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ISC Class XII Board Exam 2018 : Computer Science

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COMPUTER SCIENCE PAPER 1 (THEORY) (Maximum Marks: 70) (Time allowed: 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 six questions from Part-II, choosing two 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 (20 Marks) Answer all questions. While answering questions in this Part, indicate briefly your working and reasoning, wherever required. Question 1 (a) State the Commutative law and prove it with the help of a truth table. [1] (b) Convert the following expression into its canonical POS form: [1] F(X, Y, Z) = (X+Y ) (Y +Z) (c) Find the dual of: [1] (A +B) (1+B ) = A +B (d) Verify the following proposition with the help of a truth table: [1] ( P Q ) ( P ~Q ) = P (e) If F(A, B, C) = A (BC + B C), then find F [1] Question 2 (a) What are Wrapper classes? Give any two examples. [2] (b) A matrix A[m][m] is stored in the memory with each element requiring 4 bytes of storage. If the base address at A[1][1] is 1500 and the address of A[4][5] is 1608, determine the order of the matrix when it is stored in Column Major Wise. [2] --------------------------------------------------------------------------------------------------------------------This Paper consists of 9 printed pages and 1 blank page. 1218-868A Turn over Copyright reserved. (c) Convert the following infix notation to postfix form: [2] A+(B C (D/E) F) (d) Define Big O notation. State the two factors which determine the complexity of an algorithm. [2] (e) What is exceptional handling? Also, state the purpose of finally block in a try catch statement. [2] Question 3 The following is a function of some class which checks if a positive integer is a Palindrome number by returning true or false. (A number is said to be palindrome if the reverse of the number is equal to the original number.) The function does not use modulus (%) operator to extract digit. There are some places in the code marked by ?1?, ?2?, ?3?, ?4?, ?5? which may be replaced by a statement / expression so that the function works properly. (i) (ii) (iii) (iv) (v) boolean PalindromeNum( int N ) { int rev= ?1?; int num=N; while( num>0) { int f= num/10; int s = ?2?; int digit = num ?3?; rev= ?4? + digit; num /= ?5?; } if( rev= =N ) return true; else return false; } What is the statement or expression at ?1? What is the statement or expression at ?2? What is the statement or expression at ?3? What is the statement or expression at ?4? What is the statement or expression at ?5? [ [1] [1] [1] [1] [1] ------------------------------------------------------------------------------------------------------------------------------- 2 1218-868A PART II (50 Marks) Answer six questions in this part, choosing two questions from Section A, two from Section B and two from Section C. SECTION - A Answer any two questions. Question 4 (a) Given the Boolean function F(A, B, C, D) = (0,2,4,8,9,10,12,13). (i) Reduce the above expression by using 4-variable Karnaugh map, showing the various groups (i.e. octal, quads and pairs). Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs. (ii) (b) [4] [1] Given the Boolean function: F(A, B, C, D) = (3,4,5,6,7,10,11,14,15). (i) Reduce the above expression by using 4-variable Karnaugh map, showing the various groups (i.e. octal, quads and pairs). [4] (ii) Draw the logic gate diagram for the reduced expression. Assume that the [1] variables and their complements are available as inputs. Question 5 (a) A training institute intends to give scholarships to its students as per the criteria given below : [5] The student has excellent academic record but is financially weak. OR The student does not have an excellent academic record and belongs to a backward class. OR The student does not have an excellent academic record and is physically impaired. The inputs are: INPUTS A F C I Has excellent academic record Financially sound Belongs to a backward class Is physically impaired (In all the above cases 1 indicates yes and 0 indicates no). Output : X [1 indicates yes, 0 indicates no for all cases] Draw the truth table for the inputs and outputs given above and write the SOP expression for X(A,F,C,I). ------------------------------------------------------------------------------------------------------------------------------- 3 1218-868A Turn over (b) (c) Using the truth table, state whether the following proposition is a tautology, contingency or a contradiction: ~( A B ) V ( ~A => B ) Simplify the following expression, using Boolean laws: [3] [2] A ( A + B ) C ( A + B ) Question 6 (a) What is an Encoder? Draw the Encoder circuit to convert A-F hexadecimal numbers to binary. State an application of a Multiplexer. [5] (b) Differentiate between Half Adder and Full Adder. Draw the logic circuit diagram for a Full Adder. [3] (c) Using only NAND gates, draw the logic circuit diagram for A + B. [2] SECTION 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 7 Design a class Perfect to check if a given number is a perfect number or not. [ A number is said to be perfect if sum of the factors of the number excluding itself is equal to the original number] Example : 6 = 1 + 2 + 3 (where 1, 2 and 3 are factors of 6, excluding itself) [10] Some of the members of the class are given below: Class name Data members/instance variables: num Methods/Member functions: Perfect (int nn) : Perfect : to store the number : parameterized constructor to initialize the data member num=nn int sum_of_factors(int i) : returns the sum of the factors of the number(num), excluding itself, using recursive technique void check( ) : checks whether the given number is perfect by invoking the function sum_of_factors( ) and displays the result with an appropriate message Specify the class Perfect giving details of the constructor( ), int sum_of_factors(int) and void check( ). Define a main( ) function to create an object and call the functions accordingly to enable the task. ------------------------------------------------------------------------------------------------------------------------------- 4 1218-868A Question 8 Two matrices are said to be equal if they have the same dimension and their corresponding elements are equal. For example the two matrices A and B given below are equal: Matrix A 1 2 3 2 4 5 [10] Matrix B 3 5 6 1 2 3 2 4 5 3 5 6 Design a class EqMat to check if two matrices are equal or not. Assume that the two matrices have the same dimension. Some of the members of the class are given below: Class name Data members/instance variables: a[ ][ ] m n Member functions/methods: EqMat(int mm, int nn) : EqMat : : : to store integer elements to store the number of rows to store the number of columns : parameterised constructor to initialise the data members m = mm and n = nn to enter elements in the array checks if the parameterized objects P and Q are equal and returns 1 if true, otherwise returns 0 void readarray( ) int check(EqMat P, EqMat Q) : : void print( ) : displays the array elements Define the class EqMat giving details of the constructor( ), void readarray( ), int check(EqMat, EqMat) and void print( ). Define the main( ) function to create objects and call the functions accordingly to enable the task. ------------------------------------------------------------------------------------------------------------------------------- 5 1218-868A Turn over Question 9 A class Capital has been defined to check whether a sentence has words beginning with a [10] capital letter or not. Some of the members of the class are given below: Class name : Capital sent : to store a sentence freq : stores the frequency of words beginning with a capital letter Capital( ) : default constructor void input( ) : to accept the sentence boolean isCap(String w) : checks and returns true if word begins with a capital letter, otherwise returns false void display( ) : displays the sentence along with the frequency of the words beginning with a capital letter Data member/instance variable: Member functions/methods: Specify the class Capital, giving the details of the constructor( ), void input( ), boolean isCap(String) and void display( ). Define the main( ) function to create an object and call the functions accordingly to enable the task. ------------------------------------------------------------------------------------------------------------------------------- 6 1218-868A SECTION 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 10 A super class Number is defined to calculate the factorial of a number. Define a sub class Series to find the sum of the series S = 1! + 2! + 3! + 4!+ ......+n! [5] The details of the members of both the classes are given below: Class name Data member/instance variable: n Member functions/methods: Number(int nn) : Number : to store an integer number : parameterized constructor to initialize the data member n=nn int factorial(int a) : returns the factorial of a number (factorial of n = 1 2 3 n) void display( ) : displays the data members Class name: Data member/instance variable: sum Member functions/methods: Series( ) Series : to store the sum of the series : void calsum( ) : parameterized constructor to initialize the data members of both the classes calculates the sum of the given series void display( ) : displays the data members of both the classes Assume that the super class Number has been defined. Using the concept of inheritance, specify the class Series giving the details of the constructor( ),void calsum( ) and void display( ). The super class, main function and algorithm need NOT be written. ------------------------------------------------------------------------------------------------------------------------------- 7 1218-868A Turn over Question 11 Register is an entity which can hold a maximum of 100 names. The register enables the user to add and remove names from the top most end only. Define a class Register with the following details: Class name : Register Data members / instance variables: stud[ ] : array to store the names of the students cap : stores the maximum capacity of the array top : to point the index of the top end : constructor to initialize the data member cap = max, top = 1 and create the string array void push(String n) : to add names in the register at the top location if possible, otherwise display the message OVERFLOW String pop( ) : removes and returns the names from the top most location of the register if any, else returns $$ void display( ) : displays all the names in the register Member functions: Register (int max) (a) Specify the class Register giving details of the functions void push(String) and String pop( ). Assume that the other functions have been defined. [4] The main function and algorithm need NOT be written. (b) Name the entity used in the above data structure arrangement. [1] Question 12 (a) A linked list is formed from the objects of the class Node. The class structure of the [2] Node is given below: class Node { int n; Node link; } Write an Algorithm OR a Method to search for a number from an existing linked list. The method declaration is as follows: void FindNode( Node str, int b ) ------------------------------------------------------------------------------------------------------------------------------- 8 1218-868A [2] (b) Answer the following questions from the diagram of a Binary Tree given below: A E G B C D H F (i) Write the inorder traversal of the above tree structure. [1] (ii) State the height of the tree, if the root is at level 0 (zero). [1] (iii) List the leaf nodes of the tree. [1] ------------------------------------------------------------------------------------------------------------------------------- 9 1218-868A Turn over [1]

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