item; ListNodes next; Write a method OR an algorithm to compute and return the sum of all integers items stored in the linked list. The method declaration is specified below: int listsum(listnodes start); (b) What is Big O notation? State its significance. (c) Answer the following from the diagram of a Binary tree given below: i) Name the parent node of E. [1] ii) Write the postorder tree traversal. [1] iii) Write the internal nodes of the tree. [1] iv) State the level of the root of the tree. [1]

20 COMPUTER SCIENCE PAPER 1 THEORY YEAR 2011 Question 1. (a) State the two absorption laws. Verify any one of them using truth table. (b) Reduce the following expression : F(A,B,C)= Σ(0,1,2,3,4,5,6,7) Also find the complement of the reduced expression. (c) Name the logic gate for the following circuit diagram and write its truth table. (d) Using truth table, verify whether the following is true or false: (p q) = (q p ) (e) If A=1, B=0, C=1 and D=1 find its i) maxterm ii) minterm [2 x 5 =10] Question 2. (a) How can we override a method in inheritance? (b) A square matrix A[m x m] is stored in the memory with each element requiring 2 bytes of storage. If the base address A[1][1] is 1098 and the address at A[4][5] is 1144, determine the order of the matrix A[mxm] when the matrix is stored column majorwise. (c) What is Big O Notation? (d) What is an exception? (e) Convert the infix expression to its postfix form: A+B*C-D/E [2 x 5 =10] Question 3. (a) The following is a part of some class. What will be the output of the function mymethod( ) when the value of counter is equal to 3? Show the dry run/ working. void mymethod(int counter) if(counter= =0) System.out.println( ); else System.out.println( Hello + counter); mymethod(- -counter); System.out.println( + counter); [5]

21 (b) The following function is a part of some class which computes and returns the greatest common divisor of any two numbers. There are some places in the code marked by?1?,?2?,?3?,?4?, and?5? which must be replaced by statement/expression so that the function works correctly. int gcd(int a, int b) int r; while(?1?) r=?2?; b=?3?; a=?4?; if(a==0) return?5?; else return -1; i) What is the expression or statement at?1? ii) What is the expression or statement at?2? iii) What is the expression or statement at?3? iv) What is the expression or statement at?4? v) What is the expression or statement at?5? [1 x 5 = 5] Part II Answer seven questions in this Part, choosing three questions from Section A and two questions from Section B and two questions from Section C. Section A Answer any three questions from this Section Question 4. (a) State the principle of duality. Give the dual of the following: (A B)+(C.1)=(A +C)(B+C) [3] (b) Reduce the following Boolean expressions to their simplest forms:- i) (CD) +A + A+ C.D + A.B ii) A.B+C(A.B + A.C) [4] (c) Verify using a truth table if: [3] Question 5. (a) Given F(P,Q,R,S)= π(2,3,6,7,9,11,12,13,14,15) Reduce the above expression using four variable K-map. Draw the logic gate diagram of the reduced expression using NOR gates only. [5] (b) Given F(A,B,C,D)= A B C D + A B C D + AB C D + AB C D + A BC D +A BCD. Reduce the above expression by using four variable K-map. Draw the logic gate diagram of the reduced expression using NAND gates only. [5]

22 Question 6. (a) Show with the help of a logic diagram how a NAND gate is equivalent to an OR gate. [3] (b) Verify if the following is valid: (A B) ^ (A C)= A (B^C) [3] (c) What is a decoder? Draw the truth table and logic circuit diagram for a 2 to 4 decoder. [4] Question 7. (a) What is a Full Adder? Draw the truth table for a Full Adder. Also derive SOP expression for the Full Adder and draw its logic circuit. [4] (b) State how a decoder is different from a multiplexer. Also state one use of each. [3] (c) Convert the following cardinal expression into its canonical form and reduce it using Boolean laws: F(L,M,O,P) = π(0,2,8,10) [3] Section B Answer any 2 questions. Each program should be written in such a way that it clearly depicts the logic of the problem. This can be achieved by using mnemonic names and comments in the program. Question 8. Input a sentence from the user and count the number of times, the words an and and are present in the sentence. Design a class Frequency using the description given below: Class name : Frequency Data Members text : stores the sentence countand : to store the frequency of the word and. countan : to store the frequency of the word an. len : stores the length of the string. Member functions Frequency() : constructor to initialize the data variables. void accept(string n) : to assign n to text where the value of the parameter should be in lowercase. void checkandfreq() : to count the frequency of and. void checkanfreq() : to count the frequency of an. void display() : to display the frequency of an and and with suitable messages. Specify class Frequency giving details of the constructor(), void accept(string), void checkand freq() and void display(). Also define the main function to create an object and call methods accordingly to enable the task. [10] Question 9. A class DeciOct has been defined to convert a decimal number into its equivalent octal number. Some of the members of the class are given below: Class name : DeciOct n : stores the decimal number oct : stores the equivalent octal number Member functions: DeciOct() : constructor to initialize the data members to 0 void getnum(int nn) : assigns nn to n void deci_oct() : calculates the octal equivalent of n and stores it in oct using the recursive technique

23 void show() : displays the decimal number n calls the function deci_oct() and displays its octal equivalent (a) Specify the class DeciOct, giving details of the constructor(), void getnum(int), void deci_oct() and void show(). Also define a main function to create an object and call the functions accordingly to enable the task. [8] (b) State any two disadvantages of using recursion. [2] Question 10. You are given a sequence of n integers, which are called pseudo arithmetic sequences ( sequences that are in arithmetic progression). Sequence of n integers : 2, 5, 6, 8, 9, 12 We observe that = = 6 +8 = 14 The sum of the above sequence can be calculated as 14 x 3 = 42 For sequence containing an odd number of elements the rule is to double the middle element, for example 2, 5, 7, 9, 12 =2 +12 = 5 +9 = 7 +7 = x 3 = 42 [ middle element = 7] A class pseudoarithmetic determines whether a given sequence is pseudo-arithmetic sequence. The details of the class are given below:- Class name : Pseudoarithmetic n : to store the size of the sequence a[ ] : integer array to store the sequence of numbers ans, flag : to store the status sum : to store the sum of sequence of numbers r : to store the sum of 2 numbers Member functions : Pseudoarithmetic( ) : default constructor void accept(int nn ) : to assign nn to n and to create an integer array. Fill in the elements of the array. boolean check( ) : return true if the sequence is a pseudo-arithmetic sequence otherwise return false. Specify the class Pseudoarithmetic, giving details of the constructor(), void accept(int) and Boolean check(). Also define the main function to create an object and call methods accordingly to enable the task. [10] Section C Answer any 2 questions. Each program/algorithm should be written in such a way that it clearly depicts the logic of the problem step wise. This can also be achieved by using pseudo codes. (Flowcharts are not required) The programs must be written in Java. The algorithm must be written in general standard form wherever required. Question 11. A super class Record has been defined to store the names and ranks of 50 students. Define a sub class Rank to find the highest rank along with the name. The details of both classes are given below: Class name : Record name[] : to store the names of students

24 rnk[] : to store the ranks of students Member functions: Record() : constructor to initialize data members void readvalues() : to store names and ranks void display() : displays the names and the corresponding ranks class name : Rank index : integer to store the index of the topmost rank Member functions Rank() : constructor to invoke the base class constructor and to initialize index to 0. void highest() : finds the index location of the topmost rank and stores it in index without sorting the array void display() : displays the name and ranks along with the name having the topmost rank. Specify the class Record giving details of the constructor(), void readvalues(), void display(). Using the concept of inheritance, specify the class Rank giving details of constructor(), void highest() and void display(). The main function and algorithm need not be written. Question 12. Stack is a kind of data structure which can store elements with the restriction that an element can be added or removed from the top only. The details of class Stack are given below: Class name : Stack st[] : the array to hold names. size : the maximum capacity of the string array top : the index of the topmost element of the stack ctr : to count the number of elements of the stack Member functions Stack() : default constructor Stack(int cap) : constructor to initialize size=cap and top=-1 void pushname(string n) : to push a name into the stack. If the stack is full, display the message overflow. String popname() : removes a name from the top of the stack and returns it. If the stack is empty, display the message underflow. void display() : Display the elements of the stack. (a) Specify class Stack giving details of the constructors(), void pushname(string n), String popname() and void display(). The main function and algorithm need not be written. (b) Under what principle does the above entity work? Question 13. (a) A linked list is formed from the objects of the class, class Node int info; Node link; Write an algorithm OR a method for deleting a node from a linked list. The method declaration is given below: void deletenode(node start)

25 (b) Distinguish between worst-case and best-case complexity of an algorithm. (c) Answer the following from the diagram of a Binary tree given below: i) Write the postorder tree traversal ii) Name the leaves of the tree iii) Height of the tree iv) Root of the tree

26 COMPUTER SCIENCE PAPER 1 THEORY YEAR 2012 Part I While working questions in this part, indicate briefly your working and reasoning wherever required. Question 1. (a) Using truth table, verify the following expression: X + ( Y + Z ) = ( X + Y ) + Z Also state the law. (b) Given, F(X, Y, Z)= (X + Y ). (Y + Z ) write the function in canonical product of sum form. (c) Draw the truth table and logic circuit for a 2 input XNOR gate. (d) Find the complement of the following expression: (e) X + XY (f) If (X Y) then write its: i) Converse ii) Contra positive [2 x 5 = 10] Question 2. (a) Differentiate between the keyword extends and implements. (b) State how a binary tree is a recursive data structure. (c) A matrix B[10][7] is stored in the memory with each element requiring 2 bytes of storage. If the Base address at B[x][1] is 1012 and the address B[7][3] is 1060, determine the value x where the matrix is stored in column major wise. (d) Convert the following infix notation into its postfix form: A + (( B+ C) + ( D + E) * F ) / G (e) What is a constructor? State one difference between a constructor and any other member function of a class. [2 x 5 = 10] Question 3. (a) The following function is a part of some class which computes and sorts an array arr[] in ascending order using the bubble sort technique. There are some places in the code marked by?1?,?2?,?3?,?4?,?5? which must be replaced by a statement/ expression so that the function works properly: class Trial void bubblesort(intarr[]) inti,j,k,tmp; for(i=0;?1?;i++) for(j=0;?2?;j++) if(arr[j]>?3?) tmp=arr[j];?4?=arr[j+1]; arr[j+1]=?5?;

27 i) What is the expression or statement at?1? ii) What is the expression or statement at?2? iii) What is the expression or statement at?3? iv) What is the expression or statement at?4? v) What is the expression or statement at?5? [1 x 5 = 5] (b) The following function witty() is a part of some class. What will be the output of the function witty() when the value of n is SCIENCE and the value of p is 5. Show the dry run/ working: class Trial1 public void witty(string n, int p) if(p<0) System.out.println(""); else System.out.println(n.charAt(p)+"."); witty(n,p-1); System.out.print(n.charAt(p)); [5] Part II Answer seven questions in this part, choosing three questions from Section A, two from Section B and two from Section C. Section A Answer any three questions Question 4. (a) Given the Boolean function F(A,B,C,D)= Σ(4,6,7,10,11,12,14,15) (i) Reduce the above expression by using 4 variable K- map, showing the various groups (i.e. octals, quads and pairs). (ii) Draw the logic gate diagram of the reduced expression. Assume that the variables and their complements are available as inputs. [4 + 1 = 5] (b) Given the Boolean function F(P,Q,R,S)= π(0,5,7,8,10,12,13,14,15) (i) Reduce the above expression by using 4 variable K- map, showing the various groups (i.e. octals, quads and pairs). (ii) Draw the logic gate diagram of the reduced expression. Assume that the variables and their complements are available as inputs. [4 + 1 = 5] Question 5. The principal of a school intends to select students for admission to Class XI on the following criteria: Student is of the same school and has passed the Class X Board Examination with more than 60% marks. OR Student is of the same school, has passed the Class X Board Examination with less than 60% marks but has taken active part in co-curricular activities. OR Student is not from the same school but has either passed the Class X board Examination with more than 60% marks or has participated in Sports at the national level.

28 The inputs are : INPUTS S Student is of the same school P Has passed the Class X Board Examination with more than 60% marks. C Has taken active part in co-curricular activities. T Has participated in sports at the National Level. Output :- X Denotes admission status [ 1 indicates granted and 0 indicates refused in all the cases.] (a) Draw the truth table for the inputs and outputs given above and write the SOP expression. (b) Reduce X(S,P,C,T) using Karnaugh s map. Draw the logic gate diagram for the reduced SOP expression for X(S,P,C,T) using AND and OR gate. You may use gates with two or more inputs. Assume that the variable and their complements are available as inputs. [5 x 2 = 10] Question 6. (a) Verify algebraically if, X Y Z + X Y Z + X YZ + X YZ + XY Z + XY Z = X + Y [2] (b) Represent the Boolean expression X + YZ with the help of NOR gates only. [2] (c) Define the terms contingency, contradiction and tautology. [3] (d) Consider the following truth table where A and B are two inputs and X is the output: A B X i) Name and draw the logic gate for the given truth table. [2] ii) Write the POS of X(A,B) [1] Question 7. (a) Define multiplexer and state one of its uses. Draw the logic gate diagram for 4:1Multiplexer. [4] (b) State how a half adder is different from a full adder. Also give their respective uses. [3] (c) Minimize the following expression using Boolean laws: Q(Q +P).R.(Q+R) [3] Also draw the logic gate for the reduced Boolean expression. Section B Answer any 2 questions. Each program should be written in such a way that it clearly depicts the logic of the problem. This can be achieved by using mnemonic names and comments in the program. Question 8. A class Combine contains an array of integers which combines two arrays into a single array including the duplicate elements, if any, and sorts the combined array. Some of the members of the class are given below:

29 Class Name : Combine com[ ] : integer array size : size of the array Member functions/methods Combine(intnn) : parameterized constructor to assign size = nn voidinputarray( ) : to accept the array elements void sort() : sorts the elements of combined array in ascending order using the selection sort technique. void mix(combine A, Combine B) : combines the parameterized object arrays and stores the result in the current object array along with the duplicate elements, if any. void display( ) : displays the array elements. Specify the class Combine giving details of the constructor(int ), void inputarray( ), void sort(), void mix(combine, Combine) and void display( ). Also define the main function to create an object and call the methods accordingly to enable the task. [10] Question 9. Design a class VowelWord to accept a sentence and calculate the frequency of words that begin with a vowel. The words in the input string are separated by a single blank space and terminated by a full stop. The description of the class is given below: Class Name : VowelWord str : to store a sentence freq : to store the frequency of words beginning with a vowel. Member functions VowelWord() : constructor to initialize data members to legal initial values. voidreadstr() : to accept a sentence. voidfreq_vowel( ) : counts the frequency of the words beginning with a vowel. void display() : to display the original string and the frequency of the words that begin with a vowel. Specify the class VowelWord giving details of the constructor( ), void readstr(), void freq_vowel() and void display(). Also defing the main function to create an object and call the methods accordingly to enable the task. [10] Question 10. A happy number is a number in which the eventual sum of the square of the digits of the number is equal to 1. Example : 28 = (2)2 + ( 8 )2 = = = (6)2 + ( 8)2 = = = ( 1 )2 + ( 0 )2 + ( 0 )2 = = 1 Hence 28 is a happy number. Example : 12 = (1)2 + (2)2 = = 5 Hence 12 is not a happy number. Design a class Happy to check if a given number is a happy number. Some of the members of the class are given below: