Subjective / Written Questions (25)
1. Critically derive and explain Group actions and Burnside theorem. / का critical derivation/explanation कीजिए Group actions and Burnside theorem।
2. Compare and evaluate Sylow theorems and p-groups. / की तुलना एवं मूल्यांकन कीजिए Sylow theorems and p-groups।
3. Analyse the assumptions and limitations of Jordan-Hölder theorem. / की assumptions एवं limitations का analysis कीजिए Jordan-Hölder theorem।
4. Solve a challenging application involving Solvable and nilpotent groups. / से संबंधित कठिन application को solve कीजिए Solvable and nilpotent groups।
5. Discuss the theoretical significance of Complex differentiability and Cauchy-Riemann equations. / का theoretical significance discuss कीजिए Complex differentiability and Cauchy-Riemann equations।
6. Critically derive and explain Cauchy integral formula. / का critical derivation/explanation कीजिए Cauchy integral formula।
7. Compare and evaluate Maximum modulus theorem. / की तुलना एवं मूल्यांकन कीजिए Maximum modulus theorem।
8. Analyse the assumptions and limitations of Laurent series and singularities. / की assumptions एवं limitations का analysis कीजिए Laurent series and singularities।
9. Solve a challenging application involving Residue theorem. / से संबंधित कठिन application को solve कीजिए Residue theorem।
10. Discuss the theoretical significance of Möbius transformations and cross ratio. / का theoretical significance discuss कीजिए Möbius transformations and cross ratio।
11. Critically derive and explain Metric spaces. / का critical derivation/explanation कीजिए Metric spaces।
12. Compare and evaluate Basis and countability axioms. / की तुलना एवं मूल्यांकन कीजिए Basis and countability axioms।
13. Analyse the assumptions and limitations of Product and quotient topology. / की assumptions एवं limitations का analysis कीजिए Product and quotient topology।
14. Solve a challenging application involving Connectedness and path connectedness. / से संबंधित कठिन application को solve कीजिए Connectedness and path connectedness।
15. Discuss the theoretical significance of Compactness and separation axioms. / का theoretical significance discuss कीजिए Compactness and separation axioms।
16. Critically derive and explain Curvature and torsion. / का critical derivation/explanation कीजिए Curvature and torsion।
17. Compare and evaluate Frenet-Serret equations. / की तुलना एवं मूल्यांकन कीजिए Frenet-Serret equations।
18. Analyse the assumptions and limitations of First fundamental form. / की assumptions एवं limitations का analysis कीजिए First fundamental form।
19. Solve a challenging application involving Second fundamental form. / से संबंधित कठिन application को solve कीजिए Second fundamental form।
20. Discuss the theoretical significance of Geodesics and Gauss curvature. / का theoretical significance discuss कीजिए Geodesics and Gauss curvature।
21. Critically derive and explain Euler equations of rigid-body motion. / का critical derivation/explanation कीजिए Euler equations of rigid-body motion।
22. Compare and evaluate Lagrange equations and constraints. / की तुलना एवं मूल्यांकन कीजिए Lagrange equations and constraints।
23. Analyse the assumptions and limitations of Small oscillations and normal modes. / की assumptions एवं limitations का analysis कीजिए Small oscillations and normal modes।
24. Solve a challenging application involving Hamiltonian mechanics. / से संबंधित कठिन application को solve कीजिए Hamiltonian mechanics।
25. Discuss the theoretical significance of Poisson brackets and Hamilton-Jacobi theory. / का theoretical significance discuss कीजिए Poisson brackets and Hamilton-Jacobi theory।