CBSE has recently added Case Study Based Questions or CSQ in Maths, Science and Social Science. You can visit this article to get to practice the official Sample Papers released by CBSE by clicking over here. Also do join out telegram channel to get all the updates and to participate in Quiz by clicking here.

## What is Case Study Based Questions or CSQ?

Case Study Based or CSQ are typically questions in which the paragraph or passage is given and you simply have to answer them. This questions are not very tough to solve and are introduced so that you score better marks as schools and tuition are kept closed due to the COVID Pandemic. As a result, this had to be introduced. This is resulting to us, by having 34 MCQ which is really very good for scoring 100/100 in CBSE.

## How to start preparing for CSQ’s?

To start preparing for CSQ you will need to learn all the chapters very thoroughly especially all the chapters of Geometry. CSQ from Maths can include a mixture of many chapters thus preparing all the concepts is must. They will surely be helpful. After completing all your syllabus you will need to practice a lot. So scroll below to find more than 15 Case study based question.

## Is it Easy, Hard or Moderate?

This questions are very simple if practiced at least 20-25 questions than you can easily score lot of good marks or you can score full in Maths!! Practice all the questions below.

## How much time to give to each CSQ?

You will be getting 4 Case Study Question’s each would be having 5 sub questions out of which you have to just do 4 questions. So find the shortest and most theoretical question as theoretical questions doesn’t required much solving and it will not even take 1 min to solve. Each question should not take more than 6 min, resulting to only 24 min for 16 questions which is enough. Solving as many CSQ helps in better understanding and reducing the time for each question.

Below are more than 15 examples of CSQ’s for Maths!

#### 1st Case Study Based Question

Shankar is having a triangular open space in his plot. He divided the land into three parts by drawing boundaries PQ and RS which are parallel to BC. Other measurements are as shown in the figure.

- What is the area of this land?

i) 120 m^{2}

ii) 60 m^{2}

iii) 20 m^{2}

iv) 30 m^{2} - What is the length of PQ?

i) 2.5 m

ii) 5 m

iii) 6 m

iv) 8 m - The length of RS is

i) 5 m

ii) 6 m

iii) 8 m

iv) 4 m - Area of △APQ is

i) 7.5 m^{2}

ii) 10 m^{2}

iii) 3.75 m^{2}

iv) 5 m^{2} - What is the area of △ARS?

i) 21.6 m^{2}

ii) 10 m^{2}

iii) 3.75 m^{2}

iv) 6 m^{2}

#### 2nd Case Study Based Question

There is some fire incident in the house. The fireman is trying to enter the house from the window as the main door is locked. The window is 6 m above the ground. He places a ladder against the wall such that its foot is at a distance of 2.5 m from the wall and its top reaches the window.

- Here, be the ladder and be the wall with the window.

i) CA, AB

ii) AB, AC

iii) AC, BC

iv) AB, BC - We will apply Pythagoras Theorem to find length of the ladder. It is:

i) AB^{2}= BC^{2}– CA^{2}

ii) CA_{2}= BC^{2}+ AB^{2}

iii) BC^{2}= AB^{2}+ CA^{2}

iv) AB^{2}= BC^{2}+ CA^{2} - The length of the ladder is .

i) 4.5 m

ii) 2.5 m

iii)6.5 m

iv) 5.5 m - What would be the length of the ladder if it is placed 6 m away from the wall and the window is 8 m above the ground?

i) 12 m

ii) 10 m

iii) 14 m

iv) 8 m - How far should the ladder be placed if the fireman gets a 9 m long ladder?

i) 6.7 m (approx.)

ii) 7.7 m (approx.)

iii) 5.7 m (approx.)

iv) 4.7 m (approx.)

#### 3rd Case Study Based Question

In the school garden Ajay(A), Brijesh(B), Chinki(C) and Deepak(D) planted their flower plants of Rose, Sunflower, Champa and Jasmine respectively as shown in the following figure. A fifth student Eshan wanted to plant her flower in this area. The teacher instructed Eshan to plant his flower plant at a point E such that CE: EB = 3 : 2.

- Find the coordinates of point E where Eshan has to plant his flower plant.

i) (5, 6)

ii) (6, 5)

iii) (5, 5)

iv) (6, 7) - Find the area of △ECD.

i) 9.5 square unit

ii) 11.5 square unit

iii) 10.5 square unit

iv)12.5 square unit - Find the distance between the plants of Ajay and Deepak.

i) 8.60 unit

ii) 6.60 unit

iii) 5.60 unit

iv) 7.60 unit - The distance between A and B is:

i) 5.5 units

ii) 7 units

iii) 6 units

iv) 5 units - The distance between C and D is:

i) 5.5 units

ii) 7 units

iii) 6 units

iv) 5 units

#### 4rth Case Study Based Questions

**SUN ROOM**

The diagrams show the plans for a sun room. It will be built onto the wall of a house. The four walls of the sunroom are square clear glass panels. The roof is made using

- Four clear glass panels, trapezium in shape, all the same size.
- One tinted glass panel, half a regular octagon in shape

- Find the mid-point of the segment joining the points J (6, 17) and I (9, 16).[Refer to Top View]

i) ( 33/2 , 15/2 )

ii) ( 3/2 , 1/2 )

iii) ( 15/2 , 33/2 )

iv) ( 1/2 , 3/2 ) - The distance of the point P from the y-axis is; [Refer to Top View]

i) 4

ii) 15

iii) 19

iv) 25 - The distance between the points A and S is: [Refer to Front View]

i) 4

ii) 8

iii) 16

iv) 20 - Find the coordinates of the point which divides the line segment joining the points A and B in the ratio 1:3 internally. [Refer to Front View]

i) (8.5, 2.0)

ii) (2.0, 9.5)

iii) (3.0, 7.5)

iv) (2.0, 8.5) - If a point (x,y) is equidistant from the Q(9,8) and S(17,8), then [Refer to Front View]

i) x + y = 13

ii) x – 13 = 0

iii) y – 13 = 0

iv) x – y = 13

#### 5th Case Study based Question

Education with vocational training is helpful in making a student self-reliant and to help and serve the society. Keeping this in view, a teacher made the following table giving the frequency distribution of a student undergoing vocational training from the training institute.

- Median class of above data:

i) 20 – 24

ii) 20.5 – 24.5

iii) 19.5 – 24.5

iv) 24.5 – 29.5 - Calculate the median.

i) 24.06

ii) 30.07

iii) 24.77

iv) 42.07 - The empirical relationship between mean, median, mode:

i) Mode = 3 Median + 2 Mean

ii) Mode = 3 Median – 2 Mean

iii) Mode = 3 Mean + 2 Median

iv) 3 Mode = Median – 2 Mean - If mode = 80 and mean = 110, then find the median.

i) 200

ii) 500

iii) 190

iv) 100 - The mode is the:

i) middlemost frequent value

ii) least frequent value

iii) maximum frequent value

iv) none of these

#### 6th Case Study Based Question

Two brothers Ramesh and Pulkit were at home and have to reach School. Ramesh went to Library first to return a book and then reaches School directly whereas Pulkit went to Skate Park first to meet his friend and then reaches School directly.

- How far is School from their Home?

i) 5 m

ii) 3 m

iii) 2 m

iv) 4 m - What is the extra distance travelled by Ramesh in reaching his School?

i) 4.48 metres

ii) 6.48 metres

iii) 7.48 metres

iv) 8.48 metres - What is the extra distance travelled by Pulkit in reaching his School? (All distances are measured in metres as straight lines)

i) 6.33 metres

ii) 7.33 metres

iii) 5.33 metres

iv) 4.33 metres - The location of the library is:

i) (-1, 3)

ii) (1, 3)

iii) (3, 1)

iv) (3, -1) - The location of the Home is:

i) (4, 2)

ii) (1, 3)

iii) (4, 5)

iv) (5,4)

#### 7th Case Study Based Question

The Class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Gulmohar is planted on the boundary of the plot at a distance of 1m from each other. There is a triangular grassy lawn inside the plot as shown in Fig. The students have to sow seeds of flowering plants on the remaining area of the plot.

- Considering A as the origin, what are the coordinates of A?

i) (0, 1)

ii) (1, 0)

iii) (0, 0)

iv (-1, -1) - What are the coordinates of P?

i) (4, 6)

ii) ( 6, 4)

iii) (4, 5)

iv) (5, 4) - What are the coordinates of R?

i) (6, 5)

ii) (5, 6)

iii) ( 6, 0)

iv) (7, 4) - What are the coordinates of D?

i) (16, 0)

ii) (0, 0)

iii) (0, 16)

iv) (16, 1) - What are the coordinates of P if D is taken as the origin?

i) (12, 2)

ii) (-12, 6)

iii) (12, 3)

iv) (6, 10)

#### 8th Case Study Based Question

There exist a tower near the house of Shankar. The top of the tower AB is tied with steel wire and on the ground, it is tied with string support. One day Shankar tried to measure the longest of the wire AC using Pythagoras theorem.

- In the figure, the length of wire AC is: (take BC = 60 ft)

i) 75 ft

ii) 100 ft

iii) 120 ft

iv) 90 ft - What is the area of △ABC?

i) 2400 ft^{2}

ii) 4800 ft^{2}

iii) 6000 ft^{2}

iv) 3000 ft^{2} - What is the length of the wire PC?

i) 20 ft

ii) 30 ft

iii) 25 ft

iv) 40 ft - What is the length of the hypotenuse in △ABC?

i) 100 ft

ii) 80 ft

iii) 60 ft

iv) 120 ft - What is the area of a △POC?

100 ft^{2}

150 ft^{2}

200 ft^{2}

250 ft^{2}

#### 9th Case Study Based Question

- SCALE FACTOR AND SIMILARITY SCALE FACTOR: A scale drawing of an object is the same shape as the object but a different size. The scale of a drawing is a comparison of the length used on a drawing to the length it represents. The scale is written as a ratio. SIMILAR FIGURES: The ratio of two corresponding sides in similar figures is called the scale factor. Hence, two shapes are Similar when one can become the other after a resize, flip, slide, or turn.

- A model of a boat is made on a scale of 1:4. The model is 120cm long. The full size of the boat has a width of 60cm. What is the width of the scale model?

i) 20 cm

ii) 25 cm

iii) 15 cm

iv) 240 cm - What will affect the similarity of any two polygons?

i) They are flipped horizontally

ii) They are dilated by a scale factor

iii) They are translated down

iv) They are not the mirror image of one another - If two similar triangles have a scale factor of a: b. Which statement regarding the two triangles is true?

i) The ratio of their perimeters is 3a: b

ii) Their altitudes have a ratio a: b

iii) Their medians have a ratio a/2:b

iv)Their angle bisector have a ration a^{2}:b^{2} - The shadow of a stick 5m long is 2m. At the same time, the shadow of a tree 12.5m high is:

i) 3m

ii)3.5m

iii)4.5m

iv)5m - Below you see a student’s mathematical model of a farmhouse roof with measurements. The attic floor, ABCD in the model, is a square. The beams that support the roof are the edges of a rectangular prism, EFGHKLMN. E is the middle of AT, F is the middle of BT, G is the middle of CT, and H is the middle of DT. All the edges of the pyramid in the model have a length of 12 m.

What is the length of EF, where EF is one of the horizontal edges of the block?

i) 24m

ii) 3m

iii) 6m

iv) 10m

#### 10th Case Study Based Question

An Aeroplan leaves an Airport and flies due north at 300 km/h. At the same time, another Aeroplan leaves the same Airport and flies due west at 400 km/h.

- Distance travelled by the first Airplane in 1.5 hours

i) 450 km

ii) 300 km

iii) 150 km

iv) 600 km - Distance travelled by the second Airplane in 1.5 hours

i) 450 km

ii) 300 km

iii) 150 km

iv) 600 km - Which of the following line segment shows the distance between both the airplane?

i) OA

ii) AB

iii) OB

iv) WB - Which airplane travelled a long distance and by how many km?

i) Second, 150 km

ii) Second, 250 km

iii) First, 150 km

iv) First, 250 km - How far apart the two airplanes would be after 1.5 hours?

i) 600 km

ii) 750 km

iii) 300 km

iv) 150 km