Section C MENSURATION (30 marks) |
Answer Question No.8 (compulsory 10 marks) and any two (10 x 2 = 20 marks) from the rest. |
8. |
Answer any five of the following:
(a) | What is the area of the equilateral triangle whose sides are 8cm long? |
(b) | The circumference of a wheel is 66m. Find its diameter? |
(c) | How much fencing will be required to fence a square field of 441 square meter? |
(d) | A right pyramid stands on a square base of side 16cm and has height 15 cm. Find the volume of the pyramid. |
(e) | Find the point which divides the joining of the points (3,5) and (6,8) by a straight line in the ratio 2:1 internally. |
(f) | Find the equation of the circle whose center is (3,7) and radius is 5 units. |
(g) | Find the equation of the straight line which passes through the points (3,4) and making equal intercepts on the two axes. |
(h) | Find the vertex and the length of latus rectum of the parabola (y + 3)2 = 2 (x +2). |
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9. |
(a) |
A number of circular pieces of 0.25 cm radius is to be cut from a metal sheet of dimension 11cm by 2cm. Find the possible number of such pieces. |
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(b) |
Find vertex, axis, focus and length of the latus rectum of the curve x2 6x 3y = 3. |
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10. |
(a) |
A (-5,3) and B (2,4) are two fixed points. If a point P moves in the (x - y) plane such that PA : PB = 3:2. Find the equation to the locus of p. |
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(b) |
A hollow cylinder of iron with height 32cm, internal and external radii 4cm and 5cm respectively, is melted to form a solid sphere. Find the radius of the sphere. |
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11. |
(a) |
Find the equation of the straight line passing through (2, 3) and is perpendicular to 3x 5y + 7 = 0. |
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(b) |
The major and minor axes of an ellipse are the x and y axes respectively. Its eccentricity is 1/√2 and the length of the latus rectum is 3 units. Find the equation of the ellipse. |
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Section D ELEMENTARY STATISTICS (30 marks) |
Answer Question No.12 (compulsory 10 marks) and any two (10 x 2 = 20 marks) from the rest. |
12. |
Answer any five of the following:
(a) | Find the median of the 10 observations : 9, 4, 6, 2, 3, 4, 4, 6, 8, 7. |
(b) | If the relation between two variables x and y be 2x + 5y = 24 and mode of y be 4, find the mode of x. |
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(c) |
Find the harmonic mean of |
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| , |
| , .......... |
| , occuring with frequencies 1, 2, 3, ........ |
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n respectively. |
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(d) | For 10 values x1, x2, --------- x10 of a variable x, |
10 Σ i=1 |
xi = 110 and |
10 Σ i=1 |
(xi − 5)2 = 1000, find variance |
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of x. |
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(e) | If the relation between two variables x and y be 2x y + 3 =0 and range of x be 10, then find the range of y. |
(f) | The mean of 10 observations was found to be 20. Later one observation 24 was wrongly noted as 34. Find the correct mean. |
(g) | Runs made by two groups G1 and G2 of cricketers have means 50 and 40 and variances 49 and 36 respectively. Find which group is more consistent in scoring runs |
(h) | Calculate which of the following two distributions is more skewed?
(i) mean = 22, mode = 20, s.d. = 2, (ii) mean = 24, mode = 18, s.d. = 3 |
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13. |
(a) |
The expenditure during a year in a state is shown as below: |
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Particulars | Amount (in crores) |
Industries Irrigation Agriculture Transport & Roads Education |
100.00 92.50 127.50 92.50 68.00 |
Draw the pie diagram. |
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(b) |
The variance of a series of numbers 2, 3, 11 and x is 12¼. Find the values of x. |
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14. |
(a) |
Draw a histogram to represent the following distributions: |
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Wages/hour (in Rs) No. of workers |
: : |
5 10 10 |
10 15 25 |
15 20 30 |
20 25 20 |
25 30 15 |
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(b) |
Find the mean deviation about the mean of the following series: |
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X Frequency: |
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10 3 |
11 12 |
12 18 |
13 12 |
14 3 |
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15. |
(a) |
Calculate the median of the following frequency distribution: |
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Marks No. of students |
: : |
1-20 3 |
21-40 5 |
41-60 9 |
61-80 3 |
81-100 2 |
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(b) |
The mean and standard deviation of the marks obtained by the groups of the students consisting of 50 each are given below: |
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Calculate the mean and standard deviation of the marks obtained by all 100 students. |
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