Free ISC sample paper 2021

ISC Class 12 Sample Paper 5 Standard: 12 Subject: Computer Max Marks: 70 Max. Time 3 hours ---------------------------------------------------------------------------------------- ------------------------------------------------------------------------- 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 Question 1. [1X5=5] A) Draw the truth table to prove the proportional logic expression. a<=>b = (a => b) . (b => a) B) Reduce the following 3 input function into its simplest form F(X,Y,Z)= Σ(0,1,3,5) C) Given, F (X, Y, Z) = (X+Y). (Y+Z) write the function in canonical product-of-sum form. D) Convert the following expression F(X, Y, Z)=XY+Y’Z into minterms. E) Simplify the following expression using law of Boolean algebra. At each step clearly state the law used for simplification. xy + xz + xyz Question 2. [2 x 5 =10] a) Define a Queue. How is dequeue is different from queue b) Convert the following infix notation to postfix: A+[(B+C)+(D+E)* F]/G c) State the differences between a constructor and a function. d) For an array of real numbers x [6][20], find the address of x [5] [4 ], if x [0] [0] is stored in location 100 in the column major order. Assume that each element requires 4 bytes. e) What do you mean by time and space complexity? Question3. Give output of the following function where a and b are arguments greater than 0. Show the dry run/working. int first(int a , int b) { Int ans, sm,la; If(a<b) { sm=a; la=b; } else 1 { sm=b; la=a; } ans=la; while(ans%sum!=0) ans+=la; return ans; } (i) What will the function first (7,5) return ? [2] (ii) What will the function first (6,8) return ? [2] (iii) In one line, state what the function is doing. [1] Part II 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 F(P,Q,R,S)= Σ(0,1,2,3,5,6,7,10,13,14,15) 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 variables and their complements are available as inputs. [1] b) Given G(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 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 variables and their complements are available as inputs. [1] Question 5 a). Draw the truth table and logic circuit diagram for a decimal to Binary Encoder. [5] b) Define maxterms and minterms. Give one example of each. [2] c) State whether the following expression is a Tautology or Contradiction with the help of a truth table: (X↔Z). [(X→Y).(Y→Z)] [3] Question 6. a. How many select lines does an 8:1 multiplexer have? Briefly explain the working of a 4:1 multiplexer with the logic diagram. [5] b. Reduce the Boolean expression in to the simplest form. {(C.D)’+A’}+a+(C.D)+(A.B) [5] 2 Section B Answer 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. A class Admission contains the admission numbers of 100 students. Some of the data members/ member functions are given below: Class name : Admission Data members Adno[ ] : integer array to store admission numbers Member functions Admission( ) : constructor to initialize the array elements. void fillArray( ) : to accept the elements of array in ascending order. Int binSearch(int l,int u, int v) : to search for a particular admission number(v) using binary search and recursive technique and returns 1 if found otherwise returns -1. Specify the class Admission giving details of the constructor, void fillArray( ) and int binSearch(int,int,int). Define the main function to create an object and call the functions accordingly to enable the task. [10] Question8. 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: Class name Piglatin variables : Txt to store a word len to store the length Member functions : Piglatin( ) constructor to initialize the data members 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. [10] 3 Question 9. 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: Class name Perfect Data members/instance variables n stores an integer number Member functions: Perfect( ) Perfect(int) default constructor parameterized constructor to assign a value to ‘n'. void perfect_sq() void sum_of() to display the first 5 perfect squares larger than ‘n’ (if n = 15, the next 3 perfect squares are 16, 25, 36) 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. [10] Section C Answer any two questions 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 class Personal contains employee details and another class Retire calculates the employee’s Provident Fund and Gratuity. The details of the two classes are given below: Class name Personal Data Members: Name stores the employee name Pan stores the employee PAN number basic_pay stores the employee basic salary acc_no stores the employee bank account number Member functions: Personal( …. ) parameterized constructor to assign value to data members void display( ) to display the employee details 4 Class name Data Members: Yrs Pf Retire stores the employee years of service stores the employee provident fund amount Grat Member functions: Retire ( …. ) void provident( ) void gratuity( ) void display1( ) stores the employee gratuity amount parameterized constructor to assign value to data members of both the classes. calculates the PF as (2% of the basic pay) * years of service. calculates the gratuity as 12 months salary, if the years of service is more than or equal to 10 years else the gratuity amount is nill. Displays the employee details along with the PF and gratuity amount. Assume that the super class Personal has been defined. Using the concept of inheritance specify the class Retire giving details of the constructor, void provident () and void gratuity ().The super class and themain function need not be written. [5] Question 11. Rack is a kind of data structure which can store utmost 20 books. The Rack restriction is that a book can be kept into the rack or removed only at one end and i.e., on the top. The class Rack has the following details. Class name : Rack Data members book[] : an array of string of maximum 50 locations to store books. limit : stores the capacity of the array name : String variable to store name of the book. top: integer to indicate topmost book in the rack. Member functions Rack():constructor to store blank in the array book[]. Rack(int m) : constructor to initialize the data members m to limit and -1 to top. void putthebook() : input name of the book into variable name and adds it on the top into the array[], if possible else display the message “overflow” void removebook() : to remove a book from the top of the rack, if array is empty then display the message “Rack underflow” void disp() : displays the books present in the list Specify the class Rack giving details of only the constructor Rack(int), member function void putthebook (int), void removebook ().Assume that other functions have been defined.The main function need not be written. [5] 5 Question 12. A) A Linked List is formed from the objects of the class, [2] 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) b) Answer the following questions from the diagram of a binary tree given below:- List the nodes in the tree given below using: [3] (i) Preorder Traversal (ii) Postorder Traversal (iii) Inorder traversal F G J I K L H P M O N 6 ―――――――――― ISC Class 12 Sample Paper 6 Standard: 12 Subject: Computer Max Marks: 70 Max. Time 3 hours ---------------------------------------------------------------------------------------- ------------------------------------------------------------------------ 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. -------------------------------------------------------------------------------- ---------------------------------------------------------------- ----- PART I Answer all questions Question 1. [1X5=5 ] a) State the two compliment laws of Boolean Algebra. Verify any one using truth table. b) What do you understand by combinational circuit? c) What is Big O notation? d) Obtain the truth Table to verify the following expression: x.(y+z)=xy+xz. Also name the law stated above. e) Given, F(X,Y,Z)=(X’+Y’).(Y+Z’) write the function in canonical product-of-sum form. Question 2. [2 x 5 =10] a) Define a Queue. How is dequeue different from queue b) State two ways in which linked lists are different from arrays. c) Each element of an array A[-20……20,15…..45] requires 2 bytes of storage. If the array is stored row major wise determine the location of A[2,18]. d) What do you understand by time complexity and space complexity? e) Convert the following infix notation to postfix form: (B+D)*(G+H/K). Question 3 [5] The following function trial() perform are a part of some class. Show dry run/working. What will be the output of the function perform() when the value of p is 5? int trial(int n) { if(n==1) return 2; else if(n==2) return 3; return trial(n-2)+trial(n-1); } void perform(int p) { int x; for(inti=1;i<=p;i++) { x=trial(i); System.out.print(x+” ”); } } Part II Answer six questions in this part, choosing two from Section A, two from Section B and twofrom Section C 1 Section A Answer any two questions Question 4. a) Given F(A,B,C,D) = Σ (0,2, 6,8,10,11,14,15) (i) Reduce the above expression by using 4 - Variable K-Map, showing the various groups (i.e octal , quads and pairs). [4] (ii) Draw the Logic gate diagram of the reduced expression using NAND Gate only. [1] b) Given F(A,B,C,D) = π (5,7,8,10,12,14,15). (i) Reduce the above expression by using 4 - Variable K-Map, showing the variousgroups (i.e octal , quads and pairs). [4] (ii) Draw the Logic gate diagram of the reduced expression. [1] Question 5. (a) What is Full adder? Write the SOP expressions for sum and carry. Simplify the expressions algebraically using Boolean algebra. [5] (b) Draw the truth table and logic circuit diagram for a Decimal to Binary encoder. [5] Question 6. (a) Write the equivalent Boolean expression for the propositions F=X→Y and F=X↔Y. [2] (b) Minimize the following expression. At each step state clearly the law used Y=(A+B’).(B+CD)’ [3] (c) Draw the truth table and logic circuit diagram for a 3x8 decoder. What is the difference between a multiplexer and a decoder? [5] Section B Answer two questions Each program should be written in such a way that it clearly depicts the logic of the problem. use mnemonic names and comments in the program. (Flowcharts and algorithms are notrequired) The programs must be written in Java. Question 7. [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 4 + 64 = 68 68 = (6)2 + (8)2 36 + 64 = 100 100 = (1)2 + (0)2 + (0)2 =1+0+0=1 Here 28 is 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: Class name Data members N : Happy : stores the number 2 Member functions Happy() : constructor to assign 0 to n. void getnum(int nn) : to assign the parameter value to the number n=nn. int sum_sqdigits(int x) : returns the sum of the square of the digits of the number x,using the recursive technique. void ishappy() : checks if the given number is a happy number by calling the function sum_sq_digits(int) and displays an appropriate message. Specify the class Happy giving details of all the functions also define a main() function to create an object and call the methods to check for Happy number. Question 9. [10] A class stringop is designed to handle string related operations. Some members of the class are given below: Data member txt : to store the given string of maximum length 100. Member function stringop() : constructor void readstring() : to accept the string char caseconvert(int): to convert the letter to other case void circulardecode() : to decode the string by replacing each letter by converting it to opposite case and then by the next character in a circular way. Hence “AbZ” will decode “bCa”. Specify the class giving details of all member functions. You do not need to write function main(). Question 10. [10] A class Rearrange has been defined to insert an element and to delete an element from an array. Some of the members of the class are given below: Class name Data members : Rearrange a[] n pos1 pos2 item : integer type array : size of array (integer) : position of insertion (integer) : position of deletion : item to be inserted (integer) Member functions void enter() : to enter size, array elements and to display the entered elements. 3 void insert() void disp1() : to accept element (item) to be inserted, position of insertion and insert the element (item) at the position of insertion. : to display the array after item is inserted. void disp2() : to display the array after item is deleted. void remove() : to accept the position of deletion and delete element(item) at the position of deletion. Specify the class Rearrange giving details of the functions void enter(), void insert(), void disp1(), void disp2() and void remove(). The main function need not be written. Section C Answer any two questions 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 foralgorithms. 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 class Personal contains employee details and another class Retire calculates the employee’s provident Fund and Gratuity. The details of the two classes are given below: Class name Data Members: Name Pan basic_pay acc_no Personal stores the employee name stores the employee PAN number stores the employee basic salary stores the employee bank account number Member functions: Personal( …. ) void display( ) parameterized constructor to assign value to data members to display the employee details Class name Data Members: Yrs Pf Grat Member functions: Retire ( …. ) void provident( ) Retire stores the employee years of service stores the employee provident fund amount stores the employee gratuity amount parameterized constructor to assign value to data members of both the classes. calculates the PF as (2% of the basic pay) * years of service. 4 void gratuity( ) void display1( ) calculates the gratuity as 12 months’ salary, if the years of service is more than or equal to 10 years else the gratuity amount is nill. Displays the employee details along with the PF and gratuity amount. Assume that the super class Personal has been defined. Using the concept of inheritance specify theclass Retire giving details of the constructor, void provident() and void gratuity().The super class and themain function need not be written. [5] Question 11. A dequeue enables the user to add and remove integers from both the ends i.e. front and rear. Define a class DeQueue with the following details: Class name : Dequeue Data members ele[] : array to hold integer elements. cap : stores the maximum capacity of the array. front : to point the index of the front. rear : to point the index of the rear. Member functions Dequeue(int max) : constructor to initialize the data member cap = max, front = rear = 0 andcreate the integer array. Void pushfront(int v) : to add integers from the front index, if possible else display the message (“full from front”). Int popfront() : to remove and return element from front. If array is empty then return -999. Void pushrear(int v) : to add integers from the front index if possible else display the message(“full from rear”). Int poprear() : to remove and return elements from rear. If the array is empty then return -999. Specify the class Dequeue giving details only the constructor Dequeue(int), void pushfront(int) and int poprear(). Assume that other functions have been defined. The main function need not be written. [5] Question 12. (a) A linked list is formed from the objects of the class. [2] class Node { int info; Node link; } 5 Write an algorithm OR a method for deleting a node from a linked list. The method declaration is given: void deletenode(Node start). (c) Answer the following from the diagram of a binary Tree [3] A B C D E F G H (i) Write the Inorder tree traversal. (ii) Name the Leaves of the tree (iii) Height of the tree. 6 ―――――――――― ISC Class 12 Sample Paper 7 Standard: 12 Subject: Computer Max Marks: 70 Max. Time 3 hours ---------------------------------------------------------------------------------------- ------------------------------------------------------------------------- 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 Question 1. A) Verify if, P.(~P+Q’)=(P→Q) using truth table. B) Find the complement of F(A,B,C,D)= [A + { ( B+C) . (B’+ D’)}] C) Find the dual for the Boolean equation. AB’ + BC’ +1 =1 D) If A=1, B=0, C=1 and D=1 find its i) maxterm ii) minterm E) 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 [ 1 x 5 = 5] Question 2. a)State the different applications of stack. b) Convert the following infix notation to postfix: (A+ ( B*C)) / (C-(D*B)) c) Explainany two standard ways of traversing a binary tree. d) A two dimensional array defined as X[3…6, -2…2] requires 2 bytes of storage space for eachelement. If the array is stored in row major order, determine the address of X[5,1], given the base address as 1200. e) i) What is the worst-case complexity of the following code segment : for(inti=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. The following is a function of some class. What will be the output of the function recs( ) when the value of num is equal 1 to 4?Show the dry run / working. int recs(int num) { if(num==0) return 0; else return num+ recs(num-1); } [5] Part II 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 F(P,Q,R,S)= Σ(0,1,3,4,5,6,7,9,10,11,13,15) 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 variables and their complements are available as inputs. [1] b) Given G(X,Y,Z,W)= π(0,2,4,6,8,9,10,11) 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 variables and their complements are available as inputs. [1] Question 5. a) Differentiate between XNOR and XOR gates. Draw the truth table and logic diagrams of three input XNOR gates. [4] b) Differentiate between proposition and wff. [2] c) Define half adder. Construct the truth table and logic diagram of a halfadder. [4] Question 6. a) Draw the logic gate diagram for the Boolean function F(A,B,C)= (A’+B).(B’+C) making use of NOR gates only. [3] b) Define proposition. How does tautology differ from contradiction? [2] c) Convert (X’+Y+Z’).(X+Y’+Z).(X+Y+Z’).(X+Y+Z) into SOP form. [2] d) Briefly explain the working of a 4:1 multiplexer. Also draw the logic diagram of 4:1 multiplexer. [3] Section B Answer 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. A class Matrix contains a two dimensional integer array of order [ m x n ]. The maximum value possible for both m and n is 25. Design a class Matrix to find the difference of the two matrices. The details of the members of the class are given below: 2 Class name : Matrix Data members arr[][] : stores the matrix element m: integer to store the number of rows n: integer to store the number of columns Member functions: Matrix(int mm, intnn) : to initialize the size of the matrix m=mm and n=nn Void fillarray() : to enter the elements of the matrix Matrix SubMat(Matrix A) : subtract the current object from the matrix of parameterized object and return theresulting object. void display() : display the matrix elements. Specify the class Matrix giving details of the constructor Matrix(int,int), void fillarray(),Matrix SubMat(Matrix) and void display(). Define the main() function to create an object and call the functions accordingly to enable the task. [ 10] Question8. A class Modify has been defined with the following details: Class name : Modify Data members St : stores a string len : to store the length of the string. Member functions void read() : to accept the string in uppercase alphabets. Voidputin(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 at a distance of 2 moves ahead. For example:- “ABCD” becomes“CDEF”, “XYZ” becomes “ZAB”. Specify the class Modify giving details of the functions voidread(), void putin(int,char), void takeout(int)and void change(). The main function need not be written. [ 10 ] Question 9. A Special number is a number in which the sum of the factorial of its digits is equal to the number. Example 1445 ( 1! + 4! + 5!= 145). Thus, 145 is a special number. Design a class Special to check if thegiven number is a Special number or not. Some of the members of the class are given below: Class name : Special Data members n : integer to store the number Member functions Special() : default constructor void read() : to accept the number int factorial(int x) : return the factorial of a number using recursion technique Boolean isSpecial() : checks for the special number by invoking the function factorial() and returns true if Special, otherwise returns false. void display() : to show the result with an appropriate message Specify the class Special giving details of the constructor, void read(), int factorial() , Boolean isSpecial ()and void display(). Define the main function to create an object and call the functions accordingly to enable the task. [ 10 ] Section C Answer any two questions 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. 3 A Super class Student defines the personal data of a student while another class Marks defines the register number, name of subject and marks obtained by the student. The details of both the classes are givenbelow: Class name : Student Data members name : string to store name. sex : string to store sex age : integer to store age Member functions Void inpdetails() : to accept values for data members. void show() : to display personal data of student. Class name : Marks Data members regnum :int to store registration number. marks :int to store marks. subject : String to store subject name. Member functions Void inpdetails() : to accept values for data members. void show() : to display exam and student details. Assume that the super class Student has been defined. Using the concept of inheritance specify the class marks giving details of the constructor, void inpdetails() and void show().The super class and themain function need not be written. [5] Question 11. Define a class Repeat which allows the user to add elements from one end (rear) and remove elementsfrom the other end (front) only.The following details of the class Repeat are given below: Class name : Repeat Data members st[] : an array to hold a maximum of 100 integer elements cap : stores the capacity of the array f: to point to the index of the front r: to point to the index of the rear Member functions Repeat(int m) : constructor to initialize the data memberscap=m, f=0, r=0 and to create the integer array Void pushvalue(int v) : to add integers from the rear index if possibleelse display the message “overflow” Int popvalue() : to remove and return element from the front, ifarray is empty then return -9999 Void disp() : displays the elements present in the list Specify the class Repeat giving details of the constructor Repeat(int), member function void pushvalue(int), int popvalue().Assume that other functions have been defined.The main function need not be written. [5] Question 12. 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 declarationis given below: void deletenode(Node start) [2] 4 b) Answer the following questions from the diagram of a binary tree given below:- ii) Write the post order tree traversal. [1] iii) Write the internal nodes of the tree. [1] iv) State the level of the root of the tree. [1] 5 ―――――――――― ISC Class 12 Sample Paper 8 Standard: 12 Max Marks: 100 Subject: Computer Max. Time 3 hours ----------------------------------------------------------------------------------------------------------------- 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 1. (a) Convert … (see the PDF for the full paper)