GATE CSE 2022

Question 1
Which one of the following statements is TRUE for all positive functions f(n)?
A
f(n^2)=\theta (f(n)^2), where f(n) is a polynomial
B
f(n^2)=o (f(n)^2)
C
f(n^2)=O (f(n)^2), where f(n) is an exponential function
D
f(n^2)=\Omega (f(n)^2)
Algorithm   Asymptotic Notation
Question 2
Which one of the following regular expressions correctly represents the language of the finite automaton given below?

A
ab*bab* + ba*aba*
B
(ab*b)*ab* + (ba*a)*ba*
C
(ab*b + ba*a)*(a* + b*)
D
(ba*a + ab*b)*(ab* + ba*)
Theory of Computation   Finite Automata
Question 3
Which one of the following statements is TRUE?
A
The LALR(1) parser for a grammar G cannot have reduce-reduce conflict if the LR(1) parser for G does not have reduce-reduce conflict.
B
Symbol table is accessed only during the lexical analysis phase.
C
Data flow analysis is necessary for run-time memory management.
D
LR(1) parsing is sufficient for deterministic context-free languages.
Compiler Design   Parsing
Question 4
In a relational data model, which one of the following statements is TRUE?
A
A relation with only two attributes is always in BCNF.
B
If all attributes of a relation are prime attributes, then the relation is in BCNF.
C
Every relation has at least one non-prime attribute.
D
BCNF decompositions preserve functional dependencies.
Database Management System   Normal Form
Question 5
Consider the problem of reversing a singly linked list. To take an example, given the linked list below,

the reversed linked list should look like

Which one of the following statements is TRUE about the time complexity of algorithms that solve the above problem in O(1) space?
A
The best algorithm for the problem takes \theta(n) time in the worst case.
B
The best algorithm for the problem takes \theta(n \log n) time in the worst case.
C
The best algorithm for the problem takes \theta(n^2) time in the worst case.
D
It is not possible to reverse a singly linked list in O(1) space.
Data Structure   Link List
Question 6
Suppose we are given n keys, m hash table slots, and two simple uniform hash functions h_1 and h_2. Further suppose our hashing scheme uses h_1 for the odd keys and h_2 for the even keys. What is the expected number of keys in a slot?
A
\frac{m}{n}
B
\frac{n}{m}
C
\frac{2n}{m}
D
\frac{n}{2m}
Data Structure   Hashing
Question 7
Which one of the following facilitates transfer of bulk data from hard disk to main memory with the highest throughput?
A
DMA based I/O transfer
B
Interrupt driven I/O transfer
C
Polling based I/O transfer
D
Programmed I/O transfer
Computer Organization   IO Interface
Question 8
Let R1 and R2 be two 4-bit registers that store numbers in 2's complement form. For the operation R1+R2, which one of the following values of R1 and R2 gives an arithmetic overflow?
A
R1 = 1011 and R2 = 1110
B
R1 = 1100 and R2 = 1010
C
R1 = 0011 and R2 = 0100
D
R1 = 1001 and R2 = 1111
Digital Logic   Number System
Question 9
Consider the following threads, T_1, T_2, \text{ and }T_3 executing on a single processor, synchronized using three binary semaphore variables, S_1, S_2, \text{ and }S_3, operated upon using standard wait() and signal(). The threads can be context switched in any order and at any time.

Which initialization of the semaphores would print the sequence BCABCABCA ...?
A
S_1 = 1; S_2 = 1; S_3 = 1
B
S_1 = 1; S_2 = 1; S_3 = 0
C
S_1 = 1; S_2 = 0; S_3 = 0
D
S_1 = 0; S_2 = 1; S_3 = 1
Operating System   Process Synchronization
Question 10
Consider the following two statements with respect to the matrices A_{m \times n},B_{n \times m},C_{n \times n} \text{ and }D_{n \times n},

Statement 1: tr(AB) = tr(BA)
Statement 2: tr(CD) = tr(DC)

wheretr() represents the trace of a matrix. Which one of the following holds?
A
Statement 1 is correct and Statement 2 is wrong.
B
Statement 1 is wrong and Statement 2 is correct.
C
Both Statement 1 and Statement 2 are correct.
D
Both Statement 1 and Statement 2 are wrong.
Engineering Mathematics   Linear Algebra
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