Loyola College P.G. Mathematics Nov 2006 Mathematical Social Sciences Question Paper PDF Download

November 23, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

P.G. DEGREE EXAMINATION – COMMON PAPER

AA 28

THIRD SEMESTER – NOV 2006

MT 3925 – MATHEMATICAL SOCIAL SCIENCES

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

Answer ALL Questions.

(a) Calculate the median for the following distribution.

class interval : 131-135 135-140 140-145 145-150 150-155 155-160 160-165 165-170 170-175

Frequency : 3 11 17 19 27 22 14 8 4

(or)

What is a scatter diagram? Explain its different types. (5 marks)

Find the mean , standard deviation and variance for the following :

X : 29 33 37 38 39 40 42 43 45 47 50 59 60

F : 1 1 3 4 2 3 2 2 3 1 1 1 1

(or)

(d) Ten competitors in a musical test were ranked by three judges A, B and C in the following order .

Ranks by A : 1 6 5 10 3 2 4 9 7 8

Ranks by B : 3 5 8 4 7 10 2 1 6 9

Ranks by C : 6 4 9 8 1 2 3 10 5 7

Using rank Correlation method , find which pair of judges has been nearest approach to common

likings in music. (15 marks)

(a) Define a directed graph, an undirected graph and a multigraph with examples.

(or)

(b) Explain Konigsberg Bridge problem. Is there any solution to this problem?. If not, why?

(5 marks)

(ii) Define a walk, a path and an Eulerian graph with examples. (10 + 5 marks)

(or)

(i) In a colony there are 5 families represented by F₁, F₂,..F₅. Draw a graph with edges which denote the friendship between the families with the condition that all families are friends to the other.

(ii) The following graph represents the map of a certain area where vertices represent junction and lines represent roads. Help your postman to start from a vertex (which represents the post office) and go through all the streets exactly once and return to the post office (Vertices may be repeated).

(iii) An electrical circuit board has to be prepared with the following requirements. There are 7 terminals T₁, T₂, …, T₇. Wires have to be laid between the terminals as per the table given below.

T₁ – T₅, T₇, T₄

T₂ – T₅, T₇, T₄

T₃ – T₅, T₇, T₄

T₄ – T₂, T₆, T₃, T₁

T₅ – T₁, T₂, T₃

T₆ – T₄

T₇ – T₁, T₂, T₃

Draw a graph to represent this board. As it is always good to avoid crossing of wires (which will cause short circuit), give the best possible layout of the graph.

(4 + 5 + 6 marks)

III. (a) What are the objectives of an investigation.

(or)

(b) What is sampling? State the reasons for sampling. (5 marks)

(or)

(d) Explain the subject matter of a survey. (15 marks)

(a) The manager of an oil refinery must decide on the optimum mix of two possible blending processes of which the input and output production runs are as follows:

Process Input Output

Crude A Crude B Gasoline X Gasoline Y

1 6 4 6 9

2 5 6 5 5

The maximum amounts available of crudes A and B are 250 units and 200 units respectively. Market demand shows that at least 150 units of gasoline X and 130 units of gasoline Y must be produced. The profits per production run from process 1 and process 2 are Rs.4 and Rs.5 respectively. Formulate the problem for maximizing the profit.

(or)

(b) Construct a network diagram for the activities B, C, ….Q and N satisfying the following constraints:

B<E,F; C < G,L; E,G<H; L,H<I; L<M; H<N; H<J; I,J<P; P<Q.

The notation X<Y means that the activity X must be completed before Y can begin.

(5 marks)

(c) (i) A company makes two kinds of leather belts. Belt A is a high quality belt, and belt B is of lower quality. The respective profits are Rs.4 and Rs.3 per belt. Each belt of type A requires twice as much time as a belt of type B, and if all belts were of type B, the company could make 1000 per day. The supply of leather is sufficient for only 800 belts per day. Belt A requires a fancy buckle and only 400 per day are available. There are only 700 buckles a day available for belt B. Determine the optimum product mix by graphical method.

(ii) What are the rules to be followed for the construction of a network? (10 + 5 marks)

(or)

(d) Use simplex method to solve Maximize z = 2x₁ + 4x₂ + x₃ + x₄ subject to constraints

x₁ + 2₂ + 2x₃ + 4x₄ 80, 2x₁ + 2x₃ + x₄ 60, 3x₁ + 3x₂ + x₃ + x₄ 80,

x₁0, x₂ 0, x₃ 0, x₄ 0. (15 marks)

(a) Explain the fuzzy association of the intelligent control of a traffic light.

(or)

(b) Solve the following assignment problem.

A B C D

I 1 4 6 3

II 9 7 10 9

III 4 5 11 7

IV 8 7 8 5 (5 marks)

D₁ D₂ D₃ D₄ Availability

O₁ 5 3 6 2 19

O₂ 4 7 9 1 37

O₃ 3 4 7 5 34

Demand 16 18 31 25 (15 marks)

(or)

(d) (i) Describe FAMs as mappings.

(ii) Define Fuzzy Hebb Matrix.

(iii) Construct a fuzzy Hebb matrix M given the input A = (.3 .4 .8 1) recalled fit vector B = (.2 .6 .5) upon max-min composition: A_oM = B. (5 + 4 + 6 marks)

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Loyola College M.Sc. Mathematics Nov 2008 Mathematical Social Sciences Question Paper PDF Download

November 15, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

AB 36

P.G. DEGREE EXAMINATION – COMMON PAPER

THIRD SEMESTER – November 2008

MT 3925 – MATHEMATICAL SOCIAL SCIENCES

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

Time : 9:00 – 12:00

Answer ALL Questions.

(a) Define a research problem.

(or)

What are the essential characteristics of sampling? (5 marks)

Explain briefly all the sources of hypothesis.

(or)

Explain the utilities of Social Science research. Explain the difficulties in social science research.

(15 marks)

(a) (i) Give an example of a graph which has a cut vertex but does not have a bridge.

(ii) Find G₁ + G₂ and G₁ x G₂ if G₁ = and G₂ =

(2 + 3 marks)

(or)

(b) Define (i) closed walk, (ii) trial, and (iii) path. Give examples. (5 marks)

(ii) Find adjacency matrix and incidence matrix for the following graph.

(iii) In the following graph, find x – y walk, x – y trial, x – y path and length of the x – y walk, trial and path.

(2 + 7 + 6 marks)

(or)

(d) (i) Define directed graph, indegree and outdegree of a directed graph. Give an example.

(ii) Prove that, in a graph G every x – y walk contains an x – y path.

(iii)If G contains no odd degree vertices then prove that G contains no bridges.

(2 + 7 + 6 marks)

III. (a) Calculate the mean for the following distribution.

Cost of production: 2 – 6 6 – 10 10 – 14 14 – 18 18 – 22 22 – 26 26 – 30 30 – 34

No. of Holdings : 1 9 21 47 52 36 19 3

(or)

(b) Certain crosses of pea gave 5321 yellow and 1804 green seeds. The expectation is 25 percent of green seeds on a Mendelian hypothesis. Can the divergence from the expected value have arisen from the fluctuation of simple sampling only? (5 marks)

Series A 192 288 236 229 184 260 348 291 330 243

Series B 83 87 93 109 124 126 126 101 102 108

(or)

(d) Find the mean, median and mode for the following data.

Marks 0 – 4 4 – 8 8 – 12 12 – 16 16 – 20 20 – 24 24 – 28

No. of students 10 12 18 7 5 3 2

(15 marks)

(a) Write L-formula, P-formula, L-P formula, M.E formula, Walsch Price index formula for the

construction of index numbers.

(or)

(b) Construct quantity index numbers taking 1967 as the base:

Commodity Average Price Production

1967 1968 1969 1970

A 1.00 62 65 66 90

B 1.50 138 120 110 80

C 0.25 500 540 580 800

D 2.25 10 10 10 10

(5 marks)

(or)

(d) Prepare price and quantity index numbers for 1972 with 1961 as base year from the following data by using (i) Laspeyre’s, (ii) Paasche’s, (iii) Marshall-Edgeworth, and (iv) Fisher’s method.

Article I Article II Article III Article IV

Year Price Quantity Price Quantity Price Quantity Price Quantity

1961 5.00 5 7.75 6 9.63 4 12.50 9

1972 6.50 7 8.80 10 7.75 6 12.75 9

(15 marks)

(a) Explain briefly scaling individual test items in terms of difficulty.

(or)

(b) The fifth grade norms for a reading examination are mean = 60, s.d = 10, and for an arithmetic examination mean = 26, s.d = 4. Ram scores 55 on the reading test and 24 on the arithmetic test. Compute his -scores. In which test is he better? (5 marks)

(c) (i) Five problems are solved by 15%, 34%, 50%, 62% and 80% respectively of a large unselected group. If the zero point of ability in this test is taken to be at – 3, what is the –value of each problem as measured from this point?

(ii) A test is administered on 400 pupils. It gives mean 60 and standard deviation 12. Complete the following table of equivalent raw scores.

Raw Score : 84 78 72 66 60 54 48 42 36

– score : __ __ 1 __ 0 __ __ __ __

Standard score: __ __ __ __ __ __ 40 __ __

(10 + 5 marks)

(or)

(d) (i) Given three test items 1, 2 and 3 are passed by 50%, 40% and 30% respectively of a large group, on the assumption of normality of the distribution, what percentage of this group must pass test item 4 in order for this to be as much more difficult than 3, as 2 is more difficult than 1?

(ii) Write short notes on Intelligence Quotient. (10 + 5 marks)

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