# Computer Science (Theory) Official 2022-2023 ISC (Commerce) Class 12 Question Paper Solution

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Computer Science (Theory) [Official]
Marks: 70 CISCE
ISC (Commerce)
ISC (Science)

Academic Year: 2022-2023
Date & Time: 20th March 2023, 2:00 pm
Duration: 3h
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1. Candidates are allowed additional 15 minutes for only reading the paper.
2. They must NOT start writing during this time.
3. 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.
4. All working, including rough work, should be done on the same sheet as the rest of the answer:
5. 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.)
[10]1
[1]1.i

According to De Morgan's law (a +b + c')' will be equal to ______.

a' + b' + c'

a' + b' + c

a' · b'· c'

a' · b'· c

Concept: DeMorgan’S Law/Theorem and Their Applications
Chapter: [0.01] Boolean Algebra
[1]1.ii

The dual of (X' + 1) · (Y' + 0) = Y' is ______.

X · 0 + Y · 1 = Y

X' · 1 + Y' · 0 = Y

X' · 0 + Y' · 1 = Y

(X' + 0) + (Y' + 1) = Y'

Concept: Basic Theorems of Boolean Algebra (Eg. Duality, Idempotence, Commutativity, Associativity, Distributivity, Operations with 0 and 1, Complements, Absorption, Involution)
Chapter: [0.01] Boolean Algebra
[1]1.iii

The reduced expression of the Boolean function F(P, Q) = P' · + P · Q is ______.

P' + Q

P

P'

P + Q

Concept: Basic Theorems of Boolean Algebra (Eg. Duality, Idempotence, Commutativity, Associativity, Distributivity, Operations with 0 and 1, Complements, Absorption, Involution)
Chapter: [0.01] Boolean Algebra
[1]1.iv

If (~p ⇒ ~q), then its contrapositive will be ______.

P ⇒ q

q ⇒ p

~q ⇒ p

~p ⇒ q

Concept: Class as a Contract
Chapter: [0.1] Arrays, Strings
[1]1.v

The keyword that allows multi-level inheritance in Java programming is ______.

implements

super

extends

this

Concept: Programming in Java (Review of Class Xi Sections B and C)
Chapter: [0.04] Programming in Java (Review of Class Xi Sections B and C)
[1]1.vi

Write the minterm of F(A, B, C, D) when A = 1, B = 0, C = 0 and D = 1.

Concept: Big O Notation for Computational Complexity
Chapter: [0.14] Complexity and Big O Notation
[1]1.vii

Verify if (A + A')' is a Tautology, Contradiction or a Contingency.

Concept: Truth Tables
Chapter: [0.01] Boolean Algebra
[1]1.viii

State any one purpose of using the keyword this in Java programming.

Concept: Object as an Instance of a Class
Chapter: [0.05] Objects
[1]1.ix

Mention any two properties of the data members of an Interface.

Concept: Interfaces in Java
Chapter: [0.1] Arrays, Strings
[1]1.x

What is the importance of the reference part in a Linked List?

Concept: Recursive Data Structures - Single Linked List (Algorithm and Programming), Binary Trees, Tree Traversals (Conceptual)
Chapter: [0.13] Data Structures
[10]2
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[2]2.i

Convert the following infix notation to prefix notation.

(A - B)/C * (D + E)

Concept: Conversion of Infix to Prefix and Post Fix Notations
Chapter: [0.13] Data Structures
[2]2.ii

A matrix M[- 6, ... 10, 4 ... 15] is stored in the memory with each element requiring 4 bytes of storage. If the base address is 1025, find the address of M [4] [8] when the matrix is stored in Column Major wise.

Concept: Example Algorithms that Use Structured Data Types (E.G. Searching, Finding Maximum/Minimum, Sorting Techniques, Solving Systems of Linear Equations, Substring, Concatenation, Length, Access to Char in String, Etc.)
Chapter: [0.1] Arrays, Strings
[3]2.iii

With reference to the code given below, answer the questions that follow along with dry run/working.boolean num(int x)

{ int a=1}
for (int c=x; c>0; c/<10}
a*=10;
return (x*x%a)=x;
}
1. What will the function num() return when the value of x = 25?
2. What is the method num() performing?
Concept: Basic Theorems of Boolean Algebra (Eg. Duality, Idempotence, Commutativity, Associativity, Distributivity, Operations with 0 and 1, Complements, Absorption, Involution)
Chapter: [0.01] Boolean Algebra
[3]2.iv

The following function task() is a part of some class. Assume ‘m’ and ‘n’ are positive integers greater than 0. Answer the questions given below along with dry / run working.

int task(int m, int n)
{ if(m=n)
return m;
else if (m>n)
return task(m-n, n);
else
return task(m, n-m)
}
1. What will the function task() return when the value of m=30 and n=45?
2. What function does task() perform, apart from recursion?
Concept: Concept of Recursion
Chapter: [0.11] Recursion
PART II - 50 MARKS : Section-A (Answer any two questions.)
[10]3
[5]3.i

Given the Boolean function F(A, B, C, D) = ∑(2, 3, 6, 7, 8, 10, 12, 14, 15).

1. Reduce the above expression by using 4- variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs.
2. Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs.
Concept: Use of Karnaugh Map for Minimization of Boolean Expressions (Up to 4 Variables)
Chapter: [0.01] Boolean Algebra
[5]3.ii

Give the Boolean function F(A, B, C, D,) π(0, 1, 2, 4, 5, 8, 10, 11, 14,15).

1. Reduce the above expression by using 4-variable Karnaugh mpa, showing the various groups (i.e., octal quads and pairs)
2. Draw the logic gate diagrams for the reduced expression. Assume that the variables and their complements are available as inputs.
Concept: Use of Karnaugh Map for Minimization of Boolean Expressions (Up to 4 Variables)
Chapter: [0.01] Boolean Algebra
[10]4
[5]4.i

A shopping mall allows customers to shop using the cash or credit card of any nationalised bank. In awards bonus points to their customers on the basis of criteria given below:

• The customer is an employee of the shopping mall and makes the payment using a credit card.
OR
• The customer shops items which carry bonus points and makes the payment using a credit card with a shopping amount of less than  ₹10,000.
OR
• The customer is not an employee of the shopping mall and makes the payment not through a credit card in cash for the shopping amount above ₹10,000/-

The inputs are:

 INPUTS C Payment through a credit card. A Shopping amount in above  ₹10,000 E The customer is an employee of theshopping mall. I Item carries a bonus point.

(In all the above cases, 1 indicates yes and 0 indicates no.)

Output: X[1 indicates bonus point awarded, 0 indicates bonus point not awarded for all cases]

Draw the truth table for the inputs and outputs given above and write the POS expression for X(C, A, F, I).

Concept: Truth Tables
Chapter: [0.01] Boolean Algebra
[3]4.ii

Differentiate between half adder and full adder. Write the Boolean expression and draw the logic circuit diagram for the SUM and CARRY of a full adder.

Concept: Applications of Boolean Algebra and Logic Gates to Half Adders, Full Adders, Encoders, Decoders, Multiplexers, NAND, NOR as Universal Gates
Chapter: [0.02] Computer Hardware
[2]4.iii

Verify the following expression by using the truth table:

(A ☉ B)' = A ⊕ B

Concept: Truth Tables
Chapter: [0.01] Boolean Algebra
[10]5
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[5]5.i

What is an encodrer?

Concept: Applications of Boolean Algebra and Logic Gates to Half Adders, Full Adders, Encoders, Decoders, Multiplexers, NAND, NOR as Universal Gates
Chapter: [0.02] Computer Hardware

How is Encoder different from a decoder?

Concept: Applications of Boolean Algebra and Logic Gates to Half Adders, Full Adders, Encoders, Decoders, Multiplexers, NAND, NOR as Universal Gates
Chapter: [0.02] Computer Hardware

Draw the logic circuit for a 4 :1 multiplexer and explain its working.

Concept: Elementary Logic Gates (NOT, AND, OR, NAND, NOR, XOR, XNOR) and Their Use in Circuits
Chapter: [0.02] Computer Hardware
[3]5.ii

From the logic diagram given below, write the Boolean expression for (1) and (2). Also, derive the Boolean expression (F) and simplify it.

Concept: DeMorgan’S Law/Theorem and Their Applications
Chapter: [0.01] Boolean Algebra
[2]5.iii

Convert the following cardinal expression to its canonical form:

F(P, Q, R) = π(0, 1, 3, 4).

Concept: Reducing Boolean Expression (SOP and POS) to Its Minimal Form
Chapter: [0.01] Boolean Algebra
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)
[10]6

Design a class NumDude to check if a given number is a Dudeney number or not. (A Dudency number is a positive integer that is a perfect cube, such that the sum of its digits is equal to the cube root of the number.)

Example 5832 = (5 + 8 + 3 +2)3 = (18)3 = 5832

Some of the members of the class are given below:

 Class name unique Data member/instance variable: num to store a positive integer number Methods/Member functions: NumDude() default constructor to initialise the data member with a legal initial value void input() to accept a positive integer number int sumDigits(int x) returns the sum of the digits of number 'x' using recursive technique void isDude() checks whether the given number is a Dudeney number by invoking the function sumDigits() and displays the result with an appropriate message.

Specify the class NumDude giving details of the constructor ( ), void input( ), intsumDigits(int) and void is Dude(). Define a main() function to create an object and call the functions accordingly to enable the task.

Concept: Examples of Algorithmic Problem Solving Using Functions (Various Number Theoretic Problems, Finding Roots of Algebraic Equations)
Chapter: [0.09] Functions
[10]7

A class Trans is defined to find the transpose of a square matrix. A transpose of a matrix is obtained by interchanging the elements of the rows and columns.

Example: If size of the matrix = 3, then

 ORIGINAL 11 5 7 8 13 9 1 6 20
 TRANSPOSE 11 8 1 5 13 6 7 9 20

Some of the member of the class are given below:

 Class name Trans Data members/instance variables: arr[ ] [ ] to store integers in the matrix m integer to store the size of the matrix Methods/Member functions: Trans(int mm) parameterised constructor to initialise the data member m = mm void fillarray( ) to enter integer elements in the matrix void transpose( ) to create the transpose of the given matrix void display( ) displays the original matrix and the transposed matrix by invoking the method transpose( )

Specify the class Trans giving details of the constructor( ), void fillarray( ), void transpose( ) and void display( ). Define a main ( ) function to create an object and call the functions accordingly to enable the task.

Concept: Examples of Algorithmic Problem Solving Using Functions (Various Number Theoretic Problems, Finding Roots of Algebraic Equations)
Chapter: [0.09] Functions
[10]8

A class Sort Alpha has been defined to sort the words in the sentence in alphabetical order.

Example: Input: THE SKY IS BLUE
Output: BLUE IS SKY THE

Some of the members of the class are given below:

 Class name Short Alpha Data members/instance variables: sent to store a sentence n integer to store the number ofwords in a sentence Methods/Member functions: ShortAlpha( ) default constructor to initialise data members with legal initial values void acceptsent( ) to accept a sentence in UPPERCASE void short(SortAlpha P) sorts the words of the sentence of object P in alphabetical order and stores the sorted sentence in the current object void display( ) display the original sentence along with the sorted sentence by invoking the method sort( )

Specify the class Sort Alpha giving details of the constructor (), void acceptsent(), void sort (Sort Alpha) and void display(). Define a main()function to create an object and call the functions accordingly to enable the task.

Concept: Example Algorithms that Use Structured Data Types (E.G. Searching, Finding Maximum/Minimum, Sorting Techniques, Solving Systems of Linear Equations, Substring, Concatenation, Length, Access to Char in String, Etc.)
Chapter: [0.1] Arrays, Strings
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)
[5]9
[4]9.i

A double ended queue is a linear data structure which enables the user to add and remove integers from either ends i.e., from front or rear.

The details for the class deQueue are given below:

 Class name deQueue Data members/instance variables: Qrr[] array to hold integer elements lim maximum capacity of the dequeue front to point the index of the front end rear to point the index of the rear end Methods/Member functions: deQueue(int 1) constructor to initialise lim = 1, front = 0 and rear =0 void addFront(int v) to add integers in the dequeue at the front end if possible, otherwise display the message “OVERFLOW FROM FRONT” void addRear(int v) to add integers in the dequeue at the rear end if possible, otherwise, display the message “OVERFLOW FROM REAR” int popFront() removes and returns the integers from the front end of the dequeue if any, else returns — 999 int popRear ( ) removes and returns the integers from the rear end of the dequeue if any, else returns — 999 void show( ) displays the elements of the dequeue

Specify the class deQueue giving details of the function void addFront(int) and int popFront(). Assume that the other functions have been defined. The main() function and algorithm need NOT be written.

Concept: Basic Data Structures (Stack, Queue, Dequeue)
Chapter: [0.13] Data Structures
[1]9.ii

Differentiate between a stack and a queue.

Concept: Basic Data Structures (Stack, Queue, Dequeue)
Chapter: [0.13] Data Structures
[5]10

A super class Demand has been defined to store the details of the demands for a product. Define a subclass Supply which contains the production and supply details of the products.

The details of the member of both the classes are given below:

 Class name Demand Data members/instance variables: pid string to store the product ID pname string to store the product name pdemand integer to store the quantity demanded for the product Methods/Member functions: Demand(...) parameterised constructor to assign values to the data members void display( ) to display the details of the product Class name Supply Data members/instance variables: produced integer to store the quantity of the product produced prate to store the cost per unit of the product in decimal Methods/Member functions: Supply(...) parameterised constructor to assign values of the data members of both the classes double calculation( ) returns the difference between the amount of demand  (rate×demand) and the amount produced (rate× produced) void display( ) to display the details of the product and the difference in amount of demand and amount of supply by invoking the method calculation( )

Assume that the super class Demand has been defined. Using the concept of inheritance, specify the class Supply giving the details of the constructor(...), double calculation() and void display().

Concept: Inheritance
Chapter: [0.12] Inheritance and Polymorphism
[5]11
[2]11.i

A linked list is formed from the objects of the class given below:

class Node
{
doubel sal;
Node next;
}

Write an Algorithm OR a Method to add a node at the end of the an existing linked list. The method declaration is as follows:

void addNote(Node ptr, double ss)

Concept: Implementation of Algorithms to Solve Problems
Chapter: [0.03] Implementation of Algorithms to Solve Problems
[3]11.ii

Answer the following questions from the diagram of a Binary Tree given below:

1. Write the pre-order traversal of the above tree structure.
2. Name the parent of the nodes D and B.
3. State the level of nodes E anf F when the root is at level 0.
Concept: Recursive Data Structures - Single Linked List (Algorithm and Programming), Binary Trees, Tree Traversals (Conceptual)
Chapter: [0.13] Data Structures

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