Section C |
MENSURATION (25 marks) |
Answer Question No.8 (compulsory – 5 marks) and any two (10 x 2 = 20 marks) from the rest. |
|
8. |
(a) |
The perimeter of a rectangle is 25.5 m. Its length is 9.5 m. Find its area. |
2 |
|
(b) |
The mid points of the sides of a triabgle are (1, 4), (4, 8) and (5, 6). Find the co-ordinates of the vertices of the triangle. |
3 |
9. |
(a) |
A cubical metal box is open at the top and the cost of painting its inside at Rs. 1.60 per square cm is Rs. 392. The box is wholly filled with a liquid. Find the volume of the liquid. |
5 |
|
(b) |
In the parabola 4(y - 1)2 = − 7(x − 3) find (i) latus rectum, (ii) co-ordinates of focus and vertex. |
5 |
10. |
(a) |
A bicycle wheel makes 5000 revolutions in moving 11 km. Find the diameter of the wheel. |
5 |
|
(b) |
In a parallelogram ABCD slope of AB = −2, slope of BC = 3/5. Find the (i) gradient of AD; (ii) gradient of altitude to AD and (iii) gradient of height of the triangle ABC. |
5 |
11. |
(a) |
Two hexagonal coins of the same metal have weights in the ratio 3:2. If the sides are in the ratio 5:2, find the ratio of their thickness. |
5 |
|
(b) |
(i) | The radius of the circle x2 + y2 − 2x + 3y + λ = 0 is 2½. Find the value of λ. |
|
2 |
|
(ii) | Find the eccentricity of the ellipse whose major axis is double the minor axis. |
|
3 |
Section D |
ELEMENTARY STATISTICS (30 marks) |
Answer Question No. 12 (compulsory – 6 marks) and any two (12 x 2 = 24 marks) from the rest. |
|
12. |
(a) |
Find the harmonic mean of |
|
, |
|
, |
|
, |
|
and 1. |
| 2 |
|
(b) |
Examine the validity of the statement: If each observation in a series is increased by 10, then their A.M. changes but not their standard deviation. |
2 |
|
(c) |
The mean, middian and the coefficient of variation of 100 items are found to be 90, 84 and 60. Find the coefficient of skewness of the distribution. |
2 |
13. |
The distribution of weight of the students of a school is given below: |
4 |
|
Weight (in lbs.) | 100-105 | 105-110 | 110-115 | 115-120 | 120-125 |
No. of students | 105 | 210 | 220 | 300 | 315 |
| |
|
|
(a) | Draw a histogram. |
(b) | Draw both "less than type" and "more than type" OGIVES" and hence estimate the median. |
(c) | Compute the mean. | |
|
14. |
(a) |
Arithmetic mean of the frequency distribution is Rs. 56.47: |
12 |
|
Daily wages in Rs. | 45 | 50 | 55 | 60 | 65 | 70 | 75 | Total |
Frequency | 5 | 48 | — | 30 | — | 8 | 6 | 150 |
| |
|
|
(a) | Find the missing frequencies. |
(b) | Find the mode. |
(c) | Find the standard deviation. |
(d) | Find the coefficient of skewness. | |
|
15. |
(a) |
Following is the statement of marks obtained by two students A and B in 10 examination papers: |
8 |
|
Paper | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Marks scored by A | 44 | 80 | 76 | 48 | 52 | 72 | 68 | 56 | 60 | 54 |
Marks scored by B | 48 | 75 | 54 | 60 | 63 | 69 | 72 | 51 | 57 | 66 |
| |
|
|
If the consistency of performance is the criterion for awarding a prize, find the prize winner among A and B. |
|
|
(b) |
For a fistribution Bowley's coefficient of skewness is − 0.36, Q1 = 8.6 and median = 12.3. Find the coefficient of quartile deviation. |
4 |
__________ |