
	Trending ▼ ICSE CBSE 10th ISC CBSE 12th CTET GATE UGC NET Vestibulares ResFinder

Pune University - SY BSc (Sem - II) MATHEMATICS - II (B), April 2010

4 pages, 22 questions, 0 questions with responses, 0 total responses,

	pune_sci	+Fave Message
	Profile Timeline Uploads Q & A

Home > pune_sci >

Instantly get Model Answers to questions on this ResPaper. Try now!
NEW ResPaper Exclusive!

Formatting page ...

Total No. of Questions : 4] [Total No. of Pages : 4 P480 [3717]-202 S.Y. B.Sc. MATHEMATICS Paper - II (B) : Discrete Mathematics (Sem. - II) (New Course) Time : 2 Hours] Instructions : [Max. Marks : 40 1) Figures to the right indicate full marks. 2) Use of single memory, non-programmable scientific calculator is allowed. Q1) Attempt each of the following: [10] a) How many three letter words can be formed from letters in the set {a, b, y, z} if repeated letters are allowed? b) In how many ways can a prize winner choose three CDs from the top ten list if repeats are allowed? c) Show that if any four numbers from 1 to 6 are chosen, then two of them will add to 7. d) Which of the following is linear homogeneous recurrence relation? Why? i) an = (-2) an-1 ii) an = an-1 + 3. e) Give an example of a graph on five vertices with exactly two components. f) Tell whether the following graph has an Euler circuit. Explain. a b d c P.T.O. 3 g) Find a Hamiltonian circuit for the graph given below. h) Is a flow conserved at node 4 in the following network? Why. i) Is the following graph bipartite? Why? j) Find the chromatic polynomial for the following graph. Q2) Attempt any two of the following: a) Prove that every positive integer n > 1 can be written uniquely as s P1 1 P2 2 .... Ps , where the Pi are primes and P1< P2 < ....... < Ps. [3717]-202(Paper II B) 4 [10] -2- b) Five fair coins are tossed and results are recorded. i) How many different sequences of heads and tails are possible? ii) How many of the sequences in part (i) have exactly one head recorded. iii) How many of the sequences in part (i) have exactly three heads. c) Show that if seven points are selected in a hexagon whose sides have length 1 unit, at least two of the points must be no farther apart than 1 unit. Q3) Attempt any two of the following. [10] a) Solve the recurrence relation dn = 2dn-1 - dn-2 with initial conditions d1 = 1.5, and d2 = 3. b) Prove that if a graph G has no loops or multiple edges, then twice the number of edges is equal to the sum of the degrees of all vertices. c) Use Kruskal's algorithm to find a minimal spanning three for the following graph. Q4) Attempt any one of the following. a) i) If a graph G has more than two vertices of odd degree, then prove that there can be no Euler path in G. [3717]-202(Paper II B) 5 [10] -3- ii) Let MR be the matrix of a marriage suitability relation between five men and five women. Can each man marry a suitable women? 1 0 M R = 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 i) Let G be a bipartite graph. What is (G ) ? Explain your answer. ii) b) Find a maximum flow in the following network by using the labelling algorithm. 2 3 [3717]-202(Paper II B) 6 -4-

Formatting page ...

Additional Info : S.Y. B.Sc. Mathematics (Semister - II) : Discrete Mathematics Paper - II (B) (New Course), Pune University
Tags : pune university exam papers, university of pune question papers, pune university science, pune university courses, bsc pune university, msc pune university, pune university solved question papers, pune university model question paper, pune university paper pattern, pune university syllabus, old question papers pune university

pune_sci chat

Horizontal lines at:
Guest Horizontal lines at:
AutoRM Data:
Box geometries: