P.G Mathematics Question Paper

Loyola College P.G. Physics Nov 2006 Energy Physics Question Paper PDF Download

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                        LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

P.G. DEGREE EXAMINATION – COMMON PAPER

AC 21

THIRD SEMESTER – NOV 2006

PH 3925 – ENERGY PHYSICS

 

 

Date & Time : 08-11-2006/9.00-12.00   Dept. No.                                                       Max. : 100 Marks

 

 

 

PART – A

Answer ALL questions.                                                                 (10 x 2 = 20 Marks)

  1. Write a short note on natural gas as an energy source.
  2. How is nuclear power realized?
  3. Solar energy is the future source – Why?
  4. What are the advantages of flat-plate collectors for solar radiation?
  5. How does photosynthesis take place?
  6. How is energy consumption related to the prosperity of a country?
  7. Describe the principle of energy storage system in lead acid battery.
  8. What are the energy options for the developing countries?
  9. Discuss the phenomenon of global warming.
  10. How is hydrogen used as a fuel?

PART – B

Answer any FOUR questions.                                                   (4 x 7.5 = 30 Marks)

  1. Discuss India’s position with regard to fossil fuels.
  2. a. Describe any design of solar cooker. (5)
  3. What are the merits and demerits of solar cookers? (2.5)
  4. a. Discuss the methods for obtaining energy from biomass. (4)
  5. What are the advantages and limitations of biomass energy sources? (3.5)
  6. a. Enumerate the patterns of energy consumption. (3)
  7. Discuss the world energy future. (4.5)
  8. Discuss the possibilities of nuclear energy for peaceful purposes.

PART – C

Answer any FOUR questions.                                                   (4 x 12.5 = 50 Marks)

  1. a. Discuss the sources and prospects of renewable energy sources.             (8)
  2. Enumerate the advantages and disadvantages of renewable energy. (4.5)
  3. a. What are the components of photo-voltaics? Describe how a basic photovoltaic system is

used for power generation.                                                                        (2+4.5)

  1. Enumerate the applications of solar photo-voltaic systems. (3)
  2. What are the advantages of photo-voltaic solar energy conversion? (p.30). (3)
  3. a. What is geothermal energy? Describe how energy is extracted from a geothermal field.                                                                                                             (2.5+6)
  4. Write a note on the geothermal sources.                                                     (4)
  5. a. What is the principle of Ocean Thermal Energy Conversion?                    (4)
  6. How is electricity produced from the ocean?                                             (6)
  7. What are the merits and demerits in energy conversion from the ocean?   (2.5)
  8. a. What is nuclear fission? Discuss the products of fission. (3+4.5)
  9. Describe the process of controlled chain reaction of nuclear energy?       (5)

 

 

 

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Loyola College P.G. Mathematics Nov 2008 Graph Theory Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS

 

AB 22

 

FIFTH SEMESTER – November 2008

MT 5400 – GRAPH THEORY

 

 

 

Date : 12-11-08                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART- A

                                                                                                                                                                                 

Answer ALL the questions. Each question carries 2 marks.                                (10 x 2 = 20 marks)

 

  1. Show that every cubic graph has an even number of vertices.
  2. Let G = (V, E) be a (p, q) graph. Let and . Find the number of vertices and edges in G – v and G – e.
  3. Define a walk and a path.
  4. What is a connected graph?
  5. Give an example of a disconnected graph with 4 components.
  6. Draw all non-isomorphic trees on 6 vertices.
  7. Define an Eulerian trail and a Hamiltonian cycle.
  8. What is a cut edge? Give an example.
  9. Determine the chromatic number of Kn.
  10. Define a planar graph and give an example of a non-planar graph.

 

 

PART –  B

 

Answer any FIVE questions. Each question carries EIGHT marks.                   (5 x 8 = 40 marks)

 

  1. (a). Show that in any group of two or more people there are always two with exactly

the same number of friends inside the group.

(b). Let G be a (p, q)-graph all of whose vertices have degree k or k + 1. If G has t

vertices of degree k then show that t = p(k+1)-2q.                                                           (4+4)

 

  1. Let G1 be a (p1, q1)-graph and G2 a (p2, q2)-graph. Show that G1 + G2 is a (p1 + p2, q1 + q2 + p1p2) – graph and G1 x G2 is a (p1 p2, q1p2 + q2p1) – graph.

 

  1. (a).Prove that any self – complementary graph has 4n or 4n+1 vertices.

(b).Prove that a graph with p vertices and  is connected.                                       (4+4)

  1. (a). Prove that a closed walk of odd length contains a cycle.

(b). Find the composition of the following graphs.

 

(4+4)

 

 

 

 

 

  1. (a). Show that if G is disconnected then GC is connected.

(b). Determine the centre of the following graph.

(4+4)

  1. Let v be a vertex of a connected graph. Then prove that the following statements are equivalent:
    1. v is a cut-point of G.
    2. There exists a partition of V – {v} into subsets U and W such that for each

uU and  wW, the point v is on every (u, w) – path.

  1. There exist two points u and w distinct from v such that v is on every (u, w)-

path.

 

  1. Let G be a connected plane graph with V, E and F as the sets of vertices, edges and faces respectively. Then prove that | V | – | E | + | F | = 2.

 

  1. State and prove the five-colour theorem.

 

PART – C

 

Answer any TWO questions. Each question carries 20 marks.                            (2 x 20 = 40 marks)

 

  1. (a). Prove that the maximum number of edges among all graphs with p vertices with no

triangles is [p2 / 4], where [x] denotes the greatest integer not exceeding the real number x.

(b). Show that an edge e of a graph G is a cut edge if and only if it is not contained in any cycle

of G.                                                                                                                                (15+5)

 

  1. (a). Prove that a graph G with at least two points is bipartite if and only if all its cycles

are of even length.

(b). Let G be graph with with p ≥ 3 and. Then prove that G is Hamiltonian.                      (10+10)

  1. (a). If G is Hamiltonian, prove that for every non-empty proper subset S of V, the

number of components of G \ S , namely, ω(G \ S) ≤ | S |.

 

(b). Prove that the following statements are equivalent for a connected graph G.

  1. G is Eulerian.
  2. Every vertex of G has even degree.
  3. The set of edges of G can be partitioned into cycles.                        (5+15)

 

  1. Let G be a (p, q)-graph. Prove that the following statements are equivalent.
  2. G is a tree.
  3. Any two vertices of G are joined by a unique path.
  4. G is connected and p = q + 1.
  5. G is acyclic and p = q + 1.

(20)

 

 

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