Computer Science (Theory) Official Board Paper 2025-2026 ISC (Commerce) Class 12 Question Paper Solution

According to the Principle of Duality, the Boolean equation Q'•0+P'•Q'+P'• Q = P' will be equivalent to:

Q•0 + P•Q + P•Q' = P

Q'•1 + P•Q' + P•Q' = P'

(Q' + 1)•(P' + Q')•(P' + Q) = P'

(Q' + 0)•(P' + Q')•(P' + Q) = P'

Consider the following statement written in class Student where school_Name is its data member.

static final String school_Name = "Co-Ed School";

Which of the following statements are valid for school_Name?

1. All objects of class Student share the same value of school_Name.
2. The value of school_Name cannot be changed during program execution.
3. The keywords static and final cannot be used together for a variable.

Only I and II

Only II and III

Only I and III

Only III

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

P = You practise regularly

Q = You become skilled

S1 = P => Q

S2 = ~PVQ

Assertion: S1 and S2 are logically equivalent.

Reason: A conditional statement P => Q can be expressed as ~ PVQ.

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.

Both Assertion and Reason are false.

The Boolean equations a + 1 = a and a • 0 = 0 correspond to ______.

Involution Law

Law of Identity

Distributive Law

Law of Complements

The worst case complexity for following code segment is:

for(int i=1;i<=n;i++)
 {
  for(int j=1;j<=)
  {
     statement;
  }
 }

O(n+i)

O(n×i)

O(n)

O(n²)

Assertion: An interface in Java contains abstract and non-abstract methods.

Reason: All methods in an interface must be implemented by any class that extends this interface.

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.

Both Assertion and Reason are false.

The complement of the Boolean expression a • b' + a' + a' • b is ______.

a + b' • a • a' + b

(a' + b) • a • (a + b')

(a + b') • a' • (a + b')

a' • b + a + a • b

Assertion: The return statement enables the exit of the program control from the current method.

Reason: If a method’s return type is void, it can still contain return 0 statement to return nothing.

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.

Both Assertion and Reason are false.

Consider the two propositions given below:

A = You use ecofriendly methods.

B = Pollution is reduced.

If A implies to B, then write its Contrapositive statement.

What is Gray code in Karmaugh map?

Convert the following infix notation to prefix form.

P/Q + (S * F + X/R)

A matrix G[3...7, 2...5] is stored in the memory, with each element requiring 4 bytes of storage. If the address of G[5][4] is 6000, find the base address when the matrix is stored column-major-wise.

The following function workOut() is a part of some class. Assume 'n' is a positive integer.

String workOut (int n)

{ if (n == 0)

       return"";

    int rem = n% 16;

    char cr = (rem < 10)? (char) (rem + '0'): (char) (rem - 10+'A');

    return workOut (n/16) + cr;

}

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

1. What will the function workOut(220) return?   [2]
2. What is the function workOut() performing apart from recursion?   [1]

The following function is Tech() is a part of some class which is used to check if a given number is a Tech number or not. 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. 

A number is Tech number if the count of digits is even and the square of the sum of its two equal halves is equal to the number itself.

Example: 2025 = 20 + 25 = (45)² = 2025

boolean isTech(int n)

{

  String s = String.valueOf(n);

  int len = ?1?;

  if (len %2!= 0)

  return ?2?:

  intfirst = Integer.parselnt(s.substring(0, len/2));

  int second = Integer.parseInt(s.substring(len/2));

  int sum =first + second;

  return ?3? == n;

}

What are the expressions or statements at?1?, ?2? and ?3?

What is a decoder?

Draw the logic gate diagram for decoding the binary numbers {0011, 0100, 0101, 0111, 1011, 1110} to hexa-decimal numbers.

State any one application of a multiplexer.

The Chain rule states that [(a=>b) • (b=>e)] => (a=>c). Prove this rule using Boolean laws.

Given that P = 0, Q = 1, R = 0, S = 0, write its:

Maxterm

Given that P = 0, Q = 1, R = 0, S = 0, write its:

Minterm

According to the ancient laws of the Valley of Peace, a candidate can become the Dragon Warrior only if they satisfy any one of the following conditions:

• The candidate belongs to the Panda Clan and has been trained for more than 5 years under the Grand Master
• The candidate possesses the Secret Chi Power but does not belong to the Panda
• The Panda candidate is recommended by the Grand Master, but neither belongs to the Clan nor has been trained for more than 5 years

The inputs are:

(In all the above cases, 1 indicates YES and 0 indicates NO)

Output: X − Denotes eligibility to become the Dragon Warrior

(1 = eligible and 0 = not eligible)

Draw the truth table for the inputs and outputs given above. Write the for X(C, T, P, R).

Construct the logic gate diagram for a Full Adder using two Half Adders.

Draw a truth table to verify if the following proposition is a Tautology, a contradiction, or a Contingency.

(A∧∼B)=>(~A∨B)

Reduce the Boolean function F(A,B,C,D) = π (0,1,2,3,7,8,9,10,11,12,13,15) 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 logic gate diagram given below, derive the Boolean expression for (1), (2), and Q. Reduce the derived expression.

Draw the logic gate diagram for 2-input AND gate using NOR gates only. Show the expression at each step.

A class TimeOp has been defined to add any two accepted time periods.

Example: Time A = 6 hours 35 minutes 40 seconds

Time B = 7 hours 45 minutes 30 seconds

Time A + Time B = 14 hours 21minutes 10 seconds

(where 60 minutes = 1 hour and 60 seconds = 1 minute)

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

Specify the class TimeOp giving the details of the constructor(), void readTime(), TimeOp addTime(TimeOp) and void dispTime(). Define the main() function to create objects and call the functions accordingly to enable the task.

A class Trimorphic has been defined to accept a positive integer from the user and display if it is a Trimorphic number or not. 

[A number is said to be Trimorphic if the cube of the number ends with the number itself.]

Example 1: 24³ = 13824 ends with 24

Example 2: 5³ = 125 ends with 5

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

Specify the class Trimorphic, giving the details of the constructor(), void accept(), boolean check() and void result(). Define the main() function to create an object and call the functions accordingly to enable the task.

State any two differences between iteration and recursion.

Design a class PendulumS to perform an operation on a word containing alphabets in upper case only. Rearrange the word by putting the lowest ASCII value character at the centre and the second lowest ASCII value character to its right and the third to its left and so on.

Example 1: Input: COMPUTER

                   Output: TPMCEORU

Example 2: Input: SCIENCE

                   Output: SIECCEN

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

Specify the class PendulumS giving the details of the constructor( ), int minCharIndex(String), void arrange() and void display(). Define the main( ) function to create an object and call the functions accordingly to enable the task.

In any internet Each browser, new webpage a user can visit new webpages and go back to previously visited URL is stored in browser’s memory such that when the user clicks ‘Back’ button, the previous webpage gets displayed. The details of the members of the class are given below:

1. Specify the class Browser, giving details of the functions void visit(String) and String back(). Assume that the other functions have been defined.
2. Name the entity described above and state its principle.

A superclass Hotel has been defined to store the details of a hotel. Define a subclass Customer to calculate the total bill for a customer as per the following criteria:

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

Assume that the superclass Hotel has been defined. Using the concept of Inheritance, specify the class Customer, giving details of constructor(...), void compute() and void show()

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

A linked list is formed from the objects of the class Word. The structure of the class Word is given below:

   class Word
   {
       String value;
       Word next;
   }

Write an Algorithm OR a Method to count and display the number of nodes whose value starts with a consonant.

The method declaration is as follows:

void countConsonant(Word first)

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

1. Write the pre-order traversal of the above tree.
2. State the level of Node Q when the root is at level 0.
3. State the size of the left subtree and the right subtree.