🎯 Attachment 1: How to pass — for exam tension

Minimum study · target 30+ / 60

Breathe. You do not need all 6 units, and you do not need 60 out of 60. Passing lives around 27–30 marks out of 60. The plan below puts 45 marks on the table from just Q1 plus Q2 plus Q3 — so even with mistakes, you stay above the pass band. Add one more full question and it becomes 60 marks on the table.

Step 1 — the minimum set (learn these first, in this order)

Learn	Where it pays	Marks on the table
Q1's three fixed shorts	Equivalence · Logical equivalence · Pigeonhole	15
Q2	Inclusion–exclusion + Function composition	15
Q3	Transitive closure + Hasse / lattice	15
Total on the table (minimum set)		45

Step 2 — the safe set (add this and you cover 60 marks)

One more full question — Q5 (isomorphism + recurrence) (15) = 15 more marks. 45 + 15 = 60 out of 60 attempted; distinction (45) needs 45/60.

Step 3 — how to attempt in the hall (3 hours)

Q1 (30 min) → Q2 (35) → Q3 (35) → strongest of Q4/Q5/Q6 (35) → check with the remaining time. Use the full time on the graph questions' diagrams.

Honest note, not a guarantee. This pattern comes from only 2 papers — MU can break a slot. It raises your odds; it is not a guarantee.

⚡ Attachment 2: Inside The Papers

Read this first — the cheat code inside the papers

DSGT is the most predictable paper of the semester. Every single slot asks the same topic in both papers. Q1a is equivalence both times, Q1b is logical equivalence both times, Q1c is pigeonhole both times — all the way down to Q6b, Euler/Hamiltonian both times. If you learn the slot list below, you have learned the paper. The only thing that changes is the story wrapped around the question.

Q1 + Q2 + Q3 is 45 marks on the table from fully fixed slots — learn those three questions first and you are already past the pass line at full marks.

Exam dates are expected, not confirmed for AI & DS (taken from the AI & ML sheet: 17 / 19 / 21 / 25 / 27 Nov, 2:30–4:30 pm). Treat them as expected until the official sheet is seen.

📋 Attachment 3: Model paper — MU's strict pattern

Predicted shape · practice only

MU sets this paper to a strict template — every slot asks the same topic in both papers. The table below is that template, read off both papers slot by slot. Below it is a model paper built from the template for practice — it is NOT the real exam paper, and no question in it is claimed to be a leaked or real question. Practise each slot with the Dec / May question listed in the ranked study below.

Question	a (marks)	b (marks)	c (marks)	Evidence
Q1 — any 3	Equivalence relation (5)	Logical equivalence (5)	Pigeonhole principle (5) — Dec also Q1d Truth table, Q1e Mapping (5 each)	Q1a–c identical topics both papers; Q1d/Q1e Dec-only in the scan
Q2	Inclusion–exclusion (8)	Function composition (7)	—	Identical topics both papers
Q3	Transitive closure / Warshall (8)	Hasse diagram / lattice (7)	—	Identical topics both papers
Q4	Group under × mod 7 (8)	Mathematical induction (7)	—	Identical topics both papers
Q5	Graph isomorphism (8)	Recurrence relation (7)	—	Identical topics both papers
Q6	Ring (8)	Euler / Hamiltonian paths & circuits (7)	—	Identical topics both papers

Q1 as printed in the scans: Dec shows a–e (its heading says six — a sixth subquestion is not in the scan); May shows only a–c. May Q2a and Q4a marks are taken as 8 because each question totals 15 and the b-part is 7. May Q6b's graph figure is not legible in the scan. Nothing here is invented to fill those gaps.

The model paper to practise (predicted shape, 60 marks)

Q1 (any 3 × 5): Equivalence (polygons) · Logical equivalence (bus attendance) · Pigeonhole (socks).

Q2 (8 + 7): Inclusion–exclusion (drug trial) + Function composition (discount + tax).

Q3 (8 + 7): Transitive closure (airline network) + Hasse / lattice (permission levels).

Q4 (8 + 7): Group mod 7 (cyclic + generator) + Induction (sum series).

Q5 (8 + 7): Graph isomorphism (network layouts) + Recurrence (portfolio model).

Q6 (8 + 7): Ring (Z₄ tables) + Euler / Hamiltonian (conference venue graph).

Attempt Q1 + any three of Q2–Q6, exactly like the real paper. If you can do this practice paper cold, you can do the pattern.

📊 Attachment 4: Ranked PYQs & Question Bank

Sorted by frequency and yield. Tick the boxes as you master each topic to watch your marks tracker update live.

Unit I — Crisp Set Theory and Logic

Rank 2 · 5 questions

Logic is the Q1 engine: logical equivalence and truth tables are fixed shorts, and mathematical induction is a full 7-mark question in Q4b both times.

Mathematical induction

2 / 2 papers 7 marks both times

Mark topic done

Dec 2025 · Q4b · 7 marks

A student deposits savings in a fund according to: Daily saving: S_n = 4n − 1. They want to verify if S_n is always odd for all natural numbers n. i. Prove the statement using mathematical induction. ii. Explain the meaning for planning weekly budgets and long-term savings.

May 2026 · Q4b · 7 marks

A data analyst observes that the cumulative computational cost of a repeated process is modeled by the series: Σ_r=1ⁿ r(r + 3). The analyst claims that for every positive integer n, Σ_r=1ⁿ r(r + 3) = (1/3)n(n + 1)(n + 5), n ≥ 1, n ∈ N. Using the principle of mathematical induction: 1. Verify the result for the base case. 2. Prove the inductive step. 3. Conclude that the formula is valid for all n ≥ 1. 4. Interpret how induction helps validate formulas in algorithm analysis.

Logical equivalence

2 / 2 papers 5 marks both times

Mark topic done

Dec 2025 · Q1b · 5 marks

A college bus attendance system gives "Boarded = True" when: P: The student taps RFID card; Q: Bus mentor manually verifies student; R: The system logs boarding record. The transport officer rewrites: (P ∨ Q) → R ≡ (P → R) ∧ (Q → R). i. Prove the above using logical equivalence laws step-by-step. ii. Explain how this version ensures no boarding method is ignored, improves data consistency, and reduces false "absent" cases.

May 2026 · Q1b · 5 marks

A software security system uses logical rules to decide whether access should be granted, denied, or forwarded for further verification. Consider the following logical expressions: ((p → q) → r) and (p ∧ ¬q) ∨ r. Using a series of logical equivalences, prove that the two expressions are logically equivalent. Also interpret how logical equivalence helps simplify decision rules in software systems.

Truth table / access expression

Dec 2025 only 5 marks

Mark topic done

Dec 2025 · Q1d · 5 marks

A Cybersecurity lab access is granted if: P: Student has lab clearance; Q: Student has signed NDA; R: Student completed safety briefing. Access expression: A = (P ∧ Q) ∨ (P ∧ R). i. Construct truth table for A. ii. Identify combinations where access is wrongly granted. iii. Explain consequences for security, safety compliance, and audit records.

Unit II — Mathematical Relations

Rank 1 · 6 questions

Relations run this paper. Equivalence, Warshall's transitive closure, and Hasse diagrams with lattices fill Q1a, Q3a and Q3b in both papers — three fixed slots, six questions between them.

Transitive closure / Warshall

2 / 2 papers 8 marks both times

Mark topic done

Dec 2025 · Q3a · 8 marks

A Data Science program has a prerequisite network among modules: M1: Python Basics; M2: DS Foundation; M3: Machine Learning; M4: Deep Learning; M5: Deployment. Given relation R = {(1,2), (2,3), (3,4), (4,5), (1,1), (3,3), (5,5)}. i. Apply Warshall's Algorithm to compute transitive closure. ii. For each Mi, list all modules it can unlock. iii. Identify root modules and terminal modules. iv. Explain how this helps curriculum planners maintain valid learning paths.

May 2026 · Q3a · 8 marks

A domestic airline company maintains a directed flight network among four cities: V = {a, b, c, d}. The direct flight connections are represented by the relation: R = {(a,b), (b,d), (d,c), (d,a)}. The company wants to analyze all possible direct and indirect travel routes, including circular journeys. Based on the given flight network: 1. Identify and explain the concept of reachability / transitive closure used in the graph. 2. Determine all possible ordered pairs of cities connected through: direct routes, routes with layovers, and circular routes. 3. Analyze how graph connectivity helps optimize airline route planning. 4. Represent the final connectivity relation for the graph.

Hasse diagram / lattice

2 / 2 papers 7 marks both times

Mark topic done

Dec 2025 · Q3b · 7 marks

Data storage providers offer plans of sizes: S = {1 TB, 2 TB, 4 TB, 8 TB, 16 TB}. Relation a | b (a divides b). i. Draw the Hasse diagram. ii. List all (a,b) where a divides b. iii. Check whether S forms a lattice (meet & join for every pair). iv. Explain impact on designing upgrade/downgrade recommendations and plan combinations in the storage app.

May 2026 · Q3b · 7 marks

A cloud access-control system organizes permission levels using divisibility-based hierarchy. The permission levels are: A = {1,2,3,6,12,24,36,72}. A relation R is defined on A as: (x,y) ∈ R if x | y. Based on this hierarchy: 1. Write all ordered pairs of relation R. 2. Construct the Hasse Diagram of the poset. 3. Analyze whether the given poset forms a lattice. 4. Justify your answer using suitable meet and join examples.

Equivalence relation

2 / 2 papers 5 marks both times

Mark topic done

Dec 2025 · Q1a · 5 marks

A student-feedback system groups teacher responses using the rule: Two responses x and y are "similar" if they fall in the same satisfaction band (e.g., 1–2 = Low, 3 = Medium, 4–5 = High). i. Using definitions of reflexive, symmetric, transitive, determine whether "similarity" is an equivalence relation. ii. Explain the classroom-level meaning of each property. iii. Discuss how violating any property affects AI-based feedback analytics and dashboard reports.

May 2026 · Q1a · 5 marks

A digital geometry learning platform groups polygons based on the number of sides for automatic classification and retrieval. Let A be the set of all polygons. A relation R is defined on A as: R = {(P₁, P₂): P₁ and P₂ have the same number of sides}. Based on this classification system: 1. Analyze whether the relation R is an equivalence relation on A. 2. Verify the properties of reflexivity, symmetry, and transitivity. 3. Construct suitable equivalence classes for triangles, quadrilaterals, and pentagons. 4. Interpret how equivalence relations help organize geometric data in digital systems.

Unit III — Functions

Rank 4 · 3 questions

The smallest unit, but function composition is a fixed Q2b in both papers, and mapping types round out Q1.

Function composition

2 / 2 papers 7 marks both times

Mark topic done

Dec 2025 · Q2b · 7 marks

A university assigns raw marks to final grades using: Moderation function M(x) = x + 5; Weight conversion W(x) = 0.4x. Compute the compositions: i. W ∘ M; ii. M ∘ W; iii. M ∘ M; iv. W ∘ W. Interpret each composition in the grading context, and discuss which are academically meaningful and which may distort scores.

May 2026 · Q2b · 7 marks

A retail store offers seasonal discounts on clothing items. A customer wants to purchase a shirt priced at Rs.1000. The store first provides a 15% discount, after which an 8% sales tax is applied to the discounted price. Based on this shopping scenario: 1. Develop suitable mathematical functions representing the discount process and the tax calculation process. 2. Construct the composite function representing the final cost of the shirt. 3. Determine the final amount to be paid by the customer. 4. Analyze how composite functions help automate billing systems in retail applications.

Mapping: function / one-one / onto / many-one

Dec 2025 only 5 marks

Mark topic done

Dec 2025 · Q1e · 5 marks

Students are assigned to specialization tracks based on the following rule: Score in Coding ≥ 80 → Software Track; Score in Networks ≥ 75 → Network Security; Score in Math ≥ 85 → Data Science. (Priority: Data Science > Software > Network Security). Given sample data (Coding, Networks, Math): S1: (85, 60, 70); S2: (65, 80, 90); S3: (82, 78, 88); S4: (78, 76, 60). i. Map each student to a track. ii. Check if the mapping is function / one-one / onto / many-one. iii. Explain how these properties impact batch size planning, mentor allocation, and fairness.

Unit IV — Counting

Rank 1 · 6 questions

Counting pays in every paper. Inclusion–exclusion and recurrence are full 8- and 7-mark questions, and the pigeonhole principle is a fixed Q1 short. Three topics, all asked in both papers.

Inclusion–exclusion

2 / 2 papers 8 marks both times

Mark topic done

Dec 2025 · Q2a · 8 marks

A campus event app records students who use three app sections: E: Event Announcements; C: Clubs & Communities; R: Reels / Short videos. Survey data table: E 140; C 110; R 120; E∩C 65; E∩R 70; C∩R 55; Total Students 200. i. Using inclusion–exclusion, compute how many students use all three sections. ii. Find students who use only one section. iii. Explain how this analysis helps app developers and event committees design targeted notifications and UI improvements.

May 2026 · Q2a · 8 marks

A pharmaceutical company conducts a drug trial on 1000 people to analyze the side effects of a newly developed medicine. The following observations are recorded: 122 people develop symptom A; 88 people develop symptom B; 112 people develop symptom C; 27 people develop both symptoms A and C; 29 people develop both symptoms A and C; 32 people develop both symptoms B and C; 10 people develop all three symptoms A, B, and C. Using the Principle of Inclusion and Exclusion: 1. Analyze how many people develop at least one symptom. 2. Determine the number of people who show exactly one symptom. 3. Construct a Venn diagram and fill all regions appropriately.

Recurrence relation

2 / 2 papers 7 marks both times

Mark topic done

Dec 2025 · Q5b · 7 marks

A student club records followers using recurrence: F_n = 4F_n−1 − 4F_n−2. With, F₀ = 10 (core team); F₁ = 30 (after first promotion). i. Solve the recurrence relation. ii. Describe growth pattern (linear/exponential). iii. Comment whether such growth is realistic for a campus club in long term.

May 2026 · Q5b · 7 marks

A financial analytics company models the quarterly growth of a digital investment portfolio using a recurrence relation. Let F_n represent the portfolio value during the n^th quarter. The growth pattern is governed by: F_n = 3F_n−1 + 10F_n−2 + 7·5ⁿ, with initial conditions: F₀ = 4, F₁ = −3. Based on this predictive model: 1. Solve the given recurrence relation using an appropriate method. 2. Determine the general expression for F_n. 3. Analyze the effect of the exponential forcing term 7·5ⁿ on the sequence growth. 4. Interpret how recurrence relations are useful in financial forecasting and computational modeling.

Pigeonhole principle

2 / 2 papers 5 marks both times

Mark topic done

Dec 2025 · Q1c · 5 marks

A programming contest has 240 participants and 12 judging terminals. i. Using Pigeonhole Principle, find the minimum number of contestants who must end up using the same terminal. ii. Explain how this insight helps in contest scheduling, load balancing, and avoiding terminal bottlenecks.

May 2026 · Q1c · 5 marks

A quality control department stores 10 pairs of socks of different colors in a drawer for packaging verification. Using the Pigeonhole Principle, analyze the minimum number of socks that must be selected randomly to guarantee that at least one matching pair of the same color is obtained. Justify your answer with suitable reasoning.

Unit V — Algebraic Structures

Rank 3 · 4 questions

Groups and rings are Q4a and Q6a in both papers — the same two slots, the same 8 marks each, only the modulus changes.

Group under × mod 7

2 / 2 papers 8 marks both times

Mark topic done

Dec 2025 · Q4a · 8 marks

A QR-based token system transforms token number a into: T(a) = (a × k) mod 7, with a ∈ {1…6}. i. Construct multiplication table (×₇). ii. Find modular inverses of 2, 3, 5 under mod 7. iii. Determine if ({1…6}, ×₇) forms a group. iv. Comment on whether this token transformation ensures reversibility, forgery prevention, and predictable validation.

May 2026 · Q4a · 8 marks

A cryptographic system uses non-zero residue classes modulo 7 for secure key generation. Consider the set: G = {1,2,3,4,5,6} under multiplication modulo 7. Based on this system: 1. Construct the multiplication table of G under multiplication modulo 7. 2. Determine the multiplicative inverses of 2,3,5, and 6. 3. Analyze whether G forms a cyclic group. 4. If it is cyclic, identify at least one generator and justify your answer.

Ring

2 / 2 papers 8 marks both times

Mark topic done

Dec 2025 · Q6a · 8 marks

The college uses modulo-6 operations to rotate lab batches: Addition: a ⊕ b = (a + b) mod 6; Multiplication: a ⊗ b = (a × b) mod 6. i. Check if (Z₆, ⊕) is an abelian group. ii. Check closure, associativity of (Z₆, ⊗). iii. Verify distributive property of ⊗ over ⊕. iv. Conclude whether (Z₆, ⊕, ⊗) forms a ring, and discuss why this matters in designing timetable rotation logic.

May 2026 · Q6a · 8 marks

A cryptographic system uses arithmetic operations on residue classes modulo 4 for encoding and verification. Consider the set: Z₄ = {0,1,2,3} with addition and multiplication defined modulo 4. Based on this algebraic structure: 1. Construct the addition and multiplication tables for Z₄. 2. Verify whether Z₄ satisfies the required ring properties. 3. Analyze the role of additive identity, additive inverse, multiplicative associativity, and distributive laws. 4. Conclude whether Z₄ forms a ring under addition and multiplication modulo 4.

Unit VI — Graph Theory

Rank 3 · 4 questions

Graphs close the paper: isomorphism in Q5a and Euler/Hamiltonian in Q6b, both asked in both papers.

Graph isomorphism

2 / 2 papers 8 marks both times

Mark topic done

Dec 2025 · Q5a · 8 marks

Two lab surveillance networks are modeled as undirected graphs: Graph G₁ (Cameras A,B,C,D): A: B, C; B: A, D; C: A, D; D: B, C. Graph G₂ (Cameras P,Q,R,S): P: Q, R; Q: P, S; R: P, S; S: Q, R. i. Determine whether G₁ and G₂ are isomorphic. ii. If yes, provide the mapping. iii. Explain how detecting isomorphic patterns helps in reusing surveillance layouts and minimizing storage of duplicate designs.

May 2026 · Q5a · 8 marks

A computer networking company proposes two communication network layouts represented by graphs G₁ and G₂. The organization wants to verify whether both network structures provide the same connectivity pattern even though the device labels are different. The graphs are represented as: V(G₁) = {A,B,C,X,Y,Z}; E(G₁) = {(A,X), (A,Y), (B,X), (B,Y), (C,Y)}; V(G₂) = {1,2,3,4,5,6}; E(G₂) = {(1,4), (1,5), (2,4), (2,5), (3,5)}. Based on the above network structures: 1. Define isomorphism of graphs. 2. Analyze whether graphs G₁ and G₂ are isomorphic. 3. If they are isomorphic, determine a valid one-to-one correspondence between the vertices. 4. Justify your answer by comparing degree sequence and adjacency preservation.

Euler / Hamiltonian paths & circuits

2 / 2 papers 7 marks both times

Mark topic done

Dec 2025 · Q6b · 7 marks

A research conference venue is modeled as graph V = {A,B,C,D,E,F} with edges: E = {AB, AC, BC, BD, CE, DE, DF, EF}. i. Determine existence of Euler Path, Euler Circuit, Hamiltonian Path, Hamiltonian Circuit. ii. Construct them if they exist. iii. Explain what this means for planning visitor flow, inspection rounds, and avoiding repeated walking paths.

May 2026 · Q6b · 7 marks

A city transport authority is analyzing a road network connecting six important locations A, B, C, D, E, and F. The network is represented by the following graph: [graph figure not legible in scan]. Based on the given road network: 1. Determine whether the graph has an Euler Path. 2. Determine whether the graph has an Euler Circuit. 3. Determine whether the graph has a Hamiltonian Path. 4. Determine whether the graph has a Hamiltonian Circuit. 5. Justify your answer using degree of vertices and graph traversal conditions.

💡 Attachment 5: Solutions — Coming Tomorrow

Solutions for DSGT. Step-by-step solutions land here, one per question, in the same order as the ranked topics above.

Solution: Q1 — short skills