LEEE 2026 Memory-Based Question Bank

Note

Community-compiled, memory-based question bank for LEEE 2026 (exam date: 2 May 2026, results: 11 May 2026). Questions reconstructed from participant recalls; answers verified where possible against GATE solutions.

Exam Structure & Overview

LEEE 2026 Paper Breakdown

Section	Questions	Notes
General Aptitude / LR	30	Verbal, quant, logical reasoning
CS Core A (Easy Theory)	10	First 2 weeks of programming-class level
CS Core B (In-depth)	25	Algorithmic, time complexity, digital
Engineering Mathematics	15	Calc, LA, DM, Probability
Total	80

• One attempted student reported 59/80 total: 18/30 LR + 42/50 CSE Core.
• Another student attempted 60 questions. Many students attempted 55-70.
• The CS section was completed by prepared students in 20-30 minutes.
• Questions appeared in different order for different test-takers (randomised).
• Marking scheme: $+1$ / $-0.25$ (negative marking present throughout).
• No OS, CN, or DBMS-heavy questions this year - pattern shifted significantly from 2025.
• One participant said DM was easy.

Results & Cutoffs (Released 11 May 2026, 6:20 PM)

• Cutoffs are subject-wise (not aggregate).
• Subject cutoff for shortlisting: 26.00
• General Aptitude (GA) cutoff for shortlisting: 13.00

Subject Distribution (CS Section) - What Actually Came

Topic	Appeared?	Notes
2s Complement / COA	✓ Heavy (4-5 Qs)	Biggest surprise
Heaps	✓ $\approx$3 Qs	Both build-heap and operations
Trees / BST / AVL	✓ $\approx$3 Qs
Sorting algorithms	✓ $\approx$2 Qs	Merge sort, Stooge sort
Graph algorithms	✓ $\approx$2 Qs	BFS/DFS for components/cycles
C Programming	✓ $\approx$4 Qs	Short-circuit, static, recursion, pointers
Discrete Math	✓ $\approx$3 Qs	Functions, graph edges, propositional logic
Asymptotic Notation	✓ 1-2 Qs
DBMS	✓ 1 Q (R-S cond.)	Light
Operating Systems	▲ 1 Q about tables	Very light
Computer Networks	✗	Did not appear
Hashing	✗	Did not appear
Flip-flops / Counters / Registers / MUXes	✗	Did not appear
Laplace / Fourier / Z-Transform	✗	Did not appear

GATE PYQs - Direct Reuse (Confirmed)

Many CS questions were directly lifted from GATE with no modification:

• Sorted linked list insertion $\to O(n^2)$ (GATE 2020)
• Insert $n^2$ into AVL tree (GATE PYQ)
• Decoder $m+n=1034$ (GATE CSE 2020 Q20) - referred to in chat as “C3D8”
• GATE CSE 2009 Q59 appeared directly
• Stooge sort recurrence (GATE PYQ)
• GCD time complexity (GATE PYQ)

Experiences, Tips & Strategy

Student Experiences

• Overall difficulty: Rated easy-to-moderate. Math was easy; GATE questions heavily repeated.
• Paper surprises: 5-8 out-of-syllabus questions. 2s complement was unexpectedly heavy; flip-flops (which many prepared) were absent.
• CS section speed: Prepared students finished CS in 20-30 min.
• Aptitude: Considered easy but time-constrained. Last part of aptitude was easier - check all sections before skipping.
• Pattern shifts year to year: Students who prepared OS & DBMS based on 2025 pattern found almost nothing this year. COA/digital arithmetic dominated instead.
• K-map ambiguity: A K-map question had 2 correct options ($ab+bc+ca$ AND $(a+b)(b+c)(c+a)$) in a single-choice format - management may award bonus marks.

Cutoff Estimates (2026)

Estimate Source	Cutoff
Conservative estimate	$\approx$40-50
Higher estimates	50-60
Probable cutoff	$\approx$50

• Paper was rated easier than 2025; cutoffs expected to rise.
• $\approx$200 interview slots available.
• $\approx$7,000-10,000 students register annually; fewer actually sit the exam. 2026 had lower turnout due to endsem clashes.

Eligibility

• CSD: Completing 4 semesters of B.E./B.Tech. in CSE / IT / AI & ML / Data Science / Software Engineering / Maths & Computing / Computer Engineering by July 2026.
• ECD: Electronics & Communication Engineering equivalent.
• Backlogs must be cleared before the exam.
• CGPA is asked in some interview panels - low CGPA may invite questions about extra-curricular activities.
• Internships and projects strengthen the SOP and interview.

Results & Process

• Results sent via email; can also check IIITH official site.
• Results expected: 12-14 May 2026
• Interview: 23 May 2026

Prep Tips (from Students Who Sat the Exam)

1. Practice GATE PYQs - many appear verbatim. Focus on easy-to-mid difficulty GATE questions; solving those comfortably is sufficient to qualify.
2. Don’t chase specific topics - syllabus focus shifts every year. Broad coverage beats deep focus on a few topics.
3. Don’t rely on senior predictions - seniors predicted op-amps and small-signal for ECE; exact opposite came.
4. 2s complement was the single biggest digital topic - know all the conversion rules cold.
5. Attempt strategy: Being overly conservative (skipping uncertain questions) can backfire. Negative marking is real, but skipping questions you’d have gotten right is equally costly.
6. CS-A section (easy theory) is very straightforward - attempt all of it first.
7. Maths appeared in every section (Aptitude + CS + Maths section) - maths was more than 30% of the paper.
8. Genuine interest matters - “If you do not like the topics, it will be impossible for you to even crack the MCQ test. The questions are made to make you think.”
9. Recommended YouTube channels:

• 3Blue1Brown, vcubingx, Mathemaniac - differential equations and complex analysis.
• Trefor Bazett - excellent discrete mathematics playlist for LEEE prep.

General Aptitude (30 Questions)

Note

This section appeared in both LEEE 2026 and PGEE 2026 - many questions were identical across both exams.

Verbal / Comprehension

Q: Narayana Murthy comprehension (4 questions)

Q: Survey comprehension (4 questions)

Q: The Internet comprehension passage (PGEE)

Quote

“The Internet can have a positive impact on the conduct of psychological research, both by changing the costs of data collection and by making visible interesting psychological phenomena…”

4 questions were asked on this passage.

Q: Who told the truth? (Logic puzzle)

Quote

4 students. Exactly one person copied and one person lied.

• Aditi: “Karan copied the assignment”
• Karan: “Rohan didn’t copy the assignment”
• Neha: “Aditi is telling the truth”
• Rohan: “Neha is telling false”

Answer: Karan copied the assignment.

Logical Reasoning

Q: River Crossing - 3 Men, 3 Lions

Quote

3 men and 3 lions must all cross a river. The boat carries 1 or 2 at a time. If lions ever outnumber men on either bank, the men are eaten. What is the minimum number of boat trips?

Answer: 11 trips.

(Classic puzzle - TED-Ed video covers it. Key insight: a lion can also row the boat back.)

Q: Variant - 3 Men vs 3 Tigers (count ways)

Quote

3 men are on one bank and 3 tigers are on the other bank. They must all cross to the opposite bank using a boat that carries 1 or 2 beings at a time. At no point (on either bank or in the boat) may the number of tigers exceed the number of men; if tigers ever outnumber men on a bank or in the boat, the men are eaten. How many distinct sequences of crossings (ways) allow everyone to cross safely?

Q: Logic / Family Relationship Puzzle (Love triangle / cheating scenario)

Quote

Widely considered confusing. Exact details unclear from discussion. Many students skipped it.

Q: Circular seating arrangement (PGEE)

Quote

7 people in a circular seating arrangement.

Answer: (C)

Q: Person travels 8 km north, turns 60, travels 7 km. How far from start? (PGEE)

Quote

Answer: 13 km, South-West

Quantitative Aptitude

Q: Day of the week - April 25, 2026

Quote

What day of the week was April 25, 2026?

Answer: Saturday.

(First question in the aptitude section. Students who knew modular day-counting tricks solved it instantly.)

Q: Work and Time

Quote

A can do work in $X$ days, B in $Y$ days, C in $Z$ days. They all start together but A leaves after 2 days. In how many days is the work completed?

PGEE version: A, B, C complete a task individually in 12, 16, and 24 days. A leaves after 2 days. How many more days are needed?

PGEE Answer: 6 more days (for B and C to complete remaining work)

Q: Train crossing a pole

Quote

A train running at 60 km/h crosses a stationary pole in 30 seconds. What is the length of the train?

Answer: 500 m

Q: 400 m Race (PGEE)

Quote

A and B compete in a 400 m race. A’s speed = 8 m/s, B’s speed = 10 m/s. A gets a head-start of 60 metres.

Answer: B wins by 2.5 seconds.

Q: Electricity Bill Calculation (PGEE)

Quote

Jan: 350 units, Feb: 80 units consumed.

• 1-100 units: Rs. 4/unit
• 101-300 units: Rs. 6/unit
• 300+ units: Rs. 9/unit
• Fixed meter charge: Rs. 50
• 10% government tax on overall cost

Answer: Rs. 2717

Q: Graph-based aptitude questions (Q10-12) (PGEE)

Quote

3 graph-based quantitative questions appeared. Exact details not recalled by respondents.

Q: Two Circles Intersecting (PGEE)

Quote

Two circles intersect at B and C. Common chord length = 16 cm, distance between centres = 21 cm, radius of larger circle = 17 cm. Find radius of smaller circle.

Answer: 10 cm

Q: Integers divisible by 3 or 7 (PGEE)

Quote

How many integers between 1 and 1000 are divisible by 3 or 7?

Inclusion-exclusion: $\lfloor 1000/3\rfloor +\lfloor 1000/7\rfloor -\lfloor 1000/21\rfloor =333+142-47=428$

Q: Number of Factors (PGEE)

Quote

How many positive integer factors does $N=2^2\times 3^3\times 4^4\times 5^5$ have?

Note: $4^4=2^8$, so $N=2^{10}\times 3^3\times 5^5$. Number of factors $=11\times 4\times 6$.

Answer: 264

Q: Power of a Power Set (PGEE)

Quote

The number of elements in $\mathcal{P}(\mathcal{P}(S))=256$. What is $n=|S|$?

$|\mathcal{P}(S)|=2^n$, $|\mathcal{P}(\mathcal{P}(S))|=2^{2^n}=256=2^8\Rightarrow 2^n=8\Rightarrow n=3$.

Answer: $n=3$

Q: AP and GP - 3 Positive Numbers

Quote

3 positive numbers are in AP with sum = 21. When 2 is added to the smallest, 3 to the middle, and 9 to the largest, they form a GP. Find the two smallest numbers.

AP: $3,7,11$. After adding $2,3,9\to 5,10,20$ (GP with ratio 2).

Answer: 3 and 7

Q: Missing Number in Table (PGEE)

Col 1	Col 2	Col 3
5	3	16
10	8	36
13	12	?

Quote

Pattern: ${\text{Col1}}^2-{\text{Col2}}^2$: $5^2-3^2=16$ , $10^2-8^2=36$ , $13^2-12^2=25$ .

Answer: 25

Q: Three dice - probability (PGEE)

Quote

Three dice are rolled independently. What is the probability that the difference between the highest and lowest value is exactly 4?

Answer: $2/9$ (TIFR 2011 question)

Q: Dhoni-Kohli sequence (PGEE)

Quote

Write natural numbers 1, 2, 3, … replacing multiples of 3 with “dhoni”, multiples of 5 with “kohli”, multiples of both with “dhoni kohli”. Only actual numbers are counted. What is the 100th number in this filtered sequence?

Answer: 187

Q: Travel preferences - set theory (PGEE)

Quote

66 people like air travel, 128 like train, 55 like car, 15 like all three, 45 like at least two. Find the number who like at least one mode. (Apply inclusion-exclusion.)

Q: Rectangle shaded region (PGEE)

Quote

Rectangle ABCD. P is midpoint of AB. Q divides BC in ratio 1:3. R divides AD in ratio 3:1. What fraction of the rectangle is shaded?

Answer: 3/4

Q: Permutations - no adjacent even numbers (PGEE)

Quote

Number of permutations of $\{1,2,3,4,5\}$ forming 5-digit numbers such that no two even numbers are adjacent and the number is not divisible by 5.

Q: Minimum people - same birth month (PGEE)

Quote

Minimum number of people such that the probability of at least 2 sharing a birth month is $\ge 50$?

Answer: 5

Q: Sum of 3 positive integers = 10

Quote

How many ways can 10 be written as the sum of three positive integers, where $(2,2,6)$, $(2,6,2)$, $(6,2,2)$ are counted as one representation? Options: 36, 360, 45, 720.

Answer: 8 (LEEE - unordered) $|$ Answer: 36 (PGEE - ordered)

Q: $3\times 3\times 3$ Cube Painting (PGEE)

Quote

Top and bottom faces painted red, remaining painted blue. How many small cubes have blue paint but NOT red?

Options: 1) 9, 2) 8 Answer: 8

Q: Cylinder + Cone + Hemisphere Volume (PGEE)

Quote

A cylinder has height 15 cm and diameter 10 cm. A cone of the same diameter and depth 6 cm is cut from the top. A hemisphere of the same diameter is added at the bottom. Find the total volume.

Answer: $1225\pi /3$

Q: Graphical probability distribution questions

Quote

Given distributions (normal, uniform, etc.) with mean and standard deviation - questions asked using the graph.

Also asked: For which distribution is mean significantly less than mode? (Retirement ages: most retire at 65, some at 40 $\to$ left-skewed distribution.)

Q: $P(A\cap B)$ can be? (PGEE)

Quote

$P(A)=0.5$, $P(B)=0.3$. What can $P(A\cap B)$ be?

Answer: 0.15 (valid range: $[0,\min (P(A),P(B))]=[0,0.3]$)

Engineering Mathematics (15 Questions)

Note

Maths appeared in every section of the paper (Aptitude, CS Core, and the Maths section). Overall rated easy; maths was more than 30% of the paper.

Calculus & Analysis

Q: Integration - King’s Rule

Quote

Evaluate:

${\int }_0^1\log \left(\frac{1}{x}-1\right)dx={\int }_0^1\log \left(\frac{1-x}{x}\right)dx$

By King’s property ${\int }_0^{1}f(x)dx={\int }_0^{1}f(1-x)dx$: $f(x)=\log \left(\frac{1-x}{x}\right)$ and $f(1-x)=-f(x)$, so the integral $=-$itself.

Answer: 0 (Equivalent forms: ${\int }_0^1\log \frac{1}{1+x}dx$ also appeared.)

(One respondent recalled this as "$\int \ln (x)dx$" with options 0 and 1 - likely imprecise recall of this question (answer 0). Note: ${\int }_1^e\ln (x)dx=1$ is another clean definite integral with the same options that may also have appeared.)

Q: Limit

Quote

$\underset{x\to \infty }{\lim }\frac{\sin x}{x}$

Answer: 0 ($\sin x$ is bounded; $1/x\to 0$)

Q: Derivative - $\sin (x)+e^x$

Quote

Differentiate $f(x)=\sin (x)+e^x$.

Answer: $f^{\prime }(x)=\cos (x)+e^x$

Q: Derivative - $\sinh (x)+e^x$

Quote

Differentiate $f(x)=\sinh (x)+e^x$.

Answer: $f^{\prime }(x)=\cosh (x)+e^x$

Q: Implicit Differentiation

Quote

$y=\sin (x-y)$. Find $dy/dx$.

$\frac{dy}{dx}=\cos (x-y)\left(1-\frac{dy}{dx}\right)⟹\frac{dy}{dx}=\frac{\cos (x-y)}{1+\cos (x-y)}$

Q: Nested Radical

Quote

$x=\sqrt{12+\sqrt{12+\sqrt{12+\cdots }}}$. Find $x$.

$x=\sqrt{12+x}\Rightarrow x^2-x-12=0\Rightarrow (x-4)(x+3)=0$; since $x>0$, $x=4$.

Answer: $x=4$

Q: Critical Points

Quote

$f^{\prime }(x)=0$ at $x=x^{\ast }$. What can be concluded about $df/dx$?

Answer: Nothing can be concluded. (Could be a maximum, minimum, or inflection point.)

Q: Partial Differentiation

Quote

$x=r\cos \theta$, $y=r\sin \theta$. Compute $\frac{\partial x}{\partial r}\cdot \frac{\partial y}{\partial \theta }$.

$\partial x/\partial r=\cos \theta$, $\partial y/\partial \theta =r\cos \theta$ $\Rightarrow$ product $=r{\cos }^2\theta$.

Q: Domain of $f\circ g$

Quote

$f(x)=\frac{1}{x-5}$, $g(x)=\sqrt{x-2}$. Find domain of $f\circ g$.

$f(g(x))=\frac{1}{\sqrt{x-2}-5}$. Need $x\ge 2$ and $\sqrt{x-2}\ne 5\Rightarrow x\ne 27$.

Answer: $[2,27)\cup (27,\infty )$

Q: Quadratic / Domain check

Quote

Question involving $x^2-3x+2$ (possibly inside a log or sqrt). Find roots / solve.

$x^2-3x+2=(x-1)(x-2)$, roots 1 and 2. If inside $\log /\sqrt{}$, domain restricts further. Must check domain - many students forgot this.

Linear Algebra

Q: Eigenvalues - $4\times 4$ Matrix

Quote

Sum of eigenvalues of a given $4\times 4$ matrix?

(Sum of eigenvalues = trace of the matrix.)

Q: Rank of Matrix - $A^{-1}$ exists

Quote

Given $3\times 3$ matrix $A$. If $A^{-1}$ exists, what is the rank of $A$?

($A^{-1}$ exists $\iff$ $A$ is invertible $\iff$ rank $=n$.)

Answer: rank = 3

Q: Orthogonal Matrix

Quote

A $3\times 3$ orthogonal matrix has entries including $1/\sqrt{2}$, $1/\sqrt{3}$, $1/\sqrt{6}$. Find unknown $c$.

Answer: $c=1/\sqrt{3}$ (rows must be orthonormal)

Q: Which grows fastest? (PGEE)

Quote

Compare as $x\to \infty$: (1) $2^{2^x}$, (2) $100000^x$, (3) $e^{e^{\ln x}}=e^{xe}$, (4) $e^{x^2}$.

Answer: $2^{2^x}$ (double exponential dominates all others)

Discrete Mathematics

Q: Number of injective (one-to-one) functions

Quote

Number of one-to-one functions from a set of $m$ elements to a set of $n$ elements?

Answer: $P(n,m)=n!/(n-m)!$

Q: Number of onto (surjective) functions

Quote

Number of onto functions from $\{a,b,c,d\}$ to $\{1,2,3,4\}$?

Answer: $4!=24$ (when $|\text{domain}|=|\text{codomain}|$, bijections count both)

Q: Number of all functions (to a smaller set)

Quote

Number of functions from a set of 5 elements to a set of 3 elements?

Answer: $3^5=243$

Q: Max edges in a complete graph $K_n$

Quote

Answer: $\frac{n(n-1)}{2}$

Q: Propositional Logic - CNF

Quote

Convert/simplify: $p\to (q\wedge p)$.

Using $p\to q\equiv \neg p\vee q$: Answer: $\neg p\vee (q\wedge p)$

Also asked: CNF of $(\neg p\vee q)\wedge (\neg p\vee r)$ - already in CNF (conjunction of disjuncts).

Q: $f(f(x))=0$ - find all $x$

Quote

$f(x)=x^2-3x+2$. Find all $x$ such that $f(f(x))=0$.

f(x) = 0 & x = 1 or x = 2

f(x) = 1 & x^2-3x+1=0 x = 352

f(x) = 2 & x^2-3x=0 x = 0 or x = 3

Answer: $\left\{0,1,2,3,\frac{3+\sqrt{5}}{2},\frac{3-\sqrt{5}}{2}\right\}$

Probability & Statistics

Q: Probability - biased coin

Quote

A box contains 4 coins. One is unfair ($P(\text{H})=0.8$); others are fair ($P(\text{H})=0.5$). A coin is chosen at random and tossed. Find $P(\text{head})$.

Answer: 0.575 $=\frac{1}{4}\times 0.8+\frac{3}{4}\times 0.5=0.2+0.375$

Q: Mutually exclusive or independent?

Quote

$P(A)=0.2$, $P(B)=0.3$, $P(A\cup B)=0.5$. Are A and B mutually exclusive or independent?

$P(A\cap B)=0.2+0.3-0.5=0\Rightarrow$ mutually exclusive.

Answer: Mutually exclusive

Q: Mutually exclusive or independent? (Variant)

Quote

$P(A)=0.3$, $P(B)=0.5$, $P(A\cup B)=0.8$. $P(A\cap B)=0.3+0.5-0.8=0$.

Answer: Mutually exclusive

Q: $P(A\cup B)=0.6$ variant (PGEE)

Quote

$P(A)=0.2$, $P(B)=0.3$, $P(A\cup B)=0.6$. What can be said?

$P(A\cap B)=0.2+0.3-0.6=-0.1<0$ - impossible. Error in question or options.

Answer: None of the above

Q: Distribution - mean $<$ mode

Quote

For which distribution is the mean significantly less than the mode? Retirement ages: most retire at 65, some at 40 - left-skewed distribution has mean pulled toward lower values while mode stays at the peak.

CS Core - Algorithms & Data Structures

Q: Insert $n^2$ elements into an AVL tree of $n$ elements

Quote

An AVL tree already has $n$ elements. Time complexity to insert $n^2$ more?

Each insertion into an AVL tree of $\approx n^2$ nodes takes $O(\log n^2)=O(\log n)$. Total: $n^2\times O(\log n)$.

Answer: $O(n^2\log n)$ (confirmed GATE PYQ - appeared directly)

Q: Insert $n$ elements into a sorted linked list

Quote

Time complexity to insert $n$ elements one by one into an initially empty sorted linked list?

$i$-th insertion traverses $i$ elements $\Rightarrow$ total $=1+2+\cdots +n=n(n+1)/2$.

Answer: $O(n^2)$ (GATE 2020 PYQ - appeared with no modification)

Q: Number of binary trees with 3 unlabelled nodes

Quote

How many distinct binary trees are possible with 3 unlabelled nodes?

Answer: 5 (Catalan number $C_3=5$)

Q: Number of distinct BSTs with 5 nodes

Quote

Answer: 42 (Catalan number $C_5=42$)

Q: Build binary tree from traversals + find height

Quote

Postorder: $\{8,6,7,3,4,2,5,1\}$, Inorder: $\{8,6,3,7,2,4,1,5\}$ (or similar). Reconstruct the tree and find its height.

Answer: 4 (if root is counted as level 0)

Q: Stooge Sort recurrence

Quote

What is the recurrence relation for Stooge Sort?

Answer: $T(n)=3T(2n/3)+O(1)$

(confirmed by multiple students; confirmed GATE PYQ)

Q: Which sorting algorithm has $O(n\log n)$ in all cases?

Quote

Which sort guarantees $O(n\log n)$ worst-case time complexity?

Answer: Merge Sort (Quick sort has $O(n^2)$ worst case)

Q: Data structure for delete-max and search in $O(n)$

Quote

Which data structure supports deleting the max element and searching for an element both in $O(n)$ time?

Answer: BST (delete-max: $O(h)=O(\log n)$ avg, $O(n)$ worst; search: $O(n)$ worst)

(Some interpretations say heap for delete-max; confirmed PGEE answer is BST.)

Q: Heap operations - which is $O(n)$?

Quote

Which heap operation has time complexity $O(n)$?

1. Build Heap (bottom-up using heapify)
2. $N$ heapify-max operations
3. $N$ heap insertions

Answer: Option 1 - Build Heap (bottom-up build is $O(n)$; options 2 and 3 are $O(n\log n)$)

Q: Two heap-building algorithms

Quote

Algorithm 1 (bottom-up): heapify at each index from $n/2$ down to 1.

Algorithm 2 (top-down): insert elements one by one from $i=2$ to $n$.

• Time complexity: Algo 1 is $O(n)$; Algo 2 is $O(n\log n)$ - NOT the same.
• Both build a valid max-heap but can produce different outputs (different valid arrangements).

Q: Time complexity to build a Max Heap from $n^2$ elements

Quote

Build a max heap from $n^2$ elements. Compare the two methods:

• Bottom-up Build-Heap: $O(n)$ in number of elements $\Rightarrow O(n^2)$ for $n^2$ elements.
• Inserting $n^2$ elements one by one: each insertion is $O(\log n^2)=O(\log n)$ $\Rightarrow$ total $O(n^2\log n)$.

Answer: Build-Heap is $O(n^2)$; repeated insertion is $O(n^2\log n)$.

(Options recalled: “Build-Heap” vs “Insert for already existing heap” - Build-Heap is the faster method.)

Q: Heap/BST insertion

Quote

Insertion time in a max-heap or balanced BST?

Answer: Both $O(\log n)$

Q: Max heap - structure property

Quote

The max-heap property requires each parent $\ge$ its children; it does NOT require any ordering relationship between nodes at the same level.

Q: GCD - Euclid’s Algorithm

Quote

Time complexity of Euclid’s GCD algorithm?

Answer: $O(\log n)$ (where $n$ is the smaller of the two inputs; options included $\log n$, $n$, “none of these” - $\log n$ confirmed)

Q: Number of connected components - time complexity

Quote

Most efficient algorithm for finding the number of connected components?

Answer: $O(V+E)$ using BFS or DFS

Q: Cycle detection in undirected graph

Quote

Options: a) Topological Sort b) Prim’s c) Union-Find d) Dijkstra’s

Answer: Union-Find (DFS also works, but given answer was Union-Find)

Q: Which algorithm checks if a graph is disconnected?

Quote

Answer: BFS or DFS - $O(V+E)$. If not all vertices are visited from one source, graph is disconnected.

Q: Matrix Multiplication - Strassen’s Algorithm property

Quote

A question about a static property of Strassen’s algorithm (not asking to run it).

Answer recalled as: (5, 3) - exact question form unclear.

Q: Inversion pairs - worst case of insertion sort

Quote

A permutation $a_1,\dots ,a_n$ has inversions: pairs $(i,j)$ with $i<j$ and $a_i>a_j$. Worst-case time complexity of insertion sort?

Answer: $O(n^2)$ (max inversions $=n(n-1)/2$)

Q: Matrix chain multiplication - which order is valid? (PGEE)

Quote

Matrices P, Q, R with different dimensions. Which product - $Q\times R\times P$, $P\times Q\times R$, or $R\times Q\times P$ - is valid?

Answer: QPR (check dimension compatibility based on given sizes)

Q: Asymptotic equivalence - $\log (n^n)$ vs $n\log n$

Quote

$F_1=\log (n^n)$, $F_2=n\log n$. Are they asymptotically equivalent?

Answer: Yes. $\log (n^n)=n\log n$, so $F_1=\Theta (F_2)$.

Q: $\log (n!)$ vs $n\log n$ - asymptotic comparison

Quote

$f(n)=\log (n!)$, $g(n)=n\log n$. Which statements are true?

1. $g(n)=O(f(n))$
2. $f(n)=O(g(n))$
3. Both (A) and (B)
4. $f(n)\ne O(g(n))$

By Stirling: $\log (n!)\approx n\log n-n$, so $f(n)=\Theta (g(n))$ - both dominate each other.

Answer: Both $g(n)=O(f(n))$ AND $f(n)=O(g(n))$, i.e. $f(n)=\Theta (g(n))$.

(One respondent recalled the answer as ”$g(n)=O(f(n))$ and $f(n)\ne O(g(n))$” - but $f(n)\ne O(g(n))$ is incorrect; they are $\Theta$-equivalent.)

CS Core - C Programming

Q: Short-circuit evaluation - && operator

Quote

“`c int i = -1, j = -1, k = 1, l = 2, m; m = i++ && j++ || k++ && l++; printf(”

`i++`: used as $-1$ (truthy), then becomes 0. `j++`: used as $-1$ (truthy). $-1\ \texttt{\&\&}\ -1 = 1$. LHS of `||` is true, so `k++` and `l++` are **NOT** evaluated (short-circuit).

: `0 0 1 2 1` (`i=0, j=0, k=1, l=2, m=1`)

Q: Short-circuit - l++ never evaluated

Quote

Simpler variant: left operand of && is 0/false; right operand contains l++.

When left side of && is 0, the right side is never evaluated - l++ is skipped.

: l stays at 2 (does not increment to 3).

Q: Short-circuit with bitwise & - $k=0$ variant

Quote

int i = -1, j = -1, k = 0, l = 2, m;
m = i++ & j++ || k++ & l++;
printf("

Parses as (i++ & j++) || (k++ & l++).

• i++ & j++: uses $-1$ and $-1$ (post-incremented), $(-1)\&(-1)=-1$ (all bits set, non-zero).
• || short-circuits: k++ & l++ is not evaluated; k stays 0, l stays 2.
• Logical || returns 1 when left side is non-zero $\Rightarrow$ m = 1.

Options: 0 0 0 2 1 / 0 0 1 3 1

: 0 0 0 2 1

(Uses bitwise &, not logical &&. Short-circuit still applies at the || level.)

Q: Static variable recursion

Quote

#include <stdio.h>
int main() 
static int var = 5;
printf("
if (var)
main();
 

Static variable retains its value across recursive calls. var– prints then decrements.

: 5 4 3 2 1

Q: C keyword - storage class that survives function termination

Quote

Options: static, volatile, register

: static

Q: Recursive string function - putchar

Quote

void fun(char *a) 
if (*a && *a != ' ') 
char c = *a;
fun(a + 1);
putchar(c);
 
 
int main() 
char a[] = "ABCDE FGHIJ";
fun(a);
 

Recursion goes forward until space or null. On the way back, prints characters in reverse order.

: EDCBA

Q: Combinatorics - combinations with repetition formula

Quote

Answer formula: $\left(\genfrac{}{}{0ex}{}{n+r-1}{r-1}\right)$ or $\left(\genfrac{}{}{0ex}{}{n-1}{r-1}\right)$

(Stars and bars for distributing $r$ identical items into $n$ bins.)

Q: Pointer arithmetic - two printf variant

Quote

“`c int arr[] = 10, 20, 30, 40, 50; int *ptr = arr; printf(” printf(”

`*(ptr++)` uses **post-increment**: dereferences `ptr` first (reads `arr[0]=10`), then increments `ptr` to `arr[1]`. Second `printf` reads `arr[1]=20`.

: `10 20`

(Common trap: a student recalled ```20 20`" thinking parentheses in `(ptr++)` convert it to pre-increment - they do **not**. Pre-increment requires `*(++ptr)`, which would give `20 20`.)

Q: C expression to compute $\min (x,y)$ using bitwise operations (CS-B)

Quote

Write a C expression that computes $\min (x,y)$ without using if/else.

: y \^ ((x \^ y) & -(x < y))

Proof: if $x<y$: $(x<y)=1$, $-1=$all 1-bits, so $(x\oplus y)\&\sim 0=x\oplus y$, then $y\oplus (x\oplus y)=x$ ✓.

If $x\ge y$: $-(0)=0$, so $(x\oplus y)\&0=0$, then $y\oplus 0=y$ ✓.

Q: Best data structure to implement recursion

Quote

Answer: Stack (LIFO - exactly what the function call stack uses)

(At least one student incorrectly marked “linked list” at the last moment and regretted it.)

Q: Two threads - shared variable

Quote

Thread A: X–; Thread B: X++; $X$ shared, initial value $=0$, operations NOT atomic. Possible values of $X$ after both execute?

Answer: 0, 1, or $-1$ (race conditions - read-modify-write interleaving)

CS Core - Digital Logic & Computer Architecture

Warning

2s Complement - 4-5 questions (heaviest topic in CS section)

Students expected flip-flops/counters but got 2s complement instead. Biggest surprise of the paper.

Q: 2s complement GATE-style - C(3,8) or P(16,8) type

Quote

Answer recalled in a format like C(3,8) or P(16,8). Likely the same as the 2s complement of 8P question (GATE CSE 2010 Q8).

Q: 2s complement of 8P (GATE CSE 2010 Q8)

Quote

$P$ is a 16-bit number given in hexadecimal 2s complement form. Find the 2s complement representation of $8P$.

(Reference: gateoverflow.in/2179/gate-cse-2010-question-8)

Answer: BDC8 (exact value depends on given $P$ - check GATE solution)

Q: For which number is 2s complement the same as the original?

Quote

Options include: 1000, 0000, etc.

Answer: 1000 ($-(1000{)}_{\text{2s comp}}=1000$ due to overflow; it is its own negative)

Q: IEEE 754 Single Precision for 0.5

Quote

Represent 0.5 in IEEE 754 single-precision floating point.

$0.5=1.0\times 2^{-1}$: sign $=0$, exponent $=-1+127=126={\text{01111110}}_2$, mantissa $=0$.

Answer: (sign=0, exponent=126, mantissa=0)

Q: Which number system gives different representations of the same number? (GATE CSE 1999 Q2.17)

Quote

Options: (1) 1’s complement and 2’s complement (2) Signed magnitude and 2’s complement

(3) 1’s complement and signed magnitude (4) None

Both 1’s complement and signed magnitude have two representations of zero ($+0$ and $-0$); 2’s complement has only one.

Answer: Option 1 or 3 (depending on exact wording; reference: gateoverflow.in/1495)

Q: K-map - majority function

Quote

3-variable K-map; output is 1 when at least 2 of 3 inputs are 1. Minimised SOP?

Answer: $ab+bc+ca$

(Equivalent POS form: $(a+b)(b+c)(c+a)$ - both are correct.)

Warning

This question may receive bonus marks. The exam listed both $ab+bc+ca$ and $(a+b)(b+c)(c+a)$ as separate answer options in a single-choice format, but both are algebraically equivalent. Management is likely to award marks to all students.

Q: XOR gate as inverter

Quote

What should input B be to make an XOR gate output $A^{\prime }$?

$A\oplus 1=A^{\prime }$. Connect B to logic 1 (VCC).

Answer: B = 1 (VCC)

Q: XOR expression - $A^{\prime }B+B^{\prime }A$

Quote

Verify $A^{\prime }B+B^{\prime }A=A\oplus B$. When $B=1$: $B^{\prime }A=0$, $A^{\prime }B=A^{\prime }$; expression $=A^{\prime }$ - confirms XOR behaviour.

Q: XOR commutativity

Quote

Is $X\oplus Y=Y\oplus X$?

Answer: Yes (XOR is commutative and associative)

Q: ROM - multiplication table storage

Quote

A ROM stores the complete multiplication table of 8-bit unsigned integers. What is the ROM size?

Address space: $2\times 8=16$ address bits $\Rightarrow 2^{16}=64\text{K}$ locations. Product of two 8-bit numbers is 16 bits.

Answer (PGEE): $64\text{K}\times 16$ Answer (LEEE, approx.): $64\text{K}\times 8$

Q: Decoder for 1 KB RAM (GATE CSE 2020 Q20 - “C3D8”)

Quote

A decoder with $m$ input lines and $n$ output lines addresses a byte-addressable RAM of 1 KB. Find $m+n$.

$1\text{KB}=2^{10}$ bytes $\Rightarrow m=10$, $n=2^{10}=1024$.

Answer: $m+n=1034$

(Reference: gateoverflow.in/333211/gate-cse-2020-question-20)

Q: B+ Tree internal node capacity (PGEE)

Quote

Block size = 1024 bytes. For an internal node in a B+ tree, how many keys are required?

(Depends on key size and pointer size given - not fully recalled by respondents.)

Q: Large page size + TLB (PGEE)

Quote

If page size is very large with a TLB, how does it affect TLB misses and CPU utilisation?

Answer: Reduces TLB misses (fewer pages needed) and increases CPU utilisation.

CS Core - Operating Systems

Note

OS was very lightly represented in LEEE 2026 (one question about tables). Full OS questions appeared in PGEE 2026.

Q: Round Robin - wait time (PGEE)

Quote

Round Robin, TQ = 2, all processes arrive at $t=0$. P1 = 4 ms, P2 = 5 ms, P3 = 2 ms. Find wait time of P3.

Execution order: P1[2], P2[2], P3[2, done at $t=6$]. P3 starts at $t=4$, arrival = 0, wait = 4 ms.

Answer: 4 ms

Q: Round Robin with very high TQ (PGEE)

Quote

Round Robin with infinitely large time quantum behaves like?

Answer: FCFS (First Come First Serve)

Q: Deadlock-free process sequence (PGEE)

Quote

Processes X, Y, Z with Wait/Signal on binary semaphores a, b, c, d:

• X: Wait(a), Wait(b), Wait(c)
• Y: Wait(b), Wait(c), Wait(d)
• Z: Wait(c), Wait(d), Wait(a)

After each process, Signal() is activated. What is the deadlock-free ordering? (Break circular wait dependency.)

Q: Mutex vs Condition Variable (PGEE)

Quote

10 threads writing data to 1000 entries on a shared database (10,000 total writes). What should be used?

Options: Mutex lock, Condition variable, or both?

Q: Virtual memory - page table size (PGEE)

Quote

100 processes, 32-bit virtual address space, page size = 2 KB, each page table entry = 4 bytes. Total size of all page tables?

Entries per process $=2^{32}/2^{11}=2^{21}$. Size per process $=2^{21}\times 4=2^{23}\text{bytes}=8\text{MB}$. Total $=100\times 8\text{MB}$.

Answer: 800 MB

Q: Page fault count (PGEE)

Quote

Reference string: 1, 2, 3, 4, 2, 1, 2, …; Frame size = 3.

(Using FIFO or LRU - 4 compulsory misses on first 4 distinct pages, then hits.)

Answer: 5 page faults (for the given sequence)

CS Core - Computer Networks

Note

CN did not appear in LEEE 2026. The following questions appeared in PGEE 2026.

Q: TCP - SYN/ACK sequence number (PGEE)

Quote

Client sends SYN with sequence number $k$. What is the server’s ACK value?

Answer: ACK $=k+1$

Q: TCP timer estimation (PGEE)

Quote

Given $\alpha$ and $\beta$, calculate the TCP retransmission timer.

$\text{EstimatedRTT}=(1-\alpha )\cdot \text{EstimatedRTT}+\alpha \cdot \text{SampleRTT}$

Q: Subnet mask (PGEE)

Quote

A /24 network needs subnets each accommodating exactly 30 hosts. What subnet mask allows the maximum number of subnets?

30 hosts $\Rightarrow$ 5 host bits ($2^5-2=30$). Subnet bits $=32-5=27$.

Answer: /27 mask (3 bits for subnet ID within the /24)

CS Core - Database Management Systems

Q: $R-S$ (Set Difference) in relational algebra

Quote

For $R-S$ to be valid, what conditions are required on $R$ and $S$?

Answer: Union compatibility only - same degree (number of attributes) AND same domains.

(Incorrect answer reported: “free degree” - only union compatibility is required.)

Q: SQL - set operations (PGEE)

Quote

Condition for validity of $P-R$ where $P$ and $R$ are tables?

Answer: $P$ and $R$ must be union compatible (same number of columns, compatible data types)

Q: Which returns the most rows? (PGEE)

Quote

Cartesian product vs. outer join vs. inner join - which returns the most tuples?

Answer: Cartesian product (returns $|R|\times |S|$ rows unconditionally)

Q: Full outer join rows (PGEE)

Quote

$A$ has 7 rows, $B$ has 5 rows, 3 rows in common. Full outer join row count?

Answer: 9 ($7+5-3=9$)

Q: SQL - employees with above-average departmental salary (PGEE)

Quote

employee(EID, NAME, DID)
Department(DID)

Find employees whose income $\ge$ average income of their department.

(Use JOIN with GROUP BY DID and HAVING clause, or a correlated subquery.)

Q: Relational algebra - projection and selection commutativity (PGEE)

Quote

Is $\Pi (\sigma (R))=\sigma (\Pi (R))$ valid? (where $\sigma =$ selection, $\Pi =$ projection, and the selection condition uses only projected attributes)

Answer: Yes (operations commute when selection uses only projected attributes)

ECE / ECD Section

Note

The ECE paper was heavily loaded with Communication Theory + Semiconductor Physics. Digital Electronics was under-represented. Seniors had predicted Small Signal & Op-Amps - exact opposite came.

Exam Structure (ECE)

• Section 1: Entirely Communication Theory ($\approx$5 questions)
• $\approx$2 Control Theory questions
• $\approx$2-3 Network Theory questions
• $\approx$3-4 Digital Logic questions
• A few Laplace transform questions (no Fourier, no Z-transform)
• Aptitude and maths: same as CSE - easy, contributing $\approx$40 attempted questions

Experience

• ECE students felt disadvantaged compared to CSE students (who could attempt 70+).
• The ECE paper may have been the same as the PGEE (ECE) paper this year.
• Out-of-syllabus questions affect everyone equally - relative impact is reduced.

Semiconductor Physics

Q: Avalanche breakdown - what does it depend on?

Quote

Questions were basic conceptually but options were confusing.

Q: Diffusion capacitance

Quote

Theory-heavy. Rarely studied deeply. Came from 1st-year content.

Q: Diode - exponential V-I relation (Community response)

Quote

Why does a diode have an exponential V-I relation?

Q: BJT vs MOSFET current (Community response)

Quote

Why is current in BJT greater than in MOSFET?

Q: Why is a diode inefficient at high frequencies? (Community response)

Q: Early Effect (PGEE ECE)

Quote

Early effect is caused by: base-width modulation due to variation in collector-base voltage.

Q: Operating mode of MOSFET (Community response)

Quote

Identify the operating mode given circuit parameters.

Q: CMOS downscaling components (Community response)

Quote

What components are used in CMOS downscaling?

Options: 1) PMOS 2) PMOS and logic gates 3) Logic/combinational circuits 4) Non-linear elements

Q: Avalanche breakdown (Community response)

Quote

Avalanche breakdown is caused by: thermal runaway / charge carrier multiplication?

Communication Theory

Q: FSK Modulation - bandwidth

Quote

Find bandwidth of FSK modulation given bitrate. (Part of $\approx$5 communication theory questions; considered out of syllabus by many.)

Q: AM, FM, DSBSC, FSK, PSK, PWM, PPM

Quote

Multiple questions covering these modulation types. Required conceptual understanding, not formula plug-and-play.

Q: Delta Modulation & DPCM

Quote

Additional questions from delta modulation and DPCM. No one in the Discord channel got the delta modulation question correct - considered truly out of syllabus.

Q: LTI system - time scaling (Community response)

Quote

For a given stable causal LTI system, if $y(0.25t)$ is applied to another system with the same conditions, find $h(t)$ and $x(t)$.

Q: Bandwidth of product of two signals (Community response)

Control Systems

Q: Two control theory questions appeared

Quote

One was relatively easy; topic was considered out of syllabus for most students.

Q: Clock limitation in sequential circuits (Community response)

Quote

Reason for clock frequency limitation in sequential circuits?

Network Theory

Q: 2-3 questions from network theory (fewer than expected)

Q: 2 simple circuit theory questions (Community response)

Q: Op-amp with capacitor as negative feedback (Community response)

Quote

What is the output?

Signals & Systems

Q: A few Laplace transform questions appeared

Quote

No Fourier transform or Z-transform questions appeared.

Q: Time scaling property of convolution (Community response)

Digital Electronics (ECE)

Q: Only 3-4 digital logic questions appeared (less than expected)

Quote

Boolean logic derived from a given circuit.

ECE Prep Advice

1. Focus on: Semiconductor Physics (including 1st-year theory) + Signals/DSP/Communication Theory + Control Systems + Engineering Maths.
2. Don’t rely on seniors’ predictions - syllabus focus shifts every year.
3. Broad knowledge $>$ deep knowledge in a few topics.
4. Consistent revision beats last-3-month cramming; attend classes regularly.
5. Low selection rate is primarily due to very few seats - not because questions are impossibly hard.

Aggregated Community Responses

Note

Submitted via anonymised community responses on 2-3 May 2026. Raw responses grouped by branch.

CSE Students

Combined feedback from CSE participants:

• Difficulty rated easy to moderate; prepared students clustered around 3/10 to 5/10.
• Repeatedly recalled technical topics: linked list insertion complexity, AVL insertion complexity, heapify/build-heap complexity, Stooge sort recurrence, graph connected components and cycle detection, matrix rank/eigenvalue questions, and binary tree reconstruction from traversals.
• COA/digital arithmetic themes: IEEE 754 (0.5), 2’s complement variants, XOR-as-inverter, ROM size for multiplication tables, and decoder addressing ($m+n=1034$).
• Probability/discrete math recalls: biased coin probability (0.575), mutual exclusivity checks, and function/counting questions.
• Calculus/math recalls: $\lim \sin (x)/x$, ${\int }_0^1\log (1/x-1)dx$, implicit differentiation, nested radical, AP-GP, and work/time problems.
• Aptitude highlights: RC passages, truth/logic puzzles, train/pole, calendar/day questions.
• “Time management is necessary.” (heap build complexity, King’s rule integral, and C short-circuit variant recalled)
• “Paper was memory based and tests your basics.” Worst-case merge sort TC was asked with explicit options: O(nlogn) / O(n^2^) / O(n) / O(logn). Answer: O(nlogn).
• Anonymous respondent (CSD): Aptitude (30 Qs) felt difficult; subjective CS+Maths section was comparatively easy. Paper structure confirmed: Aptitude 30Qs $|$ CS 35Qs $|$ Maths 15Qs, with questions equally distributed over all syllabus topics. Recommended channels: 3Blue1Brown, vcubingx, Mathemaniac (differential equations, complex analysis); Trefor Bazett (discrete mathematics). “If you do not like the topics, it will be impossible for you to even crack the MCQ test. The questions are made to make you think.”
• Anonymous respondent (CSD, difficulty 5/10): Recalled a limits-at-infinity question, aptitude questions on work/time/wages, probability, time complexity and sorting (bubble sort and selection sort), and permutations/combinations. Early aptitude felt easy, then the difficulty increased. Digital logic included SOP/POS form, discrete math included tautology/statements and graph/spanning tree questions, C had tricky output questions plus a register/storage-class question (“extern” recalled), and one long paragraph-style reading question was time-consuming. Eigenvalues/eigenvectors also appeared. The overall advice was to prepare broadly, stay fast, and focus on conceptual understanding.

ECE Students

Combined feedback from ECE participants:

• Difficulty mostly reported in moderate range (5/10 to 8/10).
• Semiconductor/device questions: diode exponential V-I, diffusion/high-frequency behaviour, avalanche breakdown, BJT vs MOSFET current, BJT theory (general), MOSFET operating regions, and Early effect.
• Signals/systems and communication topics: LTI time-scaling, convolution scaling, bandwidth-of-signals, FSK bandwidth.
• Circuit/digital/control: logic from circuits, MUX-based questions, op-amp with capacitive feedback, basic circuit theory, and clock limitations in sequential circuits.
• Basic math/calculus snippets also appeared ($\lim \sin (x)/x$, log-based integrals).

Overall Difficulty Distribution (Aggregated)

Note

Average difficulty: $\approx$4.44/10 (CSD responses) and $\approx$5.75/10 (ECD responses).

Paper rated fairly easy by prepared students.

Appendix - GATE Questions Directly Referenced

GATE Reference	Topic	Answer
GATE CSE 2020 Q20	Decoder for 1 KB RAM ($m+n$)	1034
GATE CSE 2010 Q8	2s complement of $8P$	BDC8 (depends on $P$)
GATE CSE 2009 Q59	(Exact topic unknown)	See gateoverflow.in
GATE CSE 1999 Q2.17	Number system representation	Check gateoverflow.in
GATE CSE 2018 Q20	Data structures (tree)	See gateoverflow.in
GATE 2020 (DS)	Sorted linked list insertion	$O(n^2)$
(various)	Stooge sort, AVL insert, Catalan	Standard answers

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Community-compiled question bank based on memory-based reports.

Last updated: 2026-05-06

Related

• previous-year-questions-pyqs
• leee-2026-interview-experiences