The volume of a hemisphere is 2425 $\frac{1}{2}$ cm^3. Find its curved surface area. 

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

Tangents PA and PB are drawn from an external point P to two concentric circle with centre O and radii 8 cm and 5 cm respectively, as shown in Fig., If AP = 15 cm, then find the length of BP.

In fig., an isosceles triangle ABC, with AB =AB, circumscribes a circle. Prove that the point of contact P bisects the base BC.

                                            OR

In fig., the chord AB of the larger of the two concentric circles, with centre O, touches the smaller circle at C. Prove that AC = CB.

In fig., OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region.  $\left[\mathrm{Use} \mathrm{\pi } = \frac{22}{7}\right]$

Find the sum of all three digit natural numbers, which are multiples of 7.

Find the values (s) of k so that the quadratic equation  3x² - 2kx + 12 = 0 has equal roots.

A point P divides the line segment joining the points A(3,-5) and B(-4, 8) such that $\frac{\mathrm{AP}}{\mathrm{PB}} = \frac{\mathrm{K}}{1}$ . If P lies on the line x + y = 0, then find the value of K.

If the vertices of a triangle are (1, -3), (4, p) and (-9, 7) and its area is 15 sq. units, find the value (s) of p.

Prove that the parallelogram circumscribing a circle is a rhombus.

                                       OR

Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

20.

From a solid cylinder of height 7 cm and base diameter 12 cm, a conical cavity of same height and same base diameter is hollowed out. Find the total surface area of the remaining solid.  $\left[\mathrm{Use} \mathrm{\pi } = \frac{22}{7}\right]$

                                    OR

A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, then find the radius and slant height of the heap.