Case Study Based Questions Class 10

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

CASE STUDY -1, CHAPTER -1, REAL NUMBERS

The diagram shown below is a prime factor tree

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

Q1) The value of a is

a) 2

b) 3

c) 5

d) 6

Q2) The value of 'b' is

a) 3

b) 5

c) 7

d) 11

Q3) ' c + d' has a value equal to

a) 22

b) 24

c) 26

d) 28

Q4) HCF of (a, b, c) is

a) a

b) b

c) c

d) 1

Q5) The HCF of Smallest Prime Number and smallest composite number is

a) 1

b) 2

c) 3

d) 4

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

CASE STUDY 2 CHAPTER -1 REAL NUMBERS

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.

Q1) 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?

a) 144

b) 128

c) 288

d) 272

Q2) 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

Q3) 36 can be expressed as a product of its primes as

a) 2² x 3²

b) 2¹ x 3³

c) 2³ x 3¹

d) 2⁰ x 3⁰

Q4) 7 X 11 X 13 X 15 + 15 is a

a) Prime number

b) Composite number

c) Neither prime nor composite

d) None of the above

Q5) If p and q are positive integers such that p = ab² and q = a²b, where a, b are prime numbers, then LCM (p, q) is

a) ab

b) a²b²

c) a³b²

d) a³b³

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

CASE STUDY -1 CHAPTER -2 POLYNOMIALS

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

Based on the above information, answer the following questions

Q 1) What is the shape of the curve EFG ?
a) Parabola
b) Ellipse
c) Straight line
d) Circle

Q 2) If the curve ABC is represented by the polynomial -(x² + 4x + 3), then its zeroes are :
a) 1 and -3
b) -1 and 3
c) 1 and 3
d) -1 and -3

Q 3) If the path traced by the car has zeroes at -1 and 2, then it is given by

a) x² + x + 2

b) x² - x + 2

c) x² - x – 2

d) x² + x – 2

Q 4) The number of zeroes of the polynomial representing the whole curve is :
a) 4
b) 3
c) 2
d) 1

Q 5) The distance between C and G is :

a) 4 units
b) 6 units
8 units
7 units

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

CASE STUDY -2 CHAPTER -2 POLYNOMIALS

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. The shape of the poses shown is

a) Spiral

b) Ellipse

c) Linear

d) Parabola

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?

a) 0

b) 1

c) 2

d) 3
Q4) The two zeroes in the above shown graph are

a) 2, 4

b) -2, 4

c) -8, 4

d) 2,-8
5. The zeroes of the quadratic polynomial    $4\sqrt{3}x^{2}+5x-2\sqrt{3}$ are
a) $\frac{2}{\sqrt{3}},\: \frac{\sqrt{3}}{4}$

b) $-\frac{2}{\sqrt{3}},\: \frac{\sqrt{3}}{4}$

c) $\frac{2}{\sqrt{3}},\: -\frac{\sqrt{3}}{4}$

d) $-\frac{2}{\sqrt{3}},\: -\frac{\sqrt{3}}{4}$
Question

Answer

1

d

2

c

3

c

4

b

5

b

CASE STUDY -1, CHAPTER -5,

ARITHMETIC PROGRESSION

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

I	If the first circular row has 30 seats, how many seats will be there in the 10th row?	1
II	For 1500 seats in the auditorium, how many rows need to be there?	1
III	If there were 17 rows in the auditorium, how many seats will be there in the middle row?	2

CASE STUDY -1, CHAPTER -7,

COORDINATE GEOMETRY

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

Q1) If O is the origin, then what are the coordinates of S ?

a) (-6, -4)

b) (6, 4)

c) (-6, 4)

d) (6, -4)

Q2) 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)

Q3) 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

Q4) 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

Q5) 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

CASE STUDY -2, CHAPTER -7,

COORDINATE GEOMETRY

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

CASE STUDY -3, CHAPTER -7, COORDINATE GEOMETRY

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)

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

CASE STUDY -4, CHAPTER -7, COORDINATE GEOMETRY

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:

I	What is the length of the line segment joining points B and F?	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?	1
III	What are the coordinates of the point on y axis equidistant from A and G?	2

CASE STUDY -1, CHAPTER -9,

APPLICATION OF TRIGONOMETRY

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.

Find the distance PA.

Find the distance PB

III

Find the width AB of the river.

[OR]

Find the height BQ if the angle of the elevation from P to Q be 30°.

CASE STUDY -1, CHAPTER -12,

AREA RELATED TO CIRCLES

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

CASE STUDY -2, CHAPTER -12,

AREA RELATED TO CIRCLES

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

Download PDF file Here

THANKS FOR YOUR VISIT

PLEASE COMMENT BELOW

Search This Blog

Maths MCQ

FEATURED POST ON MATHS MCQ

Maths MCQ Class IX Ch-14 | Statistics