**Case study of CBSE standard math 2022 – 2023 class 10**

**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 the 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:- (i) Modal class of the data = 600-800**

**(ii)**

Rain fall(mm) | 200-400 | 400-600 | 600-800 | 800-1000 | 1000-1200 | 1200-1400 | 1400-1600 | 1600-1800 |

Number of sub-divisions(F) | 2 | 4 | 7 | 4 | 2 | 3 | 1 | 1 |

C.F. | 2 | 6 | 13 | 17 | 19 | 22 | 23 | 24 |

l = 600, N = 24, C.F. = 6, F = 7, h = 100

⇒

⇒

⇒

⇒

**(iii)**

Rain fall(mm) |
200-400 |
400-600 | 600-800 | 800-1000 | 1000-1200 | 1200-1400 | 1400-1600 | 1600-1800 | |||

Number of sub-divisions(F) | 2 | 4 | 7 | 4 | 2 | 3 | 1 | 1 | 24 | ||

x |
300 | 500 | 700 | 900 | 1100 | 1300 | 1500 | 1700 | |||

fx | 600 | 2000 | 4900 | 3600 | 2200 | 3900 | 1500 | 1700 |
20,400 |

Mean =

Mean =

**(iii)** If sub-division having at least 1000 mm rainfall during monsoon season, is considered good rainfall sub-division, then sub-division had good rainfall** = 2 + 3+ 1 + 1 =7**

**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:- See full solution**

**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 ?

**Solution:- See full solution**