Question
Show that points $\mathrm{A}(-3,2), \mathrm{B}(1,-2)$ and $\mathrm{C}(9,-10)$ are collinear.
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If the points $(-2, -1), (1, 0), (x, 3)$ and $(1, y)$ form a parallelogram, find the values of $x$ and $y.$
→An oil funnel made of tin sheet consists of a cylindrical portion 10 cm long attached to a frustum of a cone. If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and the diameter of the top of funnel is 18 cm. Find the area of tin required to make the funnel.
$x+3 y=7 ; 2 x+y=-1$
→The following is the distribution of height of students of a certain class in a certain city:
Find the median height.
|
Height (in cms)
|
160-162
|
163-165
|
166-168
|
16-171
|
172-174
|
|
No. of students
|
15
|
118
|
142
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127
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18
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An incomplete distribution is given as follows:
You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula, fill up the missing frequencies.
|
Variable
|
0-10
|
10-20
|
20-30
|
30-40
|
40-50
|
50-60
|
60-70
|
|
Frequency
|
10
|
20
|
?
|
40
|
?
|
25
|
15
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A wizard having powers of mystic in candations and magical medicines seeing a cock, fight going on, spoke privately to both the owners of cocks. To one he said, if your bird wins, than you give me your stake-money, but if you do not win, I shall give you two third of that'. Going to the other, he promised in the same way to give three fourths. From both of them his gain would be only 12 gold coins. Find the the stake of money each of the cock-owners have.
The mean of the following frequency distribution is 50. Find the value of f :
| Class interval | 10 - 20 | 20 - 40 | 40 - 60 | 60 - 80 | 80 - 100 |
| Frequency | 14 | f | 32 | 24 | 19 |
Side of eqilateral triangle $PQR$ is $8\ cm$ then find the area of triangle whose side is half of side of triangle $PQR$
→Prove the following identities:
$\frac{\tan\theta}{\big(1+\tan^2\theta\big)}+\frac{\cot\theta}{\big(1+\cot^2\theta\big)}=\sin\theta\cos\theta$
→$\frac{\tan\theta}{\big(1+\tan^2\theta\big)}+\frac{\cot\theta}{\big(1+\cot^2\theta\big)}=\sin\theta\cos\theta$
Given below is the distribution of total household expenditure of 200 manual workers in a city:
Find the expenditure done by maximum number of manual workers.
| Expenditure (in Rs) | No. of manual workers |
| 1000-1500 | 24 |
| 1500-2000 | 40 |
| 2000-2500 | 31 |
| 2500-3000 | 28 |
| 3000-3500 | 32 |
| 3500-4000 | 23 |
| 4000-4500 | 17 |
| 4500-5000 | 5 |