Previous Year Questions (PYQs)

PGEE 2023 Memory-Based Questions

Memory Based Question Paper - PGEE 2023

Exam Pattern

• Total: 100 Questions - 50 Aptitude + 50 Technical
• Duration: Two sections of 90 minutes each
• Difficulty (Technical): Slightly easier than GATE
• Calculator: Scientific calculator, similar to GATE

1. Digital Logic (DL)

1. Multiplexers

• Which MUX is required to design a given MUX?
• Given a $1\times 4$ MUX, determine the output for given inputs. (Candidate’s note was incomplete in source.)

2. Flip-Flops

• Characteristic equation of a JK Flip-Flop.
• D Flip-Flop (negative-edge triggered) with a given initial state - find the next state after a specified number of clock pulses.

3. Logic Gates

• Identity element of the NOR gate.
• Minimum number of NAND gates to implement: $Y=(A+B)(C+D)$.

4. Counters

• Minimum number of flip-flops required to construct a mod-50 counter.

5. Number Representation

• Find the number of differing bits between the BCD and binary representations of a given number.

2. Discrete Mathematics (DM)

1. Definition-based question on the relation between matching number and chromatic number of a graph.
2. Topological ordering of a given tree/graph.
3. Propositional Logic [GATE CS 2015] S1: If a candidate is known to be corrupt, he will not be elected. S2: If a candidate is kind, he will be elected. Which of the following follows from S1 and S2 as per sound inference rules of logic?
4. If a person is known to be corrupt, he is kind.
5. If a person is not known to be corrupt, he is not kind.
6. If a person is kind, he is not known to be corrupt.
7. If a person is not kind, he is not known to be corrupt. Answer: C

3. Data Structures

1. Stacks and Queues: A sequence of push, pop, enqueue, and dequeue operations is given. Find the final order of elements.
2. Time Complexity

• Time complexity of operations on a min-heap.
• Time complexity of operations on an AVL tree.

4. Algorithms

1. Sorting: Minimum number of swaps required to sort a given array.
2. Recurrence Relation: Solve $T(n)=2T(n-1)-1$, given $T(0)=1$.
3. Graph Algorithms

• Maximum flow from source $s$ to sink $t$ in a given graph.
• Question on Prim’s algorithm and Kruskal’s algorithm.
• Question on bottleneck spanning tree.

4. Greedy / Trees

• Huffman coding question.
• Let $S$ = the set of all binary search trees constructible with four distinct keys, and let $H$ = the average height of all trees in $S$. Find $H$.

5. Database Management Systems (DBMS)

1. Normalization (approx. 2-3 questions)

• Given a set of functional dependencies: identify the normal form, count the number of super keys, and analyse a decomposition.
• BCNF - conceptual question.
• Schema $R=(S,T,U,V)$ with FDs: $S\to T$, $T\to U$, $U\to V$, $V\to S$. Decomposition $R=(R_1,R_2)$ where $R_1\cap R_2=\varnothing$. Which of the following is true?
• Not in 2NF
• In 2NF but not 3NF
• In 3NF but not in 2NF
• In both 2NF and 3NF
• Relation $(A,B,C,D)$ with FDs: $A\to C$, $B\to D$. Identify the highest normal form.

2. SQL

• A query is given - identify the correct result.
• Which of the following is not a DML command? Options: DROP, UPDATE, DELETE, INSERT, None of the above
• Theoretical question on GROUP BY and HAVING clauses.

3. Indexing: When is an index said to be a clustered index?

6. Operating Systems (OS)

1. Memory Management

• What is the purpose of the dirty bit in a page table?
• Page replacement algorithm - conceptual/numerical question.

2. Page Fault [GATE CS 2000] Average page fault service time = 10ms; memory access time = 1$\mu$s; hit ratio = 99.99%. Find the average memory access time.
3. 1.9999 milliseconds
4. 1 millisecond
5. 9.999 microseconds
6. 1.9999 microseconds
7. Synchronisation: Semaphore variable $s$ initialised to 0. If thread $t$ calls wait(s), what happens to $t$?
8. Processes: Question on parent and child process IDs.
9. File Systems [GATE CS 2004] A Unix-style i-node has 10 direct pointers, one single, one double, and one triple indirect pointer. Disk block size = 1KB; block address = 32 bits; i-nodes = 48 bits. What is the maximum possible file size?
10. $2^{34}$ bytes
11. $2^{35}$ bytes
12. $2^{36}$ bytes
13. $2^{37}$ bytes

7. Computer Organisation & Architecture (COA)

1. DMA - Cycle Stealing [GATE-style] Disk specifications: 16 surfaces, 512 tracks/surface, 512 sectors/track, 1KB/sector, rotation speed = 3000rpm. DMA cycle reads one 4-byte word at a time; memory cycle time = 40ns. Find the maximum percentage of time the CPU is blocked during DMA.
2. 10
3. 25
4. 40
5. 50

8. Computer Networks (CN)

1. Subnetting

• Select the correct subnet mask from given options.
• A network has 5 subnets, each requiring at least 16 hosts. Which classful subnet mask is appropriate?
• 255.255.255.192
• 255.255.255.224
• 255.255.255.240
• 255.255.255.248

2. IP Fragmentation [GATE PYQ-style] Find the fragmentation offset, more-fragment (MF) flag, and packet size for a given scenario.
3. MTU [GATE CS 2014, Set-3 - same question, values modified, 2 marks] MTU-based fragmentation numerical question.
4. Ethernet: Conceptual question on Ethernet.

9. C Programming

1. Output-based questions (2-3 total); includes questions involving static variables.
2. What is the output of the following? “`c if(printf(“PGEE2024”))

3. `arr = 6,7,8,9,10,11,12,13`. What is the output of `**arr`?
4. What is the return type of `calloc()`?
5. What is the output?
```c
int x = –10;
printf(x);

10. Engineering Mathematics

1. Find the maxima of $f(x)=2x^3-9x^2+12x+5$ on the interval $[0,3]$.
2. Property-based question on orthogonal matrices.
3. Application of the Mean Value Theorem.
4. Three questions on simple differential equations in two variables, ODEs, and limits.
5. Evaluate: ${\lim }_{p\to 4}\frac{\sin \left(\frac{p\pi }{4}\right)}{p-4}$
6. Items 6-8 below were recalled separately by the candidate and appended after a section break in the source:
7. Two points are given in the $XY$-plane. Which surface does this locus represent in 3D space?
8. A differential equation is given. Identify the family of curves it represents: parabola, ellipse, circle, or hyperbola.
9. $(2^{32}+1)$ is completely divisible by a whole number $k$. Which of the following is also divisible by $k$?
10. $2^{16}+1$
11. $2^{16}-1$
12. $7\times 2^{23}$
13. $2^{96}+1$

11. Probability & Set Theory

1. Set Theory / Inclusion-Exclusion: In an examination: 43% passed Maths, 52% passed Physics, 52% passed Chemistry; 14% passed Maths & Physics; 21% passed Maths & Chemistry; 20% passed Physics & Chemistry; 8% passed all three. Total students = 200. How many students passed Maths only?
2. Probability -Ball Draw: A person picks two numbers from 1 to 25. A box contains balls numbered 1 to 25; two are drawn simultaneously. What is the probability the person wins (both drawn balls match their chosen numbers)?
3. Probability -even-Segment Display: A display currently shows digit 8 using seven LEDs. The probability that any single LED switches off is $p$. What is the probability that the display changes to show 3?

12. Miscellaneous

1. Four statements are given; identify which statement(s) are correct / incorrect. (Specific topic not recalled by candidate.)

PGEE 2025 Memory-Based Questions

Memory Based Question Paper -PGEE 2025

Exam Pattern

• Total: 90 Questions -40 Aptitude + 40 Core + 10 Mathematics
• Duration: Two sections of 90 minutes each Section 1: Aptitude (40 Q) | Section 2: Core + Maths (50 Q)
• Marking: $+1$ for correct, $-0.25$ for incorrect
• Note: Negative marking was present; no calculator policy stated.

1. Verbal / Reading Comprehension (Aptitude)

1. Passage 1 - Marie Curie [Q3 in source] (Full passage provided in exam. Questions below are fill-in-the-blank vocabulary based on the passage.)
2. The Curies’ collaboration helped to unlock the secrets of the atom. (a) friendly (b) competitive (c) courteous (d) industrious
3. Marie had a bright mind and a personality. (a) strong (b) lighthearted (c) humorous (d) strange
4. When she learned that she could not attend the university in Warsaw, she felt . (a) hopeless (b) annoyed (c) depressed (d) worried
5. Marie by leaving Poland and travelling to France to enter the Sorbonne. (a) challenged authority (b) showed intelligence (c) behaved (d) was distressed
6. Her began to fade when she returned to the Sorbonne to succeed her husband. (a) misfortune (b) anger (c) wretchedness (d) disappointment
7. Passage 2 - Research and Integrity in Indian Academia [Q4 in source] (Full passage provided in exam. Questions not recalled by candidate. Passage covered: Dr. Manmohan Singh’s 2008 speech at the Chinese Academy of Social Sciences on India-ina research collaboration; and a plagiarism case at Sri Venkateswara University involving 70+ publications.)

2. Quantitative Aptitude / Logical Reasoning

1. Number Comparison: [Q1] Which number is larger: $(7{)}^{33}$ or $(19{)}^{22}$?
2. Weighing Puzzle: [Q2] You have 10 stacks of 10 gold coins. Each coin weighs 10gm, except coins in one stack which weigh 9gm each. How many total measurements (weighings) are required to identify the defective stack?
3. Cube Painting and Cutting: [Q6] A cube of side 12cm is painted: two opposite faces in red, another pair of opposite faces in blue, and one of the two remaining faces in black (the last face unpainted). The cube is then cut into $1{\text{cm}}^3$ unit cubes. How many unit cubes have exactly two coloured faces?
4. Path Counting: [Q7] Three points $A$, $B$, $C$. Travel from $A$ to $B$ is the same as travel from $A$ to $C$ (i.e. both routes available). Travel from $B$ to $C$ is one-way only, and from $C$ to $A$ is one-way only. Starting from $A$, in how many ways can one travel to $C$ without retraversal of $A$?
5. Rope-Walking Physics: [Q9] Two persons $T$ and $J$, both 60kg, where $T$ is 40cm taller than $J$. Both walk on a rope with a 1kg weight on their ankle. What is the relation between the distances they cover?
6. Tennis Betting Puzzle: [Q20] $A$ and $B$ play tennis with a $1 bet per match. At the end, $A$ has won $3 more than they started and $B$ has won $2 more than they started. How many matches were played in total?

3. Engineering Mathematics

1. Laplace Transform: [Q8] Find the Laplace transform of $f(x)=x+3$.

2. Matrix Determinant (Maximum Value): [Q11] A matrix is given; find the maximum value of its determinant. (Options in source involve expressions with $\sin$ and $\cos$; exact matrix not fully recalled - options were garbled in source rendering.)

3. Circle Geometry - Yellow Area: [Q12] Three mutually tangent circles of equal radius $r$ are arranged so that their centres form an equilateral triangle. Find the area of the curvilinear (yellow) region enclosed between all three circles, given the radius.

4. Matrix Rank: [Q18] A matrix is given. Find its rank. $M=\left(\begin{array}{ccc}2& -3& 6\\ -4& 6& -12\end{array}\right)$ (Note: Row 2 $=-2\times$ Row 1, so rank $=1$.)

5. Divisibility: [Q21] $49^{15}-1$ is completely divisible by which of the following? (a) 48 (b) 8 (c) 50 (d) 31

6. Number of Solutions: [Q22] How many integer solutions does $x^2-3y^2=1$ have?

7. Ordinary Differential Equation: [Q23] Given $e^{dy/dx}=(x+1)$, find $y(1)$.

8. Equation of Lines: [Q24] Two lines pass through the point $(3,4)$ with given slopes. Identify which equations correspond to the lines.

9. Gaussian Distribution: [Q28] Conceptual/numerical question on Gaussian (normal) distribution.

10. Eigenvalues: [Q31] A matrix is given. Find the sum of eigenvalues.

4. Probability & Statistics

1. Probability - Coloured Balls (With Replacement): [Q16] A bag contains 25 red balls and 25 white balls. Two balls are drawn randomly with replacement. What is the probability that both balls drawn are the same colour?
2. Mode and Statistics: [Q29] Conceptual/numerical question on mode and related descriptive statistics.

5. Data Structures

1. Huffman Coding -Invalid Code: [Q5] A message is composed of characters from $X=\{P,Q,R,S,T\}$ with the following probabilities: | Character | Probability | | — | — | | P | 0.22 | | Q | 0.34 | | R | 0.17 | | S | 0.19 | | T | 0.08 | | Total | 1.00 | (Note: $P=1.00-0.34-0.17-0.19-0.08=0.22$; not explicitly shown in source table.) Which of the given Huffman codes is not valid?
2. Merging Two Min-Heaps: [Q13] What is the time complexity of merging two min-heaps of sizes $m$ and $n$?
3. $n$ Insertions into a Heap: [Q14] What is the total time taken for $n$ successive insertions into a heap?
4. $X^n$ Without pow(): [Q15] What is the time complexity of computing $X^n$ (i.e. finding the power of a number) without using the pow() library function?

6. Algorithms

1. Minimum Spanning Tree / Shortest Path: [Q27] A directed weighted graph $G^{\prime }$ with nodes $\{A,B,C,S,T\}$ is given (hand-drawn in source; structure is a rectangle $A$-S$-C$-$B$ with diagonals, and node $T$ connected below; edge weights approx.
   $A$-$S$=3, $A$-B$=2,$S$-$C$=4,$B$-$C$=6,diagonals$ 5$and$7$).Findtheminimumcostpathfrom$S$to$T$. (Exact edge weights and directions may vary - source notes “structure was somewhat same but direction and edge weight could vary.”)
2. Stable Sorting: [Q34] Which of the following sorting algorithms is not stable?

7. Digital Logic (DL)

1. Counter Comparison: [Q25] Conceptual question comparing ring counter, Johnson counter, and synchronous counter (differences in structure, states, or output behaviour).
2. Synchronous Counter - Output Frequency: [Q26] Given specifications of a synchronous counter, find its output frequency.
3. LED String Logic: [Q33] A question on how an LED string circuit works. (Exact question not fully recalled by candidate.)

8. Database Management Systems (DBMS)

1. Normalization: [Q17] A relation $R(A,B,C,D)$ is given with a set of functional dependencies. Identify the highest normal form satisfied by $R$.
2. Serializability: [Q19] Two transaction schedules are given. Determine whether each is serializable.

9. Operating Systems (OS)

1. No Deadlock Condition: [Q10] Which of the following conditions, if violated, prevents deadlock? (Tests knowledge of the four Coffman conditions: mutual exclusion, hold and wait, no preemption, circular wait.)
2. exec() System Call and PID: [Q32] A process has PID = 217 and makes an exec() call. What will the PID of the resulting process be?

10. Computer Networks (CN)

1. Subnetting - Maximum Subnets: [Q30] How many maximum subnets can be formed when the subnet mask is 255.255.255.224?

Quora: The LEEE Written Exam - Multiple Accounts

Multiple exam experiences shared on Quora:

Topic Priority Distribution (from a 2019 exam taker):

“Data Structures + Discrete Mathematics $>$ Aptitude $>$ Programming $>$ Digital Logic $>$ CSO”

This is one candidate’s observation from a single year, but it aligns with the general pattern across years. DS and DM consistently carry the most technical weight.

Important warning: “In the syllabus they didn’t mention algorithms, but questions were from algorithms also.” The official syllabus is not a complete guarantee of what appears - treat GATE-level algorithms as in-scope regardless.

Note on question papers: Papers are collected at the end of the exam and never officially released. This is why no authentic previous year papers exist publicly - only memory-based reconstructions.

Experience 1 (2022 exam):

“The LEEE 2022 written exam was divided into two sections. Section 1 was aptitude (30 questions, 60 minutes). Section 2 was the technical paper (50 questions, 120 minutes).

Aptitude was straightforward - similar to CAT/GATE aptitude but easier. I finished in 40 minutes.

Technical section had:

• 10 math questions: eigenvalues, integration, probability
• 15 data structures: BST, heap, linked list
• 10 algorithms: complexity analysis, graph algorithms
• 5 C programming: output-based
• 5 digital logic
• 5 discrete math

No DBMS/OS/CN in the technical paper for CSE in 2022.”

Experience 2 (2023 exam, CSE):

“2023 LEEE CSE had questions from DBMS and OS that surprised many students. Normalization, SQL, virtual memory questions appeared. This was unusual compared to previous years. The difficulty was GATE level.”

Experience 3 (2024 exam):

“In 2024, LEEE and PGEE had separate papers but covered similar topics. My experience: aptitude was easy, math was easy to medium, CS was GATE-level. Data structures had the most questions. Huffman coding appeared. One network flow question.”

Interview Experiences (Quora):

Interview Story 1: “My interview was about 20 minutes. They asked me about my favorite subject (I said Data Structures). Then they asked me to explain a hash table, analyze its time complexity in different scenarios, and resolve a hash collision. They also asked why I wanted to do research. The professors were friendly.”

Interview Story 2: “I chose Discrete Mathematics as my favorite. They asked me to prove that $\sqrt{2}$ is irrational, then moved to graph theory (Hamiltonian path vs. Euler path), and then asked me about my SOP research interests.”

Interview Story 3: “My interview went deep into algorithms. They gave me a problem and asked me to come up with the most efficient solution, then analyze the complexity. They were testing my thought process, not just the answer.”

Interview Story 4: “They asked about Operating Systems - scheduling algorithms, thrashing, and then moved to asking about my project. Since I mentioned a web development project, they asked basic questions about databases (SQL).”

Interview Story 5: “Very friendly professors. Started with: ‘What subject excites you the most?’ I said Probability. They asked Bayes’ theorem, conditional probability problems, and then the Monty Hall problem. I hadn’t prepared for Monty Hall but reasoned through it.”

Interview Story 6: “Digital Logic was my chosen subject. They asked about flip-flops, asked me to design a 3-bit counter, then moved to combinational logic. One professor asked about Shannon entropy (which confused me).”

Interview Story 7 (ECE): “For ECD stream, they asked about BJT amplifier analysis, Laplace transform of a circuit, and then went into digital logic (K-map minimization). About 25 minutes total.”

Interview Format Variation - Printed Questions (one reported format):

One Quora respondent described a distinctly different interview structure:

1. Candidates were formed into groups of $\sim$25, then sub-groups of 4
2. Each sub-group was taken to the main building and given 3 printed questions on paper with approximately 15 minutes to work on them
3. The actual interview then revolved entirely around those 3 printed questions, not the standard subject-choice format
4. The questions in this instance were: a conic sections geometry question (what shape when cut at different axes), an everyday chemistry question (what happens chemically when you fry food on a pan), and a word-mapping/translation task (for those who had filled linguistics interest)
5. The interviewers started with light conversation to make the candidate comfortable, then probed the candidate’s thinking from those 3 questions

Note: This format is substantially different from the standard “favorite subject” format and may reflect format variation across years or panels. Be mentally prepared for either structure.

ECD Interview Format: For the ECD (LED) track, the interview panel is typically 5-6 professors and candidates are given chalk and a board to work on. Questions are purely technical - no HR questions. Duration is approximately 25-35 minutes. The chalk-and-board format means you should practice solving circuit problems, signal analysis, and digital logic by hand.

On the role of luck: “Honestly, the interview is partly luck-based. Me and another guy prepared for LEEE together from my college; we both made it to interview, but only I got in despite the other guy having better DSA skills than me.” The panel’s composition and the direction questions take introduces genuine variability beyond your preparation level. Prepare well, but don’t read too much into individual outcomes.

Questions build on each other: Within the interview, questions are rarely isolated. Once you state your favorite topic, the next question builds on your answer to the previous one. The session is a progressive chain, not a random set.

Related

• leee-2026-memory-based-question-bank
• leee-2026-interview-experiences