CBSE Class 10 Maths Important Case Study Questions

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Important Case Study Questions from CBSE Class 10 Maths: CBSE Class 10 Maths board exam 2023 is on 21st March, 2023. With the exam approaching fast, CBSE Board exam candidates are trying to cover the complete syllabus along with practise and revision of all important topics as well. To help students in CBSE Class 10 Maths board exam 2023 preparation, we have shared these important case study questions.

According to the latest CBSE 10th Maths question paper design, Maths Standard and Basic Question Paper will have 5 Sections A, B, C, D, and E.

Section A : 20 Multiple Choice Questions (MCQs) carrying 1 mark each.
Section B : 5 Short Answer-I (SA-I) type questions carrying 2 marks each.
Section C : 6 Short Answer-II (SA-II) type questions carrying 3 marks each.
Section D : 4 Long Answer (LA) type questions carrying 5 marks each.
Section E : 3 Case Based integrated units of assessment (4 marks each) with sub-parts of the values of 1, 1 and 2 marks each respectively.

Therefore, it is very important for all Board exam candidates in CBSE Class 10 to practise case study questions from all chapters very well. This will ensure that they can easily grab the 12 marks from this section.

CBSE Class 10 Maths Important Case Study Questions

1 Two Friends Geeta and Sita were playing near the river. So, they decide to play a game in which they have to throw the stone in the river, and whoever will throw the stone at maximum distance, win the game. Geeta Starts first and throws the stone in the river. During her throw, her hand was making an angle of 60° with the Horizontal plane. Sita throws at 45°.

(a) The shape of trajectory formed by stone when Geeta & Sita throw it in the river, is:

Straight Line
Circle
Parabola
Semi circle

(b) If we make a mathematical equation of the path followed by stone when Geeta & Sita threw it in the river, then the resulting mathematical equation would be:

Linear
Cubic
Quadratic
Bi-Quadratic

(c) Let there be a Polynomial y=2x2-3x+1, then the curve formed by this Polynomial would be:

Parabola Open Upward
Parabola Open Downward
Hyperbola Open Upward
Hyperbola Open downward

(d) There is a Polynomial y=x2+x+1. It will intersect the x-axis at:

Two Real Points
One Real Point
Three Real Points
nowhere

(e) It will not intersect the x-axis.y-intercept of Polynomial can be found by

Putting y=0 in given Polynomial
Putting y=1 in the given Polynomial
Putting x=0 in the given Polynomial.
Putting x=1 in the given Polynomial.

2 The department of Computer Science and Technology is conducting an International Seminar. In the seminar, the number of participants in Mathematics, Science and Computer Science are 60, 84 and 108 respectively. The coordinator has made the arrangement such that in each room, the same number of participants are to be seated and all of them being in the same subject. Also, they allotted the separate room for all the official other than participants.

(i) Find the total number of participants.

(a) 60

(b) 84

(d) none of these

(ii) Find the LCM of 60, 84 and 108.

(a) 12

(b) 504

(d) 3780

(iii) Find the HCF of 60, 84 and 108.

(iv) Find the minimum number of rooms required, if in each room, the same number of participants are to be seated and all of them being in the same subject.

(a) 12

(b) 20

(d) none of these

(v) Based on the above (iv) conditions, find the minimum number of rooms required for all the participants and officials.

(a) 12

(b) 20

(d) none of these

3 A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.

In the standard form of quadratic polynomial, ax2 + bx + c, what are a, b and c ?
If the roots of the quadratic polynomial are equal, what is the discriminant D ?
If α and 1/α are the zeroes of the quadratic polynomial 2×2 – x + 8k, then find the value of k ?

4 Special offers are short-term pricing strategies that businesses, especially shops, will adopt to encourage customers to buy from them. During winter season, a shopkeeper sells a jacket at 8% profit and a sweater at 10 % discount thereby getting a sum of ₹1008. If she had sold the jacket at 10 % profit and the sweater at 8 % discount, she would have got ₹1028. Denoting the cost price of one jacket by ₹ x and the list price of one sweater by ₹ y, answer the following situations.

Represent the first situation algebraically.

a) 12x+10y=11200

b) 10x+12y=11200

c) 12x-10y=11200

d) 10x-12y=1120

2 Represent the second situation algebraically

a) 46x+55y=51400

b) 55x+46y=51400

c) 55x-46y=51400

d) 46x-55y=51400

3 The system of linear equations representing both the situations will have.

a) Infinite number of solutions

b) Unique solution

c) No Solutions

d) Exactly two solutions

4 The graph of the system of linear equations representing both the situations will be

a) Parallel lines

b) Coincident lines

c) Intersecting lines

d) None of these

5 An alumni association is an association of former students. These associations often organize social events, publish newsletters or magazines and raise funds for the organisation.The alumni meet of two batches of a college- batch A & batch B were held on the same day in the same hotel in two separate halls “Rose” and “Jasmine”. The rents were the same for both the halls. The expense for each hall is equal to the fixed rent of each hall and proportional to the number of persons attending each meet. 50 persons attended the meet in “Rose” hall, and the organisers had to pay ₹ 10000 towards the hotel charges. 25 guests attended the meet in “Jasmine” hall and the organisers had to pay ₹ 7500 towards the hotel charges. Denote the fixed rent by ₹ x and proportional expense per person by ₹ y.

Represent algebraically the situation in hall “Rose”.

a) 50x + y = 10000

b) 50x − y = 10000

c) x + 50y = 10000

d) x − 50y = 10000

2 Represent algebraically the situation in hall “Jasmine”

a) x + 25y = 7500

b) x − 25y = 7500

c) 25x + y = 7500

d) 25x − y = 7500

3 What is the fixed rent of the halls?

a) ₹2500

b) ₹3300

c) ₹ 4000

d) ₹5000

4 Find the amount the hotel charged per person.

a) ₹ 150

b) ₹ 190

c) ₹130

d) ₹ 100

6 Riya has a field with a flowerbed and grassland. The grassland is in the shape of a rectangle while the flowerbed is in the shape of a square. The length of the grassland is found to be 3 m more than twice the length of the flowerbed. Total area of the whole land is 1260m2

(a)If the length of the square is x m then find the total length of the field i

(b) What will be the perimeter of the whole figure in terms of x?

(c )Find the value of x if the area of total field is 1260 m2

(d) Find the area of grassland and the flowerbed separately.

7 Your friend Veer wants to participate in a 200m race. He can currently run that distance in 51 seconds and with each day of practice it takes him 2 seconds less. He wants to do it in 31 seconds.

1 Write first four terms are in AP for the given situation.

2 What is the minimum number of days he needs to practice till his goal is achieved.

3 How many seconds it takes after the 5th day .

8 Helicopter Patrolling: A helicopter is hovering over a crowd of people watching a police standoff in a parking garage across the street. Stewart notices the shadow of the helicopter is lagging approximately 57 m behind a point directly below the helicopter. If he is 160 cm tall and casts a shadow of 38 cm at this time,

(i) what is the altitude of the helicopter?

(ii) What will be length of shadow of Stewart at 12:00 pm

(iii) Write the name of triangles formed for this situation.

9 Seema has a 10 m × 10 m kitchen garden attached to her kitchen. She divides it into a 10 ×10 grid and wants to grow some vegetables and herbs used in the kitchen. She puts some soil and manure in that and sow a green chilly plant at A, a coriander plant at B and a tomato plant at C. Her friend Kusum visited the garden and praised the plants grown there. She pointed out that they seem to be in a straight line. See the below diagram carefully and answer the following questions:

(i) Find the distance between A and B is

(ii) Find the mid- point of the distance AB

(iii) Find the distance between B and C

10 A heavy-duty ramp is used to winch heavy appliances from street level up to a warehouse loading dock. If the ramp is 2 meter high and the incline is 4 meter long.

(Use √3 = 1.73)

a What angle does the dock make with the street?

b How long is the base of the ramp? ( In round figure)

11 Mohan, a class X student is a big foodie. Once his mother has made a sandwich for him. A thought has come into his mind by seeing a piece of sandwich. He thought if he increases the base length and height, he can eat a bigger piece of sandwich.

If the length of the base is 12 cm and the height is 5 cm then the length of the hypotenuse of that sandwich is:

(a) 17 cm (b) 7 cm (c) 169 cm (d) 13

If he increases the base length to 15 cm and the hypotenuse to 17 cm, then the height of the sandwich is :

(a) 7 cm (b) 8 cm (c) 32 cm (d) none of these

The value of tan 45° + cot 45°

(a) 1 (b) 2 (c) 3 (d) 4

12 A flag pole ‘h’ metres is on the top of the hemispherical dome of radius ‘r’ metres. A man is standing 7 m away from the dome. Seeing the top of the pole at an angle 45° and moving 5 m away from the dome and seeing the bottom of the pole at an angle 30°.

(i) the height of the pole

(ii) radius( height) of the dome

(iii) Is it possible to see the pole at the angle of 60 0

(iv) If the height of pole is increased, the angle elevation will …..

13 In an international school in Hyderabad organised an Interschool Throwball Tournament for girls just after the pre-board exam. The throw ball team was very excited. The team captain Anjali directed the team to assemble in the ground for practices. Only three girls Priyanshi, Swetha and Aditi showed up. The rest did not come on the pretext of preparing for pre-board exam. Anjali drew a circle of radius 5m on the ground. The centre A was the position of Priyanshi. Anjali marked a point N, 13 m away from centre A as her own position. From the point N, she drew two tangential lines NS and NR and gave positions S and R to Swetha and Aditi. Anjali throws the ball to Priyanshi, Priyanshi throws it to Swetha, Swetha throws it to Anjali, Anjali throws it to Aditi, Aditi throws it to Priyanshi, Priyanshi throws it to Swetha and so on.

14 John had a farm with many animals like cows, dogs, horses etc. He had sufficient grass land for the cows and horses to graze, One day Three of his horses were tied with 7 metre long ropes at the three corners of a triangular lawn having sides 20m, 34m and 42m.

(a) Find the area of the triangular lawn .

(b) Find the area of the field that can be grazed by the horses.

(c) The area that cannot be grazed by the horses.

15 Arun, a 10th standard student, makes a project on coronavirus in science for an exhibition in his school. In this project, he picks a sphere which has volume 38808 cm3 and 11 cylindrical shapes, each of volume 1540 cm3 with length 10 cm.

Based on the above information, answer the following questions.

(i) Diameter of the base of the cylinder is

(ii) Diameter of the sphere is

(iii) Total volume of the shape formed is

(iv) Curved surface area of the one cylindrical shape is

(v) Total area covered by cylindrical shapes on the surface of sphere is

16 Municipality is installing playground equipment at various parks. They have to study the age group of children playing in a park of a specific colony. The classification of children according to their ages, playing in a park is shown in the following table.

Age group of children (in

years)

6-8

8-10

10-12

12-14

14-16

Number of children

Based on the above information answer the following:

In which age group, will the maximum number of children belong?
Find the mode of the ages of children playing in the park?

17 Piggy bank or Money box( a coin container) is normally used by children. Piggy bank serves as a pedagogical device to teach about saving money to children. Generally, piggy banks have openings besides the slot for inserting coins but some do not have openings. We have to smash the piggy bank with a hammer or by other means, to get the money inside it.

A child Shreya has a Piggybank. She saves her money in her Piggybank. One day she found that her Piggybank contains hundred 50 paisa coins, fifty 1 rupees coin, twenty 2 rupees coin, and ten 5 rupees coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down.

Based on the above information, answer the following questions.

(a) The probability that the fallen coin will be 50 paisa coin, is ——-

(b) The probability that the fallen coin will be 5 rupees coin, is———

(c) The probability that the fallen coin will be 2 rupees coin, is———

(d) The probability that the fallen coin will be 2 rupees coin or 5 rupees coin, is——–

18 A game consists of tossing a one-rupee coin 3 times & noting its outcome each time.