India meteorological department observes seasonal

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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

 

\text{Median} = l + \dfrac{\frac{N}{2}-C.F.}{F}\times h

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

\text{Median} = 600 + \dfrac{\frac{24}{2}-6}{7}\times 200

⇒\text{Median} = 600 + \dfrac{12 - 6}{7}\times 200

⇒\text{Median} = 600 + \dfrac{6}{7}\times 200

⇒ \text{Median} = 600 + 171.428

⇒ \text{Median} =771.428

(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 = \dfrac{\Sigma fx}{\Sigma f}

Mean = \dfrac{20,400}{24}= 850

(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

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