# Department of Mathematics/Viva Voce Questions

## Viva Voce Questions[edit]

# | Question | Answer | Professor | Year |
---|---|---|---|---|

1 | Time complexity of bubble sort (worst case and best case), Archimedean principle, comparing cardinality of infinite sets, and vector space solution of a matrix equation. | Simply keep your cool while answering. If they think you are not getting the answers, they will throw some additional hints for you to answer. Just keep calm, and be confident in your answers. | Chair: DK Gupta, S Choudhury, Ratna Datta, D Biswas, Gyaneshwar, J Kumar, K Ghoshal | 3rd(2017) |

2 | Fundamental questions on Linear Algebra ( Example of a vector space of particular dimension, Whether a particular equation represents a vector space or not), Proof of a theorem in Group Theory (Don't remember the exact one), Friend functions in CPP (Was made to write code on the whiteboard) | Do not try to answer if you are not sure about it. Simply accept that you are not sure and let them move on. Prof. Somesh Kumar is sure to bombard some statistical problems, so being prepared in Probability and Stats always helps in case you happen to fall into his panel. They will most probably ask your topic of interest. Make sure you have a good command of the fundamentals of the topic. | Chair : Prof Somesh Kumar, GP Rajashekhar, Bappaditya Bhowmick, Pawan Kumar | 3rd |

3 | Pawan Kumar (Algo): Write a java program which includes public, private, protected functions, objects Asis Gangoli(Mathematical Methods: Singular point, pole definition.VK Jain: open set, closed set, contact point, interior point definitions, Allu Vasudevara(Linear Algebra, Measure theory and Integration), measurable function | do not try to answer if you are not sure about it. Simply accept that you are not sure and let them move on. | Chair: Asish Gangoli, Pawan Kumar, MP Biswal, VK Jain,Allu Vasudevara | 3rd |

4 | Question regarding PDE like general form, how to identify the type of PDE, Canonical Form and Numerical Solution of the PDE. Ratna Datta asked basics of DFA, NFA and epsilon NFA and then Regular Grammar. Prof. Bhowmick will ask basic definitions and proofs he has recently done in class. Pro. Panda will ask basic of transportation problem and assignment problem mainly. | Just know the basic concept of every subject. @Juniors try to prepare short notes of every subject you study in a semester. It will help you a lot during the Viva bcoz Vivas are generally held in near the exams so you won't have much time preparing for it. | 3rd | |

5 | Definitions of a poset, lattice, and boolean algebra. Diagonalization of a matrix and conditions for it. The condition where sin and cosine transforms are applicable. | Prepare at least one subject very well. | Chair: Prof. PVSN Murthy, Ratna Datta, B Bhowmick, Geetanjali Panda | 3rd |

6 | Questions were mostly from the subjects taught in the current sem.Some definitions from Automata theory, Boundary conditions and discretization schemes from ANT, Real Analysis definitions(open sets, closed sets etc.) In the end, there was some discussion regarding my future path. | Except Ratna Dutta, pretty much everyone tried to focus on the basics. | Chair:Prof Ratna Dutta, PVSN Murthy, J Kumar, MP Biswal, VK Jain | 3rd |

7 | Two questions on fluid mech: one on checking conditions for a given flow to be valid (incompressible and irrotational) and another one on cases of continuity equation. One on whether a 3x3 matrix is diagonalizable. One on topology (base def and ex.). And last one was reg. binomial and hypergeometric distributions. | Going through basics of courses relevant to panel very quickly will suffice. | Panel: Profs GPRS, R Dutta, S Mukhopadhyay, R Gayen, PD Srivastava, Bhowmick, D Biswas, S Kumar (absent) | 5th |

8 | Markov Chain, Topology (Compactness, Interior points, Open sets) | Prof. Somnath Bhattacharya, Gnaneshwar, Nahak, T Rajshekar, V K Jain, Nitin Gupta | 5th | |

9 | What is a Poissons process, inner product space, positive definite matrix, finite vector space | Prof. Somnath Bhattacharya, Gnaneshwar, Nahak, T Rajshekar, V K Jain, Nitin Gupta | 5th | |

10 | Linear independance in a Vector space comprised of all continous function in (-1,1). Definition of Topology, Topological space, Basis, Subbase. Example of a topology. Housedorf Space. | If you are assigned to this panel, chill out and relax. Also, try and practice listening to Gnaneshwar speak because it gets extremely hard to understand him with his accent. By far the hardest part of the viva. Prepare Linear Algebra as it will be helpful in basically any panel. | Prof. Somnath Bhattacharya, Gnaneshwar, Nahak, T Rajshekar, V K Jain, Nitin Gupta | 5th |

11 | Second order PDE & ODE IVP, Compactness defition, Given a proof on topology and asked to prove! Rank Nullity Theorem and its proof in infinite space, Defitions of NFA n DFA, Difference between NFA n DFA, What is regular expression. And what are the difference between regular language and context free language. Two more questions from Functional Analysis. (Didn't remember exactly) and one proof from SFA | If GPRS is iin your panel. Do prepare PDE. If you answer a single question then there will be no further questions from other panalists. Hardly you'll have to face two more questions from other topics. And Linear Algebra will be our saviour for that day no matter which panel you'll get. | Panel: Profs GPRS, R Dutta, S Mukhopadhyay, R Gayen, PD Srivastava, Bhowmick, D Biswas, S Kumar (absent) | 5th |

12 | What is countable set?(0,1) countable or not? what is the difference between DFA & turing machine? given stream function find velocity potential. Regular expression definition. 0^n1^n -> regular expression or not. | say "Fluid Mechanics" in ur favourites if Prof. GPRS is in ur panel, he will save you. Just go through basics of Fluid Mechanics like Navier stokes, Bernoulis etc. Dont panic. Answer only if you know perfectly. Know at least the topics(names) of SFA. | Panel: Profs GPRS, R Dutta, S Mukhopadhyay, R Gayen, PD Srivastava, Bhowmick, D Biswas, S Kumar (absent) | 5th |

13 | Basic questions from Linear Algebra ( Span , Eigen values and Linear Transforamtion), ellipitical PDE and change into cannonical from (Proof was required), Statistics(pdf of Normal distribution and question related to confidence interval ), Topology (Hausdroff Space , subspaces) | Panel: Profs GPRS, R Dutta, S Mukhopadhyay, R Gayen, PD Srivastava, Bhowmick, D Biswas | 5th | |

14 | Basic Questions from Probability(Mutually Exclusive events.Definitions of pdf, mean , median, mode and their value for normal distribution).Basic idea of measure(properties like countable subadditivity and one or two problems using that property).Basic calculus questions(topics taught in Maths-I, Maths-II) | With this panel, just be optimistic that you aren't grilled on the topics of PDE.Most of the profs seemed friendly, even praising you if you answer correctly.However,M.P.Biswal's entry provided a deathly blow to the benevolence of the panel. | Panel:Profs A.Ganguly, V.Allu, M.P.Biswal, J.Kumar, K. Ghosal,R. Nanduri,S.R.Khare | 5th |

15 | Some questions from Linear Algebra (pretty straight forward provided u remember them) - Define Inner Product Space, Is a set of real numbers a vector space, (over which field and what dimension), Cauchy Schawrz Inequality, Grahm Schmidt Diagonalization Process, Heini Borel Theorem, some tough PDE questions - Method of Separation, when is it used, Characteristic curve Properties, canonical form etc.), Statistics - distributions which possess memory less property, some questions on geometric distribution, | Well frankly the panels wont be same as we had. So I would suggest make sure you strongly prepare 2-3 subjects because almost every panel would ask what u know, In my case, Prof. S bhattacharya just went out when my GV started, so i was at loss as I had prepared his subjects well. Linear Algebra is a must as we have a lot of profs. who have an expertise in that field . One thing I would want to say is - if its not a strictly roll no. wise call, try to go early as the Profs. would then ask you basic questions,. In our panel, the GV got tougher as time went by. Do not forget to prepare the Depth courses of the semester you are in. Dont say subjects which no prof in the panel knows, else they would start questioning you from random subjects then.Dont Panic, it would hardly last for 15 minutes | Chair : Prof. N Gnaneshwar, V K Jain, Nitin Gupta, T Raja Sekhar, B Adhikari.. | 5th |

16 | Questions spread over analysis - what's a real number?, Lebesgue measurable functions, Riemann integrable functions, Vector spaces examples. Crypto and Information Theory - measurement of information, GF(8) finite field, primitive polynomials. | Chair : Prof. N Gnaneshwar, V K Jain, T Raja Sekhar, B Adhikari.. | 5th | |

17 | 1. Diagonizable matrices 2.) What is the dimension of R(Q) 3.) How do you define vector spaces with infinite dimension 4.) Fourier series expansion derivation 5.) Sufficient and necessary conditions for a minima 6.) What do you mean by eigen vectors and eigen values 6.) what are the restrictions on eigen vectors 7.) explain nelder mead method 7.) Thomas Algorithm | Mention only those subjects which you have read thoroughly! Prof. Allu will ask difficult questions in Linear algebra, so when you mention the topics you have prepared for GV think at least twice before saying Linear Algebra, R Gayen and Panda are cool profs, just go through the basics of NLP and ANT. | Chair: D K G, Allu, Nahak, Somesh kumar, R Gayen, Geetanjali Panda, GPRS, Khare | 5th |

18 | 1. Diagonizable matrices 2.) What is the dimension of R(Q) 3.) How do you define vector spaces with infinite dimension 4.) Fourier series expansion derivation 5.) Sufficient and necessary conditions for a minima 6.) What do you mean by eigen vectors and eigen values 6.) what are the restrictions on eigen vectors 7.) explain nelder mead method 7.) Thomas Algorithm | Chair: K.Ghosal,R.Gayen,P.Panigrahi,R.Dutta | 5th | |

19 | Algebra: What is eigen vector, eigrn values? Eigen values of AB or BA will be same or not? prove it. Goswami sir asked about timestamp protocol and basics of dbms. Stats: Give example of one contn. and one discrete distribution function. mean, variance of such functions. What is uniform continuity whether 1/x is uni.cont. in (0.1) or not? in(1,2)? The condition other than continuity for unfiorm cont. will be ? (boundedness) | Chair: Biswal, Bhowmick, B Adhikari, Nitin Gupta, N Gnaneshwar, PVSN Murthy, Nanduri, Adrijit Goswami | 5th |