Case Study Based Questions Class 10 Maths
Case Study Based Questions Class 10 Maths
- To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.
(i) What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B?
(ii) Express 36 as a product of its primes
(iii) 7 is a ________ number
(iv) If p and q are positive integers such that p = a and q= b, where a , b are prime numbers, then find the LCM (p, q) - Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial.
(i) Write the shape of the path traced shown in figure below.
(ii) Write the condition for ‘a’ if graph of quadratic polynomial ax2 + bx +c opens upwards.
(iii) Observe the above graph and answer how many zeroes are there for the polynomial?
(iv) Write the three zeroes in the above shown graph.
3. Two schools P and Q decided to award prizes to their students for 2 games of Hockey Rs.x per student and Cricket Rs.y per student. School P decided to Award a total of Rs. 9500 for the two games to 5 and 4 Students respectively, while School Q decided to award Rs.7374 for the two games 4 and 3 students respectively.
(i) Represent the following information algebraically ( in terms of x and y).
(ii)Â What is the price amount of hockey?
(iii)On which game  the price amount is more and by how much ?
(iv) What will be the total Price amount if there are two student each part 2 games
4. The speed of a motor boat is 20 km/hr in still water. For covering the distance of 15 km the boat took 1 hour more for upstream than downstream.Â
(i) Let speed of the stream be x km/hr. then write speed of the motorboat in upstream.
(ii). Write the quadratic equation for the speed of the current?
(iii) What is the speed of current?
(iv) How much time boat took in downstream?
Case Study Based Questions Class 10 Maths
5. Raj and Ajay are very close friends. Both the families decide to go to Ranikhet by their own cars. Raj’s car travels at a speed of x km/h. While Ajay’s car travels 5 km/h faster than Raj’s car. Raj took 4 hours more than Ajay to complete the journey of 400km
(i)What will be the distance covered by Ajay’s car in two hours?
(ii) What is the speed of Ajay’s car ?
(iii). much time took Ajay to travel 400 km ?
(iv)Which of the following quadratic equation describe the speed of Raj’s car?
a) x2 – 5x – 500 = 0
b) x2 + 4x – 400 = 0
c) x2 + 5x – 500 = 0
d) x2 – 4x + 400 = 0
6. Your elder brother wants to buy a car and plans to take loan from a bank for his car. He repays his total loan of Rs1,18,000 by paying every month starting with the first instalment of Rs1000. If he increases the instalment by Rs100 every month, answer the following:
(i) Find the amount paid by him in 30th instalment.
(ii) What amount does he still have to pay after 30th installment?
(iii). If total installments are 40 then find the amount paid in the last installment?
(iv). Find the ratio of the 1st installment to the last installment
7. Vijay is trying to find the average height of a tower near his house. He is using the properties of similar triangles. The height of Vijay’s house is 20m when Vijay’s house casts a shadow 10m long on the ground. At the same time, the tower casts a shadow 50m long on the ground and the house of Ajay casts 20m shadow on the ground.
(i). What is the height of the tower?
(ii).What will be the length of the shadow of the tower when Vijay’s house casts a shadow of 12m?
(iii). What is the height of Ajay’s house?
(iv)When the tower casts a shadow of 40m, same time what will be the length of the shadow of Ajay’s house?
8. In order to conduct Sports Day activities in your School, lines have been drawn with chalk powder at a distance of 1 m each, in a rectangular shaped ground ABCD,100 flowerpots have been placed at a distance of 1 m from each other along AD, as shown in given figure below. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 th distance AD on the eighth line and posts a red flag.
(i)Find the position of green flag
(ii)Find the position of red flag
(iii)What is the distance between both the flags?
(iv)If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?
9. Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure, including microwave dishes. They are among the tallest human made structures. There are 2 main types: guyed and self-supporting structures. On a similar concept, a radio station tower was built in two sections A and B. Tower is supported by wires from a point O. Distance between the base of the tower and point O is 36 m. From point O, the angle of elevation of the top of section B is 300 and the angle of elevation of: the top of section A is 450
- Find the length of wire from point O to the top of Section B
- Find the distance AB
- Find the area of triangle OPB
(iv)Find the height of the Section A from the base of the tower.
10. A Ferris wheel (or a big wheel in the United Kingdom) is an amusement ride consisting of a rotating upright wheel with multiple passenger-carrying components (commonly referred to as passenger cars, cabins, tubs, capsules, gondolas, or pods) attached to the rim in such a way that as the wheel turns, they are kept upright, usually by gravity. After taking a ride in Ferris wheel, Aarti came out from the crowd and was observing her friends who were enjoying the ride . She was curious about the different angles and measures that the wheel will form. She forms the figure as given below.
In the given figure
(i) Find ROQ
(ii) Find RQP
(iii)Find RSQÂ Â Â
(iv) Find ORP
11. A brooch is a small piece of jewelry which has a pin at the back so it can be fastened on a dress, blouse or coat. Designs of some brooch are shown below. Observe them carefully.
Design A:Â Brooch A is made with silver wire in the form of a circle with diameter 28mm. The wire used for making 4 diameters which divide the circle into 8 equal parts.
Design B:Â Brooch B is made of two colours – Gold and silver. Outer part is made with Gold. The circumference of silver part is 44mm and the gold part is 3mm wide everywhere.
Refer to Design A
1. Find the total length of silver wire required
2. Find the area of each sector of the brooch
Refer to Design B
3. Find the circumference of outer part (golden)
4. Find the difference of areas of golden and silver parts5. A boy is playing with brooch B. He makes revolution with it along its edge. How many complete revolutions must it take to cover 80 mm?
12. A golf ball is spherical with about 300-500 Â dimples that help increase its velocity while in play. Golf balls are traditionally white but available in colours also. In the given figure, a Golf ball has diameter 4.2 cm and surface has 315 dimples (hemispherical) of radius 2 mm. Â
 Based on the above information answer the following questions
(i)Find the surface area of one such simple
(ii) Find the volume of the material dug out to make one dimple.
(iii)Find the total surface area exposed to the surroundings
(iv)Find the volume of the Gulf ball
13. The COVID-19 pandemic, also known as coronavirus pandemic, is an ongoing pandemic
of coronavirus disease caused by the transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) among humans. The following tables shows the age distribution of case admitted during a day in two different hospitals      Â
                                      Table 1
| Ages (yrs) | 5-15 | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 |
| no. of cases | 6 | 11 | 21 | 23 | 14 | 5 |
TABLE-2
| Ages (yrs) | 5-15 | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 |
| No. of cases | 8 | 16 | 10 | 42 | 24 | 12 |
Refer to table 1)
1. Find the average age for which maximum cases occurred
2. What is the upper limit of modal class?
3. Find the mean of the given data
Refer to table 2)
- Find the mode of the given data
- Find the median of the given data
14. Rahul and Ravi planned to play Business ( board game) in which they were supposed to use two dice.
(i). Ravi got first chance to roll the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is 8?
(ii)Rahul got next chance. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is 13?
(iii)Now it was Ravi’s turn. He rolled the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is less than or equal to 12?
(iv)Rahul got next chance. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is equal to 7?
(v). Now it was Ravi’s turn. He rolled the dice. What is the probability that he got the sum of two numbers appearing on the top face of the dice is greater than 8?
Case Study Based Questions Class 10 Maths
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