RUCHI TUTORIAL
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SA2
SAMPLE PAPER 2 MATHS CLASS 10
FEB 2016
From the top of a building 60 m high the angles of depression of the top and the bottom of a tower
are observed to be 300 and 600. Find the height of the tower.
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field,
which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/hr, in
how much time will the tank be filled.
An A.P. has 21 terms. The sum of 10th, 11th and 12th terms is 129 and the sum of the last 3 terms is
237. Find the A.P.
If the radii of the ends of a bucket 24 cm high are 5 cm and 15 cm, find the surface area of the bucket
provided it is closed from the smaller end.
A circus tent is cylindrical to a height of 3 m and conical above it. If its diameter is 105 m and slant
height of the cone is 53 m, calculate the total area of the canvas required for the tent.
From a station, two trains start at the same time. One train moves in west direction and other in
North direction. First train moves 5 km/hour faster than the second train. If after two hours, distance
between the two trains is 50 km, find the average speed of each train.
The product of ram’s age (in years) five years ago and his age ten year later is 16. Determine ram’s
present age.
From a station, two trains start at the same time. One train moves in west direction and other in
North direction. First train moves 5 km/hour faster than the second train. If after two hours, distance
between the two trains is 50 km, find the average speed of each train.
A person observed the angle of elevation of the top of a tower as 30 . He walked 50 m towards the
foot of the tower along level ground and found the angle of elevation of the top of the tower as 60 .
Find the height of the tower.
10 A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm 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 approximately 8 g mass. .
11 The
slant height of a frustum of a cone is 4 cm and the perimeter of circular ends are 18 cm and 6
cm. Find the cost of painting its curved surface at Rs. 10 per square centimeter.
12 A vessel is in the form of an inverted cone. Its height is 8 cm. It is fill with water up to brim. When
100 lead shots each of which is a solid sphere of radius 0.5 cm are dropped in the vessel, one fourth
of water flows out. Find the diameter of its top.
13 A hollow metallic cylinder whose outer radius is 4.3 cm and internal radius is 1.1 cm and whole length
is 4 cm, is melted and recast into a solid cylinder 12 cm long. Find the diameter of solid cylinder.
14 The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how
many terms are there and what is their sum ?
15 A
student scored a total of 32 marks in class tests in mathematics and science. Had he scored 2
marks less in Science and 4 more in Mathematics, the product of his marks would have been 253.
Find his marks in two subjects.
16 A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car
at an angle of depression of 30 , which is approaching the foot of the tower with a uniform speed.
Six seconds later, the angle of depression of the car is found to be 60 . Find the time taken by the
car to reach the foot of the tower from this point.
17 The sum of first 6 terms of an A.P. is 42. The ratio of its 10th term to its 30th term is 1 : 3. Find the
first term and the thirteenth term of the A.P.
18 A person standing on the bank of a river, observes that the angle of elevation of the top of the tree
standing on the opposite bank is 60 . When he retreats 20 m from the bank, he finds the angle of
elevation to be 30 . Find the height of the tree and the breadth of the river.
19 A fez, the cap used by the Turks, is shaped like the frustum of a cone. If its radius of the open side is
10 cm, radius at the upper base is 4 cm and its slant height is 15 cm. Find the area of material used
for making it.
20 A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone
is 2 cm and the diameter of the base is 4 cm. Determine the volume of the toy. If a right circular
cylinder circumscribes the toy, find the difference of the volume of the cylinder and toy.
21 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, find the radius and slant height of the heap.