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ISC Class XII Prelims 2025 : Computer Science

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HALF YEARLY EXAMINATION 2025-2026 CLASS: XII FULL MARKS: 35 COMPUTER Science Time: One and half hour Instructions to Candidates You are allowed additional 15 minutes for only reading the question paper. You must NOT start writing during the reading time. This question paper has 5 printed pages. It is divided into two parts and has 8 questions in all. Part I is compulsory and has two questions. Answer all questions. Part II is divided into three sections: A, B and C. While attempting Multiple Choice Questions in Part I, you are required to write only ONE option as the answer. Each section in Part II has two questions. Any one question have to be attempted from each section. The intended marks for questions are given in brackets [ ]. PART I 10 MARKS Answer all questions. While answering questions in this Part, indicate briefly your working and reasoning, wherever required. Question 1 i) Assume int [ ] [ ] x = { {8,9} , {5,6,7},{1,2,3,4}}, what are x[0].length, [1] x[1].length, and x[2].length ? (a) 2, 3 and 3 (b) 2, 3 and 4 (c) 3, 3 and 3 (d) 2, 2 and 2 ii) If binary search technique uses recursion instead of iteration, the code: [1] i. will contain two base cases. ii. will contain two recursive cases. iii. when executed will lead to an exception, stack overflow. Which of the above is valid? (a) i and ii (b) ii and iii (c) i and iii (d) Only iii iii) Assertion (A): In Boolean Algebra, dual of the Boolean expression (A+B) .1 [1] is equal to 0. Reason (R): In Boolean Algebra, the complement of an OR operation is equal to the AND operation of complement of the individual variables. (a) Both A and R are true, and R is (b) Both A and R are true, but R is not the correct explanation of A the correct explanation of A. (c) A is true, but R is false. (d) A is false, but R is true. Page 1 of 5 iv) Assertion (A): The contrapositive of p => q is q => p Reason (R): Contrapositive is the conditional statement, obtained after interchanging antecedent and consequent. (a) Both A and R are true, and R is (b) Both A and R are false the correct explanation of A (c) A is true, but R is false. (d) A is false, but R is true. v) Which one of the following keywords will make the data member as a class variable? (a) static (b) final (c) abstract (d) public Question 2 i) A 2 to 4 decoder contains 2 inputs denoted by A1 and A0 and 4 outputs denoted by D0, D1, D2, D3. Write the minterm representations for D1 and D3. ii) Following method is a part of a class MyArray. int check(int m[ ], int i) { if (i<= 0) { return 0; } return check(m, i-2 ) + m[i-1]; } public static void main( ) { int m[ ] = {1, 2, 3, 4}; int ans = check(m, m.length); System.out.println(ans); } a) Predict the output of the code considering there is no compilation error. Show the working. b) Considering the if condition is changed to if(i<0) , how will it affect the output? [1] [1] [2] [2] [1] PART II 25 MARKS Answer 3 questions in this part, choosing one question from Section A, one from Section B and one from Section C. SECTION - A Answer any one questions. Question 3 i) A student from the Electronics department is asked to design a digital alarm for a smart home security system for the outside area. It comprises a sensor and a digital identification (ID) card with six-digit personal identification number (PIN). The alarm is supposed to buzz if wrongful entry is attempted, either by breaking the glass window or by entering the wrong PIN. Following statements are the criteria for the alarm to buzz: The sensor detects the door opening without scanning a digital ID card. or The sensor detects the door opening by breaking of the door lock. or Page 2 of 5 The sensor detects the wrong pin entry thrice of the digital ID card while opening the door. The inputs are: Inputs D Door opening B Breaking of door lock S Scanning security card P Entering correct six-digit pin less than three times (In all the above cases 1 indicates Yes and 0 indicates No). Output: A Denotes the buzz of security alarm system (1 indicates yes and 0 indicates no) Draw the truth table for the inputs and outputs given above. Write the canonical POS expression for the A (D, B, S, P). ii) Reduce the above expression A(D,B,S,P) by using 4 variable K Map, showing the various groups (I.e. octate, quad or pair) Draw the logic gate diagram for the reduced expression. Assume that the variables and their compliments are available as inputs. Question 4 a) Given the Boolean function F (P,Q,R,S) = (2,3,5,7,8,10,11,12,13,15). i) Reduce the above expression by using a 4-variable Karnaugh map, showing the various groups (i.e. octal, quads and pairs). ii) Draw the logic gate diagram for the reduced expression using NAND gate only. Assume that the variables and their complements are available as inputs. b) f (a, b, c ) = a.b + a.c + b.c . Find its corresponding Cardinal and Canonical sumof- product expression? c) If a=1, b=0, c=1, d=0, then write maxterm and minterm for F(a, b, c, d) in canonical form? [5] [4] [1] [4] [1] [3] [2] SECTION B Answer any one question 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 5 An Automorphic number is a number whose square ends with the given number itself. E.g. (5)2 = 25, (25)2 = 625, (76)2 = 5776. Design a class Automorphic to check if numbers in the given range are Automorphic numbers or not. The member functions and data members of the class are given below: Class Name : Automorphic Data members/instance variables: l, u :lower and upper limits of the range count :frequency of the automorphic numbers in the range l and u Page 3 of 5 [10] Member functions : Automorphic(int l, int u): parameterised constructor to assign values to data members boolean check(int n) : to check if n is an automorphic number. If yes it returns true otherwise returns false. void list( ) : to check all the numbers between the range l and u, by calling check(int n) and to display only the automorphic numbers. Also to display the frequency of the automorphic numbers in the given range. Specify the class Automorphic giving details of the parameterised constructor, boolean check(int n) and void list( ). Create one object in the main( )method and call all the methods appropriately. Sample input Enter the lower limit of the range->1 Enter the upper limit of the range->1000 Sample output List of Automorphic numbers from 1 to 1000 : Number Square 1 1 5 25 6 36 25 625 76 5776 376 141376 625 390625 Frequency of Automorphic numbers between 1 to 1000 : 7 Question 6 Design a class Spy to check if a number is a Spy number or not. A spy number is a number where the sum of its digits equals the product of its digits. For example, 1124 is a spy number, the sum of its digits is 1+1+2+4=8 and the product of its digits is 1*1*2*4=8. Class name : Spy Data Members: num : to store the number Member methods: Spy(int nn) : initialize the data member num=nn int sumOfDigits(int i) : returns the sum of digits of num using recursive technique Page 4 of 5 [10] int prodOfDigits( int i) : returns the product of digits of num using recursive technique void check( ) : checks whether the given number is a Spy number or not by invoking the functions sumOfDigits( ) and prodOfDigits( ) and displays appropriate message Specify the class Spy giving details of the functions int sumOfDigits(int ), void check( ), int prodOfDigits(int). Assume that the data member and constructor are already defined. Define a main method to create an object and call the functions accordingly to enable the task. SECTION C Answer any One question Question 7 a) If A = It is cloudy and B = It is raining , then write the proposition for (i) Contrapositive (ii) Converse b) Write the cardinal Product-of-Sum (POS) expression for the sum and carry of a full adder. c) Simplify the following expression: AB C + AB C + ABC Question 8 a) Using a truth table, state whether the following proposition is a Tautology, Contradiction or Contingency: ~(P =>Q)<=>(~P Q) b) How is a decoder different from a multiplexer? c) Find the output of following snippet: String S1= "AB" , S2= "BC"; for(int i=0, j=0 ; i< S1.length( ) ; i++, j++) System.out.println(S1.charAt(i)+S2.charAt(j)); d) What is the length of the array int arr[ ], if its first index is x and the last index is y? ************** Page 5 of 5 [2] [2] [1] [2] [1] [1] [1]

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