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Find the area of a right-angled triangle, the radius of whose circumcircle measure 8cm and the altitude drawn to the hypotenuse measures 6cm.
Find the mean, marks per stufdent, using assumed-mean method:
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Marks
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$0-10$
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$10-20$
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$20-30$
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$30-40$
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$40-50$
|
$50-60$
|
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Number of students
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$12$
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$18$
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$27$
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$20$
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$17$
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$6$
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In a hospital, the ages of diabetic patients were recorded as follows. Find the median age.
| Age (in years) | 0-15 | 15-30 | 30-45 | 45-60 | 60-75 |
| Number of patients | 5 | 20 | 40 | 50 | 25 |
Prove that the point A(2, 4), B(2, 6) and $\text{C}(2+\sqrt{3},5)$ are the vertices of an equilateral triangle.
→Following is the cumulative frequency distribution of employees in a certain office according to age.
Find the median age of employee.
| Age | less than 20 | less than 25 | less than 30 | less than 35 | less than 40 | less than 45 | less than 50 | less than 55 | less than 60 |
| Cumulative frequency | 0 | 2 | 8 | 22 | 51 | 88 | 105 | 108 | 110 |
Show that the points A(1, -2), B(3, 6), C(5, 10) and D(3, 2) are the vertices of a parallelogram.
Find the condition that the zeros of the polynomial $f(x) = x^3 + 3px^2 + 3qx + r$ may be in A.P.
→Solve the following equations by using the method of completing the square:
$\text{x}^2-\big(\sqrt2+1\big)\text{x}+\sqrt2=0$
→$\text{x}^2-\big(\sqrt2+1\big)\text{x}+\sqrt2=0$
From a solid cylinder of height $14\ cm$ and base diameter $7\cm,$ two equal conical holes each of radius 2.1cm and height 4cm are cut: off. Find the volume of the remaining solid.
→A drinking glass is in the shape of a frustum of a cone of height $14\ cm.$ The diameters of its two circular ends are 16cm and $12\ cm.$ Find the capacity of the glass.
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