While designing the school year book a teacher asked

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Case study of CBSE standard math 2022 – 2023 class 10

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.

While designing the school year book a teacher asked

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 ?              [CBSE 2023]

Solution:- (i) The original photo is 18 cm long and 12 cm wide

Increase length of the photo = x cm

And Increase width of the photo = x cm

New length of the photo = (18 + x) cm

New breadth of the photo = (12 + x) cm

According to the question

(18 + x)(12 + x) = 2(18×12)

(ii) From question (i)

(18 + x)(12 + x) = 2(18×12)

⇒ 216 + 18 x + 12 x + x² = 432

⇒ x² + 30 x – 216 = 0  .   .   .(i)

Equation (i) is the standard form of quadratic equation

(iii) x² + 30 x – 216 = 0

⇒ x² + 36 x – 6 x – 216 = 0

⇒ x(x + 36) – 6(x – 36) = 0

⇒ (x + 36)(x – 6) = 0

Now the value of x

x = -36 and x = 6

x = -36 not possible

Hence, x = 6 cm

New length of the phota = 18 + 6 = 24 cm

New breadth of the photo = 12 + 6 = 18 cm

OR

According to the question

(18 + x)(12 + x) = 220

⇒ 216 + 18 x + 12 x + x² = 220

⇒ x² + 30 x + 216 – 220 = 0

⇒ x² + 30 x -4 = 0

a = 1, b = 30, c = -4

b² – 4ac= (30)² – 4(1)(-4) = 900 + 16

= 916

x= \dfrac{- b \pm \sqrt{b^2 - 4ac}}{2(1)}

x= \dfrac{- 30 \pm \sqrt{916}}{2(1)}

⇒ x= \dfrac{- 30 \pm \sqrt{916}}{2}

There are no any rational value of x for which area will be 220 cm²

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 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

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