AKTU Discrete Structures & Theory of Logic · Important Questions 2026Source: ryzenstudy.com PYQs
BCS303 Discrete Structures & Theory of Logic Important Questions 2026 (AKTU)
Repeat analysis + most-asked questions, unit-wise
What we did: built from all 5 AKTU Discrete Structures & Theory of Logic papers (2021-22–2025-26): 119 questions grouped into 75 distinct questions, 23 of which were asked in more than one paper.
- of marks were repeat questions
- 49%
- of marks were repeat questions
- questions asked in 2+ papers
- 23
- questions asked in 2+ papers
- papers analysed (2021-22–2025-26)
- 5
- papers analysed (2021-22–2025-26)
- units, mapped to current syllabus
- 5
- units, mapped to current syllabus
How much of the paper repeats?
- Repeats are real: when we checked each newer BCS303 paper against the papers before it, on average 49% of its marks were questions already asked in an earlier paper.
- 2023-24 paper: 46% of marks were repeats (9 of 10 repeated questions were in our top list).
- 2024-25 paper: 67% of marks were repeats (9 of 14 repeated questions were in our top list).
- 2025-26 paper: 35% of marks were repeats (3 of 8 repeated questions were in our top list).
- Topic weightage is a guide, not a guarantee: our Tier 1 + Tier 2 topics covered 71% of the next paper's marks — picking the same number of topics at random would have covered about 54%.
Across 10 subjects and 23 papers we tested, 43% of marks repeated earlier questions on average.
1.Unit-wise most-asked questions
Ranked by how many papers asked them, then by how recently. Click a paper to open it.
Unit 1: Set Theory& Relations · Relations
12% of past marks| Question | Asked |
|---|---|
| Examine R = {(a, b) | a ≡ b (mod m)} is an equivalence relation on Z. Also ensure that if x1 ≡ y1 and x2 ≡ y2 then (x1 + x2) ≡ (y1 + y2). | Asked 2× |
| Let R = {(1, 2), (2, 3), (3, 1)} defined on A = {1, 2, 3}. Calculate the transitive closure of R using Warshall's algorithm. | Asked 2× |
| Let R be a binary relation on the set of all strings of 0 and 1 such that R = {(a,b): a and b have same number of 0's}. Show that whether R is reflexive, symmetric, transitive or a partial order relation. | Asked 2× |
| What is meant by a reflexive relation? State its basic property. 2 marks2025-26 Q1(b) | Asked 1× |
Unit 2: POSET & Lattices · Functions
18% of past marks| Question | Asked |
|---|---|
| i) Justify that (D42, \) is lattice. ii) Let L1 be the lattice defined as D6 and L2 be the lattice (P(S), ≤), where P(S) be the power set defined on set S = {a, b}. Justify that the two lattices are isomorphic. | Asked 3× |
| Calculate the composite mapping gof if f: R→R is given by f(x) = e^x and g: R→R is given by g(x) = sin x. | Asked 3× |
| Let f(x) = 3x + 5 and g(x) = x^2 − 2x + 1. Evaluate f(3) and classify f(x) and g(x) as one-to-one, onto, or neither. | Asked 2× |
| Construct the Hasse Diagram for (P(S), ⊆) where P(S) is a power set defined on set S = {a, b, c}. Determine whether it is a Lattice or not. | Asked 2× |
Unit 3: Boolean Algebra · Theory of Logics · Predicate Logic
31% of past marks| Question | Asked |
|---|---|
| Use a Karnaugh map to find a minimal sum for E = y't' + y'z't + x'y'zt + yzt'. | Asked 5× |
| Show the validity of the following argument: Hypotheses: "It is not sunny this afternoon and it is colder than yesterday. We will go swimming only if it is sunny. If we do not go swimming, then we will take a canoe trip. If we take a canoe trip, then we will be home by sunset." Conclusion: "We will be home by sunset." | Asked 4× |
| Translate the following statements in symbolic form: (i) The sum of two positive integer is always positive. (ii) Everyone is loved by someone. (iii) Some people are not admired by everyone. (iv) If a person is female and is a parent, then this person is someone's mother. | Asked 3× |
| Construct inverse of the following statement "If I wake up early in the morning, then I will be healthy." | Asked 3× |
Unit 4: Algebraic Structures
22% of past marks| Question | Asked |
|---|---|
| Let H be a subgroup of a finite group G. Prove that order of H is a divisor of order G. | Asked 2× |
| How many generators are there of the cyclic group G of order 10. | Asked 2× |
| Let G = {1, −1, i, −i} with the binary operation multiplication be an algebraic structure, where i = √−1, then determine whether G is an Abelian group. Also if G is cyclic group, then determine the generator of G. | Asked 2× |
| Define zero divisor of a ring. 2 marks2025-26 Q1(e) | Asked 1× |
Unit 5: Graphs · Combinatorics
19% of past marks| Question | Asked |
|---|---|
| Show that in any room of people who have been doing handshaking there will always be at least two people who have shaken hands the same number of times. | Asked 5× |
| Express the following (i) Euler graph and Hamiltonian graph (ii) Chromatic number of a graph (iii) Walk and path (iv) Bipartite graph. | Asked 3× |
| Let G be a 3-regular graph with n vertices. What is the sum of the degree of the vertices? Show that in such a graph n must be even. | Asked 2× |
| Illustrate the following graph using an adjacency matrix: A graph with vertices V = {A, B, C, D} and edges E = {(A, B), (B, C), (C, D), (D (see original paper) | Asked 2× |
2.Topic weightage: which topics carry the marks
Blue = Tier 1 + Tier 2 (topics that carried ~80% of past marks). Grey = the rest. It shows where marks have gone, not a promise of what comes next.
Theory of inference · U3
8.4% (cum 8%)
Karnaugh maps · U3
7.8% (cum 16%)
Graph terminology and degrees · U5
6.9% (cum 23%)
Propositions and truth tables · U3
6% (cum 29%)
Cyclic groups · U4
5.8% (cum 35%)
Groups and algebraic structures · U4
5.7% (cum 41%)
Lattice definition and properties · U2
5.5% (cum 46%)
Cosets and Lagrange theorem · U4
4.3% (cum 50%)
Pigeonhole principle · U5
4.1% (cum 55%)
Classification of functions · U2
3.9% (cum 58%)
Types and properties of relations · U1
3.5% (cum 62%)
Equivalence relations and classes · U1
3.2% (cum 65%)
POSET and Hasse diagrams · U2
3.2% (cum 68%)
Predicates and quantifiers · U3
2.9% (cum 71%)
Algebraic manipulation of Boolean expressions · U3
2.8% (cum 74%)
Set operations and power sets · U1
2.8% (cum 77%)
Special lattices · U2
2.5% (cum 79%)
Composite and inverse functions · U2
2.3% (cum 82%)
Rings and fields · U4
2.2% (cum 84%)
Composite relations and closure · U1
2.1% (cum 86%)
Subgroups · U4
2.1% (cum 88%)
Planar graphs · U5
1.7% (cum 90%)
Counting techniques · U5
1.3% (cum 91%)
Inference in predicate logic · U3
1.3% (cum 92%)
Euler and Hamiltonian paths · U5
1.3% (cum 94%)
Isomorphism and homeomorphism · U5
1.2% (cum 95%)
Group homomorphisms · U4
1% (cum 96%)
Graph representation · U5
1% (cum 97%)
Boolean algebra laws · U3
0.9% (cum 98%)
Special graphs · U5
0.9% (cum 99%)
Growth of functions · U2
0.4% (cum 99%)
Tautology and logical equivalence · U3
0.4% (cum 99%)
Normal subgroups · U4
0.4% (cum 100%)
| Topic | Papers | Share |
|---|---|---|
| Theory of inference · Unit 3 · Tier 1 | 4/5 | 8.4% |
| Karnaugh maps · Unit 3 · Tier 1 | 5/5 | 7.8% |
| Graph terminology and degrees · Unit 5 · Tier 1 | 4/5 | 6.9% |
| Propositions and truth tables · Unit 3 · Tier 1 | 4/5 | 6% |
| Cyclic groups · Unit 4 · Tier 1 | 5/5 | 5.8% |
| Groups and algebraic structures · Unit 4 · Tier 1 | 3/5 | 5.7% |
| Lattice definition and properties · Unit 2 · Tier 1 | 4/5 | 5.5% |
| Cosets and Lagrange theorem · Unit 4 · Tier 1 | 3/5 | 4.3% |
| Pigeonhole principle · Unit 5 · Tier 2 | 5/5 | 4.1% |
| Classification of functions · Unit 2 · Tier 2 | 4/5 | 3.9% |
| Types and properties of relations · Unit 1 · Tier 2 | 4/5 | 3.5% |
| Equivalence relations and classes · Unit 1 · Tier 2 | 3/5 | 3.2% |
| POSET and Hasse diagrams · Unit 2 · Tier 2 | 3/5 | 3.2% |
| Predicates and quantifiers · Unit 3 · Tier 2 | 3/5 | 2.9% |
| Algebraic manipulation of Boolean expressions · Unit 3 · Tier 2 | 3/5 | 2.8% |
| Set operations and power sets · Unit 1 · Tier 2 | 4/5 | 2.8% |
| Special lattices · Unit 2 · Tier 2 | 2/5 | 2.5% |
| Composite and inverse functions · Unit 2 · Tier 2 | 4/5 | 2.3% |
| Rings and fields · Unit 4 · Tier 3 | 3/5 | 2.2% |
| Composite relations and closure · Unit 1 · Tier 3 | 2/5 | 2.1% |
| Subgroups · Unit 4 · Tier 3 | 2/5 | 2.1% |
| Planar graphs · Unit 5 · Tier 3 | 3/5 | 1.7% |
| Counting techniques · Unit 5 · Tier 3 | 2/5 | 1.3% |
| Inference in predicate logic · Unit 3 · Tier 3 | 2/5 | 1.3% |
| Euler and Hamiltonian paths · Unit 5 · Tier 3 | 2/5 | 1.3% |
| Isomorphism and homeomorphism · Unit 5 · Tier 3 | 1/5 | 1.2% |
| Group homomorphisms · Unit 4 · Tier 3 | 1/5 | 1% |
| Graph representation · Unit 5 · Tier 3 | 2/5 | 1% |
| Boolean algebra laws · Unit 3 · Tier 3 | 2/5 | 0.9% |
| Special graphs · Unit 5 · Tier 3 | 1/5 | 0.9% |
| Growth of functions · Unit 2 · Tier 3 | 1/5 | 0.4% |
| Tautology and logical equivalence · Unit 3 · Tier 3 | 1/5 | 0.4% |
| Normal subgroups · Unit 4 · Tier 3 | 1/5 | 0.4% |
3.Paper pattern (2025-26)
| Section | Questions | Rule |
|---|---|---|
| A | 7 × 2 marks | Attempt all |
| B | 5 × 2.3333333333333335 marks | Attempt any 3 |
| C | 10 × 7 marks | Attempt any 1 |
4.In the syllabus, never asked yet
Low priority, but read them once — a new paper can always start here.
- Order relations · U1
- Permutation and symmetric groups · U4
- Graph coloring · U5
5.Study order
- 1Theory of inference (Unit 3, Tier 1)
- 2Karnaugh maps (Unit 3, Tier 1)
- 3Graph terminology and degrees (Unit 5, Tier 1)
- 4Propositions and truth tables (Unit 3, Tier 1)
- 5Cyclic groups (Unit 4, Tier 1)
- 6Groups and algebraic structures (Unit 4, Tier 1)
- 7Lattice definition and properties (Unit 2, Tier 1)
- 8Cosets and Lagrange theorem (Unit 4, Tier 1)
- 9Pigeonhole principle (Unit 5, Tier 2)
- 10Classification of functions (Unit 2, Tier 2)
- 11Types and properties of relations (Unit 1, Tier 2)
- 12Equivalence relations and classes (Unit 1, Tier 2)
- 13POSET and Hasse diagrams (Unit 2, Tier 2)
- 14Predicates and quantifiers (Unit 3, Tier 2)
- 15Algebraic manipulation of Boolean expressions (Unit 3, Tier 2)
- 16Set operations and power sets (Unit 1, Tier 2)
- 17Special lattices (Unit 2, Tier 2)
- 18Composite and inverse functions (Unit 2, Tier 2)
FAQ
Which units of BCS303 carry the most marks?
Unit 3 (Boolean Algebra · Theory of Logics · Predicate Logic, 31% of past marks) and Unit 4 (Algebraic Structures, 22% of past marks).
Do AKTU Discrete Structures & Theory of Logic questions repeat?
Yes. On average 49% of the marks in each newer BCS303 paper came from questions already asked in an earlier paper, and 23 questions have appeared in more than one paper.
How is this list made?
Every question from the 5 papers (2021-22–2025-26) was mapped to the current AKTU syllabus and grouped with the same question from other years. Questions are ranked by how many papers they appeared in, then by how recently.
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Note: this is based on past AKTU papers, not a guarantee. Questions are mapped to the current syllabus; topics that are no longer in the syllabus are left out.