 ## ISC sample paper

ISC sample paper
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 [ ].

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PART I

Question 1.                                                                          [1X5=5]
A)Write the truth table for a 2 input disjunction in a propositional logic.

B) Using a truth table verify the following expression: (X+Y). Z=/=(Z.X)+Y

C) Find the complement of X.(Y.Z’+ Y’X) using De Morgan’s law. Do not reduce the expression.

D) State and verify the Distributive law using the truth table.

E) Reduce the following expression to its simplest form using law of Boolean algebra. At each step clearly state the law used for simplification. D’ +A +A+C’D’+A.B

Question 2.                                                                                                                                                              [2 x 5 =10]

1. What is the use of implements keyword?
2. Convert the following infix notation to postfix:
p+q*r- s/t
3. State the differences between throw and throws keyword?
4. A matrix of 2D array defined as A[4,….7][-1….3] requires 2 bytes of storage space for each element. Calculate the address of x [6,2], if x   is stored in location 100 in the row major order.
5. What is the difference between the best case and worst case complexity of an algorithm?

Question3.
The following function month() is a part of a class. What will be the output of the following function month() when the value of n is ‘January ‘ and the value of R is 5?  Show the dry run/working.

void month(String n, int R)

{

If(R<0)

System.out.print(“  “);

else

{

System.out.println (n.charAt(R) +” .”);

month(n, R-1);

}

}

Part II
Answer six questions in this part, choosing two questions from Section A, two from Section B and twofrom Section C.
Section A

Question 4.
a) Given F(P,Q,R,S)= Σ(0,1,2,3,5,7,8,9,10,11)

1. i) Reduce the above expression by using 4 variable Karnaugh map, showing the various groups( i.e. octal, quads and pairs).                                                                                                                                                                                 
ii) Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs.                                                                                                                                                           
2. b) Given P(A,B,C,D)= ABC’D’ + A’BC’D’+ A’BC’D+ ABC’D+A’BCD+ABCD
3. i) Reduce the above expression by using 4 variable Karnaugh map, showing the various groups (i.e. octal, quads and pairs).                                                                                                                                                                                 
ii) Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs.                                                                                                                                                            

Question 5

a) Draw the truth table and logic circuit diagram for a 3X 8 decoder.                                                                                  

b) What do you understand by a multiplexer? State any one application of a multiplexer circuit.                                

c) Draw the logic gate diagram to implement the AND gate by using NOR gate and NAND gate.                                 

Question 6.

1. Draw a logic diagram for the following function using only NAND gate.                                                                  

F(A, B, C, D)=(A’+B’). (B+C’)(C’+A)

1. A combinational logic circuit with three inputs P, Q, R produces output 1 if there are odd number of 0’s as inputs. Draw its truth table and write its SOP expression. Find the complement of the above derived expression using De Morgan’s theorem.                                                                                                                                                
2. What is an abstract class?                                                                                                                                                     

Section B

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 7.                                                                                                                                                    [ 10 ]

 A class RecFact defines a recursive function to find the factorial of a number.   The details of the class are given below: Class name RecFact Data members 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-2)!/  (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.

Question8.

A Transpose of any array is obtained by interchanging the elements of the 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                                          :           Transarray

Data members

arr[][]                                                  :           stores the matrix elements

m                                                         :           integer to store the number of rows

n                                                          :           integer to store the number of columns

Member functions      :

Transarray()                                        :           default constructor

Transarray(int mm, int nn)                 :           to initialize the size of the matrix, m=mm, n=nn

void fillaray()                                      :           to enter the elements of the matrix

void transpose(Transarray A)             :           to find the transpose of a given matrix

void disparray()                                   :           displays the array in a matrix form

Specify the class Transarray giving the details of the constructor and other member functions. You need not to write the main function.                                                                                                                                                                 

Question 9.

Class ChaArray contains an array of n characters (n<=100). You may assume that the array contains only the letters of the English alphabet. Some of the member functions/methods of ChaArray are given below:

Class Name                                                                        ChaArray

Data Members/instance variables :

char ch[]                                                                              : An array of characters

int size                                                                                  : The size of array of characters

Member functions/methods:

ChaArray()                                                                          : Constructor to assign to initialize instance  variables to null.

ChaArray(char c[])                                                           : Constructor to assign character array c to  the instance variable.

void displayArray()                                                          : to display the list of n characters.

void move()                                                                        : to move all the upper case letters to the right side of the array                                                                                                     and the lower case   letters to the left side of the array without                                                                                                     using any standard sorting technique.

Example:

Input: t D f s X v d

Output: t d f s v X D

Specify the class ChaArray giving the details of the two constructors and the functions void displayArray(), and void move() only. You do not need to write the main function.                                                                                                

Section C

Each program 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 comments in the program and mnemonic names or pseudo codes for algorithms. The program must be written in Java and the algorithms must be written in general/standard form, wherever required/ specified. (Flowcharts are not required.)

Question 10.

A consumer wants to computerized his electricity bill calculations for his/her own purpose. There is class meter which contains meter details and another class ElectricityBill which calculates the bill amount. The details of both the classes are as given below:

Class name                             :           Meter

Data members                       :

meternum                    :           long integer data to store meter number.

name                             :           string data to store name of consumer.

mcharge                       :           double type data to store meter rental charges.

Member functions                 :

Meter(long m, double ch, long p)       :           a constructor to assign m to meternum, ch to mcharge and p to prRread.

void readname()                                      :           to accept name of consumer.

Class name                             :           ElectricityBill

Data members                       :

rate                              :           stores rate per unit.

units                            :           stores total units consumed

amt                              :           stores total bill amount

Member functions                 :

ElectricityBill(……..) :           constructor to initialize the data members and assign 3.50 to rate.

double calculations()   :           to find total units consumed and returns the bill amount (units * rate per unit) to be                                                            paid by the consumer.

void dispBill()             :           to display electricity bill in the following format

Meter              Name  Rental             Previous         Current          Rate                Total               Bill

Question 11.
Link is an entity which can hold a maximum of 100 integers. Link enables to add elements from the rear end and remove integers from the front end of the entity. Define a class Link with the following details:

Data members

lnk[]                                         entity to hold the integer elements.

max                                         stores the maximum capacity of the entity.

begin                                       to point to the index of the front end.

end                                          to point to the index of the rear end.

Member functions

Link(int nn)                              constructor to initialize max=mm, begin=0, end=0.

the message “OUT OF SIZE”.

int dellink()                              to remove and return an element from the front index, if possible

Otherwise display the message “EMPTY…” and return -99.

void display()               displays the elements of the entity.

Specify the class Link giving details of all the functions.                                                                                                          

Question 12.
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, int x)

b) Answer the following questions from the diagram of a binary tree given below:-
List the nodes in the tree given below using:                                                                                                                               

• Preorder Traversal
• Postorder Traversal
• Inorder traversal 