Subjective / Written Questions (25)
1. Critically derive and explain Eisenstein criterion and field extensions. / का critical derivation/explanation कीजिए Eisenstein criterion and field extensions।
2. Compare and evaluate Splitting fields and separability. / की तुलना एवं मूल्यांकन कीजिए Splitting fields and separability।
3. Analyse the assumptions and limitations of Galois correspondence. / की assumptions एवं limitations का analysis कीजिए Galois correspondence।
4. Solve a challenging application involving Finite fields. / से संबंधित कठिन application को solve कीजिए Finite fields।
5. Discuss the theoretical significance of Cyclotomic extensions. / का theoretical significance discuss कीजिए Cyclotomic extensions।
6. Critically derive and explain Banach spaces. / का critical derivation/explanation कीजिए Banach spaces।
7. Compare and evaluate Hahn-Banach theorem. / की तुलना एवं मूल्यांकन कीजिए Hahn-Banach theorem।
8. Analyse the assumptions and limitations of Open mapping and closed graph theorems. / की assumptions एवं limitations का analysis कीजिए Open mapping and closed graph theorems।
9. Solve a challenging application involving Weak and weak-star topology. / से संबंधित कठिन application को solve कीजिए Weak and weak-star topology।
10. Discuss the theoretical significance of Hilbert spaces and Riesz representation. / का theoretical significance discuss कीजिए Hilbert spaces and Riesz representation।
11. Critically derive and explain Spectral theorem. / का critical derivation/explanation कीजिए Spectral theorem।
12. Compare and evaluate ODE existence and uniqueness. / की तुलना एवं मूल्यांकन कीजिए ODE existence and uniqueness।
13. Analyse the assumptions and limitations of Linear systems and stability. / की assumptions एवं limitations का analysis कीजिए Linear systems and stability।
14. Solve a challenging application involving Boundary-value problems. / से संबंधित कठिन application को solve कीजिए Boundary-value problems।
15. Discuss the theoretical significance of Phase-plane analysis. / का theoretical significance discuss कीजिए Phase-plane analysis।
16. Critically derive and explain Continuity equation. / का critical derivation/explanation कीजिए Continuity equation।
17. Compare and evaluate Euler equations of fluid flow. / की तुलना एवं मूल्यांकन कीजिए Euler equations of fluid flow।
18. Analyse the assumptions and limitations of Navier-Stokes equations. / की assumptions एवं limitations का analysis कीजिए Navier-Stokes equations।
19. Solve a challenging application involving Vorticity and circulation. / से संबंधित कठिन application को solve कीजिए Vorticity and circulation।
20. Discuss the theoretical significance of Boundary layers. / का theoretical significance discuss कीजिए Boundary layers।
21. Critically derive and explain Riemannian metrics. / का critical derivation/explanation कीजिए Riemannian metrics।
22. Compare and evaluate Riemann curvature tensor. / की तुलना एवं मूल्यांकन कीजिए Riemann curvature tensor।
23. Analyse the assumptions and limitations of Fundamental group and homotopy. / की assumptions एवं limitations का analysis कीजिए Fundamental group and homotopy।
24. Solve a challenging application involving Riemannian geometry. / से संबंधित कठिन application को solve कीजिए Riemannian geometry।
25. Discuss the theoretical significance of Algebraic topology. / का theoretical significance discuss कीजिए Algebraic topology।