Computer Science (Theory) Specimen Paper 2024-2025 ISC (Commerce) Class 12 Question Paper Solution

The compliment of the Boolean expression Aꞌ • (B • Cꞌ + Bꞌ • C).

Aꞌ • (B + C + Bꞌ + C)

A + (B + Cꞌ) • (B + Cꞌ)

A + (Bꞌ + C) • (B + Cꞌ)

Aꞌ • (Bꞌ + Cꞌ + Bꞌ • C)

Assertion: Recursion utilises more memory as compared to iteration.

Reason: Time complexity of recursion is higher due to the overhead of maintaining the function call stack.

Both Assertion and Reason are true and Reason is the correct explanation for Assertion.

Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.

Assertion is true and Reason is false.

Assertion is false and Reason is true.

According to the Principle of duality, the Boolean equation (Aꞌ + B) • (1 + B) = Aꞌ + B will be equivalent to ______.

(A + Bꞌ) • (0 + B) = A + Bꞌ

(Aꞌ • B) + (0 • B) = Aꞌ • B

(Aꞌ • B) + (0 • B) = Aꞌ + B

(Aꞌ + B) • (0 + B) = Aꞌ + B

Distributive law states that ______.

A + B • C = (A + B) • (A +C)

A + ( A • B) = A

A • (B + C) = (A • B) + (B • C)

A + B • C = A • B + A • C

The complement of the reduced expression of F(A,B) = ∑ (0,1,2,3) is ______.

1

A • B

0

Aꞌ + Bꞌ

Study the given propositions and the statements marked Assertion and Reason that follow it. Choose the correct option on the basis of your analysis.

p = I am a triangle

q = I am a three-sided polygon

s1 = p → q

s2 = q → p

Assertion: s2 is converse of s1

Reason: Three-sided polygon must be a triangle.

Both Assertion and Reason are true and Reason is the correct explanation for Assertion.

Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.

Assertion is true and Reason is false.

Assertion is false and Reason is true.

Assertion: In Java, the String class is used to create and manipulate strings, and it is immutable.

Reason: Immutability ensures that once a String object is created, its value cannot be changed.

Both Assertion and Reason are true and Reason is the correct explanation for Assertion.

Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.

Assertion is true and Reason is false.

Assertion is false and Reason is true.

Consider the following statement written in class Circle where pi is its data member.

static final double pi = 3.142;

Which of the following statements are valid for pi?

1. It contains a common value for all objects class Circle.
2. Its value is non-changeable.
3. At a time two access modifiers, static and final, cannot be applied to a single data member pi.

I and II

II and III

I and III

Only III

For Big O notation, state the difference between O(n) and O(n² ).

A full adder needs five gates and those are 3 AND gates, 1 OR gate and 1 XOR gate. When a full adder is constructed using 2 half adders, it also requires 5 gates. State the names along with the quantity those gates.

Convert the following infix notation to prefix form.

( A – B ) / C * ( D + E )

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.

The following function getIt() is a part of some class. Assume x is a positive integer, f is the lower bound of arr[ ] and l is the upper bound of the arr[ ].

Answer the questions given below along with dry run/working.

public int getIt(int x,intarr[],int f,int l)
  {
   if(f>l)
     return-1;
   int m=(f+l)/2;
   if(arr[m]<x)
     return getIt(x,m+1,l);
   else if(arr[m]>x)
     return getIt(x,f,m-1);
   else
     return m;
}

1. What will the function getIt( ) return if arr[ ] = {10,20,30,40,50} and x = 40?

2. What is function getIt( ) performing apart from recursion?

The following is a function of class Armstrong. This recursive function calculates and returns the sum of the cubes of all the digits of num, where num is an integer data member of the class Armstrong.

[A number is said to be Armstrong if the sum of the cubes of all its digits is equal to the original number].

There are some places in the code marked by ?1?, ?2?,?3? which may be replaced by a statement/expression so, that the function works properly.

public int sumOfPowers(int num) 
  {
     if(num == 0) 
        return ?1?
     int digit = ?2?;
        return(int)Math.pow(digit, 3) + ?3?;
}

1. What is the expression or statement at ?1?
2. What is the expression or statement at ?2?
3. What is the expression or statement at ?3?

A shopping mall announces a special discount on all its products as a festival offer only to those who satisfy any one of the following conditions.

• If he/she is an employee of the mall and has a service of more than 10 years.
                                   OR
• A regular customer of the mall whose age is less than 65 years and should not be an employee of the mall.
                                   OR
• If he/she is a senior citizen but not a regular customer of the mall.

The inputs are:

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

Output: X - Denotes eligible for discount [1 indicates YES and 0 indicates NO in all cases]

Draw the truth table for the inputs and outputs given above and write the SOP expression for X ( E, R, S, C ).

Reduce the above expression X ( E, R, S, C ) 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.

Reduce the Boolean function F(P,Q,R,S) = (P+Q+R+S) • (P+Q+R+Sꞌ) • (P+Q+Rꞌ+S) • (P+Qꞌ+R+S) • (P+Qꞌ+R+Sꞌ) • (P+Qꞌ+Rꞌ+S) • (P+Qꞌ+Rꞌ+Sꞌ) •(Pꞌ+Q+R+S) • (Pꞌ+Q+R+Sꞌ) 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.

From the given logic diagram:

1. Derive Boolean expression and draw the truth table for the derived expression
2. If A=1, B=0 and C=1, then find the value of X.

Draw the logic circuit to decode the following binary number (0001, 0101, 0111, 1000, 1010, 1100, 1110,1111) to its hexadecimal equivalents. Also, state the Hexadecimal equivalents of the given binary numbers.

Verify if the following proposition is valid using the truth table:

(X ∧ Y) =>Z = (Y => Z) ∧ (X => Y).

Answer the following questions related to the below image:

1. What is the output of the above gate if input A=0, B=1?
2. What are the values of the inputs if output =1?

Given are two strings, input string and a mask string that remove all the characters of the mask string from the original string.

A class StringOp is defined as follows to perform above operation.

Some of the members of the class are given below:

Specify the class StringOp giving details of the constructor( ), void accept( ), void form() and void display( ). Define a main( ) function to create an object and call all the functions accordingly to enable the task.

A class Mixarray contains an array of integer elements along with its capacity (More than or equal to 3). Using the following description, form a new array of integers which will contain only the first 3 elements of the two different arrays one after another.

Example:

Array1: { 78, 90, 100, 45, 67 }

Array2: {10, 67, 200, 90 }

Resultant Array: { 78, 90, 100, 10, 67, 200}

The details of the members of the class are given below:

Specify the class Mixarraygiving details of the constructor(int), void input( ), Mixarray mix(Mixarray,Mixarray) and void display( ). Define a main( ) function to create objects and call all the functions accordingly to enable the task.

A class LCM has been defined to find the Lowest Common Multiple of two integers.

Some of the data members and member functions are given below:

Specify the class LCM giving details of the constructor( ), void accept( ), int getLCM() and void display( ). Define a main ( ) function to create an object and call the member functions accordingly to enable the task.

Recycle is an entity which can hold at the most 100 integers. The chain enables the user to add and remove integers from both the ends i.e. front and rear.

Define a class ReCycle with the following details:

1. Specify the class ReCycle giving details of the functions void pushfront(int) and int poprear( ). Assume that the other functions have been defined.
   The main( ) function and algorithm need NOT be written.
2. Name the entity described above and state its principle.

A library issues books on rental basis at a 2% charge on the cost price of the book per day. As per the rules of the library, a book can be retained for 7 days without any fine. If the book is returned after 7 days, a fine will also be charged for the excess days as per the chart given below:

A super class Library has been defined. Define a sub class Compute to calculate the fine and the total amount. The details of the members of both the classes are given below:

Assume that the super class Library has been defined. Using the concepts of Inheritance, specify the class Compute giving the details of constructor, void fine ( ) and void show ( ) functions.

The super class, main function and algorithm need NOT be written.

A linked list is formed from the objects of the class Node. The class structure of the 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)

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

1. Name the root of the left sub tree and its siblings.
2. State the size and depth of the right sub tree.
3. Write the in-order traversal of the above tree structure.