The discus throw is an event in which an athlete attempts

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Case study of CBSE standard math 2022 – 2023 class 10

Case study 1:- The discus throw is an event in which an athlete attempts to throw a discus. The athlete spins anti-clockwise around one a half times through a circle, then release the throw,. When released, the discus travels along tangent to the circular spin orbit.

In the given figure, AB is one such tangent to a circle of radius 75 cm. Point O is a centre and ∠ABO = 30º. PQ is parallel to OA.

Based on above information:

(a) Find the length of AB.            [1 marks]

(b) Find the length of OB.           [1 marks]

(c) Find the lenth of AP.              [2 marks]

OR

Find the length of PQ.

Solution:- In given Figure

(i) In triangle ΔOAB

\tan 30 = \dfrac{OA}{AB}

⇒ \dfrac{1}{\sqrt{3}} = \dfrac{75}{AB}

⇒ AB = 75\sqrt{3} cm

(ii) In triangle ΔOAB

\sin 30 = \dfrac{OA}{OB}

⇒ \dfrac{1}{2} = \dfrac{75}{OB}

⇒  OB = 150 cm

(iii) Since, OQ = Radius of circle

OQ = 75 cm

Now, QB = OB – OQ = 150 – 75

⇒ QB = 75 cm

Now, in triangle ΔQPB

\cos 30 = \dfrac{PB}{QB}

⇒ \dfrac{\sqrt{3}}{2} = \dfrac{PB}{75}

⇒ PB = \dfrac{150}{\sqrt{3}}

⇒ PB =\dfrac{150\sqrt{3}}{\sqrt{3}\sqrt{3}}

⇒ PB = \dfrac{150\sqrt{3}}{3} = 25\sqrt{3} cm

OR 

(iii) Since, OQ = Radius of circle

OQ = 75 cm

Now, QB = OB – OQ = 150 – 75

⇒ QB = 75 cm

Now, in triangle ΔQPB

\sin 30 = \dfrac{PQ}{QB}

⇒ \dfrac{1}{2} = \dfrac{PQ}{75}

⇒ PQ = \dfrac{75}{2} = 37.5 cm

Case study 2:- While designing the school year book, a teacher asked the student that the length and width of a particular photo is increased by x units each to double the area of the photo. The original photo is 18 cm long and 12 cm wide.

Based on the above information, answer the following questions :

(I) Write an algebraic equation depicting the above information.     [1 marks]

(II) Write the corresponding quadratic equation in standard form.      [1 marks]

(III) What should be the new dimensions of the enlarged photo ?      [2 marks]

OR

Can any rational value of x make the new area equal to 220 cm² ?

Case study 3:- India meteorological department observes seasonal and annual rainfall every year in different sub- divisions of our country.

It help them to compare and analyse the results. The table given below shows sub-division wise seasonal(monsoon) rainfall(mm0 in 2018 :

Based on the above information, answer the following question :

(I) Write thee modal class.                        [1 marks]

(II) find the median of the given data.      [2 marks]

OR

Find the mean rainfall in this season.      [2 marks]

(III) If sub-division having at least 1000 mm rainfall during monsoon season, is considered good rainfall sub-division, then how many sub-division had good rainfall ?             [1 marks]

Solution:- See full solution

Case study from CBSE sample paper Basic math 2024 – 2025 class 10

Case study 1:- A group of students conducted a survey to find out about the preferred mode of transportation to school among their classmates. They surveyed 200 students from their school. The results of the survey are as follows:

120 students preferred to walk to school.

25% of the students preferred to use bicycles.

10% of the students preferred to take the bus.

Remaining students preferred to be dropped off by car.

Based on the above information, answer the following questions:

(i) What is the probability that a randomly selected student does not prefer to walk to school ?

(ii) Find the probability of a randomly selected student who prefers to walk or use a bicycle.

(iii) (A) One day 50% of walking students decided to come by bicycle. What is the probability that a randomly selected student comes to school using a bicycle on that day?

OR

(iii) (B) What is the probability that a randomly selected student prefers to be dropped off by car?

Solution:- See full solution

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