LU B.Sc Sem 1 Mathematics Matrices and Algebra Important Questions 2026 | PYQ Pattern
LU B.Sc 1st Semester Mathematics (Matrices and Algebra) Important Questions 2026 – Lucknow University (LU) aur affiliated colleges ke B.Sc NEP Semester I (PCM group) students ke liye Mathematics – Matrices and Algebra (Paper-II) ke sabse important questions, bilkul previous year question paper (PYQ) pattern me. Saare questions neeche page par hi hain – section-wise.
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Paper Details – B.Sc Sem 1 Mathematics (LU NEP 2026)
| University | University of Lucknow (LU) + affiliated colleges |
| Course | B.Sc. I Semester (NEP) – PCM |
| Paper | Mathematics – Matrices and Algebra (Paper-II) |
| Time / Marks | 2 Hours / 75 Marks |
| Pattern | Kul 4 questions: Section A se 1 (15 marks) + Section B se 3 (20 marks each) |
Section A – Important Questions (15 Marks)
Note: Section A se koi ek question attempt karna hai.
Q1. (a) Bring A = [[1, 2, 0, –1], [3, 4, 1, 2], [–2, 3, 2, 5]] to normal form and find its rank.
(b) Give the statement and proof of the Cayley-Hamilton theorem and use it to find the inverse of [[0, 0, 1], [3, 1, 0], [2, 1, 4]]. [15 Marks]
Q2. (a) Find the values of λ for which the system x + y + z = 1, x + 2y + 4z = λ, x + 4y + 10z = λ² is consistent, and solve it completely in each case.
(b) Show that any square matrix can be written uniquely as P + iQ with P and Q Hermitian. [15 Marks]
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Section B – Important Questions (20 Marks)
Note: Section B se koi teen questions attempt karne hain.
Q3. (a) Obtain the eigenvalues and eigenvectors of [[2, 0, 1], [0, 2, 0], [1, 0, 2]].
(b) Show that ‘congruence modulo n’ is an equivalence relation on the set of integers. [20 Marks]
Q4. (a) Prove that a non-empty subset H of a group G is a subgroup if and only if ab⁻¹ ∈ H for all a, b ∈ H.
(b) Show that the intersection of two subgroups of G is a subgroup, and give an example showing that their union need not be a subgroup. [20 Marks]
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Q5. (a) Decide whether σ = (1 2 3 4 5 6 7 8 9 → 2 5 4 3 6 1 7 9 8) is an even or odd permutation and find its order.
(b) Show that the set Aₙ of all even permutations of degree n is a subgroup of Sₙ of order n!/2. [20 Marks]
Q6. (a) Give the statement and proof of the fundamental theorem of homomorphism.
(b) Prove that Z/nZ ≅ Zₙ. [20 Marks]
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Q7. (a) State Fermat’s theorem and use it to find the remainder when 3⁴⁷ is divided by 23.
(b) What is a normal subgroup? Prove that a subgroup H of G is normal if and only if gHg⁻¹ = H for every g ∈ G. [20 Marks]
Q8. (a) What is a cyclic group? Show that every group of prime order is cyclic.
(b) List the generators of (Z₁₂, ⊕) and find the subgroup generated by 2̄. [20 Marks]
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Q9. (a) Show that every finite integral domain is a field, and give an example of an integral domain that is not a field.
(b) Show that the characteristic of an integral domain is either zero or a prime. [20 Marks]
Q10. (a) Give the statement and proof of Lagrange’s theorem.
(b) Let f : R → R′ be a ring homomorphism. Prove that Ker f is an ideal of R. [20 Marks]
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Exam Tips – Mathematics (Matrices and Algebra)
- Section A ke long answers ke short notes bana lo – 15 marks pakke karo.
- Section B ke derivations / numericals / diagrams ki practice karo.
- Upar ke questions ko 2 ghante me PYQ ki tarah solve karke dekho.
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FAQs
LU B.Sc 1st Semester Mathematics (Matrices and Algebra) exam me kitne questions attempt karne hote hain?
Ye 75 marks ka 2 ghante ka paper hai. Kul 4 questions attempt karne hote hain – Section A se 1 question (15 marks) aur Section B se 3 questions (20-20 marks).
Kya ye LU B.Sc Sem 1 Mathematics ka official previous year question paper (PYQ) hai?
Nahi. Ye LUUPDATE team ka banaya 2026 exam ke liye most important questions ka set hai, jo Lucknow University ke previous year papers ke pattern aur NEP syllabus par based hai.
B.Sc Sem 1 Mathematics Matrices and Algebra ke answers / solutions kahan milenge?
LUUPDATE ke Most Important Questions course (BA, B.Sc, B.Com Sem I, III & V) me har question ka pura solution milta hai – sirf ₹99 me, LUUPDATE App par.
Ye paper kis group ke liye hai – PCM ya ZBC?
Mathematics (Matrices and Algebra) LU B.Sc NEP Semester I ke PCM group ke students ke liye hai.
Disclaimer: Ye LUUPDATE team dwara taiyar kiye gaye expected important questions hain (previous year pattern par), Lucknow University ka official question paper nahi. Exam pattern aur syllabus ke liye university ka official notice zaroor dekhein.
