Home > ISC_Computer Science > ISC Specimen Paper ( Computer Science Theory) – 2013

ISC Specimen Paper ( Computer Science Theory) – 2013

February 9, 2013 Leave a comment Go to comments
COMPUTER  SCIENCE
PAPER 1 
(THEORY) 
Three hours
(Candidates are allowed additional 15 minutes for only reading the paper.
They must NOT start writing during this time.)
—————————————————————————————————————-
Answer all questions in Part I (compulsory) and seven questions from Part-II,  choosing
three questions  from  Section-A,  two  from Section-B and two from Section-C . 
All working, including rough work, should be done on the same sheet as the
rest of the answer.
The intended marks for questions or parts of questions are given in brackets [  ].
—————————————————————————————————————-
PART I
Answer all questions.
While answering questions in this Part, indicate briefly your working and reasoning,
wherever required.
Question 1      
(a)  State the two distributive laws of Boolean Algebra.  Prove any one of them with the help of Truth Table.  [2]
(b) Draw the truth table to verify the expression :
p ⇒ q is equivalent to ∼ q ⇒ ∼ p   (∼ q =  q = q’)       [2]
(c) Find the complement of the following:
         [(xy)′ • x] [ (xy)′ • y]             [2]
(d) Simplify the following Boolean Expression using laws of Boolean Algebra.  At each step, clearly state the law used for simplification.
z . ( z + x ) x ( y +  y )           [2]
(e)  Given     F ( x, y, z ) = xz + xy + yz
Write the function in canonical sum of products form.    [2]
Question 2 
(a) What do LIFO and FIFO stand for?  [2]
(b) For an array of real numbers x [ − 6… 8 , -12… 20 ] , find the address of
  x [5] [4 ],  if x  [1] [1]  is stored in location 100 in the column major order.
Assume that each element requires 4 bytes.  [2]
(c)  State the difference between an abstract class and an interface  [2]
(d) Convert the following infix expression to its postfix form:
     b * [ (a / d )  -   ( c * ( e  -  f ) ) ]      [2]
(e) Define a binary tree.  [2]
Question 3
(a) The following function is a part of some class.  It returns the value 1 when the number is an Armstrong number, otherwise it returns 0.
/* An Armstrong number  is a number which is equal to the sum of the cube of
its individual digits */
           int arms ( int n )
           {
                int digit = 0, sum = 0 ;
                int rem = n;
                while ( ? 1 ? )
                 {
                     digit = ? 2 ?;
                     sum = sum + ? 3 ? ;
                     rem = ? 4 ? ;
                 }
                if (? 5 ? )
                   return 1 ;
                else
                   return 0 ;
           }
(i) What is the expression/value at ? 1 ?  [1]
(ii) What is the expression/value at ? 2 ?  [1]
(iii) What is the expression/value at ? 3 ?  [1]
(iv) What is the expression/value at ? 4 ?  [1]
(v) What is the expression/value at ? 5 ?  [1]
(b)  Give output of the following function where x and y are arguments greater than 0. Show the dry run/working.
 int strange (int x, int y)
     {
      //Assuming x>0 and y>0
        if(x>=y)
         {
             x = x-y;
             return strange(x , y);
          }
        else
             return x;
      }
(i) What will the function strange(20,5) return ?                           [2]
(ii) What will the function strange(15,6) return ?                           [2]
(iii) In one line, state what the function is doing.  [1]
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 ( P, Q, R, S ) = ∑ ( 0, 1, 3, 4, 5, 6, 7, 9, 10, 11, 13, 15 )
Use Karnaugh’s map to reduce the 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 variable and their complements are available as inputs.   [5]
(b) Given  the Boolean function :
     X ( P, Q, R, S )  =  π ( 3, 8, 10, 12, 13, 14, 15 )
Use Karnaugh’s map to reduce this function X using the given 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]
Question 5  
The main safe in the nationalized bank can be opened by means of a unique password consisting of three parts.  Different parts of the  password are held by the
Chairman, Regional Manager, Bank Manager and Head cashier of the bank, respectively. In order to open the safe, any one of the following conditions must be
satisfied:
The password of the Chairman, together with passwords of any two other officials, must be entered.
OR
The password of all the three bank officials, excluding the chairman, must be entered.
The inputs are: 
        A :  Denotes the Chairman’s password.
        B :  Denotes the Regional Manager’s password.
        C :  Denotes the Bank Manager’s password.
        D : Denotes the Head Casher’s password.
Output: 
        X – Denotes that the safe can be opened.
               [1 indicates Yes and 0 indicates No in all cases]
(a)  Draw the truth table 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, if possible. 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 two or more inputs.  Assume that the variables and their complements are
available as inputs.  [5]
Question  6 
(a) Draw the truth table and logic circuit diagram for a Decimal to Binary Encoder.  [5]
(b)  Given :  F(x, y, z) = ∑ (1,3,7)  Verify :   F(x, y, z) = π (0,2,4,5,6)     [2]
(c)  Simplify the following expression by using Boolean laws. Show the working and also mention the laws used :
           X’Y’Z’ + XYZ’ + XY’Z’ + X’YZ’       [3]
Question 7 
(a)  Define Cardinal Form of an expression and Canonical Form of  an expression.  Give an example for each.  [3]
(b)  Which gate is equivalent to :          (NOR) OR (XOR)      [3]
(c)  Define a Half Adder.  Draw the Truth Table and Logic diagram of a Half Adder.  [4]
     
 SECTIO N– B 
Answer any two 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 Java.
Question 8    
 A perfect square is an integer which is the square of another integer.  For example, 4, 9, 16 .. are perfect squares. Design a Class Perfect with the following description:   [10]
Class name :  Perfect
Data members/instance variables   
 n : stores an integer number
Member functions:  
 Perfect( ) : default constructor
 Perfect(int) : parameterized constructor to assign a value to ‘n’
 void perfect_sq() : to display the first 5 perfect squares larger than ‘n’ (if  n = 15, the next 3 perfect squares are 16, 25, 36)
 void sum_of() : to display all combinations of consecutive integers whose sum is equal to n. ( the number n = 15 can be expressed as
        1      2     3      4     5
        4      5     6
        7      8
Specify  the  class  Perfect  giving details of the constructors, void perfect_sq( ) and void sum_of().  Also define the main function to create an object and call methods
accordingly to enable the task.
Question 9 
A class RecFact defines a recursive function to find the factorial of a  number.  The details of the class are given below:  [10]
Class name :  RecFact
Data members/instance variables   
 n : stores the number whose factorial is required.
 r : stores an integer
Member functions :  
 RecFact( ) : default constructor
 void readnum( ) : to enter values for ‘n’ and ‘r’
 int factorial(int) : returns the factorial of the  number using the Recursive Technique.
 Void factseries(  )   : to calculate and display the value of  n! /  r!*(n-r )!
Specify the class RecFact  giving the details of the  constructor and member functions void readnum( ), int factorial(int) and void factseries( ).  Also define the main function
to create an object and call methods accordingly to enable the task.
Question 10 
In “Piglatin” a word such as  KING is replaced by INGKAY , while TROUBLE becomes OUBLETRAY and so on . The first vowel of the original word becomes
the start of the translation, any  preceding letters being shifted towards the end and followed by AY.  Words that begin with a vowel or which do not contain
any vowel are left unchanged. Design a class  Piglatin using the description of the data members and member functions given below:   [10]
Class name                                                 :    Piglatin
Data members /instance variables  : 
       Txt                                                  :   to store a word
       len                                                   :   to store the length
Member functions : 
     Piglatin( )                                          :   constructor to initialize the data mrmbers
     void readstring( )                              :   to  accept the word input in UPPER CASE
     void convert ( )                                 :   converts  the word into its  piglatin form
 and displays the word  (changed or unchanged)
     void  consonant( )                             :   counts and displays the number of
consonants present in  the given word.
Specify the class  Piglatin  giving the details of the constructor, void readstring( ), void convert( ) and void consonant( ).   Also define the main function to create an
object and call methods accordingly to enable the task.
SECTIO N– C 
Answer any two questions.
Each program should be written in such a way that it clearly depicts the logic of the problem
stepwise.
This can be achieved by using comments in the program and mnemonic names or
pseudo codes for algorithms.  The programs must be written in Java and the algorithms must be
written in general / standard form, wherever required / specified.
 (Flowcharts are not required.)
Question 11  
A class Author contains details of the author and another class Book List contains details of the books written by him.  The details of the two classes are given below:   [10]
Class name :  Author
Data members   
 authorno : stores the author’s number
 name : stores the author’s name
Member functions  
 Author ( ) : default constructor
 Author ( … ) : parameterised  constructor to assign values to author number and name
 void show( ) : to display the author’s details
Class name :  Booklist
Data members/instance variables   
 bookno : Long type variable to the store book number
bookname : stores the book name
price : float variable to store the price
 edition : integer type variable to store the edition number
Member functions
 Booklist (…) :  parameterized constructor to assign values to data members of both the classes
void show( ) : to display all the details
Specify the class  Author giving details of the  constructors and member function  void show( ).  Using the concept of Inheritance, specify the class Booklist giving details of the
constructor and the member function  void show( ). Also define the main function to create an object and call methods accordingly to enable the task.
Question 12 
In a computer game, a vertical column and a pile of rings are displayed.  The objective of the game is to pile up rings on the column till it is full.  It can hold 10 rings at the
most.  Once the column is full, the rings have to be removed from the top till the column is empty and then the game is over.  Define the class RingGame with the following
details:   [10]
Class name :  RingGame
Data members/instance variables   
 ring [ ] : array to hold rings (integer)
 max : integer to hold maximum capacity of ring array
 upper : integer to point to the upper most element
Member functions
 RingGame(int m) : constructor to initialize, max = m & upper to – 1.
 void jump-in(int ) : adds a ring to the top of the column, if possible. otherwise,
displays a message “Column full. Start removing rings”.
 void jump-out( ) : removes the ring from the top, if column is not empty.  otherwise,
outputs a message, “Congratulations. The game is Over”.
Specify the class  RingGame giving the details of the  constructor and functions  void jump-in(int) and void jump-out( ).  Also define the main function to create an object and
call methods accordingly to enable the task.
Question 13 
(a) A Linked List is formed from the objects of the class,
                        Class Node
                             {
                                 int num;
                                 Node next;
                              }
Write the algorithm OR a method for inserting a node in the end of the list. The method declaration is given below :
  void insertnode(Node start)   [4]
(b) State the complexity for the following algorithms :  [3]
 (i) Linear Search
 (ii) Binary Search
 (iii) Selection Sort
(c)  List the nodes  in the tree given below using:   [3]
 (i) Preorder Traversal
 (ii) Postorder Traversal
 (iii) Inorder traversal
F
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