Notesale: Turn your study into money

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REAL NUMBERS- CASE STUDY
CASE STUDY 1
...
There are two sections- section A and
section B of grade X
...


1
...
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
a) 2
b) 4
c) 6
d) 8

3
...
7

is a

a) Prime number
b) Composite number
c) Neither prime nor composite
d) None of the above
5
...
c) 288
2
...
a)
4
...
b)
CASE STUDY 2:
A seminar is being conducted by an Educational Organisation, where the
participants will be educators of different subjects
...


1
...
What is the minimum number of rooms required during the event?
a) 11
b) 31
c) 41
d) 21
3
...
The product of HCF and LCM of 60,84 and 108 is
a) 55360
b) 35360
c) 45500
d) 45360
5
...
b) 12
2
...
a)
4
...
d)

CASE STUDY 3:
A Mathematics Exhibition is being conducted in your School and one of your friends
is making a model of a factor tree
...

Observe the following factor tree and answer the following:

x

5

2783

y

253

11

1
...
What will be the value of y?
a) 23
b) 22
c) 11
d) 19
3
...
According to Fundamental Theorem of Arithmetic 13915 is a
a) Composite number
b) Prime number
c) Neither prime nor composite
d) Even number
5
...
b) 13915
2
...
b) 23
4
...
c)
POLYNOMIALS- CASE STUDY
CASE STUDY 1:
The below picture are few natural examples of parabolic shape which is represented
by a quadratic polynomial
...
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,

, a, b and c are

a) All are real numbers
...

c) ‘a’ is a non zero real number and b and c are any real numbers
...

2
...
If

are the zeroes of the qudratic polynomial 2

then k is

a) 4
b)
c)
d)

2

4
...

b) Touches x‐axis at a point
...

d) Either touches or intersects x‐ axis
...
If the sum of the roots is –p and product of the roots is - , then the quadratic
polynomial is
a) k (

)

b) k (

)

c) k (

)

d) k (

)
ANSWERS

1
...

2
...
b)
4
...

5
...
In the figure, one can observe that poses can be related to
representation of quadratic polynomial
...
The shape of the poses shown is
a) Spiral
b) Ellipse
c) Linear
d) Parabola
2
...
In the graph, how many zeroes are there for the polynomial?

a) 0
b) 1
c) 2
d) 3
4
...
The zeroes of the quadratic polynomial √
a)

√

,

b)
c)

√

,

√

√

d) -

,√

√

√

√

,

ANSWERS
1
...
c) a < 0
3
...
b) -2, 4
5
...
Even though an athlete
dribbles the ball in both sports, a basketball player uses his hands and
a soccer player uses his feet
...
The projectile (path
traced) of soccer ball and basketball are in the form of parabola representing
quadratic polynomial
...
The shape of the path traced shown is
a) Spiral
b) Ellipse
c) Linear
d) Parabola
2
...
Observe the following graph and answer

In the above graph, how many zeroes are there for the polynomial?
a) 0
b) 1
c) 2
d) 3
4
...
What will be the expression of the polynomial?
a)
b)
c)
d)

ANSWERS
1
...
c) a > 0
3
...
c) -3, -1, 2
5
...
One mark is awarded for every correct
answer while ¼ mark is deducted for every wrong answer
...
Rest of the questions he attempted by guessing
...


Type of Question

Marks given for correct

Marks deducted for

answer

wrong answer

1

0
...
If answer to all questions he attempted by guessing were wrong, then how
many questions did he answer correctly?
2
...
If answer to all questions he attempted by guessing were wrong and
answered 80 correctly, then how many marks he got?
4
...
He answered 96 questions correctly
...
He attempted 24 questions by guessing
...
Marks = 80- ¼ 0f 40 =70
4
...
The design and the
measurement has been made such that areas of two bedrooms and kitchen together
is 95 sq
...


Based on the above information, answer the following questions:
1
...

2
...

3
...

4
...

5
...
50 per sq
...
Area of two bedrooms= 10x sq
...
m
10x + 5y = 95
2x + y =19
Also, x + 2+ y = 15
x + y = 13
2
...
On solving two equation part(i)
x= 6m and y =7m
area of bedroom = 5 x 6= 30m
area of kitchen = 5 x 7= 35m
4
...
m
5
...
The auto charges in a city comprise of a fixed charge together with
the

charge

for

the

Name of the city

distance

covered
...
)

10

75

15

110

8

91

14

145

City B

Situation 1: In city A, for a journey of 10 km, the charge paid is Rs 75 and for a
journey of 15 km, the charge paid is Rs 110
...

Refer situation 1
1
...
A person travels a distance of 50km
...
155
b) Rs
...
355
d) Rs
...
What will a person have to pay for travelling a distance of 30km?
a) Rs
...
289
c) Rs
...
305
4
...
B
2
...
B
4
...
Both the families decide to go to Ranikhet by
their own cars
...
Raj took 4 hours more than Ajay to complete the journey of 400
km
...
What will be the distance covered by Ajay’s car in two hours?
a) 2(x +5)km
b) (x – 5)km
c) 2( x + 10)km
d) (2x + 5)km
2
...
What is the speed of Raj’s car?
a) 20 km/hour
b) 15 km/hour
c) 25 km/hour
d) 10 km/hour
4
...
a) 2(x + 5)km
2
...
a) 20km/ hour
4
...
For covering the distance of 15 km the boat
took 1 hour more for upstream than downstream
...
Let speed of the stream be x km/hr
...
What is the relation between speed ,distance and time?
a) speed = (distance )/time
b) distance = (speed )/time
c) time = speed x distance
d) speed = distance x time
3
...


x2+ 30x − 200 = 0
x2+ 20x − 400 = 0
x 2+ 30x − 400 = 0
x2− 20x − 400 = 0
What is the speed of current ?

a) 20 km/hour
b) 10 km/hour

c) 15 km/hour
d) 25 km/hour
5
...
c) (20 – x)km/hr
2
...
c) x 2+ 30x – 400= 0
4
...
c) 45 minute
ARITHMETIC PROGRESSION
CASE STUDY 1:
India is competitive manufacturing location due to the low cost of manpower and
strong

technical

and

engineering

capabilities

contributing

to

higher

quality production runs
...
It produced 16000 sets in 6 th year and 22600 in 9th
year
...
Find the production during first year
...
Find the production during 8th year
...
Find the production during first 3 years
...
In which year, the production is Rs 29,200
...
Find the difference of the production during 7th year and 4th year
...
Rs 5000
2
...
Production during first 3 year= 5000 + 7200 + 9400=21600
4
...
Difference= 18200-11600=6600
CASE STUDY 2:
Your friend Veer wants to participate in a 200m race
...
He
wants to do in 31 seconds
...
Which of the following terms are in AP for the given situation
a) 51,53,55…
...


c) -51, -53, -55…
...
What is the minimum number of days he needs to practice till his goal is
achieved
a) 10
b) 12
c) 11
d) 9
3
...
If nth term of an AP is given by
an = 2n + 3 then common difference of an AP is
a) 2
b) 3
c) 5
d) 1
5
...
b
2
...
b
4
...
a

CASE STUDY 3:
Your elder brother wants to buy a car and plans to take loan from a bank for his
car
...
If he increases the instalment by Rs 100
every month , answer the following:

1
...
The amount paid by him in the 30 installments is
a) 37000
b) 73500
c) 75300
d) 75000
3
...
If total installments are 40 then amount paid in the last installment?

a) 4900
b) 3900
c) 5900
d) 9400
5
...
a) 3900
2
...
c) 44500
4
...
b) 10 : 49
SIMILAR TRIANGLES
CASE STUDY 1:

Vijay is trying to find the average height of a tower near his house
...
The height of Vijay’s house if 20m when Vijay’s house
casts a shadow 10m long on the ground
...


1
...
What will be the length of the shadow of the tower when Vijay’s house casts a
shadow of 12m?
a) 75m
b) 50m
c) 45m
d) 60m
3
...
When the tower casts a shadow of 40m, same time what will be the length of
the shadow of Ajay’s house?
a) 16m
b) 32m
c) 20m
d) 8m
5
...
c)100m
2
...
b)40m
4
...
d) 8m

CASE STUDY 2:
Rohan wants to measure the distance of a pond during the visit to his native
...
To find the distance between the points, he makes a right-angled
triangle using rope connecting B with another point C are a distance of 12m,
connecting C to point D at a distance of 40m from point C and the connecting D
to the point A which is are a distance of 30m from D such the ADC=900
...
Which property of geometry will be used to find the distance AC?
a) Similarity of triangles
b) Thales Theorem
c) Pythagoras Theorem
d) Area of similar triangles
2
...
Which is the following does not form a Pythagoras triplet?
a) (7,24,25)
b) (15,8,17)
c) (5,12,13)
d) (21,20,28)
4
...
Find the length of the rope used
...
c)Pythagoras Theorem
2
...
d)(21,20,28)
4
...
c)82m
SCALE FACTOR
Case study;
A scale drawing of an object is the same shape at the object but a different size
...
The scale is written as a ratio
...

Hence, two shapes are similar when one can become the other after a resize, flip,
slide or turn
...
Scale
factor is 1:200

This means that a length of 1 cm on the photograph above corresponds to a length
of 200cm or 2 m, of the actual engine
...

1
...
What will affect the similarity of any two polygons?
a) They are flipped horizontally
b) They are dilated by a scale factor
c) They are translated down
d) They are not the mirror image of one another
...
What is the actual width of the door if the width of the door in photograph is
0
...
7m
b) 0
...
07cm
d) 0
...
If two similar triangles have a scale factor 5:3 which statement regarding the
two triangles is true?
a) The ratio of their perimeters is 15:1
b) Their altitudes have a ratio 25:15
c) Their medians have a ratio 10:4
d) Their angle bisectors have a ratio 11:5
5
...
a)22m
2
...
a)0
...
b)Their altitudes have a ratio 25:15
5
...
Niharika runs 1/4 th the distance AD on the 2nd line
and posts a green flag
...


1
...
25)
c) (25,2)
d) (0, -25)
2
...
2)
3
...
√41
a) √11
b) √61
c) √51
4
...
5)
b) (10,22)
c) (2,8
...
5,20)
5
...
5,24)
b) (0
...
5)
c) (2
...
5)
d) (25,20)
ANSWERS:
1
...
c) (8,20)
3
...
a) (5, 22
...
a) (3
...
Saplings of Gulmohar are planted on the boundary
at a distance of 1 m from each other
...
The students are to sow seeds of flowering plants on the
remaining

area

of

1
...
What will be the coordinates of R, if C is the origin?
a) (8,6)
b) (3,10)
c) (10,3)
d) (0,6)
3
...
Calculate the area of the triangles if A is the origin
a) 4
...


d) 6
...
Calculate the area of the triangles if C is the origin
a) 8
b) 5
c) 6
...
5
ANSWERS:
1
...
c) (10,3)
3
...
a) 4
...
d) 4
...

After taking a ride in Ferris wheel, Aarti came out from the crowd and was observing
her friends who were enjoying the ride
...
She forms the figure as given below
...
In the given figure find ROQ
a) 60
b) 100
c) 150
d) 90
2
...
Find RSQ
a) 60
b) 75
c) 100
d) 30
4
...
c) 150
2
...
b) 75
4
...
The logo design is as given in the figure and he is working on the
fonts and different colours according to the
theme
...
The lengths of sides AB, BC and CA are 12 cm, 8 cm and 10 cm
respectively
...
Find the length of AD
a) 7
b) 8
c) 5
d) 9
2
...
Find the length of CF
a) 9
b) 5
c) 2
d) 3
4
...
Find area of ∆ABC
a) 50
b) 60
c) 100
d) 90

ANSWERS:
1
...
b) 5
3
...
c) 24
5
...
The teacher
and students had interest in history as well
...
The teacher also said that India Gate, which is
located at the eastern end of the Rajpath (formerly called the Kingsway), is about
138 feet (42 metres) in height
...
What is the angle of elevation if they are standing at a distance of 42m away
from the monument?
a) 30
b) 45
c) 60
d) 0
2
...
So, they want to know the
distance where they should stand and hence find the distance
...
24 m
b) 20
...
64 m
3
...
The ratio of the length of a rod and its shadow is 1:1
...
The angle formed by the line of sight with the horizontal when the object viewd
is below the horizontal level is
a) corresponding angle
b) angle of elevation
c) angle of depression
d) complete angle
ANSWERS:
1
...
a) 25
...
a) 20√ m
4
...
a) corresponding angle
CASE STUDY 2:

A Satellite flying at height h is watching the top of the two tallest mountains in
Uttarakhand and Karnataka ,them being Nanda Devi(height 7,816m) and
Mullayanagiri (height 1,930 m)
...
If the distance
between the peaks of two mountains is 1937 km , and the satellite is vertically above
the midpoint of the distance between the two mountains
...
The distance of the satellite from the top of Nanda Devi is
a) 1139
...
52 km
c) 1937 km
d) 1025
...
The distance of the satellite from the top of Mullayanagiri is
a) 1139
...
52 km
c) 1937 km
d) 1025
...
The distance of the satellite from the ground is
a) 1139
...
52 km
c) 1937 km
d) 1025
...
What is the angle of elevation if a man is standing at a distance of 7816m from
Nanda Devi?
a) 30
b) 45
c) 60
d) 0
5
...
So, find the distance of this mile stone form the mountain
...
327 km
b) 566
...
36 km
ANSWERS:

1
...
4 km
2
...
b) 577
...
b) 45
5
...
It is
similar as Rangoli in North India and Kolam in Tamil Nadu
...
Your friend who is a partner in competition , suggests two designs given
below
...


Design I: This design is made with a circle of radius 32cm leaving equilateral
triangle ABC in the middle as shown in the given figure
...


Refer Design I:
1
...
The altitude of the equilateral triangle is
a) 8 cm
b) 12 cm
c) 48cm
d) 52cm
Refer Design II:
3
...
Area of each circular design is
a) 124 cm2
b) 132 cm2

c) 144 cm2
d) 154 cm2
5
...
b) 32√ cm
2
...
b) 1764 cm2
4
...
a) 378 cm2
A Brooch
CASE STUDY 4:
A brooch is a small piece of jewellery which has a pin at the back so it can be
fastened on a dress, blouse or coat
...


Observe

them

carefully
...
The wire used for making 4 diameters which divide the circle into 8 equal
parts
...
Outer part is made with
Gold
...

Refer to Design A
1
...
The area of each sector of the brooch is
a) 44 mm2
b) 52 mm2
c) 77 mm2
d) 68 mm2
Refer to Design B
3
...
49 mm
b) 82
...
50 mm
d) 62
...
The difference of areas of golden and silver parts is
a) 18
b) 44
c) 51
d) 64
5
...
He makes revolution with it along its edge
...
b) 200mm
2
...
d) 62
...
c) 51
5
...
Some
students of a school reached for adventure at Sakleshpur
...
After that they went for
a jungle trek
...
As dusk fell, it was time to take
shelter
...
Each group
had to make a conical tent to accommodate all the four students
...
The radius of the tent is 7m
...
The volume of cylindrical cup is
a) 295
...
5cm3
c) 384
...
25cm3
2
...
67cm3
b) 89
...
25 cm3
d) 210
...
Which container had more juice and by how much?
a) Hemispherical cup, 195 cm3
b) Cylindrical glass, 207 cm3
c) Hemispherical cup, 280
...
42 cm3
4
...
How much space on the ground is occupied by each student in the conical
tent
a) 54m2
b) 38
...
d) 404
...
b) 89
...
d) Cylindrical glass, 314
...
c) 24m
5
...
5m2

CASE STUDY 2:

Top View

The Great Stupa at Sanchi is one of the oldest stone structures in India, and an
important monument of Indian Architecture
...
Its nucleus was a simple hemispherical
brick structure built over the relics of the Buddha
...
A big hemispherical dome with a cuboidal structure
mounted on it
...
Calculate the volume of the hemispherical dome if the height of the dome is
21 m –
a) 19404 cu
...
m
c) 15000 cu
...
m
2
...
The cloth require to cover the hemispherical dome if the radius of its base is
14m is
a) 1222 sq
...
m
c) 1200 sq
...
m

4
...
e
...
m
b) 1232 sq
...
m
d) 1932 sq
...
The volume of the cuboidal shaped top is with dimensions mentioned in
question 4
a) 182
...
45 m3
c) 292m3
d) 192m3
Answers
1
...
m
2
...
b) 1232 sq
...
c) 1392 sq
...
d) 192m3
CASE STUDY 3:
On a Sunday, your Parents took you to a fair
...

Observe the figures and answer the questions-:

1
...
Volume of the solid figure if the length of the edge is 7cm isa)256 cm3
b) 196 cm3
c) 343 cm3
d) 434 cm3
3
...
Slant height of a cone if the radius is 7cm and the height is 24 cm___
a) 26cm
b) 25 cm
c) 52 cm
d) 62cm
5
...
d) 6√
2
...
b) 308 cm2
4
...
a) 858 cm2
STATISTICS
CASE STUDY 1:
COVID-19 Pandemic
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
...
of cases

5-15

15-25

25-35

35-45

45-55

55-65

6

11

21

23

14

5

Table 2
Age (in years)

5-15

15-25

25-35

35-45

45-55

55-65

No
...
The average age for which maximum cases occurred is
a) 32
...
36
c) 36
...
24

2
...
The mean of the given data is
a) 26
...
4
c) 33
...
4
Refer to table 2
4
...
4
b) 48
...
3
d) 64
...
The median of the given data is
a) 32
...
2
c) 42
...
6
ANSWERS
1
...
82
2
...
d) 35
...
a) 41
...
b) 40
...
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)
...
The following tables gives the
weekly consumption of electricity of these families
...
of families

The similar survey is conducted for 80 families of Colony B and the data is recorded
as below:
Weekly consumption (in

0-10

10-20

20-30

30-40

40-50

50-60

0

5

10

20

40

5

units)
No
...
The median weekly consumption is
a) 12 units
b) 16 units
c) 20 units
d) None of these
2
...
64 units
b) 22
...
The modal class of the above data is I
a) 0-10
b) 10-20
c) 20-30
d) 30-40
Refer to data received from Colony B
4
...
2 units
b) 43
...
The mean weekly consumption is
a) 15
...
8 units
c) 38
...
c) 20 units
2
...
64 units
3
...
b) 43
...
c) 38
...
The deck has 52 cards
...


1
...

a)
b)
c)
d)
2
...

a)
b)
c)
d)
3
...

a)
b)
c)
d)
4
...

a)
b)
c)
d)
5
...

a)
b)
c)
d)

ANSWERS
1
...
d)
3
...
a)
5
...


1
...
What is the probability that he got the
sum of the two numbers appearing on the top face of the dice is 8?
a)
b)
c)
d) 0
2
...
What is the probability that he got the sum of the two
numbers appearing on the top face of the dice is 13?
a)
b)
c)
d) 0

3
...
He rolled the dice
...
Rahul got next chance
...
Now it was Ravi’s turn
...
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 ?
a)
b)
c)
d)
ANSWERS
1
...
d) 0
3
...
c)
5

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