About This Solved Paper
| Prepared by | Unnati Education, IGNOU-experienced academic content team |
|---|---|
| Qualification | Graduate with specialization in Computer Science and Algorithm Design |
| Programme | IGNOU Bachelor of Computer Applications (BCA_NEW) |
| Institution Reference | IGNOU Term-End Examination December 2025 |
BCS-042 tests how well you understand the logic behind computing, not just the code. The BCS 042 Question Paper December 2025 covered algorithm complexity, searching and sorting techniques, graph algorithms including Dijkstra's and DFS, divide and conquer methods, and the Master Theorem. It is a 50-mark paper with one compulsory question worth 20 marks alone. Getting the compulsory section right is essential since it covers multiple algorithm concepts simultaneously. Structured, stepwise answers with clear complexity analysis are what IGNOU BCA examiners consistently reward in this paper.
What is BCS-042 Question Paper December 2025?
The BCS-042 December 2025 question paper is a 50-mark IGNOU Term-End Examination for BCA students covering Introduction to Algorithm Design, with one compulsory 20-mark question and any three optional questions attempted in 2 hours.
BCS-042 is a core paper in the IGNOU Bachelor of Computer Applications programme. It builds systematic thinking about how algorithms work, how efficient they are, and how to choose the right approach for a given problem. The December 2025 paper tested both theoretical understanding of complexity and hands-on application of algorithms like Dijkstra, bubble sort, binary search, and DFS on actual data sets and graphs provided in the questions.
About IGNOU BCS-042 | Introduction to Algorithm Design
BCS-042 develops your ability to design, analyse, and compare algorithms across different problem types. You study time and space complexity using Big O notation, algorithm design paradigms including greedy, divide and conquer, and branch and bound, sorting and searching methods, graph traversal techniques, and shortest path algorithms. Most students notice that the numerical questions in this paper, such as applying Dijkstra's algorithm to a given graph or running bubble sort iterations on a specific list, require very careful stepwise presentation to earn full marks. Skipping steps costs marks even when the final answer is correct.
BCS 042 Question Paper Exam Pattern and Marks Breakdown
This paper carries 50 marks in total. Question 1 is compulsory and carries 20 marks split across four sub-parts of 5, 5, 6, and 4 marks respectively. Students then attempt any 3 questions from Q2 to Q5, each carrying 10 marks with two sub-parts of 5 or 6 marks each. The examination duration is 2 hours. All answers require algorithm steps, complexity analysis, or numerical applications on specific data provided within the question itself.
All Questions | BCS 042 Question Paper December 2025 IGNOU (Complete List)
(a) Explain the concept of the space complexity in context of algorithm analysis. How is it different from time complexity ? Provide an example to illustrate the calculation of space complexity. 5 (b) Given a list of distinct integers, write an algorithm to determine the position of an integer in the list using linear search and count the number of comparison operations required. 5 (c) Describe any three of the following : 3x2=6 (i) Greedy technique (ii) Cycle in a Directed Graph (iii) Upper Bound (iv) Branch and Bound (d) Use Master Theorem to give tight asymptotic bounds of the following : 2x2=4 (i) T(n) = 4T(n/2) + n2 (ii) T(n) = 2T(n/2) + nVn
(a) State Euclid's algorithm and find GCD (595, 252) by this algorithm. 5 (b) Write the iterations for sorting the following list of numbers using bubble sort and selection sort : 5 45, 67, 13, 90, 2, 35, 28, 10
(a) Differentiate between Kruskal's algorithm and Prim's algorithm. 4 (b) Apply Dijkstra's algorithm to find shortest path from source vertex A to each of the other vertices of the following directed graph : 6
(a) Consider the following sorted array A with 13 elements : 7, 15, 19, 27, 30, 48, 56, 59, 75, 87, 94, 110, 111 Illustrate the working of Binary search algorithm while searching for ITEM : 5 (i) 19 (ii) 94 (b) Show that the runtime of QUICK SORT algorithm in the best case is Theta(n log n). 5
(a) Multiply 1026732 x 0732920 using divide and conquer technique using Karatsuba method. 5 (b) Write an algorithm for Depth First Search (DFS) and traverse the following graph using DFS. Starting vertex is A : 5
BCS 042 Syllabus Topics Covered in Question Paper
The December 2025 paper covers complexity analysis through space and time complexity comparison and Master Theorem application. Algorithm design techniques are tested via greedy method, branch and bound, and divide and conquer including Karatsuba multiplication. Sorting algorithms appear through bubble sort and selection sort iterations on a given list. Graph algorithms cover Kruskal versus Prim differences, Dijkstra's shortest path on a directed graph, and DFS traversal. Searching is tested through binary search illustration and linear search comparison count. Quick Sort best case complexity proof completes the coverage.
Sample Answer Preview | BCS 042 Introduction to Algorithm Design Solved Question Paper
Take Question 2(b) on bubble sort and selection sort for the list 45, 67, 13, 90, 2, 35, 28, 10. Here's the important part: IGNOU expects you to show every pass separately for bubble sort, identifying which elements are compared and swapped in each step. For selection sort, show the minimum element identified in each pass and its new position after swapping. Both must be shown as iteration tables with the list state after each pass. Get the complete BCS-042 solved question paper from Unnati Education for all five questions answered with this level of stepwise detail.
How to Write High-Scoring Answers in BCS 042 Question Paper
For Q1 sub-parts, write concise and precise algorithmic answers within the given mark allocation. A 5-mark sub-part needs around 100 to 120 words plus the algorithm or example. For graph-based questions like Q3(b) on Dijkstra, present your answer as a step-by-step table showing distance updates for each vertex at every iteration. Binary search in Q4(a) must show mid calculation, comparison result, and range update for each step. Complexity proofs like Q4(b) need both the recurrence derivation and the final Big O notation clearly stated with justification.
Who Should Use This BCS-042 Solved Question Paper December 2025?
First-attempt BCA students who find algorithm complexity or graph traversal questions difficult to present in IGNOU's exam format will benefit from this resource. Repeat candidates can identify exactly where their previous stepwise solutions were incomplete. Self-study learners preparing without coaching get a verified reference for every section of the December 2025 paper. Students who understand algorithms conceptually but struggle to present Dijkstra iterations, sort passes, or Master Theorem proofs in the format IGNOU expects will find the solved paper particularly useful.
Why This Is Better Than Free BCS-042 December 2025 Question Paper PDFs and Telegram Files
Free Telegram PDFs show you what questions were asked. They do not show you how to run Dijkstra's algorithm step by step on that specific graph, how to present bubble sort passes in the correct tabular format, or how to apply the Karatsuba multiplication method with all intermediate steps shown. These are exactly the details that determine your marks. Unnati Education's BCS-042 December 2025 solved paper provides verified, stepwise algorithm solutions with correct complexity notation and IGNOU-format presentation for every compulsory and optional question.
Student Reviews | BCS-042 Solved Question Paper by Unnati Education
"The Dijkstra's algorithm solution in the BCS-042 December 2025 solved paper showed every distance update table clearly. That specific graph question would have cost me marks without it." — Ankit Joshi, BCA Student Delhi
"Master Theorem application and Quick Sort complexity proof were explained with full working in Unnati's BCS 042 solved paper. Much clearer than anything I found online." — Nidhi Gupta, IGNOU Pune
"I kept losing marks on sorting questions because I was not showing all iterations. After using this solved paper I understood exactly what IGNOU expects for each pass." — Rahul Sinha, BCA Repeat Candidate
How to Get the BCS-042 Solved Question Paper December 2025 | Step by Step
WhatsApp Unnati Education and mention BCS-042 December 2025. Share your name and IGNOU BCA programme details. Our team confirms your requirement and sends you the complete solved paper digitally without any delay.
Frequently Asked Questions
What is BCS-042?
BCS-042 is a core algorithm design course titled Introduction to Algorithm Design offered in the IGNOU Bachelor of Computer Applications (BCA) programme. It covers algorithm complexity analysis using time and space complexity, the Master Theorem, greedy and divide and conquer design techniques, sorting algorithms including bubble sort, selection sort, and Quick Sort, searching algorithms including linear and binary search, graph algorithms including Dijkstra's shortest path, Kruskal and Prim algorithms, and DFS traversal. The Term-End Examination carries 50 marks with one compulsory question attempted in 2 hours.
What is the exam pattern and marks distribution for BCS 042 December 2025?
The BCS 042 December 2025 paper has 5 questions. Question 1 is compulsory and carries 20 marks split across four sub-parts. Students then attempt any 3 from Q2 to Q5, each carrying 10 marks with two sub-parts of 5 or 6 marks. The total is 50 marks and the duration is 2 hours. Students must attempt the compulsory question first and then strategically choose their three optional questions based on algorithm preparation strength. Graph-based numerical questions like Dijkstra and sorting iteration questions require the most preparation time before the exam.
Which algorithm design topics are most important in BCS-042?
Key topics from the December 2025 paper include space complexity versus time complexity with examples, linear search algorithm with comparison count, greedy technique, cycle in directed graph, upper bound, branch and bound, Master Theorem application for two recurrence relations, Euclid's algorithm for GCD with numerical application, bubble sort and selection sort iterations on a given list, Kruskal versus Prim algorithm differences, Dijkstra's shortest path on a directed graph, binary search illustration for specific items, Quick Sort best case complexity proof, Karatsuba multiplication using divide and conquer, and DFS algorithm with graph traversal.
How can I download the IGNOU BCS-042 question paper for December 2025?
You can get the BCS-042 December 2025 question paper with complete stepwise solved answers directly from Unnati Education by WhatsApp. The IGNOU official website also publishes question papers after the examination cycle ends. For exam-ready solved versions with verified algorithm step solutions, iteration tables for sorting questions, graph traversal answers, complexity proofs, and IGNOU BCA-aligned answer depth for both compulsory and optional questions, Unnati Education is the most reliable preparation resource available for IGNOU BCA algorithm students.
About Unnati Education | IGNOU Study Material Experts
Unnati Education supports IGNOU students across India with solved question papers, study material, and important questions for Term-End Examinations. Our computer science and algorithm resources are prepared by subject-experienced academic writers who understand how IGNOU BCA technical papers are structured and assessed. We know that stepwise algorithm presentation, iteration tables, and correct complexity notation together determine scores in BCS-042. Students from Delhi, Haryana, Uttar Pradesh, Bihar, Rajasthan, and across India preparing for IGNOU BCA examinations have consistently relied on our resources.
Explore More IGNOU BCS-042 Solved Papers and Study Material
Explore the BCS-042 Important Questions Booklet for the current session. Access BCS-042 Assignment Solutions prepared by Unnati Education. Find chapter-wise notes on graph algorithms, sorting, and complexity analysis for BCS-042. Browse IGNOU BCA previous year solved question papers across all computer science and algorithm design courses.
Get Your BCS 042 Question Paper December 2025 Solved Paper Now
The BCS-042 Question Paper December 2025 with complete solutions is ready for you. Do not go into your exam without knowing how to present Dijkstra iterations, sorting passes, or Master Theorem applications in IGNOU's expected format. WhatsApp Unnati Education today and we will send it immediately.