Case study from CBSE sample paper Basic math 2024 – 2025 class 10
Case study 1:- A group of students conducted a survey to find out about the preferred mode of transportation to school among their classmates. They surveyed 200 students from their school. The results of the survey are as follows:
120 students preferred to walk to school.
25% of the students preferred to use bicycles.
10% of the students preferred to take the bus.
Remaining students preferred to be dropped off by car.
Based on the above information, answer the following questions:
(i) What is the probability that a randomly selected student does not prefer to walk to school ?
(ii) Find the probability of a randomly selected student who prefers to walk or use a bicycle.
(iii) (A) One day 50% of walking students decided to come by bicycle. What is the probability that a randomly selected student comes to school using a bicycle on that day?
OR
(iii) (B) What is the probability that a randomly selected student prefers to be dropped off by car?
Solution:- No of student preffered to walk to school = 120
The number of students preferred to use bicycles = 
The number of students preferred to take the bus = 
The number of students preferred to be dropped off by car = 200 – 120 – 50 – 20 = 10
(i) The probability that a randomly selected student does not prefer to walk to school = 
(ii) The selected student who prefers to walk or use a bicycle = 120 + 50 = 170
The probability of a randomly selected student who prefers to walk or use a bicycle =
(iii) (A) No of student preffered to walk to school = 120
One day 50% of walking students decided to come by bicycle, Number of student = 
= 60
The number of students preferred to use bicycles = 50
Now, The number of students use bicycles = 60 + 50 = 110
Then the probability use bicycles = 
OR
(iii) (B) The number of students preferred to be dropped off by car = 200 – 120 – 50 – 20 = 10
The probability of students preferred to dropped off by car = 
Case study 2:- Radha, an aspiring landscape designer, is tasked with creating a visually captivating pool design that incorporates a unique arrangement of fountains. The challenge entails arranging the fountains in such a way that when water is thrown upwards, it forms the shape of a parabola. The graph of one such parabola is given below.
The height of each fountain rod above water level is 10 cm. The equation of the downward-facing parabola representing the water fountain is given by
𝑝(𝑥) = −𝑥² + 5𝑥 − 4.
Based on the above information, answer the following questions:
(i) Find the zeroes of the polynomial p(x) from the graph [1 marks]
(ii) Find the value of x at which water attains maximum height. [1 marks]
(iii)(A) If h is the maximum height attained by the water stream from the water level of the pool, then find the value of h. [2 marks]
OR
(iii)(B) At what point(s) on x- axis, the height of water above x- axis is 2 m? [2 marks]
Solution:- See full solution
Case study 3:- Rinku was very happy to receive a fancy jumbo pencil from his best friend Rohan on his birthday. Pencil is a basic writing tool, when sharpened its shape is a combination of cylinder & cone as given in the picture. Cylindrical pencil with conical head is a common shape worldwide since ages. Commonly pencils are made up of wood & plastic but we should promote pencils made up of eco-friendly material (many options available in the market these days) to save environment.
The dimensions of Rinku’s pencil are given as follows:
Length of cylindrical portion is 21cm. Diameter of the base is 1 cm and height of the conical portion is 1.2 cm
Based on the above information, answer the following questions:
(i) Find the slant height of the sharpened part. [1 marks]
(ii) Find curved surface area of sharpened part (in terms of 𝜋). [1 marks]
(iii) (A) Find the total surface area of the pencil (in terms of 𝜋). [2 marks]
OR
(iii)(B) The pencil’s total height decreases by 8.2 cm after sharpening it many times, what is the volume of the cylindrical part of the shortened pencil (in terms of 𝜋) ? [2 marks]