Understudies can discover the chapter astute vital questions for course 10th Basic Maths within the table underneath. These imperative questions incorporate questions that are regularly inquired in a long time. Moreover, arrangements are to give for these questions, with extraordinary accentuation on ease-of-study. Tap on the joins underneath to begin investigating.
Case Study Question for Class 10 Basic Maths Ch 1 to 15
Case Study 01:
A lighthouse is a tall tower with light near the top. These are often built on islands, coasts or on cliffs. Lighthouses on water surface act as a navigational aid to the mariners and send warning to boats and ships for dangers. Initially wood, coal would be used as illuminators. Gradually it was replaced by candles, lanterns, electric lights. Nowadays they are run by machines and remote monitoring. Prongs Reef lighthouse of Mumbai was constructed in 1874-75. It is approximately 40 meters high and its beam can be seen at a distance of 30 kilometres. A ship and a boat are coming towards the lighthouse from opposite directions. Angles of depression of flash light from the lighthouse to the boat and the ship are 300 and 600 respectively. (CBSE Sample Paper 2022)
i) Which of the two, boat or the ship is nearer to the light house. Find its distance from the lighthouse?
Solution;
The ship is nearer to the lighthouse as its angle of depression is greater.
In ∆ACB, tan 600 = /BC
= √3 = 40/BC
∴ BC = 40/√3
= 40√3/3 m
ii) Find the time taken by the boat to reach the light house if it is moving at the rate of 20 km per hour.
Solution:
In ∆ ADB, tan 300 = /
⇒ 1/√3 = 40/
∴ DB = 40√3
Time taken to cover this distance = (60/2000 × 40√3) minutes
= 60√3/100
= 2.076 minutes
Case Study 02:
Krishnanagar is a small town in Nadia District of West Bengal. Krishnanagar clay dolls are unique in their realism and quality of their finish. They are created by modelling coils of clay over a metal frame. The figures are painted in natural colours and their hair is made either by sheep’s wool or jute. Artisans make models starting from fruits, animals, God, goddess, farmer, fisherman, weavers to Donald Duck and present comic characters. These creations are displayed in different national and international museums.
The ratio of diameters of red spherical apples in Doll-1 to that of spherical oranges in Doll-2 is 2:3. In Doll-3, male doll of blue colour has cylindrical body and a spherical head. The spherical head touches the cylindrical body. The radius of both the spherical head and the cylindrical body is 3cm and the height of the cylindrical body is 8cm. Based on the above information answer the following questions: (CBSE Sample Paper 2022)
i) What is the ratio of the surface areas of red spherical apples in Doll-1 to that of spherical oranges in Doll-2.?
Solution:
Let 1 2 be respectively the radii of apples and oranges
∵ 21: 22 = 2: 3
⇒ 1: 2 = 2: 3
421 : 422 = (1/2)2
= (2/3)2
= 4: 9
ii) The blue doll of Doll-3 is melted and its clay is used to make the cylindrical drum of Doll-4. If the radius of the drum is also 3cm, find the height of the drum.
Solution:
Let the height of the drum be h.
Volume of the drum = volume of the cylinder + volume of the sphere
π32h = (π32 × 8 + 4/3π33) 3
⇒ ℎ = (8 + 4)
⇒ ℎ = 12 cm
Case Study 03:
India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year. (CBSE Sample Paper 2023)
1) In which year, the production is Rs 29,200.
2) Find the production during 8th year Find the production during first 3 years.
3) Find the difference of the production during 7th year and 4th year
Solution:
a6 =16000 a9 = 22600
Solution:
a + 5d=16000 ——-(1)
a = 16000 – 5d
a + 8d = 22600 ——–(2)
substitute in (2)
16000 – sd + 8d = 22600
3d = 22600 – 16000
3d = 6600
d = 6600/3 = 2200
a = 16000 – 5 (2200)
a = 16000 – 11000
a = 5000
(i) an = 29200 a = 5000 d = 2200
an = a + (n-1)d
29200 = 5000 + (n – 1)2200 1/2
29200-5000 = 2200n – 2200
24200 + 2200 = 2200n
26400 = 2200n
n = 264/22
n = 12
in 12th year the production was Rs 29200
(ii) n = 8, a = 5000, b = 2200
an = a + (n-1)d
= 5000+ (8-1) 2200
= 5000 +7 x 2200
= 5000+15400
= 20400
The production during 8th year is = 2040
Or
n = 3, a = 5000, b = 2200
Sn = n/2 [2a + (n – 1) d]
= 3/2 [2(5000) + (3 – 1) 2200]
S3 = 3/2 (10000 + 2 x 2200)
= 3/2 (10000 + 4400)
= 3 x 7200
= 21600
The production during first 3 year is 21600
(iii) a4 = a + 3d
= 5000 + 3 (2200)
= 5000 + 6600
= 11600
a7 = a + 6d
= 5000 + 6 x 2200
= 5000 + 13200
= 18200
a7 – a4 = 18200 – 11600 = 7400
Case Study 04:
A boy is standing on the top of light house. He observed that boat P and boat Q are approaching the light house from opposite directions. He finds that angle of depression of boat P is 45° and angle of depression of boat Q is 30°. He also knows that height of the light house is 100 m. (CBSE Sample Paper 2023)
Based on the above information, answer the following questions.
(i) What is the measure of ∠ACD?
(ii) If ∠YAB = 30°, then ∠ABD is also 30°, Why?
(iii) Find length of CD.
Or
Find length of BD.
Solution:
(i) XY ║CD and AC is transversal.
Solution:
Photo
∠ACD = ∠CAX (alt.int ∠S)
∠ACD=30˚
(ii) ∠YAB = 30˚
∠ABD = 30˚
Because XY || CD and AB is a transversal so alternate interior angles are equal
∠YAB = ∠ABD
(iii) CD = ?
In ∆ ADC = 45˚
tan = P/B
1 = 100/B
B = 100 m
CD = 100 m
Or
BD = ?
In ∆ABD = 30˚
tan = P/B
tan 30 = 100/BD
1/√3 = 100/BD
BD = 100√3 m
Case Based Questions Class 10 Basic Maths Chapterwise
Chapter 1 | Real Numbers | Chapter 9 | Some Applications of Trigonometry |
Chapter 2 | Polynomials | Chapter 10 | Circles |
Chapter 3 | Pair of Linear Equations in Two Variables | Chapter 11 | Constructions |
Chapter 4 | Quadratic Equations | Chapter 12 | Areas Related to Circles |
Chapter 5 | Arithmetic Progressions | Chapter 13 | Surface Areas and Volumes |
Chapter 6 | Triangles | Chapter 14 | Statistics |
Chapter 7 | Coordinate Geometry | Chapter 15 | Probability |
Chapter 8 | Introduction to Trigonometry | Chapter 16 |
Key questions for 10th review Basic Maths are outlined agreeing to the CBSE NCERT program. All address sorts are accessible within the PDF, from one-word to one-line answers, brief reply sorts to five point long reply sorts. Hence, understudies can plan for exams and indeed clarify their concepts through them. On the off chance that they refer to these questions, it’ll get ready their minds to pick up a competitive advantage. Understudies will gotten to be commonplace with question patterns and the sorts of questions that will show up on exams.