Tamil Nadu Open University (TNOU) 2009-2nd Year B.Sc Mathematics " STATISTICS AND MECHANICS " UG 479 BMS 22 - Question Paper
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UG-479 BMS-22B.Sc. DEGREE EXAMINATION -JANUARY 2009.
Second Year Mathematics STATISTICS AND MECHANICS
Time : 3 hours Maximum marks : 75
PART A (5 x 5 = 25 marks)
Answer any FIVE questions from the following.
1. Calculate mean deviation from the median :
Class interval : 20-25 25-30 30-40 40-45 45-50 Frequency : 6 12 17 30 10
Class interval : 50-55 55-60 60-70 70-80 Frequency : 10 8 5 2
2. Fit a straight line trend by the method of least squares
Year 1996 1997 1998 1999 2000
Sales (000) 4 6 7 8 10
3. The regression line of Y on X and X on Y are given by
Y = 11.64 - 0.5 I andl = 19.13 - 0.87 Y
Find mean of X and Y and r.
4. Find whether A and B are independent in the following case :
(AB) = 256, (aB) =768, (A/3) = 48, (a p) = 144 .
5. The following are the group index numbers and the group weights of an average working class familys budget. Construct the cost of living index number.
Group : Food Fuel Clothing Rent Others Index no. 352 220 230 160 190 Weight : 48 10 8 12 15
6. Suppose x is a random variable with probability mass function
x2 +1
P(X) = Z x = o 12, ..., 7 148
= 0 for x > 7.
Compute E (2x2 + 3x).
7. A random sample of 600 bulbs was drawn from a large consignment and 74 was found to be defective. Find the limits of percentage of defective bulbs in the consignment.
8. Find the angle of projection when the range on a horizontal plane is 4a/3 times the greatest height attained.
Answer any FIVE questions from the following.
9. Calculate Karl Pearsons coefficient of skewness for the following data :
Years : 0-5 5-10 10-15 15-20 20-25 25-30 30-35
Frequency : 449 705 507 281 109 53 11
10. Find the Karl Pearsons coefficient of correlation between the variables X and Y.
X : 71 68 66 67 70 71 70 73 72 65 66
Y : 69 64 65 63 65 62 65 64 66 59 62
11. Find the function Ux from the data below and
hence estimate the value for x = 2 .
x: 0 14 5 U : 8 11 78 123
|
12. Compute (a) Laspeyres |
(c) s e h c s a a P e | |||
|
index numbers Item |
Price |
Quantity | ||
|
Base |
Current Base |
Current | ||
|
A |
6 |
10 |
50 |
50 |
|
B |
2 |
2 |
100 |
120 |
|
C |
4 |
6 |
60 |
60 |
|
D |
10 |
12 |
30 |
25 |
13. Fit a Poisson distribution to the following data : x : 0 1 2 3 4 5 f: 142 156 69 27 5 1
14. The following data related to Production in kg of three varieties A, B and C of paddy sown in 12 plots.
A 14 16 18 - -B 14 13 15 22 -C 18 16 19 19 20
Is there any significance in the production of the three varieties?
15. Two smooth spheres of masses m1 and m2 and coefficient of restitution e, collide obliquely with velocities u, U whose directions are inclined to the common normal at angles a], a2. Find the velocities of the spheres after impact. Also find the impulse of the blow on the sphere of mass m .
16. Obtain the differential equation of a central orbit in p - r coordinates.
4 UG-479
ws8
UG-479 BMS-22B.Sc. DEGREE EXAMINATION -JANUARY 2009.
Second Year Mathematics STATISTICS AND MECHANICS
Time : 3 hours Maximum marks : 75
PART A (5 x 5 = 25 marks)
Answer any FIVE questions from the following.
1. Calculate mean deviation from the median :
Class interval : 20-25 25-30 30-40 40-45 45-50 Frequency : 6 12 17 30 10
Class interval : 50-55 55-60 60-70 70-80 Frequency : 10 8 5 2
2. Fit a straight line trend by the method of least squares
Year 1996 1997 1998 1999 2000
Sales (000) 4 6 7 8 10
3. The regression line of Y on X and X on Y are given by
Y = 11.64 - 0.5 I andl = 19.13 - 0.87 Y
Find mean of X and Y and r.
4. Find whether A and B are independent in the following case :
(AB) = 256, (aB) =768, (A/3) = 48, (a p) = 144 .
5. The following are the group index numbers and the group weights of an average working class familys budget. Construct the cost of living index number.
Group : Food Fuel Clothing Rent Others Index no. 352 220 230 160 190 Weight : 48 10 8 12 15
6. Suppose x is a random variable with probability mass function
x2 +1
P(X) = Z x = o 12, ..., 7 148
= 0 for x > 7.
Compute E (2x2 + 3x).
7. A random sample of 600 bulbs was drawn from a large consignment and 74 was found to be defective. Find the limits of percentage of defective bulbs in the consignment.
8. Find the angle of projection when the range on a horizontal plane is 4a/3 times the greatest height attained.
Answer any FIVE questions from the following.
9. Calculate Karl Pearsons coefficient of skewness for the following data :
Years : 0-5 5-10 10-15 15-20 20-25 25-30 30-35
Frequency : 449 705 507 281 109 53 11
10. Find the Karl Pearsons coefficient of correlation between the variables X and Y.
X : 71 68 66 67 70 71 70 73 72 65 66
Y : 69 64 65 63 65 62 65 64 66 59 62
11. Find the function Ux from the data below and
hence estimate the value for x = 2 .
x: 0 14 5 U : 8 11 78 123
|
12. Compute (a) Laspeyres |
(c) s e h c s a a P e | |||
|
index numbers Item |
Price |
Quantity | ||
|
Base |
Current Base |
Current | ||
|
A |
6 |
10 |
50 |
50 |
|
B |
2 |
2 |
100 |
120 |
|
C |
4 |
6 |
60 |
60 |
|
D |
10 |
12 |
30 |
25 |
13. Fit a Poisson distribution to the following data : x : 0 1 2 3 4 5 f: 142 156 69 27 5 1
14. The following data related to Production in kg of three varieties A, B and C of paddy sown in 12 plots.
A 14 16 18 - -B 14 13 15 22 -C 18 16 19 19 20
Is there any significance in the production of the three varieties?
15. Two smooth spheres of masses m1 and m2 and coefficient of restitution e, collide obliquely with velocities u, U whose directions are inclined to the common normal at angles a], a2. Find the velocities of the spheres after impact. Also find the impulse of the blow on the sphere of mass m .
16. Obtain the differential equation of a central orbit in p - r coordinates.
4 UG-479
|
Attachment: |
| Earning: Approval pending. |
