You are Samina Zaveri, Class X, Vadodara, Gujarat. You come across the following information on a local library’s notice board.
You wish to participate but require more information. Write a letter to Teen-Toggle Games Pvt.Ltd in about 120 words, enquiring about rules, scholarship details and deadlines. Also enquire about specifications for solo or group entries.
Krishnanagar is a small town in Nadia District of West Bengal. Krishnanagar clay dolls are unique in their realism and quality of their finish. They are created by modelling coils of clay over a metal frame. The figures are painted in natural colours and their hair is made either by sheep’s wool or jute. Artisans make models starting from fruits, animals, God, goddess, farmer, fisherman, weavers to Donald Duck and present comic characters. These creations are displayed in different national and international museums. Here are a few images (not to scale) of some clay dolls of Krishnanagar.
The ratio of diameters of red spherical apples in Doll-1 to that of spherical oranges in Doll-2 is 2:3. In Doll-3, male doll of blue colour has cylindrical body and a spherical head. The spherical head touches the cylindrical body. The radius of both the spherical head and the cylindrical body is 3cm and the height of the cylindrical body is 8cm. Based on the above information answer the following questions:
(i) What is the ratio of the surface areas of red spherical apples in Doll-1 to that of spherical oranges in Doll-2.?
(ii) The blue doll of Doll-3 is melted and its clay is used to make the cylindrical drum of Doll-4. If the radius of the drum is also 3cm, find the height of the drum.
A lighthouse is a tall tower with light near the top. These are often built on islands, coasts or on cliffs. Lighthouses on water surface act as a navigational aid to the mariners and send warning to boats and ships for dangers. Initially wood, coal would be used as illuminators. Gradually it was replaced by candles, lanterns, electric lights. Nowadays they are run by machines and remote monitoring. Prongs Reef lighthouse of Mumbai was constructed in 1874-75. It is approximately 40 meters high and its beam can be seen at a distance of 30 kilometres. A ship and a boat are coming towards the lighthouse from opposite directions. Angles of depression of flash light from the lighthouse to the boat and the ship are 300 and 600 respectively.
(i) Which of the two, boat or the ship is nearer to the light house. Find its distance from the lighthouse?
(ii) Find the time taken by the boat to reach the light house if it is moving at the rate of 20 km per hour.
The following age wise chart of 300 passengers flying from Delhi to Pune is prepared by the Airlines staff.
|Age||Number of passengers|
|Less than 10||14|
|Less than 20||44|
|Less than 30||82|
|Less than 40||134|
|Less than 50||184|
|Less than 60||245|
|Less than 70||287|
|Less than 80||300|
Find the mean age of the passengers
Draw a pair of tangents to a circle of radius 6cm which are inclined to each other at an angle of 60°. Also find the length of the tangent.