This question is similar to Chapter 6 Class 12 Application of Derivatives - Ex 6.3
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CBSE Class 12 Sample Paper for 2025 Boards
Question 2
Question 3
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Question 5 Important
Question 6
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Question 8 Important
Question 9 Important
Question 10 Important
Question 11
Question 12 Important
Question 13 Important
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Question 16 Important
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Question 19 [Assertion Reasoning] Important
Question 20 [Assertion Reasoning] Important
Question 21 Important
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Question 23 (A)
Question 23 (B)
Question 24 (A)
Question 24 (B) Important
Question 25 Important
Question 26 Important
Question 27 Important
Question 28 (A)
Question 28 (B)
Question 29 (A) Important
Question 29 (B)
Question 30 Important
Question 31 (A) Important
Question 31 (B)
Question 32 Important
Question 33 Important
Question 34 (A)
Question 34 (B)
Question 35 (A)
Question 35 (B) Important
Question 36 (i) [Case Based] You are here
Question 36 (ii)
Question 36 (iii) (A) Important
Question 36 (iii) (B) Important
Question 37 (i) [Case Based]
Question 37 (ii) Important
Question 37 (iii) (A) Important
Question 37 (iii) (B)
Question 38 (i) [Case Based] Important
Question 38 (ii) Important
CBSE Class 12 Sample Paper for 2025 Boards
Last updated at Oct. 3, 2024 by Teachoo
This question is similar to Chapter 6 Class 12 Application of Derivatives - Ex 6.3
Please check the question here
Question 36 (Case Based Questions) Ramesh, the owner of a sweet selling shop, purchased some rectangular card board sheets of dimension 25 cm by 40 cm to make container packets without top. Let 𝒙 𝐜𝐦 be the length of the side of the square to be cut out from each comer to give that sheet the shape of the container by folding up the flaps.Let 𝑥 be the length of a side of the removed square Thus, Length after removing = 40 – 𝑥 –𝑥 = 40 – 2𝑥 Breadth after removing = 25 –𝑥 –𝑥 = 25 – 2𝑥 Height of the box = 𝑥 Question 36 (i) Express the volume (V) of each container as function of 𝒙 only.Let V be the volume of a box Volume of a cuboid = 𝑙 × 𝑏 × ℎ = (𝟒𝟎−𝟐𝒙)(𝟐𝟓−𝟐𝒙)(𝒙) = [40(25−2𝑥)−2𝑥(25−2𝑥)]𝑥 = (1000−80𝑥−50𝑥+4𝑥^2 )𝑥 =1000𝑥−80𝑥^2−50𝑥^2+4𝑥^3 = 1000𝑥−130𝑥^2+4𝑥^3 = 2(500𝑥−65𝑥^2+2𝑥^3 ) = 2(𝟐𝒙^𝟑−𝟔𝟓𝒙^𝟐+𝟓𝟎𝟎𝒙) cm3