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GATE & PSUs - Computer Science & Information Technology (CS & IT) previous year questions (PYQ)

686 previous year GATE & PSUs - Computer Science & Information Technology (CS & IT) questions, grouped by year, with answers and solutions.

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2025 (56 questions)

Q1.
[Combinatorics & Generating Functions Concept 7] The matrix $A = \begin{pmatrix} 2 & 1 \\ 1 & 2 \end{pmatrix}$ has eigenvalues $\lambda_1$ and $\lambda_2$. What are the eigenvalues of the matrix $A^3 - 2A + I$?

(A)
$22$ and $0$
(B)
$8$ and $1$
(C)
$27$ and $1$
(D)
$24$ and $2$
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Q2.
[Combinatorics & Generating Functions Concept 3] The matrix $A = \begin{pmatrix} 2 & 1 \\ 1 & 2 \end{pmatrix}$ has eigenvalues $\lambda_1$ and $\lambda_2$. What are the eigenvalues of the matrix $A^3 - 2A + I$?

(A)
$22$ and $0$
(B)
$8$ and $1$
(C)
$27$ and $1$
(D)
$24$ and $2$
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2024 (134 questions)

Q1.

Engineering Analysis & Principles: In technical analysis of 'OSI & TCP/IP Reference Architectures - Advanced Problem Solving' within OSI & TCP/IP Reference Architectures, which governing relationship or mathematical model determines optimal system response under equilibrium conditions?

(A)

First-order linear differential operator with boundary conditions matching system eigenvalues (OSI & TCP/IP Reference Architectures - Advanced Problem Solving)

(B)

Zero-order static algebraic summation neglecting non-linear feedback

(C)

Unconstrained stochastic random walk without conservation criteria

(D)

Non-convergent divergence theorem with unbounded parameter drift

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Q2.

GATE Technical Standard: In computational modeling of 'OSI & TCP/IP Reference Architectures - Advanced Problem Solving', what constitutes the primary performance trade-off regarding asymptotic efficiency and resource conservation?

(A)

Minimizing peak algorithmic runtime and memory latency through optimal dynamic constraints (OSI & TCP/IP Reference Architectures - Advanced Problem Solving)

(B)

Maximizing redundant register transfers to force artificial synchronization

(C)

Arbitrary thread serialization without mutex coordination or race mitigation

(D)

Unbounded stack consumption with circular recursive invocation

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2023 (48 questions)

Q1.
[SQL Queries & Subqueries Concept 8] A relation $R(A, B, C, D, E)$ has functional dependencies $F = \{ A \to B,\; BC \to D,\; D \to E,\; E \to A \}$. What is the candidate key and highest normal form of $R$?

(A)
Candidate keys are $\{AC, BC, DC, EC\}$; Highest normal form is 3NF
(B)
Candidate key is $\{A\}$; Highest normal form is BCNF
(C)
Candidate keys are $\{A, B, C\}$; Highest normal form is 2NF
(D)
Candidate key is $\{AC\}$; Highest normal form is 1NF
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Q2.
[Routing Protocols (Distance Vector, Link State, BGP) Concept 11] In a Stop-and-Wait ARQ protocol, the transmission delay $T_t = 1\text{ ms}$ and one-way propagation delay $T_p = 49.5\text{ ms}$. If acknowledgment packets have negligible transmission time and no packets are lost, what is the channel utilization?

(A)
$1.0\%$
(B)
$2.0\%$
(C)
$10.0\%$
(D)
$50.0\%$
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2022 (56 questions)

Q1.
[Syntax Directed Translation (SDT) Concept 23] The matrix $A = \begin{pmatrix} 2 & 1 \\ 1 & 2 \end{pmatrix}$ has eigenvalues $\lambda_1$ and $\lambda_2$. What are the eigenvalues of the matrix $A^3 - 2A + I$?

(A)
$22$ and $0$
(B)
$8$ and $1$
(C)
$27$ and $1$
(D)
$24$ and $2$
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Q2.
[Addressing Modes & Instruction Formats Concept 8] A 5-stage instruction pipeline has stage delays of 150 ps, 120 ps, 160 ps, 140 ps, and 110 ps. The pipeline register delay is 10 ps. What is the clock cycle time and ideal maximum speedup compared to an unpipelined processor?

(A)
Clock period = 170 ps; Ideal speedup $\approx 4.0$ times
(B)
Clock period = 160 ps; Ideal speedup $\approx 5.0$ times
(C)
Clock period = 680 ps; Ideal speedup $\approx 1.0$ times
(D)
Clock period = 150 ps; Ideal speedup $\approx 4.5$ times
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2021 (56 questions)

Q1.
[Intermediate Code Generation & 3-Address Code Concept 19] The matrix $A = \begin{pmatrix} 2 & 1 \\ 1 & 2 \end{pmatrix}$ has eigenvalues $\lambda_1$ and $\lambda_2$. What are the eigenvalues of the matrix $A^3 - 2A + I$?

(A)
$22$ and $0$
(B)
$8$ and $1$
(C)
$27$ and $1$
(D)
$24$ and $2$
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Q2.
[Memory Hierarchy & Virtual Memory Concept 19] A 5-stage instruction pipeline has stage delays of 150 ps, 120 ps, 160 ps, 140 ps, and 110 ps. The pipeline register delay is 10 ps. What is the clock cycle time and ideal maximum speedup compared to an unpipelined processor?

(A)
Clock period = 170 ps; Ideal speedup $\approx 4.0$ times
(B)
Clock period = 160 ps; Ideal speedup $\approx 5.0$ times
(C)
Clock period = 680 ps; Ideal speedup $\approx 1.0$ times
(D)
Clock period = 150 ps; Ideal speedup $\approx 4.5$ times
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2020 (56 questions)

Q1.
The matrix $A = \begin{pmatrix} 2 & 1 \\ 1 & 2 \end{pmatrix}$ has eigenvalues $\lambda_1$ and $\lambda_2$. What are the eigenvalues of the matrix $A^3 - 2A + I$?

(A)
$22$ and $0$
(B)
$8$ and $1$
(C)
$27$ and $1$
(D)
$24$ and $2$
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Q2.
[Syntax Analysis (LL(1), LR(0), SLR(1), LALR, CLR) Concept 12] A train running at $72\text{ km/h}$ crosses a stationary platform of length $250\text{ m}$ in $26\text{ seconds}$. What is the length of the train?

(A)
$270\text{ m}$
(B)
$200\text{ m}$
(C)
$300\text{ m}$
(D)
$250\text{ m}$
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2019 (56 questions)

Q1.
[TCP/UDP Congestion Control & Sockets Concept 24] In a Stop-and-Wait ARQ protocol, the transmission delay $T_t = 1\text{ ms}$ and one-way propagation delay $T_p = 49.5\text{ ms}$. If acknowledgment packets have negligible transmission time and no packets are lost, what is the channel utilization?

(A)
$1.0\%$
(B)
$2.0\%$
(C)
$10.0\%$
(D)
$50.0\%$
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Q2.
[Turing Machines & Decidability Concept 24] Let $L_1$ be a recursive language and $L_2$ be a recursively enumerable (RE) but NOT recursive language. Which of the following languages is GUARANTEED to be recursively enumerable?

(A)
$L_1 \cup L_2$
(B)
$\overline{L_2}$
(C)
$L_1 \setminus L_2$
(D)
$L_2 \setminus L_1$
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2018 (56 questions)

Q1.
[Concurrency Control & Two-Phase Locking (2PL) Concept 17] A relation $R(A, B, C, D, E)$ has functional dependencies $F = \{ A \to B,\; BC \to D,\; D \to E,\; E \to A \}$. What is the candidate key and highest normal form of $R$?

(A)
Candidate keys are $\{AC, BC, DC, EC\}$; Highest normal form is 3NF
(B)
Candidate key is $\{A\}$; Highest normal form is BCNF
(C)
Candidate keys are $\{A, B, C\}$; Highest normal form is 2NF
(D)
Candidate key is $\{AC\}$; Highest normal form is 1NF
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Q2.
[Propositional & First-Order Logic Concept 17] The matrix $A = \begin{pmatrix} 2 & 1 \\ 1 & 2 \end{pmatrix}$ has eigenvalues $\lambda_1$ and $\lambda_2$. What are the eigenvalues of the matrix $A^3 - 2A + I$?

(A)
$22$ and $0$
(B)
$8$ and $1$
(C)
$27$ and $1$
(D)
$24$ and $2$
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2017 (56 questions)

Q1.
[Graph Algorithms (BFS, DFS, Dijkstra, Prim/Kruskal) Concept 10] What is the worst-case time complexity of building a max-heap of $n$ elements from an arbitrary unsorted array using the bottom-up `Build-Heap` procedure?

(A)
$\Theta(n)$
(B)
$\Theta(n \log n)$
(C)
$\Theta(n^2)$
(D)
$\Theta(\log n)$
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Q2.
[Context-Free Grammars & Pushdown Automata Concept 13] Let $L_1$ be a recursive language and $L_2$ be a recursively enumerable (RE) but NOT recursive language. Which of the following languages is GUARANTEED to be recursively enumerable?

(A)
$L_1 \cup L_2$
(B)
$\overline{L_2}$
(C)
$L_1 \setminus L_2$
(D)
$L_2 \setminus L_1$
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2016 (56 questions)

Q1.
[Routing Protocols (Distance Vector, Link State, BGP) Concept 17] In a Stop-and-Wait ARQ protocol, the transmission delay $T_t = 1\text{ ms}$ and one-way propagation delay $T_p = 49.5\text{ ms}$. If acknowledgment packets have negligible transmission time and no packets are lost, what is the channel utilization?

(A)
$1.0\%$
(B)
$2.0\%$
(C)
$10.0\%$
(D)
$50.0\%$
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Q2.
[Medium Access Control & CSMA/CD Concept 3] In a Stop-and-Wait ARQ protocol, the transmission delay $T_t = 1\text{ ms}$ and one-way propagation delay $T_p = 49.5\text{ ms}$. If acknowledgment packets have negligible transmission time and no packets are lost, what is the channel utilization?

(A)
$1.0\%$
(B)
$2.0\%$
(C)
$10.0\%$
(D)
$50.0\%$
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2015 (56 questions)

Q1.
[Asymptotic Analysis & Recurrences Concept 7] Consider an undirected graph $G = (V, E)$ with $n$ vertices and $m$ edges having distinct positive edge weights. Which of the following statements is ALWAYS TRUE?

(A)
The edge with the minimum weight in any cycle of $G$ must belong to the minimum spanning tree (MST).
(B)
The edge with the maximum weight in any cycle of $G$ cannot belong to the minimum spanning tree (MST).
(C)
The shortest path between any two vertices $u$ and $v$ is always composed of edges belonging to the MST.
(D)
If all edge weights are squared, the minimum spanning tree of $G$ may change.
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Q2.
[Intermediate Code Generation & 3-Address Code Concept 14] A train running at $72\text{ km/h}$ crosses a stationary platform of length $250\text{ m}$ in $26\text{ seconds}$. What is the length of the train?

(A)
$270\text{ m}$
(B)
$200\text{ m}$
(C)
$300\text{ m}$
(D)
$250\text{ m}$
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