LU B.Sc Sem 5 Mathematics Analysis Important Questions 2026 | PYQ Pattern
LU B.Sc 5th Semester Mathematics (Analysis) Important Questions 2026 – Lucknow University (LU) aur affiliated colleges ke B.Sc NEP Semester V (PCM group) students ke liye Mathematics – Analysis (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 5 Mathematics (LU NEP 2026)
| University | University of Lucknow (LU) + affiliated colleges |
| Course | B.Sc. V Semester (NEP) – PCM |
| Paper | Mathematics – Analysis (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) What is a metric space? If (X, d) is a metric space, prove that d₁(x, y) = d(x, y)/(1 + d(x, y)) is also a metric.
(b) Prove that a Cauchy sequence having a convergent subsequence is convergent. [15 Marks]
Q2. (a) Let fₙ(x) = nx/(1 + n²x²), 0 ≤ x ≤ 1. Show that ⟨fₙ⟩ does not converge uniformly and find the point of non-uniform convergence.
(b) Prove that u(x, y) = ½ log(x² + y²) is harmonic and find its harmonic conjugate. [15 Marks]
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Section B – Important Questions (20 Marks)
Note: Section B se koi teen questions attempt karne hain.
Q3. (a) Prove that A is closed if and only if it contains all its limit points.
(b) Give the statement and proof of Cantor’s intersection theorem. [20 Marks]
Q4. (a) State the Weierstrass M-test and examine the uniform convergence of 1 + e⁻ˣ cos x + e⁻²ˣ cos 2x + … on [α, ∞), α > 0.
(b) Prove that the uniform limit of continuous functions on [a, b] is continuous. [20 Marks]
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Q5. Give the statement and proof of the Cauchy-Riemann equations and obtain their polar form. Show that f(z) = |z|² is differentiable only at the origin. [20 Marks]
Q6. (a) Give the statement and proof of Liouville’s theorem.
(b) Evaluate ∮_C e^(2z)/(z + 4)³ dz, C: |z| = 3, and ∮_C sin 3z/(z + π/2) dz, C: |z| = 5. [20 Marks]
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Q7. (a) Find the Laurent series of f(z) = 1/((z + 1)(z + 3)) in |z| < 1 and 0 < |z + 1| < 2.
(b) Classify the singularities of (z − sin z)/z³ at z = 0 and e^(2z)/(z − 1)² at z = 1. [20 Marks]
Q8. (a) Give the statement and proof of Cauchy’s residue theorem.
(b) Find the poles of f(z) = z²/((z − 1)²(z + 2)) and the residue at each. [20 Marks]
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Q9. Using contour integration, prove that ∫₀^2π cos 2θ/(5 + 4 cos θ) dθ = π/6 and ∫₀^∞ cos mx/(a² + x²) dx = (π/2a) e^(−ma), m ≥ 0. [20 Marks]
Q10. (a) Find the fixed points and normal form of f(z) = (3iz + 1)/(z + 1).
(b) Find the bilinear transformation sending z₁ = 2, z₂ = i, z₃ = −2 to ω₁ = 1, ω₂ = i, ω₃ = −1. [20 Marks]
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Exam Tips – Mathematics (Analysis)
- 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 5th Semester Mathematics (Analysis) 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 5 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 5 Mathematics Analysis 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 (Analysis) LU B.Sc NEP Semester V 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.
