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1
GATE CSE 2025 Set 1
MCQ (More than One Correct Answer)
+1
-0

Let $X$ be a 3-variable Boolean function that produces output as ' 1 ' when at least two of the input variables are ' 1 '. Which of the following statement(s) is/are CORRECT, where $a, b, c, d, e$ are Boolean variables?

A
$X(a, b, X(c, d, e))=X(X(a, b, c), d, e)$
B
$X(a, b, X(a, b, c))=X(a, b, c)$
C
$X(a, b, X(a, c, d))=(X(a, b, a)$ AND $X(c, d, c))$
D
$X(a, b, c)=X(a, X(a, b, c), X(a, c, c))$
2
GATE CSE 2024 Set 2
MCQ (More than One Correct Answer)
+1
-0

For a Boolean variable x, which of the following statements is/are FALSE?

A

x . 1 = x

B

x + 1 = x

C

x . x = 0

D

x + x̄ = 1

3
GATE CSE 2019
MCQ (Single Correct Answer)
+1
-0.33
Which one of the following is NOT a valid identity?
A
(x ⊕ y) ⊕ z = x ⊕ (y ⊕ z)
B
(x + y) ⊕ z = x ⊕ (y + z)
C
x ⊕ y = x + y, if xy = 0
D
x ⊕ y = (xy + x'y')'
4
GATE CSE 2016 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Let, $${x_1} \oplus {x_2} \oplus {x_3} \oplus {x_4} = 0$$ where $${x_1},\,{x_2},\,{x_3},\,{x_4}$$ are Boolean Variables, and $$ \oplus $$ is the $$XOR$$ operator.

Which one of the following must always be TRUE?

A
$${x_1}{x_2}{x_3}{x_4} = 0$$
B
$${x_1}{x_3} + {x_2} = 0$$
C
$${\overline x _1} \oplus {\overline x _3} = {\overline x _2} \oplus {\overline x _4}$$
D
$${x_1} + {x_2} + {x_3} + {x_4} = 0$$
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GATE CSE Subjects
Theory of Computation
Finite Automata and Regular Language Push Down Automata and Context Free Language Undecidability Recursively Enumerable Language and Turing Machine
Operating Systems
Process Concepts and Cpu Scheduling Synchronization and Concurrency Deadlocks Memory Management File System IO and Protection
Algorithms
Complexity Analysis and Asymptotic Notations Searching and Sorting Divide and Conquer Method Greedy Method P and NP Concepts Dynamic Programming
Digital Logic
Number Systems Boolean Algebra K Maps Combinational Circuits Sequential Circuits
Database Management System
Er Diagrams Functional Dependencies and Normalization Structured Query Language Relational Algebra Transactions and Concurrency File Structures and Indexing
Data Structures
Arrays Stacks and Queues Linked List Trees Graphs Hashing
Computer Networks
Concepts of Layering Data Link Layer and Switching Network Layer Application Layer Protocol Routing Algorithm TCP UDP Sockets and Congestion Control Lan Technologies and Wi-Fi Network Security
Software Engineering
Software Engineering
Compiler Design
Lexical Analysis Parsing Syntax Directed Translation Code Generation and Optimization
Web Technologies
Web Technologies
General Aptitude
Verbal Ability Logical Reasoning Numerical Ability
Discrete Mathematics
Set Theory & Algebra Linear Algebra Graph Theory Combinatorics Mathematical Logic Probability Calculus
Programming Languages
Basic of Programming Language Function and Recursion Pointer and Structure in C
Computer Organization
Computer Arithmetic Pipelining Machine Instructions and Addressing Modes Memory Interfacing IO Interface Alu Data Path and Control Unit Secondary Memory
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