Case Study Based Questions Class 10

Real numbers, Polynomials, Pair of Linear Equations in two variables, Coordinate Geometry, Area Related to Plane figures, Probability

CHAPTER -1, REAL NUMBERS

CASE STUDY -1

The diagram shown below is a prime factor tree

Based on the information given in the above factor tree, answer the following questions.

Question 1) Find the value of a ?

Question 2) Find the value of 'b' ?

Question 3) Find the value of ' c + d' ?

Question 4) Find the HCF of (a, b, c) ?

Question 5) What is the HCF of Smallest Prime Number and smallest composite number ?

Question	Answer
1	3
2	7
3	24
4	1
5	2

CASE STUDY -2

Teaching mathematics through activities is a powerful approach that enhances students understanding and engagement.
Keeping this in mind, Ms. Mukta planned a prime number game for class 5 students.
She announces the number 2 in her class and asked the first student to multiply it by a prime number and then pass it to the next student. Second student also multiplied it by a prime number and passed it to third student.
In this way by multiplying to a prime number, the last student got 173250

Now, Mukta asked some questions as given below to the students:

(i) What is the least prime number used by students ?

(ii) (a) How many students are in the class ?

(b) What is the highest prime number used by students ?

(iii) Which prime number has been used maximum times ?

Question	Answer
1	3
2(a)	7 Students
2(b)	11
3	5

CASE STUDY 3

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.

Question 1

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?

Question 2

If the product of two positive integers is equal to the product of their HCF and

LCM is true then, then find the HCF (32 , 36)

Question 3

Express 36 as a product of primes.

Question 4

Check whether 7 X 11 X 13 X 15 + 15 is prime or composite.

Question 5

If p and q are positive integers such that p = ab² and q = a²b, where a, b are prime numbers, then find the LCM (p, q).

Question	Answer
1	288
2	4
3	2² x 3²
4	Composite Number
5	a²b²

CASE STUDY 4

A morning walk is one of the best ways to stay healthy and active. It refreshes the mind, improves blood circulation, and keeps the body fit.

Walking in the fresh morning air gives energy for the whole day and reduces stress. It also helps in building strong immunity, controlling weight, and keeping diseases away.

On a morning walk, three persons A, B, and C step out together and their steps measure 30 cm, 36 cm and 40 cm respectively.

Based on the above information answer the following questions.

Question 1

Find the prime factors of 30, 36, 40.

Question 2

What is the minimum distance each should walk so that each can cover the same distance in complete steps.

Question 3

Find the number of steps taken by A, B and C to cover that minimum distance.

Question	Answer
1	30 = 2 ✕ 3 ✕ 5 36 = 2 ✕ 2 ✕ 3 ✕ 3 40 = 2 ✕ 2 ✕ 2 ✕ 5
2	360 cm
3	31 steps

CHAPTER -2 POLYNOMIALS

CASE STUDY -1

A car moves on a highway. The path it traces is given below

Based on the above information, answer the following questions

Question 1

What is the shape of the curve EFG ?

Question 2

If the curve ABC is represented by the polynomial -(x² + 4x + 3), then its zeroes are :

Question 3

If the path traced by the car has zeroes at -1 and 2, then it is given by

Question 4

The number of zeroes of the polynomial representing the whole curve is :

Question 5

The distance between C and G is :

Question	Answer
1	Parabola
2	1 and 3
3	x² - x – 2
4	4 zeroes
5	6 units

CASE STUDY -2

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.

Based on the above information answer the following questions

1. What is the shape of the poses shown.

2. The graph of parabola opens downwards, if _______

a) a ≥ 0

b) a = 0

c) a < 0

d) a > 0

3. In the graph, how many zeroes are there for the polynomial?

Q4) The two zeroes in the above shown graph are
a) 2, 4
b) - 2, 4
c) - 8, 4
d) 2, -8

5. Find the zeroes of the quadratic polynomial $4\sqrt{3}x^{2}+5x-2\sqrt{3}$ .

Question	Answer
1	Parabola
2	a < 0
3	2
4	-2, 4
5	$-\frac{2}{\sqrt{3}},\: \frac{\sqrt{3}}{4}$

CHAPTER -5, ARITHMETIC PROGRESSION

Case Study-1

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 Rs 1,18,000 by paying every month starting with the first instalment of Rs 1000. If he increases the instalment by Rs 100 every month , answer the following:

Read the above information and answer the following questions

Question 1:What is the amount paid by him in 30th installment

Question 2: If total installments are 40 then amount paid in the last installment?

Question 3: The ratio of the 1st installment to the last installment is

Question 4: What is the total amount paid in first 15 installments.

Answer Key:

1) 3900 2) 4900 3) 10:49 4) Rs 25500

CHAPTER -5, ARITHMETIC PROGRESSION

Case Study - 2

The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.

Based on the above information answer the following question

S.No	Questions	Marks
I	If the first circular row has 30 seats, how many seats will be there in the 10th row? Ans 120	1
II	For 1500 seats in the auditorium, how many rows need to be there? Ans 15	1
III	If there were 17 rows in the auditorium, how many seats will be there in the middle row? Ans 110	2

CHAPTER -5, ARITHMETIC PROGRESSION

Case Study - 3

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 in 31 seconds .

Based on the above informations answer the following questions

Question 1

Write the AP sequence for this situation.

Question 2

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

Question 3

Find the value of x, for which 2x, x+ 10, 3x + 2 are three consecutive terms of an AP

Answer Key:

1) 51, 49, 47, .........

2) 11 Days 3) x = 6

Case Study - 3

CHAPTER -7, COORDINATE GEOMETRY

Case Study - 1

Shivani is an interior decorator, To design her own living room she designed wall shelves. The graph of intersecting wall shelves is given below.

Based on the above information, answer the following questions

Question1

If O is the origin, then what are the coordinates of S ?

a) (-6, -4)

b) (6, 4)

c) (-6, 4)

d) (6, -4)

Question 2

The coordinates of the mid – point of the line segment joining D and H is :

a) (-3, 2/3)

b) (3, -1)

c) (3, 1)

d) (-3, -2/3)

Question 3

The ratio in which the x-axis divides the line segment joining the points A and C is :

a) 2:3

b) 2:1

c) 1:2

d) 1:1

Question 4

The distance between the points P and G is :

a) 16 units

b) 3 $\sqrt{74}$ units

c) 2 $\sqrt{74}$ units

d) $\sqrt{74}$ units

Question 5

The coordinates of the vertices of rectangle IJKL are :

a) I(2, 0), J(2, 6), K(8, 6), L(8, 2)

b) I(2, -2), J(2, -6), K(8, -6), L(8, -2)

c) I(-2, 0), J(-2, 6), K(-8, 6), L(-8, 2)

d) I(-2, 0), J(-2, -6), K(-8, -6), L(-8, -2)

Question	Answer
1	c
2	b
3	d
4	c
5	b

CHAPTER -7, COORDINATE GEOMETRY

CASE STUDY -2

A rough coordinate map of Lahiri’s Locality is shown below

Read the above information and answers the questions given below

Q1) The coordinates of the grocery store are :

a) (11, 8)

b) (7, 2)

c) (2, 7)

d) (8, 6)

Q2) The distance between the hotel and the post office is :

a) 5 units

b) $\sqrt{5}$ units

c) $\sqrt{17}$ units

d) 17 units

Q3) If a point (x, y) is equidistant from both laundry and the post office, then :

a) x = y = 4

b) x + y = 7

c) x + y = -7

d) x – y = 7

Q4) Anuradha goes first to the laundry from the post office, and then from there to the grocery store, The total distance travelled by her is :

a) 34 units

b) 28 units

c) ( $\sqrt{4}+\sqrt{6}$ ) units

d) ( $\sqrt{8}+\sqrt{26}$ ) units

Q5) The co-ordinates of the reflection of the post office on the y – axis are :

a) (-4, -5)

b) (4, -5)

c) (-4, 5)

d) (0, 5)

Question

Answer

1

b

2

c

3

b

4

d

5

c

CHAPTER -7, COORDINATE GEOMETRY

CASE STUDY - 3
Coordinate geometry is the combination of algebra and geometry. In other words we can say that coordinate geometry is a technique in which we solve the geometrical problems algebraically.

In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. Shyam and Ekta walk into the class and after observing for a few minutes tries to find the answers of the following questions.

Q 1) Coordinates of points A, B, C, D are

a) A(2,3), B(3,5), C(5,1), D(0, -1)

b) A(-2,3), B(3,5), C(5,1), D(0, -1)

c) A(-2,3), B(-3,5), C(5,1), D(0, -1)

d) A(-2,3), B(3,5), C(-5,1), D(0, -1)

Q 2) Distances: |AB|, |BC| are

a) |AB| = $\sqrt{20}$ , |BC| = $\sqrt{29}$

b) |AB| = $\sqrt{30}$ , |BC| = $\sqrt{20}$

c) |AB| = $\sqrt{29}$ , |BC| = $\sqrt{29}$

d) |AB| = $\sqrt{29}$ , |BC| = $\sqrt{20}$

Q 3) Distances: |AC| and |BD|

a) |AC| = $\sqrt{53}$ , |BD| = $\sqrt{45}$

b) |AC| = $\sqrt{53}$ , |BD| = $\sqrt{53}$

c) |AC| = $\sqrt{45}$ , |BD| = $\sqrt{45}$

d) |AC| = $\sqrt{45}$ , |BD| = $\sqrt{53}$

Q 4) What type of Quadrilateral ABCD is
a) Rectangle
b) Parallelogram
c) Rhombus
d) Square

Q 5) What are the coordinates of point of intersection of diagonals AC and BD

a) $\left (\frac{3}{2},2 \right )$

b) $\left (\frac{3}{2},-2 \right )$

c) $\left (-2,\frac{3}{2} \right )$

d) (5, -2)

Answer Key:

1) b 2) d c) a 4)b 5)

CHAPTER -7, COORDINATE GEOMETRY

CASE STUDY - 4

A tiling or tessellation of a flat surface is the covering of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. Historically, tessellations were used in ancient Rome and in Islamic art.

You may find tessellation patterns on floors, walls, paintings etc. Shown below is a tiled floor in the archaeological Museum of Seville, made using squares, triangles and hexagons.

A craftsman thought of making a floor pattern after being inspired by the above design. To ensure accuracy in his work, he made the pattern on the Cartesian plane. He used regular octagons, squares and triangles for his floor tessellation pattern

Use the above figure to answer the questions that follow:

Q. No.	Question	Marks
I	What is the length of the line segment joining points B and F? Ans √58	1
II	The centre ‘Z’ of the figure will be the point of intersection of the diagonals of quadrilateral WXOP. Then what are the coordinates of Z? Ans (-1/2, 11/2)	1
III	What are the coordinates of the point on y axis equidistant from A and G? Ans (0, 57/10)	2

CHAPTER -9, APPLICATION OF TRIGONOMETRY

CASE STUDY -1

Lakshaman Jhula is located 5 kilometers north-east of the city of Rishikesh in the Indian state of Uttarakhand. The bridge connects the villages of Tapovan to Jonk. Tapovan is in Tehri Garhwal district, on the west bank of the river, while Jonk is in Pauri Garhwal district, on the east bank. Lakshman Jhula is a pedestrian bridge also used by motorbikes. It is a landmark of Rishikesh. A group of Class X

Students visited Rishikesh in Uttarakhand on a trip. They observed from a point (P) on a river bridge that the angles of depression of opposite banks of the river are 60° and 30° respectively. The height of the bridge is about 18 meters from the river

Based on the above information answer the following questions.

Q. No.

Question

Marks

I

Find the distance PA. Ans. 12√3m

1

II

Find the distance PB Ans. 36m

1

III

Find the width AB of the river. Ans. 24√3m
[OR]
Find the height BQ if the angle of the elevation from P to Q be 45°.
Ans 18(√3+1)m

2

CHAPTER -11,  AREA RELATED TO CIRCLES

Case Study - 1
A protractor is a measuring instrument that is used for measuring angles. It is usually made of transparent plastic or metal materials

Some protractors are simple half discs. More advanced protractors, such as the bevel protractor, have one or two swinging arms which can be used for measuring angles.
A semicircular protractor of diameter 14 cm

Based on the above information, answer the following questions.
Q1) The perimeter of the given protractor (in cm) is
a) 22
b) 44
c) 36
d) 58

Q2) The area of the protractor given in the question in sq. cm is
a) 77
b) 154
c) 308
d) 616

Q3) If the diameter of the protractor is increased by 2.1 cm, then the perimeter will increased by
a) 3.5 cm
b) 6.6 cm
c) 5.4 cm
d) 7.3 cm

Q4) If the original protractor is divided into six equal sectors, what will be the area of each sector (in sq. cm) ?
a) 77/6
b) 77/3
c) 154/3
d) 308/3

Q5) The perimeter of each of the above sectors (in cm) will be
a) 53/3
b) 64/3
c) 95/3
d) 106/3

Question
Answer
1
c
2
a
3
c
4
a
5
a

CHAPTER -11,  AREA RELATED TO CIRCLES
Case Study - 2
A regular polygon of side 14 cm is drawn. Further circles of equal radii are constructed inside the polygon as shown below.
Based on the above information, answer the following questions.
Q1) What is the angle at each vertex of the polygon ?
a)   108^o
b) 120^o
c)   135^o
d)  150^o
Q2) What fraction of a circle is drawn at each vertex ?
a) 3/10
b) 1/3
c) 3/8
d) 5/12

Q3) What area (in sq. cm ) of this polygon is covered by circle and parts of circles ?
a) 1232
b) 924
c) 616
d) 462

Q4) What is the area of the polygon in sq. cm
a)   $49\sqrt{\frac{3}{4}}$
b)   $49\sqrt{3}$
c)   $147\sqrt{\frac{3}{2}}$
d)   $294\sqrt{3}$

Q5) What is the area (in sq. cm) of the unshaded part of the figure
a) 294 $\sqrt{3}$ - 154
b) 294 $\sqrt{3}$ - 308
c) 294 $\sqrt{3}$ - 462
d) None of these

Question
Answer
1
b
2
b
3
d
4
d
5
c

Chapter - 12: Surface Area and Volume

Case Study 1

Rohit was doing an experiment to find the radius r of a sphere. For this he look a cylindrical container with radius R = 7 cm and height = 10 cm.

He filled the container almost half by water as shown in the left figure. Now he dropped the yellow sphere in the container he observed as shown in the right figure. the water level in the container raises from A to B equal to 3.40 cm.

Based on the given information, answer the following questions.

Q1) If the water in the cylinder is filled to a height of 5 cm. What is the volume (in cu.cm) of water in the cylinder?

Q2) Volume (in cm³) of water displayed when sphere submerged is

Q3) Volume (in cm³) of the sphere is equal to

Q4) The radius of sphere in cm is approximately

Q5) The ratio of the curved surface areas of the sphere and the container is

Question	Answer
1	245π
2	166.6π
3	166.6π
4	5
5	5:7

CHAPTER - 12 SURFACE AREA AND VOLUME

Case Study - 2

State government wants to arrange a camp in a remote area for the welfare of villagers, who are facing health issues. They make a tent as shown in the figure below

Based on the above information answer the following questions

Q1) Slant height of the conical part is

a) 6m b) 8m c) 10m d) 7.5m

Q2) Curved surface area of the conical part is

a) 40π m²b) 80π m²c) 120π m²d) 100π m²

Q3) Curved surface area of the cylindrical part is

a) 96π m²b) 69π m²c) 80π m²d) 40π m²

Q4) Volume of air in the tent is

a) 125π m³b) 256π m³c) 314π m³d) 512π m³

Q5) Cost of canvas required to make the tent at the rate of ₹ 3.50 / m²

a) ₹ 1936 b) ₹ 1639 c) ₹ 1369 d) ₹ 1963

Question	Answer
1	c
2	b
3	a
4	d
5	a

CHAPTER - 12, SURFACE AREA AND VOLUME

Case Study - 3

Mathematics teacher of a school took her 9th standard students to show Gol Gumbaz. It was a part of their educational trip. The teacher had interest in history as well.

She narrated the facts of Gol Gumbaz to students. Gol Gumbaz is the tomb of king Muhammad Adil Shah, Adil Shah Dynasty. Construction of the tomb, located in Vijayapura, Karnataka, India, was started in 1626 and completed in 1656.

It reaches up to 51 meters in height while the giant dome has an external diameter of 44 meters, making it one of the largest domes ever built.

At each of the four corners of the cube is a dome shaped octagonal tower seven stories high with a staircase inside.

Q1) What is the total surface area of a cuboid?

a) lb + bh + hl

b) 2(lb + bh + hl)

c) 2(lb + bh)

d) 1² + b² + h²

Q2) What is the curved surface area of hemispherical dome ?

a) 908π m²b) 968π m²c) 340π m²d) 780π m²

Q3) What is the height of the cuboidal part ?

a) 14 m b) 7 m c) 29 m d) 18 m

Q4) What is the circumference of the base of the dome ?

a) 34 π m b) 22 π m c) 44 π m d) 55 π m

Q5) The total surface area of a hemispherical dome having radius 7 cm is

a) 462 cm² b) 294 cm² c) 588 cm² d) 154 cm²

^{Question Option Answer
1 b 2(lb + bh + hl)
2 b 968π m²
3 c 29 m
4 c 44 π m
5 a 462 cm²

CHAPTER - 12, SURFACE AREA AND VOLUME

Case Study - 4
A construction company is installing a solid iron pole for supporting a
large structure. The pole is made by joining two cylindrical
sections. The lower section is a cylinder of height 220 cm and base diameter 24
cm. On top of it, another cylindrical section of height 60 cm and radius 8 cm
is fixed.
The company needs to determine the total mass of the pole before
transporting it to the construction site. It is given that 1 cm³ of iron has a
mass of approximately 8 g. Take π = 3.14.

Answer the following questions:

I

Find the volume of the Pole lower cylindrical section.

1

II

Find the total volume of iron used in making the pole.

2

III

Calculate the mass of the complete iron pole in kilograms.

1

Answer Key
I) 99475.2 cm².

II)
111532.2 cm².

III) 892.2624
Kg}

CHAPTER - 14 PROBABILITY

Case Study - 1

Dice are small, throwable objects with marked sides that can rest in multiple positions. They are used for generating random numbers, commonly as part of tabletop games, including dice games, board games, role playing games and games of chance.

A traditional die is a cube with each of its six faces marked with a different number of dots (pips) from one to six. When thrown or rolled, the die comes to rest showing a random integer from one to six on its upper surface, with each value being equally likely.

A die is rolled, then find

Q1) The probability of getting a prime number is

Q2) The probability of getting a non-prime number is

Q3) The probability of getting a composite number is

Q4) The probability of getting a divisor of 24 is

Q5) The probability of getting a number less than 8 is

Answer: 1) 3/6, 2) 3/6 3) 2/6 4) 5/6 5) 1

CHAPTER - 14 PROBABILITY

Case Study - 2

Pack of playing cards contain 52 cards in which half cards are black and half cards are red. Jack, King and Queen are called face card and the cards written one are called ace card.

One-fourth of the cards are spade, club, diamond and heart. One card is drawn from the deck of 52 playing cards.

Find the probability of getting.

i) A red face card.

ii) A card of spade or ace.

iii) Either king or queen.

iv) Neither red nor queen.

Answer: i) 3/26 ii) 4/13 iii) 2/13 iv) 6/13]

I	Find the volume of the Pole lower cylindrical section.	1
II	Find the total volume of iron used in making the pole.	2
III	Calculate the mass of the complete iron pole in kilograms.	1

Search This Blog