Discrete Structures & Theory of Logic Unit 4 – Algebraic Structures (Group Theory): AKTU previous year questions
33 AKTU questions from Unit 4 (Algebraic Structures (Group Theory)) asked in 2020–2026, tagged by marks, year and topic. In short: about 26 marks of every paper come from this unit; the most asked topic is Groups & Subgroups (13 times); 8 questions came back in a later year. The latest ones are listed below; on the page you can filter them by 2-mark or long questions, topic and repeats.
Unit 4 previous year questions
- Let H be a subgroup of a finite group G. Prove that order of H is a divisor of order G. (7 marks, 2026, Cosets & Lagrange's Theorem)
- How many generators are there of the cyclic group G of order 10. (7 marks, 2026, Groups & Subgroups)
- State and prove Lagrange’s theorem. (7 marks, 2026, Cosets & Lagrange's Theorem)
- Define zero divisor of a ring. (2 marks, 2026, Rings & Fields)
- Define Abelian group. (2 marks, 2025, Groups & Subgroups)
- Solve in how many ways can you arrange the letters in the word "DISCRETE"? (2 marks, 2025, Groups & Subgroups)
- In the group Z12 under addition modulo 12, consider the subgroup H = {0, 4, 8}. Compute all the distinct Cosets of H. (7 marks, 2025, Cosets & Lagrange's Theorem)
- Calculate the number of generators of the cyclic group of order 8. (7 marks, 2025, Groups & Subgroups)
- Determine whether the set H = {0, 1, 5} is a subgroup of Z6 under addition modulo 6. (7 marks, 2025, Groups & Subgroups)
- Show that identity element is unique in a group. (2 marks, 2024, Groups & Subgroups)
- 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. (7 marks, 2024, Groups & Subgroups)
- Describe Algebraic structure, semigroup, monoid and group. Also explain the relationship among them. (7 marks, 2024, Groups & Subgroups)
Most asked Unit 4 topics
- Groups & Subgroups – asked 13 times
- Rings & Fields – asked 13 times
- Cosets & Lagrange's Theorem – asked 6 times
Unit 4 question pattern
- 2-mark questions: 15 asked in 2020–2026
- 7-mark questions: 9 asked in 2020–2026
- 10-mark questions: 9 asked in 2020–2026
- About 26 marks from Unit 4 in every paper
- 8 questions were asked again in a later year
Unit 4 questions year by year
- 2026: 4 Unit 4 questions asked (23 marks across that year's papers)
- 2025: 5 Unit 4 questions asked (25 marks across that year's papers)
- 2024: 4 Unit 4 questions asked (23 marks across that year's papers)
- 2023: 4 Unit 4 questions asked (32 marks across that year's papers)
- 2022: 6 Unit 4 questions asked (36 marks across that year's papers)
- 2021: 5 Unit 4 questions asked (18 marks across that year's papers)
- 2020: 5 Unit 4 questions asked (26 marks across that year's papers)