Periodic Test-III(2021-22)
Class- X Mathematics)
Time Allowed: 1 Hour
(Set A)
Maximum Marks: 20
General Instructions:
(i)
(ii)
(iii)
(iv)
All questions are compulsory
There are three sections-A, B, and C contains 8 questions in all.
Section- A comprises of 5 questions of 2 marks each.
Section -B comprises of 2 questions of 3 marks each.
Section -C comprises of Case Study of 4 marks.
There is an internal choice. However internal choice has been provided in two
questions of2 marks and onequestion of 3 marks.
Section- A
Very Short Type Answer Questions:
Q1.
If given fig. the angles of depression from the observing positions 0 1 and 02 of the
object A are________ and _______.
Q2.
A ladder, leaning against a wall, makes an angle of 60° with the horizontal. If the foot
of the ladder is 2.5 m away from the wall, find the length of the ladder.
(OR)
If a tower 30 m high, casts a shadow 10√3 m long on the ground, then what is the
angle of elevation of the sun?
Q3.
Volume and surface area of a solid hemisphere are numerically equal. What is the
diameter of hemisphere?
Q4.
If the total surface area of a solid hemisphere is 462 cm 2, find its volume.
[Take π = 22/7]
(OR)
The volume of a right circular cylinder with its height equal to the radius is 176/7
cm3. Find the height of the cylinder.
Q5.
A solid ball is exactly fitted inside the cubical box of side a. What is the volume of the ball?
Section- B
Short Type Answer Questions:
Q6.
In Figure, a decorative block, made up of two solids, a cube and a hemisphere. The
base of the block is a cube of side 6 cm and the hemisphere fixed on the top has a
diameter of 3.5 cm. Find the total surface area of the block.(use π=22/7)
Q7.
In the figure, AB is a 6 m high pole and CD is a ladder inclined at an angle of 60° to
the horizontal and reaches up to a point D of pole. If AD = 2.54 m. Find the length of
the ladder. (Use √3 = 1.73)
(OR)
An observer, 1.7 m tall, is 20√3 m away from a tower. The angle of elevation from
the eye of observer to the top of tower is 30°. Find the height of tower.
Section- C
Case Study:
Q8.
On a Sunday, your Parents took you to a fair. You could see lot of toys displayed, and
you wanted them to buy a RUBIK’s cube and strawberry ice-cream for you. Observe
the figures and answer the questions:-
i.
find the length of the diagonal if each edge measures 6cm.
ii
find the Volume of the solid figure if the length of the edge is 7cm.
iii
What is the curved surface area of hemisphere (ice cream) if the base radius is 7cm?
iv
what will be the Slant height of a cone if the radius is 7cm and the height is 24 cm?