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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI 600 034
B.Sc.DEGREE EXAMINATION COMPUTER SCIENCE
FIRSTSEMESTER APRIL 2018
17/16UCA1AL01- MATHEMATICS FOR COMPUTER SCIENCE
Date: 30-04-2018 Dept. No. Max. 100 Marks
Time: 01:00-04:00
PART-A
Answer ALL the questions 10X2=20
1. What is the difference between symmetric and skew symmetric of a matrix?
2. Write the Characteristic equation of
3. Define populations and samples.
4. Match each statement in the left-hand column with the correct data set
from the right-hand column.
Sample mode is 9 10, 13, 14
Sample mean is 9 15
(iii). Sample median is 9 12, 12, 18
5. What is complete graph.
6. Give an example for cut vertices?
7. What is Eulerian graph?
8.Define Hamiltonian cycle.
9. Write the formula for Newton- Rapson method to calculate root.
10. Write the Newton's forward difference formula.
PART-B
Answer ALL the questions 5X8=40
11a) Examine the following equations are consistent or not if so find any one value.
4x-y-2z=7
OR
Find the rank of the matrix
12 Which data value is the sample 90th percentile when the sample size is
16, and 100?
OR
The following data give the yearly numbers of law enforcement officers killed in the
United states over 10 years: 164, 165, 157, 164, 152, 147, 148, 131, 147, 155
Find the sample variance of the number killed in these years.
13 Define the following with an example Walk (ii)Path Trail Bridges
OR
b)i)Prove the following statement. A closed walk of odd length contains a cycle.
ii) Prove the following statement. If G is not connected bar is connected.
2
14 What is Tree? Draw all trees with 4 and 5 vertices.
OR
i)Define planar and non-planar.
ii) Prove that K5 and K3,3 are non-planar.
15a) Find the first approximation of the real root of equation by
regulaFalsi method correct to three places of decimal.
OR
Evaluate using Simpson's 1/3rd rule Simpson's 3/8th rule.
PART-C
Answer any TWO 2X20=40
16 Verify Cayley Hamilton theorem A=Hence find its inverse
Compute the sample correlation coefficient of the data of Table which relates a
Person's resting pulse rate to the number of years of school completed.
Table Pulse Rate and Years of School Completed
Person
1 2 3 4 5 6 7 8 9 10
Years of school 12 16 13 18 19 12 18 19 12 14
Pulse rate 73 67 74 63 73 84 60 62 76 71
17 Draw the following graphs.
Simple graph with 5 vertices. K5 . Regular graph with 5 vertices.
Planar graph with 5 vertices.(v) Petersen graph
Let G be a graph .prove that the following statements are equivalent.
G is a tree
Every points of G are joined by a unique path.
G is connected and
G is acyclic and p=q+1.
18. If 32.4, 26.1, y(30)=23.2,y(35)=20.5 find
using Newton's forward interpolation formula and
Find the Eigen values and Eigen vectors of
List some of the properties of the sample correlation coefficient.