TEST –D 1
1. A plane left 30 min late due to bad weather, but in order to reach its destination 1500 km away on time it has to increase its speed by 250 km/hr. Find the original speed.
2. A gulab jamun contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 such gulab jamuns, each shaped like a cylinder with two hemispherical ends with total length 5 cm and diameter 2.8 cm.
OR
A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm3 of iron has 8 gm mass.
3. A spiral is made up of successive semicircles, with centers alternately at A and B, starting from A, of radius 0.5 cm, 1 cm, 1.5 cm. What is the total length of such a spiral made up of thirteen consecutive semicircles ?
4. A container open at the top and made up of a metal sheet, is in the form of a frustum of cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container, at the rate of Rs. 20 per litre. (use π =3.14).
5. Prove that the lengths of tangents drawn from an external point to a circle are equal.
6. From the top of a light house the angle of depression of a ship sailing towards it was found to be 30o. After 10 seconds the angle of depression changes to 60 o. Assuming that the ship is sailing at uniform speed, find how much time it will take to reach the light house.
OR
From a point on the ground the angle of elevation of the bottom and the top of a flagstaff situated on the top of a 120 m tall house, was found to be 30 o and 45 o respectively. Find the height of the flagstaff.
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