21.

A Group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is

(i)extremely patient

(ii) extremely kind or honest. Which of the above values you prefer more?

Sum of the areas of two squares is 400 cm2. If the difference of their perimeters is 16 cm, find the sides of the two squares.

$$\begin{gathered} \mathrm{Solve} \mathrm{that} \mathrm{following} \mathrm{for} \mathrm{x}: \\ \frac{1}{2\mathrm{a}+\mathrm{b}+2\mathrm{x}} = \frac{1}{2\mathrm{a}} + \frac{1}{\mathrm{b}} + \frac{1}{2\mathrm{x}} \end{gathered}$$

Find the number of terms of the AP -12, -9, -6,... 12. If 1 is added toeach term of this AP, then find the sum of all terms of the AP thusobtained.

If the area of triangle ABC formed by A(x, y), B(1, 2) and C(2, 1) is 6 square units, then prove that  x + y = 15.

A vessel is in the form of hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the total surface area of the vessel.
$\left|\mathrm{Use} \mathrm{\pi }= \frac{22}{7}\right|$

A wooden toy was made by scooping out a hemisphere of same radius fromeach end of a solid cylinder. If the height of the cylinder is 10 cm, and itsbase is of radius 3.5 cm, find the volume of wood in the toy.

$\left|\mathrm{Use} \mathrm{\pi } = \frac{22}{7}\right|$

In Fig., AB and CD are two diameters of a circle with centre O, which are perpendicular to each other. OB is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.  $\left|\mathrm{Use} \mathrm{\pi } = \frac{22}{7}\right|$

The horizontal distance between two poles is 15 m. The angle of depressionof the top of first pole as seen from the top of second pole is 30o. If theheight of the second pole is 24 m, find the height of the first pole.   $\left|\mathrm{Us}e \sqrt{3} = 1.732\right|$

Construct a tangent of a circle of radius 4 cm from a point on the concentriccircle of radius 6 cm.