Maths — Mathematics for Computer Engineering (N2113111)

Branches on this paper: Computer · AI&DS · CS-IoT · 60 marks · 2 hours each

Paper / Subject Code: N2113111 / Mathematics for Computer Engineering
S.E. / Sem-III / NEP / Computer / AI&DS / IoT — 17/12/2025 — Q.P. Code: 00720

Time: 2 hoursMarks: 60

Note: 1. Question No. 1 is Compulsory. 2. Attempt any 3 (Three) Questions from the remaining questions. 3. Statistical Table is allowed.

Que. 1 — Attempt any Five questions of the following

a. If A =

3	2	1
0	−1	4
0	0	−2

, find Eigen values of A⁻¹ + 6I3

b. Transform the LPP to standard form
Maximise Z = 2x₁ + x₂ + 4x₃
x₁ − x₂ + 2x₃ ≤ 5
3x₁ + x₂ + 5x₃ ≥ 14 x₁, x₂ ≥ 03

c. Find the value of a_n in the expansion of Fourier Series for f(x) = 4 − x² in (0, 2π)3

d. A random variable x defines the possible outcomes of tossing a fair die, find moment generating function of x about origin3

e. What is the remainder when 13⁷⁰ is divided by 213

f. Obtain Spearman's rank correlation coefficient for following data3

X	24	24	24	55	25
Y	24	31	51	40	38

Que. 2

a. It is known that the probability of an item produced by a certain machine will be defective is 0.001. If the produced items are sent to the market in packets of 100, find the number of packets containing at least 2 are defective in the consignment of 2000 Packets.4

b. Five students got the following percentage of marks in mathematics and statistics
Calculate the coefficient of correlation.5

Maths	28	34	18	25	75	23	24	33	37	43
Stats	24	31	11	34	65	24	23	53	53	42

c. Expand Fourier series for f(x) = x² in (0, 2)6

Que. 3

a. Obtain equations of line of regression of x on y for following data.4

X	31	44	65	49	41
Y	48	32	21	66	43

b. By using Chinese Remainder theorem, Solve
x ≡ 1 (mod 3), x ≡ 2 (mod 4), x ≡ 3 (mod 5)5

c. Find Eigen values and Eigen vectors of the matrix
A =

3	−1	1
−1	5	−1
1	−1	3

Que. 4

a. A random variable X has probability density function
f(x) = x²e^−x x ≥ 0
Find 2 moments about origin and mean.4

b. Show that the matrix A =

2	2	1
1	3	1
1	2	2

is diagonalisable, hence find it's diagonalisable matrix.5

c. In RSA System the public key (E, N) of user A is defined as (7, 187). Calculate φ(N) and private key 'D'. What is the cipher text for M = 10 using the public key.6

Que. 5

a. Verify Cayley-Hamilton theorem for matrix
A =

2	−1	1
−1	2	−1
1	−1	2

b. The height of school children of one school is normally distributed with mean of 54 inches and standard deviation 12 inches. What proportion of students have height between i. 46 and 56 inches ii. More than 565

c. Applying Simplex method, Solve the following LPP
Maximise   Z = 3x₁ + 2x₂
Subject to constraint   x₁ + x₂ ≤ 4
x₁ − x₃ ≤ 2    x₁, x₂ ≥ 06

Que. 6

a. Fit a straight line of the form y = a + bx to the following data4

X	1	4	7	9	8	10
Y	18	14	19	27	18	28

b. Find Fourier series for the function f(x) = x, 0 < x < 2π5

c. Using the method of Lagrange's multipliers solve the following NLPP
Optimize z = −x₁² − x₂² + 4x₁ + 8x₂
Subject to: x₁ + x₂ = 4 x₁, x₂ ≥ 06

********************

Paper / Subject Code: N2113111 / Mathematics for Computer Engineering
SE / Sem-III / NEP / MAY 2026 / Computer / AI&DS / CS-IoT — Date 04/06/2026 — Q.P. 14664

Time: 2 hoursMax Marks: 60

Note: (1) Question No. 1 is Compulsory. (2) Answer any three questions from Q.2 to Q.6. (3) Figures to the right indicate full marks. (4) Statistical Table to be provided.

Q.1. — Attempt any Five Questions from the following.

a) Find the sum and product of the eigenvalues of A =

−2	−9	5
−5	−10	7
−9	−21	14

b) Construct the dual of the following LPP
Maximise Z = 5x₁ + 4x₂
Subject to constraint 2x₁ + 6x₂ ≤ 5
7x₁ + 3x₂ ≤ 2
x₁, x₂ ≥ 03

c) Find value of a_n in the expansion of Fourier series for f(x) = x² in (−π, π)3

d) Calculate first 2 raw moments for probability density function
f(x) = {

xe^−x	x ≥ 0
0	Otherwise

e) What is the remainder when 5¹¹ is divided by 73

f) Obtain Spearman's rank correlation coefficient for following data3

X	18	17	13	17	19	21
Y	21	22	14	17	18	13

Q.2.

a) The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 7. Find the probability of observing exactly three accidents on this stretch of road next month.4

b) Calculate the correlation coefficient for the following heights of fathers (X) and their sons (Y)5

X	65	66	67	67	68	69	70	72
Y	67	68	65	68	72	72	69	71

c) Expand Fourier series for f(x) = x² in (0, 2)6

Q.3.

a) Fit a straight line of the form y = a + bx to the following data4

X	1	3	5	7	8	10
Y	8	4	5	7	8	4

b) By using Chinese Remainder theorem, solve x ≡ 3 (mod 4), x ≡ 5 (mod 7)5

c) Find eigen values and eigen vectors of A =

−9	4	4
−8	3	4
−16	8	7

Q.4.

a) A random variable X has the following probability distribution4

X	1	2	3	4
P(X=x)	0.2	0.3	0.3	0.2

Find moment generating function about origin of x, hence find first two raw moments.

b) The distribution of wait times at a drive-through restaurant is approximately normal with mean 185 seconds and standard deviation 15 seconds. Find the percentage of wait times that are
i. between 155 and 215 seconds.
ii. more than 170 seconds.5

c) Check whether the matrix A =

8	−8	−2
4	−3	−2
3	−4	1

is diagonalizable, if yes, find the diagonalizing matrix P and the diagonal matrix D.6

Q.5.

a) Verify Cayley-Hamilton theorem for matrix A =

3	2	1
1	2	2
3	2	1

b) Maximise Z = 7x₁ + 5x₂
Subject to constraint −x₁ − 2x₂ ≥ −6
4x₁ + 3x₂ ≤ 12
x₁, x₂ ≥ 05

c) Perform key generation, encryption and decryption for RSA Algorithm with the following parameters primes p = 3, q = 11 message, M = 56

Q.6.

a) Expand Fourier series for f(x) = x in (−π, π)4

b) Obtain the equation of line of regression of X on Y5

X	21	23	25	27	28	20
Y	8	12	15	17	18	20

c) Using the method of Lagrange's multipliers, solve the following NLPP
Maximise Z = x₁² + x₂² + x₃² − 10x₁ − 6x₂ − 4x₃
Subject to constraint x₁ + x₂ + x₃ = 7 x₁, x₂, x₃ ≥ 06

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DSGT — Discrete Structures & Graph Theory (N2113112)

Branches on these papers: Computer · CS-IoT · AI&DS · Pattern: Q1 compulsory (5M each) + any THREE of Q2–Q6 (15M each) = 60M · 3 hours

← View Ranked DSGT PYQs & Pass Plan

Subject: Discrete Structures & Graph Theory (N2113112)
Dec 2025 — QP 99814 · 3 hours · 60 marks · 19/12/2025

Scan gap flagged: Q1 heading says "any three out of six sub questions" but the scan shows only a–e (5). A sixth subquestion is not in the scan and is not invented here.

Q1 — Attempt any three out of six sub questions (5M each)

a) 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.5

b) 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.5

c) 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.5

d) 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.5

e) Students are assigned to specialization tracks by the 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.5

a) A campus event app records students who use three app sections: E: Event Announcements; C: Clubs & Communities; R: Reels / Short videos. Survey data: 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.8

b) 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.7

a) 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.8

b) 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.7

a) 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.8

b) A student deposits savings in a fund according to: Daily saving: Sₙ = 4n − 1. They want to verify if Sₙ 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.7

a) 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.8

b) A student club records followers using recurrence: Fₙ = 4Fₙ₋₁ − 4Fₙ₋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.7

a) 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.8

b) 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.7

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Subject: Discrete Structures & Graph Theory (N2113112)
May 2026 — QP 14827 · 3 hours · 60 marks · 06/06/2026

Scan gaps flagged: May Q1 shows only a–c in the scan (no d/e/f visible); May Q2a and Q4a marks are not printed on their pages and are taken as 8M (question total 15 minus b-part 7M); May Q6b's graph figure is not legible in the scan.

Q1 (5M each, as printed a–c)

a) 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.5

b) A software security system uses logical rules to decide whether access should be granted, denied, or forwarded for further verification. Consider the 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.5

c) 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.5

a) A pharmaceutical company conducts a drug trial on 1000 people to analyze the side effects of a newly developed medicine. Observations: 122 people develop symptom A; 88 develop symptom B; 112 develop symptom C; 27 develop both A and B; 29 develop both A and C; 32 develop both B and C; 10 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.8

b) 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.7

a) A domestic airline company maintains a directed flight network among four cities: V = {a, b, c, d}. 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.8

b) A cloud access-control system organizes permission levels using divisibility-based hierarchy. Permission levels: 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.7

a) 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.8

b) A data analyst observes that the cumulative computational cost of a repeated process is modeled by the series: Σ (r=1 to n) r(r + 3). The analyst claims that for every positive integer n, Σ (r=1 to n) 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.7

a) 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. Graphs: 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.8

b) A financial analytics company models the quarterly growth of a digital investment portfolio using a recurrence relation. Let Fₙ represent the portfolio value during the nᵗʰ quarter. Growth pattern: Fₙ = 3Fₙ₋₁ + 10Fₙ₋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 Fₙ. 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.7

a) 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 4.8

b) 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.7

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AOA — Analysis of Algorithms (N2113113)

Branches on these papers: Computer · CS-IoT · AI&DS · Pattern: Q1 compulsory (any 5 of 6 × 3M = 15) + any THREE of Q2–Q6 (15M each) = 60M · 2 hours · Merge Sort fixed in Q2b

← View Ranked AOA PYQs & Pass Plan

Subject: Analysis of Algorithms (N2113113)
Dec 2025 — QP 99073 · 2 hours · 60 marks · 08/12/2025

Q1 — Answer the following (Any five) — 03 each

a) Find the complexity of given recurrence relation using Master Method: T(n) = 8T(n/2) + n².3

b) Write an algorithm for Binary Search.3

c) Explain the general method of the Greedy Approach.3

d) Explain the Principle of Optimality as applied to Dynamic Programming.3

e) Differentiate between Backtracking and Branch & Bound techniques.3

f) Explain the Naive String-Matching Algorithm.3

a) Sort the following numbers using the Selection Sort, and show the array after each pass: 28, 17, 20, 75, 13, 15.5

b) Write an algorithm for Merge Sort. Derive its time complexity. Sort the following elements using Merge Sort: 32, 55, 17, 48, 64, 26.10

a) Explain Big Theta (Θ) notation with a suitable example.5

b) What is Minimum Cost Spanning Tree? Write Kruskal's algorithm and state its time complexity. Find Minimum Cost Spanning Tree for following graph using Kruskal's Algorithm: [graph: A–B 7, B–C 7, C–D 3, D–E 6, E–F 9, F–A 5, A–G 8, B–G 3, D–G 2, F–G 4].10

a) Consider a Knapsack with capacity W = 16. There are six items with following weights and profits. (P1…P6) = (10, 5, 15, 7, 6, 18); (W1…W6) = (2, 3, 5, 7, 1, 4). Find the maximum profit using Fractional Knapsack algorithm.5

b) Write an algorithm to find Longest Common Subsequences between two given strings. Derive its time complexity. Find the LCS between following strings: X = AVANTIKA; Y = KARNAVATI.10

a) What is Multistage Graph? Explain Forward Approach method to find optimal path in Multistage Graph.5

b) What is the N-Queen Problem? Design a backtracking algorithm to solve it. Provide step-by-step working of it using suitable example.10

a) Find the All-Pair Source Shortest path for all the vertices using Floyd-Warshall Algorithm: [directed graph: A→B 7, B→A 8, B→C −3, A→C 5, C→A 6].5

b) Explain Graph Coloring method with suitable example.5

c) Write Rabin Karp String Matching Algorithm. State its time complexity.5

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Subject: Analysis of Algorithms (N2113113)
May 2026 — QP 14659 · 2 hours · 60 marks · 09/06/2026 (header date; p1 handwriting says 03/06/2026)

Q1 — Answer the following (Any Five) — 03 each

a) Solve the following recurrence relation using recursion tree method: T(n) = 3T(n/3) + n².3

b) Explain Divide and Conquer strategy with diagram.3

c) Differentiate between fractional and 0/1 knapsack problem (give minimum 5 relevant points).3

d) Find the LCS for the following sequences: X = ABCDE; Y = ACE.3

e) Explain the concept of Branch and Bound.3

f) Explain the advantage of KMP algorithm over Naïve string matching algorithm.3

a) Find the Minimum spanning tree for the following graph using Prim's algorithm: [nodes 1–6; edges: 5–4: 9, 4–1: 1, 4–3: 5, 4–2: 3, 1–5: 4, 1–2: 2, 3–2: 3, 3–6: 8, 2–6: 7].5

b) Sort the following elements using Merge Sort and hence derive the complexity of Merge Sort: 34, 9, 56, 10, 78, 61, 98, 23, 38.10

a) Sort the following elements using insertion sort: 90, 1, 4, 2, 78, 45, 39, 58, 79. Show output after each pass. Also, derive complexity of insertion sort.5

b) Find the shortest path for the following graph using Dijkstra's algorithm: (Source vertex is A). [graph: A–B 3, A–D 8, B–E 6, B–D 5, D–E 3, D–F 2, E–C 9, E–F 1, F–C 3].10

a) Explain backtracking and how it is used to solve the graph coloring problem.5

b) Solve the following knapsack problem using dynamic programming: (Capacity = 7). Table: I1: Weight 1, Profit 50; I2: Weight 2, Profit 40; I3: Weight 4, Profit 70; I4: Weight 5, Profit 80; I5: Weight 1, Profit 10.10

a) Draw the partial state space tree for 15-puzzle problem. Specify the complexity of 15 puzzle problem.5

b) Find the shortest distance from vertex 1 to vertex 12 for the following graph: [multistage graph: 1→2: 9, 1→3: 7, 1→4: 3, 1→5: 2; 2→6: 4, 2→7: 2; 3→6: 2, 3→7: 7; 4→8: 11; 5→8: 11, 5→7: 8; 6→9: 6, 6→10: 5; 7→9: 4, 7→10: 3; 8→10: 5, 8→11: 6; 9→12: 4; 10→12: 2; 11→12: 6].10

a) Explain the different asymptotic notations with graphs.5

b) Explain KMP String matching algorithm with example.5

c) Solve the following sum of subset Problem: S = {3, 4, 5, 6} and sum = 9.5

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COA — Computer Organization & Architecture (N2113114)

Branches on these papers: CS-IoT · AI&DS · Computer · Note: "Calculator having number conversion function is not allowed." · Pattern: Q1 compulsory (3 of A–D × 5M = 15) + any THREE of Q2–Q6 (15M each) = 60M · 2 hours · Q5 fixed: 8086 arch (8M) + Booth's (7M)

← View Ranked COA PYQs & Pass Plan

Subject: Computer Organization & Architecture (N2113114)
Dec 2025 — QP 98169 · 2 hours · 60 marks · 10/12/2025

Q1 — Attempt any THREE (5M each)

A: Convert the following decimal number to Binary, Octal and Hexadecimal number. a) (345.35)₁₀ b) (818.55)₁₀.5

B: Explain addressing modes of 8086 with suitable example.5

C: Explain Associative memory with its usages.5

D: Explain ISA, PCI and USB buses.5

A: Draw flowchart for non restoring division algorithm and implement for (13/3).8

B: Explain memory hierarchy with diagrams and characteristics of memory.7

A: A computer has 64MB main memory and 32KB cache memory. Each line in cache stores 8 bytes. Show the format for memory address for Direct and Associative mapping.8

B: Explain and compare programmed I/O, interrupt-driven I/O, and DMA.7

A: Explain micro-programmed control unit with suitable diagram.8

B: Draw and explain the various pipeline hazards and method to resolve it.7

A: Explain with suitable diagram Architecture of 8086 microprocessor.8

B: Multiply (12)₁₀ and (−5)₁₀ using Booth's algorithm.7

A: Explain bus arbitration with examples.5

B: Explain Flynn's classification.5

C: Differentiate horizontal and vertical microinstruction.5

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Subject: Computer Organization & Architecture (N2113114)
May 2026 — QP 09161 · 2 hours · 60 marks · 11/06/2026

Q1 — Attempt any THREE (5M each)

A: Convert (74.25)₁₀ and (47.50)₁₀ into hexadecimal numbers and perform addition on converted numbers.5

B: Explain instruction pipeline.5

C: Explain characteristics of memory.5

D: Explain Associative memory.5

A: Convert (56.45)₁₀ into IEEE 754 floating point Single Precision format.8

B: Explain different pipeline hazards.7

A: Draw flow chart for nonrestoring division algorithm and solve (15)₁₀ / (2)₁₀.8

B: Explain programmed IO and interrupt-driven data transfer methods.7

A: Compare Direct, Associative, Set Associative Cache Mapping techniques.8

B: Compare Hardwired and Softwired control unit design techniques.7

A: Explain architecture of 8086 microprocessor.8

B: Multiply (−8)₁₀ and (−3)₁₀ using Booth's algorithm.7

A: Explain Flynn's classification.8

B: Differentiate between different operation modes of 80386DX processor.7

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Gen AI — Open Elective: Generative AI (2013311)

Branches on these papers: Computer · AI&DS · Formats differ: Dec 2025 is 60 marks / 2 hours; May 2026 is 30 marks / 1 hour

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Subject: Generative AI (Open Elective — 2013311)
Dec 2025 — QP 25503 (handwritten; printed code 1042312 also on header) · 2 hours · 60 marks · 12/12/2025

Pattern: Q1 compulsory, attempt any three × 5M = 15, + attempt any three of Q2–Q6 (each 15M), + Q6 attempt any three × 5M = 15. Total 15 + 3×15 = 60.

1 — Attempt any Three [15]

a: Define Generative AI. Explain its scope with suitable examples?5

b: List any three GPT variants and mention one use case for each.5

c: What is the importance of data in training the AI model?5

d: Explain "text-to-image" tools with an example.5

a: Explain How CNN Works?8

b: Explain pre-training and fine tuning and instruct tuning in gen-AI?7

a: What is the multiread mechanism in GPT? (printed "multiread"; read as multi-head attention mechanism)7

b: Explain the architecture of RNN & how it works?8

a: What are the challenges in Generative AI?8

b: Write a short note on the architecture and working of GPT models.7

a: What is chat-GPT and how does it work?7

b: What is LLM and Types of LLM explain?8

6 — Attempt any 3 [15]

a: Ethical concerns related to Generative AI.5

b: Explain the importance of Generative AI in any five real-world domains.5

c: Differentiate between traditional language models and modern language models.5

d: Explain the importance and role of self-attention in GPT models.5

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Subject: Generative AI (Open Elective — 2013311)
May 2026 — QP 3001 (handwritten) · 1 hour · 30 marks · 15/06/2026

WARNING: This is a 30-mark / 1-hour paper, NOT the 60-mark ESE format. Pattern: Q1 compulsory, attempt any five × 2M = 10, + attempt any two of Q2–Q5, each 10M (5+5). Total 10 + 2×10 = 30. Note: Q2b and Q5b are the same question (GPT architecture and working) — attempt only one.

1 — Attempt any five [10]

(a) Define Generative AI2

(b) What is GPT and Chat-GPT?2

(d) What is pre-training?2

(e) What is LSTM?2

(f) What is tokenization in transformer model?2

(a) Explain the architecture of CNN & how it works?5

(b) Explain architecture and working of GPT models.5

(a) Explain ethical issues in Generative AI.5

(b) Explain different GPT variants and their applications.5

(a) Explain the architecture and working of Transformer models.5

(b) Explain any five Generative AI tools with examples.5

(a) Explain RNN and its limitations.5

(b) Explain GPT architecture and working.5

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