✏️ Explanatory Question
In this article, we will discuss Question 1 from the ISC Class 12 Computer Science Solved Paper 2026 with accurate answers and clear explanations.
According to the Principle of Duality, the Boolean equation
\[ Q' \cdot 0 + P' \cdot Q' + P' \cdot Q = P' \]
will be equivalent to:
(a) \(Q \cdot 0 + P \cdot Q + P \cdot Q' = P\)
(b) \(Q' \cdot 1 + P' \cdot Q' + P \cdot Q' = P'\)
(c) \((Q' + 1) \cdot (P' + Q') \cdot (P' + Q) = P'\)
(d) \((Q' + 0) \cdot (P' + Q') \cdot (P' + Q) = P'\)
✅ (c) \((Q' + 1) \cdot (P' + Q') \cdot (P' + Q) = P'\)
According to the Principle of Duality, AND \((\cdot)\) is replaced by OR \((+)\), OR \((+)\) is replaced by AND \((\cdot)\), and the digit \(0\) is replaced by \(1\). Variables and complements remain unchanged.
Consider the statement written in class Student, where school_Name is its data member:
static final String school_Name = "Co-EdSchool";
Which of the following statements are valid for school_Name?
I. All objects of class Student share the same value of school_Name.
II. The value of school_Name cannot be changed during program execution.
III. The keywords static and final cannot be used together for a variable.
(a) Only I and II
(b) Only II and III
(c) Only I and III
(d) Only III
✅ (a) Only I and II
The keyword static means that the variable belongs to the class and is shared by all objects. The keyword final means that once the value is assigned, it cannot be changed. Therefore, statements I and II are correct, while statement III is incorrect.
Study the given propositions:
\(P\): You practise regularly
\(Q\): You become skilled
\(S1 = P \Rightarrow Q\)
\(S2 = \sim P \vee Q\)
Assertion: \(S1\) and \(S2\) are logically equivalent.
Reason: A conditional statement \(P \Rightarrow Q\) can be expressed as \(\sim P \vee Q\).
(a) Both Assertion and Reason are true and Reason is the correct explanation for Assertion.
(b) Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.
(c) Assertion is true and Reason is false.
(d) Both Assertion and Reason are false.
✅ (a) Both Assertion and Reason are true and Reason is the correct explanation for Assertion.
In propositional logic, a conditional statement \(P \Rightarrow Q\) is logically equivalent to \(\sim P \vee Q\). Therefore, both Assertion and Reason are true, and the Reason correctly explains the Assertion.
The Boolean equations
\[ a + 1 = 1 \] \[ a \cdot 0 = 0 \]
correspond to:
(a) Involution Law
(b) Law of Identity
(c) Distributive Law
(d) Law of Complements
✅ Domination Law / Null Law
The given Boolean equations actually represent the Domination Law, also known as the Null Law.
Identity Law is:
\[ a + 0 = a \] \[ a \cdot 1 = a \]
Therefore, if the options only contain Involution Law, Law of Identity, Distributive Law, and Law of Complements, then the given options are not fully accurate.
Find the worst-case time complexity for the following code segment:
for(int i = 1; i <= n; i++) {
for(int j = 1; j <= i; j++) {
statement;
}
}
(a) \(O(n+i)\)
(b) \(O(n \times i)\)
(c) \(O(n)\)
(d) \(O(n^2)\)
✅ (d) \(O(n^2)\)
The outer loop runs from \(1\) to \(n\). For each value of \(i\), the inner loop runs from \(1\) to \(i\).
So, the total number of executions is:
\[ 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}{2} \]
Therefore, the time complexity is:
\[ O(n^2) \]
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.
✅ Assertion is true and Reason is false.
In modern Java, an interface can contain abstract methods as well as non-abstract methods such as default methods and static methods.
However, the Reason is false because a class does not need to implement default methods of an interface. Also, a class implements an interface; it does not extend an interface.
Find the complement of the Boolean expression:
\[ a \cdot b' + a' + a' \cdot b \]
✅ \((a' + b) \cdot a \cdot (a + b')\)
To find the complement, we apply De Morgan's Law.
\[ (a \cdot b' + a' + a' \cdot b)' \]
Applying De Morgan's Law:
\[ = (a \cdot b')' \cdot (a')' \cdot (a' \cdot b)' \]
\[ = (a' + b) \cdot a \cdot (a + b') \]
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.
✅ Assertion is true and Reason is false.
The return statement is used to exit from the current method. Therefore, the Assertion is true.
However, a void method cannot return a value like 0. It can only use return; without any value. Therefore, the Reason is false.
If:
\(A\): You use eco-friendly methods
\(B\): Pollution is reduced
And \(A\) implies \(B\), write its contrapositive.
✅ If pollution is not reduced, then you did not use eco-friendly methods.
The original statement is:
\[ A \Rightarrow B \]
The contrapositive of \(A \Rightarrow B\) is:
\[ \sim B \Rightarrow \sim A \]
Therefore, the contrapositive is: If pollution is not reduced, then you did not use eco-friendly methods.
What is Gray code in Karnaugh map?
✅ Gray code is a binary sequence in which two adjacent values differ by only one bit.
In a Karnaugh Map, Gray code is used to arrange rows and columns so that adjacent cells differ by only one variable. This helps in forming valid groups and simplifying Boolean expressions easily.