MCS 212 Solved Guess Paper for the 2026 term end exams is a fifteen question, fully solved revision file prepared by the Unnati Educations subject team for learners of Discrete Mathematics in IGNOU Master of Computer Applications (MCA_NEW) and Online MCA (MCAOL). Every question in it was chosen after reading five previous year question papers, from June 2023 up to the December 2025 sitting, and every answer is written the way an examiner expects to see it on the answer sheet.
Discrete Mathematics is not a subject you can rescue by reading theory the night before. It is a paper of truth tables, proofs, automata diagrams, counting formulae and graph properties, and marks are awarded for the working, not only the final line. That is exactly what this file is built around.
MCS 212 Discrete Mathematics Key Facts
- Course code and title: MCS-212 Discrete Mathematics
- Programmes: IGNOU Master of Computer Applications (MCA_NEW) and Online MCA (MCAOL)
- Course structure: 4 blocks and 14 units
- Exam duration: 3 hours
- Maximum marks: 100 with 70% weightage for the term end exam
- Paper pattern: Question 1 compulsory (40 marks in short parts) and any three of Q2 to Q5 (20 marks each)
- Questions solved in this file: 15
- Shown on this page as samples: 5 (the remaining 10 are shared on WhatsApp)
- Sessions analysed: 5 papers from June 2023 to December 2025
- Target sittings: June 2026 and December 2026
MCS 212 Solved Guess Paper 2026 at a Glance for Discrete Mathematics
This file contains 15 IGNOU style questions with complete step by step solutions, mapped across all four blocks of MCS-212 Discrete Mathematics and prioritised by how often each topic has appeared since June 2023. It runs to roughly 15 pages of worked answers and is shared as a PDF on WhatsApp.
What separates it from a plain question list is the tagging. Each question carries a priority label of HIGH, MEDIUM or LOW, the block and section it belongs to, its likely mark value, and the sessions in which that topic last appeared. So when you have four days left, you know which six questions to attack first instead of guessing.
| Detail | Specification |
|---|---|
| Course code | MCS-212 |
| Course title | Discrete Mathematics |
| Programmes | MCA_NEW and MCAOL |
| Questions solved | 15 |
| Blocks covered | All 4 |
| Approximate length | 15 pages of solutions |
| Prepared from | IGNOU SLM plus 5 past papers |
| Format and delivery | PDF shared on WhatsApp |
| Language | English |
| Valid for | June 2026 and December 2026 |
Answers are written in plain, readable English rather than textbook density. Where a proof needs a table, the table is drawn. Where a formula applies, the formula is stated before the numbers go in. Final results are boxed, which is a small habit that helps an evaluator find your answer quickly under a heavy checking load.
5 Sample Solved Questions from the MCS 212 Guess Paper
Five of the fifteen solved questions are reproduced below in full so you can judge the answer quality before asking for the complete file. They are drawn deliberately from four different blocks, so what you see here is representative of the whole document rather than the easiest section of it.
Each sample keeps its original number from the guess paper in the chip beside the heading, so if you later receive the full PDF you will recognise exactly where these five sat in the sequence.
Sample 1 (Guess Paper Q1) | Truth Tables, Tautology and Contradiction | Block 1 | 5 marks | Priority HIGH
Question. What is a tautology and a contradiction? Verify whether [(p ā q) ā§ ~q] ā ~p is a tautology.
Solution.
Tautology. A tautology is a compound proposition whose truth value is True (T) for every possible assignment of truth values to its constituent propositions.
Contradiction. A contradiction is a compound proposition whose truth value is False (F) for every possible assignment of truth values to its constituent propositions.
Verification. Let P = [(p ā q) ā§ ~q] ā ~p. Construct the truth table.
| p | q | p ā q | ~q | (p ā q) ā§ ~q | ~p | P |
|---|---|---|---|---|---|---|
| T | T | T | F | F | F | T |
| T | F | F | T | F | F | T |
| F | T | T | F | F | T | T |
| F | F | T | T | T | T | T |
Observation. The final column contains T in all four cases.
Conclusion. Since [(p ā q) ā§ ~q] ā ~p is true for every possible combination of truth values of p and q, it is a tautology.
Sample 2 (Guess Paper Q2) | Proof by Contradiction for ā2 | Block 1 | 5 marks | Priority HIGH
Question. Using proof by contradiction, demonstrate that ā2 is irrational.
Solution.
Assume that ā2 is rational. Then it can be written as ā2 = a/b, where a and b are integers, b ā 0, and a and b have no common factor.
Squaring both sides gives 2 = a2/b2, that is a2 = 2b2. This shows that a2 is even, and therefore a is also even.
Let a = 2k. Then (2k)2 = 2b2, so 4k2 = 2b2, which gives b2 = 2k2. This shows that b2 is even, and therefore b is also even.
So both a and b are even, which means they share the common factor 2. This contradicts the assumption that a and b have no common factor.
Conclusion. Hence the assumption is false, and therefore ā2 is irrational.
Sample 3 (Guess Paper Q6) | Inverse of a Function | Block 2 | 5 marks | Priority HIGH
Question. Find the inverse of the function f(x) = (x ā 2)/(x ā 3).
Solution.
Let y = (x ā 2)/(x ā 3), where x ā 3. To find the inverse, interchange x and y, which gives x = (y ā 2)/(y ā 3).
Multiplying both sides by (y ā 3) gives x(y ā 3) = y ā 2. Expanding, xy ā 3x = y ā 2.
Bringing the y terms to one side gives xy ā y = 3x ā 2. Factoring out y gives y(x ā 1) = 3x ā 2.
Hence y = (3x ā 2)/(x ā 1), where x ā 1, and therefore fā1(x) = (3x ā 2)/(x ā 1).
Verification. Substituting fā1(x) into f, the numerator simplifies to x/(x ā 1) and the denominator to 1/(x ā 1), and their quotient is x. Similarly fā1(f(x)) = x, so the inverse is correct.
Domain and range. Domain of f(x) is x ā 3, and domain of fā1(x) is x ā 1.
Sample 4 (Guess Paper Q10) | Inclusion and Exclusion Principle | Block 3 | 5 marks | Priority HIGH
Question. Briefly discuss the Inclusion-Exclusion principle with a suitable example.
Solution.
The Inclusion-Exclusion Principle is a counting technique used to determine the number of elements in the union of two or more sets. While counting the elements of different sets, some elements belong to more than one set and get counted more than once. The principle removes this duplicate counting by subtracting the common elements.
For two finite sets A and B, n(A āŖ B) = n(A) + n(B) ā n(A ā© B).
For three finite sets A, B and C, n(A āŖ B āŖ C) = n(A) + n(B) + n(C) ā n(A ā© B) ā n(B ā© C) ā n(A ā© C) + n(A ā© B ā© C).
Example. In a class of 40 students, 25 study Mathematics, 20 study Computer Science and 10 study both. The number studying at least one subject is n(M āŖ C) = 25 + 20 ā 10 = 35.
Conclusion. The principle is widely used in combinatorics to count elements of a union accurately by avoiding multiple counting of common elements.
Sample 5 (Guess Paper Q13) | Eulerian and Hamiltonian Graphs | Block 4 | 10 marks | Priority HIGH
Question. Differentiate between Eulerian and Hamiltonian graphs. State Dirac's criterion and Ore's criterion for a graph to be Hamiltonian.
Solution.
| Eulerian graph | Hamiltonian graph |
|---|---|
| Contains an Euler circuit. | Contains a Hamiltonian cycle. |
| The circuit passes through every edge exactly once. | The cycle passes through every vertex exactly once. |
| A vertex may be visited more than once while traversing different edges. | Every vertex is visited once, except the starting vertex which repeats at the end. |
| Existence depends on the degrees of the vertices. | Existence depends on the connectivity and structure of the graph. |
| Every connected graph in which all vertices have even degree is Eulerian. | There is no simple necessary and sufficient condition for a graph to be Hamiltonian. |
| Mainly concerned with edges. | Mainly concerned with vertices. |
Dirac's criterion. Let G be a simple graph with n vertices where n ā„ 3. If deg(v) ā„ n/2 for every vertex v, then G is Hamiltonian.
Ore's criterion. Let G be a simple graph with n vertices where n ā„ 3. If deg(u) + deg(v) ā„ n for every pair of non-adjacent vertices u and v, then G is Hamiltonian.
Application. Both criteria give sufficient conditions for testing Hamiltonicity without actually constructing a Hamiltonian cycle.
Conclusion. An Eulerian graph is about traversing every edge exactly once, whereas a Hamiltonian graph is about visiting every vertex exactly once.
These are 5 of the 15 solved questions. The remaining 10 solutions, covering Boolean algebra, mathematical induction, finite automata, permutations, recurrence relations, the handshaking theorem, bipartite graphs, chromatic number, logical equivalence and Turing machines, are shared on request.
Complete Index of the MCS 212 Guess Paper File
The full file carries 15 questions in a fixed order, and the index below lists every one of them with its topic, block, mark value and priority tag. The five reproduced above are marked as shown, so nothing about what you are receiving is hidden.
| No. | Topic | Block and section | Marks | Priority | On this page |
|---|---|---|---|---|---|
| Q1 | Truth tables, tautology and contradiction | Block 1 Logic | 5 | HIGH | Shown |
| Q2 | Proof by contradiction for ā2 | Block 1 Methods of Proof | 5 | HIGH | Shown |
| Q3 | Logical equivalence and De Morgan's laws | Block 1 Logic | 5 | HIGH | In full file |
| Q4 | Mathematical induction on T(n) and 2āæ > nĀ³ | Block 1 Methods of Proof | 10 | HIGH | In full file |
| Q5 | Boolean algebra laws and logic circuits | Block 1 Boolean Algebra | 10 | HIGH | In full file |
| Q6 | Inverse of a function | Block 2 Functions | 5 | HIGH | Shown |
| Q7 | Kleene closure of a language | Block 2 Automata and Languages | 5 | HIGH | In full file |
| Q8 | Finite automata and regular expression | Block 2 Automata and Languages | 10 | HIGH | In full file |
| Q9 | Permutations and combinations | Block 3 Combinatorics | 10 | HIGH | In full file |
| Q10 | Inclusion-Exclusion principle | Block 3 Advance Counting | 5 | HIGH | Shown |
| Q11 | Recurrence relations | Block 3 Recurrences | 10 | HIGH | In full file |
| Q12 | Handshaking theorem with proof | Block 4 Basic Properties | 10 | HIGH | In full file |
| Q13 | Eulerian and Hamiltonian graphs | Block 4 Eulerian and Hamiltonian | 10 | HIGH | Shown |
| Q14 | Bipartite graphs and chromatic number | Block 4 Colourings | 10 | HIGH | In full file |
| Q15 | Turing machines with Mealy and Moore | Block 2 Computability | 10 | HIGH | In full file |
Alongside the 15 solutions the file closes with three short sections that many learners find as useful as the answers themselves: an exam pattern rule sheet, a note on topics that are not worth over preparing, and a checklist of what evaluators reward in a mathematics answer script.
MCS 212 Discrete Mathematics Blocks and Units Covered
MCS-212 is organised into 4 blocks and 14 units, and the guess paper draws questions from every one of the four blocks. The table below sets out the official structure together with the topics inside each unit that the 2026 questions actually touch.
| Block | Unit | Key topics targeted in the guess paper |
|---|---|---|
| Block 1 Elementary Logic and Proofs | Unit 1 Propositional Calculus | Tautology and contradiction, truth tables, logical equivalence, De Morgan's laws |
| Unit 2 Methods of Proof | Proof by contradiction, irrationality of ā2, mathematical induction on recurrences and inequalities | |
| Unit 3 Boolean Algebra and Circuits | Boolean laws, expression reduction, logic gate circuits, circuit truth tables | |
| Block 2 Sets, Relations and Functions | Unit 1 Sets, Relations and Functions | Inverse of a function, composition and verification, domain and range restrictions |
| Unit 2 Automata and Languages | Kleene closure, finite automata, state transition tables, regular expressions, string acceptance | |
| Unit 3 Computability and Complexity | Turing acceptable and Turing decidable languages, Mealy and Moore machine comparison | |
| Block 3 Counting Principles | Unit 1 Combinatorics | Multiplication and addition principles, permutation and combination formulae, circular seating |
| Unit 2 Advance Counting Principles | Inclusion-Exclusion for two and three sets, worked union counting example | |
| Unit 3 Recurrences Relations | Solving T(n) = 2T(nā1) + 1, back substitution, closed form derivation | |
| Unit 4 Partitions and Distributions | Arrangement of identical objects, distribution counting basics | |
| Block 4 Graph Theory | Unit 1 Basic Properties of Graphs | Degree of a vertex, handshaking theorem with proof and application |
| Unit 2 Connectedness | Walk, path, circuit and cycle distinctions, bipartite graph edge maximum | |
| Unit 3 Eulerian and Hamiltonian Graphs | Euler circuit conditions, Hamiltonian cycles, Dirac's and Ore's criteria | |
| Unit 4 Graph Colourings | Chromatic number, vertex colouring with examples |
If you are still building your base before revision, work through the official self learning material first and keep this guess paper for the final stretch. Our MCS 212 Study Material page collects the unit wise notes for the same 14 units, so the two resources line up block for block without you having to re-map anything.
How the MCS 212 Important Questions Were Selected
Selection was done by tabulating every question from five term end papers between June 2023 and December 2025, grouping them by topic, and counting appearances. Topics repeating four or more times, or appearing in the most recent sitting, were tagged HIGH and written out in full.
The December 2025 paper mattered most in this exercise because it is the freshest signal of what the paper setter is currently favouring. Reading it against the four papers before it showed which topics are permanent fixtures and which drift in and out.
Once the shortlist was fixed, each answer was written against the IGNOU self learning material rather than from a general mathematics reference, so terminology, notation and definitions match the book the examiner uses. That discipline is the same one we follow across every IGNOU Solved Guess Paper in our library, and it is the reason our answers read like the SLM rather than like a web article.
Nothing here is a prediction dressed up as a guarantee. A guess paper narrows a 14 unit syllabus to a defensible shortlist. It does not replace reading the blocks, and any honest provider will tell you the same.
MCS 212 Topic Frequency Across the Last Five Papers
Six topics have appeared in four or five of the last five MCS 212 papers, and those six carry the highest expected return for your revision hours. The table records the raw appearance count behind every priority tag in the file.
| Topic | Jun 2023 | Dec 2023 | Dec 2024 | Jun 2025 | Dec 2025 | Priority |
|---|---|---|---|---|---|---|
| Truth tables, tautology and contradiction | Yes | Yes | Yes | Yes | Yes | HIGH |
| Kleene closure | Yes | Yes | Yes | Yes | Yes | HIGH |
| Recurrence relations | Yes | Yes | Yes | Yes | Yes | HIGH |
| Logical equivalence and De Morgan's laws | Yes | Yes | Yes | Yes | No | HIGH |
| Boolean algebra and logic circuits | Yes | Yes | Yes | No | Yes | HIGH |
| Finite automata and regular expression | Yes | No | Yes | Yes | Yes | HIGH |
| Permutations and combinations | Yes | No | Yes | Yes | Yes | HIGH |
| Bipartite graphs | Yes | No | Yes | Yes | Yes | HIGH |
| Hamiltonian graph with Dirac and Ore | Yes | Yes | Yes | No | Yes | HIGH |
| Proof by contradiction for irrationality | No | No | Yes | Yes | Yes | HIGH |
| Inclusion-Exclusion principle | Yes | Yes | No | No | Yes | HIGH |
| Mathematical induction | Yes | No | Yes | Yes | No | HIGH |
| Inverse of a function | Yes | Yes | No | No | Yes | HIGH |
| Handshaking theorem | No | Yes | Yes | No | Yes | HIGH |
| Eulerian graph and circuit | Yes | No | No | Yes | Yes | HIGH |
| Chromatic number and vertex colouring | Yes | No | Yes | Yes | No | HIGH |
| Turing acceptable versus decidable | Yes | Yes | Yes | No | No | HIGH |
| Mealy and Moore machines | No | Yes | Yes | Yes | No | MEDIUM |
| Sets and symmetric difference | No | No | Yes | Yes | Yes | MEDIUM |
| Pigeonhole principle | No | Yes | Yes | No | Yes | MEDIUM |
| Graph terms such as walk, path and cycle | No | No | No | Yes | Yes | MEDIUM |
| P, NP, undecidable and halting problem | No | No | Yes | No | Yes | MEDIUM |
| Isomorphism and planar graphs | Yes | No | Yes | No | No | LOW |
Two honest caveats sit under this table. The pigeonhole principle appears often but is not developed inside the MCS-212 blocks, so it is flagged rather than solved and should be revised from your own notes. Heavy single appearance items such as Floyd-Warshall and dynamic programming are deliberately left out.
If you want to verify the counts yourself rather than take them on trust, pull the papers from our IGNOU Previous Year Question Paper archive and tally the topics the same way we did. You can also read the paper hosted on the university site at ignou.ac.in to confirm the pattern.
MCS 212 Exam Pattern and Marking Scheme Explained
The MCS 212 term end paper runs for 3 hours and carries 100 marks with 70% weightage, where Question 1 is compulsory and worth 40 marks in short parts, and you attempt any three of the remaining four questions at 20 marks each.
| Element | Detail | What it means for revision |
|---|---|---|
| Duration | 3 hours | Roughly 100 minutes of the paper goes to Q1 alone |
| Maximum marks | 100 | Term end weightage is 70% of the course |
| Question 1 | Compulsory, 40 marks | Made of short 4 to 5 mark parts spanning all four blocks |
| Questions 2 to 5 | Attempt any three, 20 marks each | Choice exists, but only if you have prepared beyond one block |
| Answer length guide | 4 to 5 mark part is about half a page | A 20 mark question needs 2 to 3 pages of working |
| Marking behaviour | Method carries marks | Correct formula and steps score even if the final number slips |
The compulsory question is where the paper is won or lost. Because it samples across logic, sets and functions, automata, counting and graphs, a learner who prepared only two blocks cannot recover the 40 marks no matter how strong those two blocks are. Breadth beats depth in Q1, and depth pays off in Q2 to Q5.
Three habits raise scores in this subject. State the definition before you solve. Use correct notation such as ā§, āØ, ā, Ī£*, Ļ(G), P(n,r) and C(n,r). Draw the table, circuit or graph neatly, because those carry visible marks even when the surrounding prose is thin.
Who Should Use This MCS 212 Guess Paper
This file suits any learner registered in MCA_NEW or MCAOL who has read the blocks at least once and now needs to convert that reading into exam ready answers. It is a revision instrument, not a first contact with the syllabus.
It fits three situations particularly well. Learners with under two weeks left who need a defensible shortlist. Repeaters who cleared other papers but carried MCS-212 forward. Working professionals studying at night who cannot read 14 units end to end and need the highest yield topics identified for them.
It is a weaker fit if you have not opened the book at all, because worked solutions in Discrete Mathematics assume you recognise the notation. In that case start with the units, then return here. Learners taking several computer science papers in the same sitting often pair this with our wider MCA guess Paper set so the whole semester is covered under one revision plan.
Ten Day Revision Plan Using the MCS 212 Guess Paper
Ten focused days are enough to cover all 15 solved questions twice, with the second pass done by hand under timed conditions. The schedule below assumes about two hours a day.
| Days | Focus | Target from the file |
|---|---|---|
| Day 1 and 2 | Block 1 logic and proofs | Q1 to Q5, with truth tables written out by hand |
| Day 3 and 4 | Block 2 functions and automata | Q6 to Q8 and Q15, redrawing every transition table |
| Day 5 and 6 | Block 3 counting and recurrences | Q9 to Q11, memorising P(n,r) and C(n,r) forms |
| Day 7 and 8 | Block 4 graph theory | Q12 to Q14, sketching each graph rather than reading it |
| Day 9 | Timed practice | Attempt a full 3 hour paper using past questions |
| Day 10 | Weak spot repair | Rewrite only the answers you fumbled on Day 9 |
One instruction matters more than the schedule itself. Write the solutions out by hand rather than reading them. Discrete Mathematics punishes recognition memory, and a proof that felt obvious on screen collapses in the hall unless your hand has already produced it once.
How to Get the Complete MCS 212 Solved Guess Paper 2026
Send a WhatsApp message to 9899436384 with the course code MCS-212, and the complete 15 question solved PDF is shared with you directly. There is no account to create and no form to complete.
Mention your programme (MCA_NEW or MCAOL) and your target sitting when you message, since it helps us confirm you are being sent the file matched to the June 2026 and December 2026 pattern rather than an older edition. If you need guess papers for other papers in the same semester, say so in the same message and we will bundle them.
Get the MCS 212 solved guess paper on WhatsApp 9899436384
MCS 212 Guess Paper Frequently Asked Questions
How many questions are there in the MCS 212 guess paper for 2026?
The MCS 212 Discrete Mathematics guess paper contains 15 questions with complete solutions across roughly 15 pages. Five of them are reproduced in full on this page as samples, and the remaining 10 solutions are shared on WhatsApp. Every question carries a priority tag, its block mapping and its likely mark value, so you can order your revision without reading the entire file first.
Is the MCS 212 guess paper valid for both the June 2026 and December 2026 exams?
Yes. The file is built for both 2026 sittings because it is based on topic frequency across five papers rather than on one session. Topics that repeat four or five times out of five do not change between a June and a December paper. If IGNOU revises the MCS-212 syllabus or pattern before your exam, we update the file and reshare it with everyone who requested it.
Which blocks of MCS 212 Discrete Mathematics does the guess paper cover?
All four. Block 1 covers logic, proofs and Boolean algebra. Block 2 covers sets, functions, automata and computability. Block 3 covers combinatorics, advanced counting and recurrence relations. Block 4 covers graph properties, connectedness, Eulerian and Hamiltonian graphs and colourings. The 15 questions are distributed across these blocks in proportion to how often each block appears in the paper.
Can I pass MCS 212 by studying only this guess paper?
It improves your odds considerably but it is not a substitute for the blocks. Question 1 is compulsory and worth 40 marks, and it samples short parts from across the whole syllabus. A guess paper narrows 14 units to a defensible shortlist and gives you model answers, but reading the self learning material at least once remains necessary for that compulsory section.
Are the MCS 212 answers written from the IGNOU book or from general sources?
Every solution is written against the IGNOU self learning material for MCS-212, so the notation, definitions and terminology match the book your examiner uses. Where a proof has several valid forms, we use the one presented in the block. This matters in Discrete Mathematics, where an unfamiliar notation for the same correct answer can cost you presentation marks.
What is the MCS 212 exam pattern and how long is the paper?
The MCS 212 term end paper runs 3 hours for 100 marks with 70% weightage. Question 1 is compulsory and carries 40 marks in short parts of 4 to 5 marks each. You then attempt any three of Questions 2 to 5, each worth 20 marks. Method carries marks in this paper, so showing correct formulae and steps earns credit even when the final figure is wrong.
How quickly will I receive the MCS 212 guess paper after messaging?
Files are shared on WhatsApp at 9899436384 during working hours, usually within a short time of your message. Send the course code MCS-212 along with your programme, whether MCA_NEW or MCAOL. If you message late at night the file goes out the next morning. You can also ask for guess papers for other courses in the same semester in that message.
Does the MCS 212 guess paper include the pigeonhole principle?
No, and that is a deliberate decision we would rather state openly. The pigeonhole principle does appear in past MCS 212 papers, but it is not developed inside the MCS-212 blocks, so we flag it as a topic to revise from your own notes instead of writing a solution that would not match the book. Everything else in the frequency table is solved in full.
Unnati Educations is an independent academic support platform and is not affiliated with, endorsed by, or connected to the Indira Gandhi National Open University (IGNOU). Course names, codes and programme titles are used for identification only. The MCS 212 guess paper is a study aid prepared by our team and is not an official IGNOU publication. Learners should always confirm the syllabus, pattern and exam dates on ignou.ac.in.