Subjective / Written Questions (25)
1. Critically derive and explain Module homomorphisms and factor modules. / का critical derivation/explanation कीजिए Module homomorphisms and factor modules।
2. Compare and evaluate Exact sequences. / की तुलना एवं मूल्यांकन कीजिए Exact sequences।
3. Analyse the assumptions and limitations of Projective modules. / की assumptions एवं limitations का analysis कीजिए Projective modules।
4. Solve a challenging application involving Injective modules. / से संबंधित कठिन application को solve कीजिए Injective modules।
5. Discuss the theoretical significance of PID and UFD. / का theoretical significance discuss कीजिए PID and UFD।
6. Critically derive and explain Chinese remainder theorem. / का critical derivation/explanation कीजिए Chinese remainder theorem।
7. Compare and evaluate Torsion modules. / की तुलना एवं मूल्यांकन कीजिए Torsion modules।
8. Analyse the assumptions and limitations of Invariant factors. / की assumptions एवं limitations का analysis कीजिए Invariant factors।
9. Solve a challenging application involving Rational canonical form. / से संबंधित कठिन application को solve कीजिए Rational canonical form।
10. Discuss the theoretical significance of Jordan canonical form. / का theoretical significance discuss कीजिए Jordan canonical form।
11. Critically derive and explain Carathéodory extension. / का critical derivation/explanation कीजिए Carathéodory extension।
12. Compare and evaluate Lebesgue outer measure. / की तुलना एवं मूल्यांकन कीजिए Lebesgue outer measure।
13. Analyse the assumptions and limitations of Measurable functions. / की assumptions एवं limitations का analysis कीजिए Measurable functions।
14. Solve a challenging application involving Lebesgue integration. / से संबंधित कठिन application को solve कीजिए Lebesgue integration।
15. Discuss the theoretical significance of Hölder and Minkowski inequalities. / का theoretical significance discuss कीजिए Hölder and Minkowski inequalities।
16. Critically derive and explain Characteristics for first-order PDE. / का critical derivation/explanation कीजिए Characteristics for first-order PDE।
17. Compare and evaluate Charpit method. / की तुलना एवं मूल्यांकन कीजिए Charpit method।
18. Analyse the assumptions and limitations of Second-order PDE canonical forms. / की assumptions एवं limitations का analysis कीजिए Second-order PDE canonical forms।
19. Solve a challenging application involving Separation of variables. / से संबंधित कठिन application को solve कीजिए Separation of variables।
20. Discuss the theoretical significance of Fredholm equations. / का theoretical significance discuss कीजिए Fredholm equations।
21. Critically derive and explain Sturm-Liouville problems. / का critical derivation/explanation कीजिए Sturm-Liouville problems।
22. Compare and evaluate Fourier series. / की तुलना एवं मूल्यांकन कीजिए Fourier series।
23. Analyse the assumptions and limitations of Fourier/Laplace transforms. / की assumptions एवं limitations का analysis कीजिए Fourier/Laplace transforms।
24. Solve a challenging application involving Euler-Lagrange equation. / से संबंधित कठिन application को solve कीजिए Euler-Lagrange equation।
25. Discuss the theoretical significance of Smooth manifolds and tangent spaces. / का theoretical significance discuss कीजिए Smooth manifolds and tangent spaces।