DATE: MARCH 4, 2022 CLASS X MATHEMATICS ASSIGNMENT (STANDARD)

1. Find the value of a25 – a15 for the AP: 6, 9, 12, 15, ………..
2. If 7 times the seventh term of the AP is equal to 5 times the fifth term, then find the value of its 12th term.
3. Find the values of k of the quadratic equations, kx (x – 2) + 6 = 0 such that it has two equal roots.
4. Find the value of 𝑚 so that the quadratic equation 𝑚𝑥(5𝑥 − 6) +9 = 0 has two equal roots.
5. Find the value of k for which the equation x2 + k(2x + k – 1) + 2 = 0 has real and equal roots.
6. From a point P, two tangents PA and PB are drawn to a circle C(0, r). If OP = 2r,
then find ∠𝐴𝑃𝐵. What type of triangle is APB?
7. From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is
hollowed out. Find the volume of the remaining solid.
8. The curved surface area of a right circular cone is 12320 cm². If the radius of its
base is 56cm, then find its height.
9. If Ritu were younger by 5 years than what she really is, then the square of her age would have been 11
more than five times her present age. What is her present age?

10. Solve the equation

11. Following is the distribution of the long jump competition in which 250 students participated. Find the
median distance jumped by the students. Interpret the median.

12. A canal is 300 cm wide and 120 cm deep. The water in the canal is flowing at a speed of 20 km/h. How
much area will it irrigate in 20 minutes if 8 cm of standing water is desired?
13. The distribution given below shows the runs scored by batsmen in one-day cricket matches. Find the
mean number of runs.

14. Two vertical poles of different heights are standing 20m away from each other
on the level ground. The angle of elevation of the top of the first pole from the
foot of the second pole is 60° and angle of elevation of the top of the second
pole from the foot of the first pole is 30°. Find the difference between the
heights of two poles. (Take √3 = 1.73)
15. Triangle ABC is circumscribing a circle. Find the length of BC.
16. The angle of elevation of an aeroplane from a point on the ground is 60°. After a flight of 30 seconds the
angle of elevation becomes 30°. If the aeroplane is flying at a constant height of 3600 √3 m, find the speed
of the aeroplane.
17. A boy 1.7 m tall is standing on a horizontal ground, 50 m away from a building. The angle of elevation of
the top of the building from his eye is 60°. Calculate the height of the building. (Take √3 = 1.73)
18. The internal and external radii of a spherical shell are 3cm and 5cm respectively. It is melted and recast
into a solid cylinder of diameter 14cm, find the height of the cylinder. Also find the total surface area of
the cylinder. (Take 𝜋 = 22 /7 )
19. Prove that the angle between the two tangents drawn from an external point to a circle is supplementary
to the angle subtended by the line segment joining the points of contact to the centre.
20. Two tangents TP and TQ are drawn to a circle with centre O from an
external point T. Prove that ∠𝑃𝑇𝑄 = 2∠𝑂𝑃𝑄

21. Mode of the following distribution is 65 and the sum of all the
frequencies is 70. Find the missing frequencies x and y

Class 0-20 20-40 40-60 60-80 80-100 100-120 120-140 140-160

Frequency 8 11 x 12 y 9 9 5

22. A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the
form of a sphere. Find the radius of the sphere.
23. A pen stand made of wood is in the shape of a cuboid with four conical
depressions and a cubical depression to hold the pens and pins, respectively. The
dimension of the cuboid is 10 cm, 5 cm and 4 cm. The radius of each of the conical
depressions is 0.5 cm, and the depth is 2.1 cm. The edge of the cubical depression
is 3 cm. Find the volume of the wood in the entire stand.
24. A juice seller was serving his customers using glasses as shown in Figure. The
inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass had a
hemispherical raised portion which reduced the capacity of the glass. If the
height of a glass was 10 cm, find the apparent capacity of the glass and its actual
capacity. (Use π = 3.14)
25. The shadow of a tower standing on level ground is found to be 40 m longer
when the Sun’s altitude is 30° than when it is 60°. Find the height of the tower.
26. The angle of elevation of the top of a tower from two points distant s and t
from its foot are complementary. Prove that the height of the tower is √st.
27. A flagstaff stands at the top of a 5m high tower. From a point on the ground,
the angle of elevation of the top of the flagstaff is 60° and from the same point,
the angle of elevation of the top of the tower is 45°. Find the height of the
flagstaff.
28. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of
the larger circle which touches the smaller circle.
29. PA and PB are tangents to the circle from an external point P. CD are another
tangent touching the circle at Q. If PA = 12 cm, QC = QD = 3 cm, then find PC + PD.

30. Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct
the pair of tangents to the circle and measure their lengths.
31. Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and
measure its length.
32. Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°
33. If the median of the distribution given below is 28.5, find the values of x and y.

34. The following distribution shows the daily pocket allowance of children of a locality. The mean pocket
allowance is Rs 18. Find the missing frequency f.
CASE STUDY:
35. Formula one Portugese Grand Prix technical team at the Algarve International Circuit are analysing last
year data of drivers’ performance to provide valuable inferences to commentators on how the drivers
can improve this year. The length of time taken by 80 drivers to complete a journey is given in the table
below:

On the basis of the above information, answer the following questions:

(i) What is the estimate of the mean time (in minutes) taken to complete the journey ?

(ii) In which interval does the median of the distribution lie?

36. A bakery is an establishment that produces and sells flour-

based food baked in an oven such as bread, cookies, cakes,
pastries, and pies. Some retail bakeries are also categorized as
cafés, serving coffee and Tania runs a bakery shop and her
bakery is very famous for her tasty biscuits. The amount of
mixture required to make one biscuit is 18 cu cm. Before it is
cooked, the mixture is rolled into a sphere. After the biscuit is
cooked, the biscuit becomes a cylinder of radius 3 cm and height
0.7 cm ( The increase in volume is due to air being trapped in
the biscuit) Biscuits are packed in a cylindrical card box of
height 14 cm.ea to customers who wish to consume the baked
goods on the premises.
On the basis of the above information, answer the following questions:
(i) What is the volume of the biscuits after it is cooked ?
(ii) What is the volume of air trapped, while cooking the biscuit ?
37. RCB Machine Pvt Ltd started making road roller 10 year ago. Company increased its production
uniformly by fixed number every year. The company produces 800 roller in the 6th year and 1130 roller
in the 9th year. On the basis of the above information, answer the following questions:
(A) What was the company’s production in first year?
(B) What was the company’s total production of the first 6 years?
38. Trigonometry in the form of triangulation forms the basis of
navigation, whether it is by land, sea or air. GPS a radio navigation
system helps to locate our position on earth with the help of
satellites. A guard, stationed at the top of a 240m tower, observed
an unidentified boat coming towards it. A clinometer or
inclinometer is an instrument used for measuring angles or
slopes(tilt). The guard used the clinometer to measure the angle of
depression of the boat coming towards the lighthouse and found it
to be 30°.

i) Make a labelled figure on the basis of the given information and calculate the distance of the boat from
the foot of the observation tower.
ii) After 10 minutes, the guard observed that the boat was approaching the tower and its distance from
tower is reduced by 240(√3 - 1) m. He immediately raised the alarm. What was the new angle of
depression of the boat from the top of the observation tower?