Case Study 10th Class
Case Study 10th Class
Case Study 10th Class
Case study
Mathematics
Class : 10th
1. To enhance the reading skills of grade X students, the school nominates you and two of 4
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. [CBSE Question
Bank]
(a) 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?
(b) If the product of two positive integers is equal to the product of their HCF and LCM is true
then, the HCF (32, 36) is
(i) 22 × 32 (ii) 21 × 33
(iii) 23 × 31 (iv) 20 × 30
(d) 7 × 11 × 13 × 15 + 15 is a
(e) If p and q are positive integers such that p = ab2, and q = a2b, where a, b are prime
numbers, then the LCM (p, q) is
(i) ab (ii) a2b2
(a) In each room the same number of participants are to be seated and all of them being in
the same subject, hence maximum number participants that can accommodated in each
room are
(b) What is the minimum number of rooms required during the event?
(i) 23 × 32 (ii) 23 × 33
(iii) 22 × 32 (iv) 22 × 33
3. A Mathematics Exhibition is being conducted in your school and one of your friends is 4
making a model of a factor tree. He has some difficulty and asks for your help in completing
a quiz for the audience. Observe the following factor tree and answer the following:
(a) What will be the value of x?
He received 480 chemistry books, 192 physics books and 672 Mathematics books of class XI.
He whishes to average these books in minimum numbers of stacks such that each stack
consists of the books on only one subject and the number of books in each stack is the
same.
(d) Difference in number of stacks of Mathematics books and sum of stacks of Physics and
Chemistry books is
(e) If the thickness of each book of physics is 2.5 cm then height of each stack is
5. To enhance the reading skills of grade X students, the school nominates you and two of 4
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?
(iii) If there are 36 students in section A and 44 students in section B, what is minimum
number of books you will acquire for the class library so that they can be distributed equally
among students of section A or B.
OR
(ii) What is the minimum number of rooms required during the event?
OR
7. Aditi plantations have two rectangular fields of the same width but different lengths. They 4
are required to plant 168 trees in the smaller field and 462 trees in the larger field. In both
fields, the trees will be planted in the same number of rows but in different number of
columns.
(i) What is the maximum number of rows in which the trees can be planted in each of the
fields?
(ii) If the trees are planted in the number of rows obtained in part (i), how many columns will
each field have?
(iii) If total cost of planted trees in one column is ` 500, then find the cost to plant the trees in
smaller field.
OR
If the total cost of planted trees in one column is ` 500, the find the cost to plant the trees in
larger field.
8. The below picture are few natural examples of parabolic shape which is represented by a 5
quadratic polynomial. 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. [CBSE Question Bank]
(a) In the standard form of quadratic polynomial, ax2 + bx + c, a, b and c are
(iii) ‘a’ is a non zero real number and b and c are any real numbers.
(c) If α and are the zeroes of the quadratic polynomial 2x2 – x + 8k, then k is
(e) If the sum of the roots is –p and product of the roots is then the quadratic
polynomial is
9. An asana is a body posture, originally and still a general term for a sitting meditation pose, 5
and later extended in hatha yoga and modern yoga as exercise, to any type of pose or
position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one
can observe that poses can be related to representation of quadratic polynomial. [CBSE
Question Bank]
(a) The shape of the poses shown is
(c) In the graph, how many zeroes are there for the polynomial?
11. The below picture are few examples of natural parabolic which is represented by a 4
quadratic polynomial. 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.
(i) If a and are the zeroes of the quadratic polynomial 2x2 – x + 8k, then find the value of k.
(iii) Write a quadratic polynomial whose one zero is 4 and product of zeroes is 0.
OR
12. 4
An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in
hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted,
twisting, and balancing poses. In the figure, one can observe that poses can be related to representation of
quadratic polynomial.
(i) In the graph, how many zeroes are there for the polynomial?
OR
13. In Maths activity period, Roma’s Maths teacher told her to draw the graph of a polynomial having at most 4
two zeroes. She draws the graph as shown below:
OR
If a and b are zeroes of the polynomial x2 – px + q2, then find the value of a + b – ab.
5-15 6
15-25 11
25-35 21
35-45 23
45-55 14
55-65 5
Table 2
5-15
8
15-25
16
25-35
10
35-45
42
45-55
24
55-65
12
Refer to table 1
Refer to table 2
15. The table given below shows the absents records of 40 number of students of a class for 4
the middle term.
Number of days 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40
Number of students 11 10 5 4 5 2 2 1
(c) Write the assumed mean formula for calculating mean of above data.
(d) If di is the deviation of xi from the assumed mean a then determine the value of ∑fidi.
16. Electricity energy consumption is the form of energy consumption that uses electric 4
energy. Global electricity consumption continues to increase faster than world population,
leading to an increase in the average amount of electricity consumed per person (per capita
electricity consumption).
A survey is conducted for 56 families of a Colony A. The following tables gives the weekly
consumption of electricity of these families.
0-10 16
10-20 12
20-30 18
30-40 6
40-50 4
50-60 0
The similar survey is conducted for 80 families of Colony B and the data is recorded as
below:
0-10 0
10-20 5
20-30 10
30-40 20
40-50 40
50-60 5
(i) 19.64 units (ii) 22.5 units (iii) 26 units (iv) None of these
(i) 38.2 units (ii) 43.6 units (iii) 26 units (iv) 32 units
(i) 15.65 units (ii) 32.8 units (iii) 38.75 units (iv) 48 units
17. What the data is continuous and is the form of frequency distribution then median, mean 4
and model are related to each other as
3Median = Mode +
2Mean
Answer the questions based on above.
(a) Mode and mean of a data are 24 k and 30 k. Median of the data is
The given distribution shows the number of runs scored by top batsman is one-day international.
3000 – 4000 5
4000 – 5000 15
5000 – 6000 10
6000 – 7000 8
7000 – 8000 6
8000 – 9000 2
9000 – 10000 3
(b) What is the frequency of the class preceeding the modal class?
(d) Write the formula for finding the mode of the above data?
Raghav and Mohan are playing with cards. The deck has 52 playing cards. Mohan drew one
card. Answer the questions based on above.
(a) What is the probability that drawn card is red colour?
21. Rahul and Ravi planned to play Business (board game) in which they were supposed to 4
use two dice
(a) 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?
(b) 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?
(c) 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 ?
(d) 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 ?
(e) 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 greater than 8 ?
22. Shiv and Raman are playing with pair of dice. They throw a pair of dice and write the 4
outcomes. Raman says, we have 36 outcomes. Then he asks some questions to Shiv. Help
Shiv to find the answer.
(a) Find the probability that number obtained have sum less than 7.
(c) Mohan says, if I throw a dice once, find the probability of getting a prime number.
(d) If the dice is thrown once, what is the probability of getting an odd number.
(e) In a single throws of two dice, find the probability of getting a doublet of even numbers.
23. Ram Gopal has 20 tickets on which numbers are written from 1 to 20. 4
He mixed thoroughly all the tickets and then a ticket is drawn at random out of them. Answer
the questions based on above.
(a) The probability that drawn ticket bears a number, which is multiple of 3 is
(i) 1
(ii) 0
(iv) –1