TAMIL NADU OPEN UNIVERSITY Chennai-15. B.Sc Maths - Second Year SPOT ASSIGNMENT COURSE Groups and Rings
COURSE CODE
BMS - 21
Time: 1 Hour
ADMISSION YEAR
CY - 2017 Total Marks: 25
Answer all questions. 1
State and prove Cayley’s theorem.
9 Marks
2
State and prove a necessary and sufficient condition for an ideal of a
8 Marks
commutative ring with identity to be a maximal ideal. 3
Define Ordered integral domain. State two of its properties and prove.
8 Marks
TAMIL NADU OPEN UNIVERSITY Chennai-15. B.Sc Maths - Second Year SPOT ASSIGNMENT COURSE
COURSE CODE
Statistics and Mechanics
ADMISSION YEAR
CY - 2017
BMS - 22
Time: 1 Hour
Total Marks: 25
Answer all questions. 1
Find the coefficient of rank correlation for the following data which
10 Marks
shows the heights a sample of 12 fathers and their sons. Height 65 of father Height 68 of son 2
63
67
64
68
62
70
66
68
67
69
71
66
68
65
69
66
68
65
71
67
68
70
The following are the gains in weights of rats fed on two different diets
10 Marks
D1 and D2. D1: 25, 32, 30, 34, 24, 14, 32, 24, 30, 31, 35, 25 D2: 44, 34, 22, 10, 47, 31, 40, 30, 32, 35, 18, 21, 35, 29, 22. Test if the two diets differ significantly as regards their effect on increase in weights.
3
A particle is projected at an angle 30 o with a velocity 490 m/sec. Find (i) the greatest height attained (ii) the time of flight and (iii) the horizontal range.
5 Marks
TAMIL NADU OPEN UNIVERSITY Chennai-15. B.Sc Maths - Second Year SPOT ASSIGNMENT COURSE
COURSE CODE
Classical Algebra and Numerical Methods
BMS - 23
Time: 1 Hour
ADMISSION YEAR CY- 2017 Total Marks: 25
Answer all questions. 1
Solve x4 – 8x3 + 14x2 + 8x – 15 = 0, it being given that the sum of two of
8 Marks
the roots is equal to the sum of the other two. 2
Use Newton – Raphson method to obtain a root correct to three decimal
8 Marks
places of the equation x3 + 3x2 – 3 = 0.
3
Given the differential equation =
x2 with y(0) = 0. y2 +1
Obtain y(0.25), y(0.5) and y(1.0) correct to four decimal places by Picard’s method of successive approximations.
9 Marks
