Class xmaths-WPS Office

Secondary school certificate examination 2021-2022
Class X TERM-II EXAMINATION
SUBJECT : MATHEMATICS
Duration : 1and 1/2 hours. M.M.: 40
General instructions:
i. All questions are compulsory

ii. Use of calculators mobile phones and other electronic devices are not permitted.
iii. If, for any reason ,you wish to re-answer any question already answered, please
cancel the previous answer.
iv. Internal choices have been provided in some questions. You have to attempt only one
of the choices in such questions.
v. Question number 10' and 14' are for visually challenged students only.
vi. Question number 1 to 3 are MCQ. Write their correct answer in the answer sheet.
vii. Question Number 1 to 3 are of ONE mark each, Question Number 4 to 6 are of TWO
marks each, Question Number 7 to 11 are of THREE marks each and Question Number
12 to 15 are of FOUR marks.
1. For the given A.P. : 1, -1 , -3 ,-5 ..........
Common difference is
a) –1 b) 2 c) 1 d) –2
2. A circus artist is climbing a 20 m long rope , which is tightly stretched and tied from the top
of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope
with the ground level is 30°.
a) 10√3 b) 20 c) 10 d) 20√3
3. Metallic spheres of Radii 6cm, 8 cm and 10 cm respectively , are melted to form a single
solid sphere,a then the radius of the resulting sphere is
a) 12 b) 6 c) 8 d ) 10
4. The angle of elevation of the top of a tower from a point on the ground, which is 30 m
away from the foot of the tower is 30°. find the height of the tower.
5. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter
of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface
area of the vessel.
6. A solid is in the shape of a cone standing on a hemisphere with both their radii being equal
to 1 cm and the height of the cone is equal to its radius.Find the volume of the solid in terms
of π.
7. In an A.P.: given a=5 ,d= 3 ,an =50 ,find n and Sn .
8. Which term of the A.P.: 3, 8, 13, 18, ........, is 78 ?
9. Two poles of equal heights are standing opposite each other on either side of the road ,
which is 80 m wide. From the point between them on the road , the angles of elevation of
top of the poles are 60° and 30° ,respectively . Find the height of the poles and the distances
of the point from the poles.
10. Two tangents TP and TQ are drawn to a circle with centre O from an external point T.
Prove that ≺PTQ = 2 ≺OPQ.
10' (For visually challenged)

From a point on the ground, the angles of elevation of the bottom and the top of a
transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find
the height of the tower.
11. A pen stand made of wood is in the shape of a cuboid with four conical depression to hold
pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the
depression is 0.5 cm and the depth is 1.4 cm. Find the volume of the wood in the entire stand.
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 6 cm and radius 8 cm. Find the mass of the pole,
given that one cm³ of iron has approximately 8g mass.
12. If the sum of the first n terms of an AP is 4n–n². what is the first term ?what is the sum of
first two terms ? what is the second term? Similarly, find 3rd, the 10th and and the n th
terms.
13. 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 the 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.
OR
A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m
from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant
is 60°.After sometime, the angle of elevation reduces 30°. Find the distance travelled by the
balloon during the interval.
14. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary
angles at the centre of the circle.
14'. (for visually challenged) Abcopper rod of diameter 1 cm and length 8 cm is drawn into a
wire of length 18 m of uniform thickness. Find the thickness of the wire.
15. Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How
much area will it irrigate in 30 minutes, if 8 cm of standing water is needed.
OR
A farmer connects a pipe of internal diameter 20cm from a canal into a cylindrical tank in her
field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3
km/h , in how much time will the tank be filled?

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Secondary school certificate examination 2021-2022

Class X TERM-II EXAMINATION

Duration : 1and 1/2 hours. M.M.: 40

i. All questions are compulsory

1. For the given A.P. : 1, -1 , -3 ,-5 ..........

7. In an A.P.: given a=5 ,d= 3 ,an =50 ,find n and Sn .

8. Which term of the A.P.: 3, 8, 13, 18, ........, is 78 ?

10' (For visually challenged)

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