The Relation between the height of the plant (y in cm) with respect to exposure to sunlight is governed by the following equation
y = 4x – 1/2  x 2 where x is the number of days exposed to sunlight.

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Question 1

The rate of growth of the plant with respect to sunlight is ______ .

(a) 4x – 1/2  x 2

(b) 4 – x

(c) x – 4

(d) x – 1/2  x 2

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Question 2

What is the number of days it will take for the plant to grow to the maximum height

(a) 4

(b) 6

(c) 7

(d) 10

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Question 3

What is the maximum height of the plant?

(a) 12 cm

(b) 10 cm

(c) 8 cm

(d) 6 cm

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Question 4

What will be the height of the plant after 2 days?

(a) 4 cm

(b) 6 cm

(c) 8 cm

(d) 10 cm

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Question 5

If the height of the plant is 7/2 cm, the number of days it has been exposed to the sunlight is ______ .

(a) 2

(b) 3

(c) 4

(d) 1

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  1. Chapter 6 Class 12 Application of Derivatives (Term 1)
  2. Serial order wise

Transcript

Question The Relation between the height of the plant (y in cm) with respect to exposure to sunlight is governed by the following equation y = 4x โ€“ 1/2 ๐‘ฅ^2 where x is the number of days exposed to sunlight. Question 1 The rate of growth of the plant with respect to sunlight is ______ . (a) 4๐‘ฅ โ€“ 1/2 ๐‘ฅ^2 (b) 4 โ€“ ๐‘ฅ (c) ๐‘ฅ โ€“ 4 (d) ๐‘ฅ โ€“ 1/2 ๐‘ฅ^2 Rate of growth of plant with respect to sunlight = ๐’…๐’š/๐’…๐’™ = d(4๐‘ฅ โˆ’ 1/2 ๐‘ฅ^2 )/๐‘‘๐‘ฅ = 4 โˆ’ 1/2 ร— 2๐‘ฅ = 4 โ€“ ๐’™ So, the correct answer is (b) Question 2 What is the number of days it will take for the plant to grow to the maximum height? (a) 4 (b) 6 (c) 7 (d) 10 Given y = 4๐‘ฅโˆ’1/2 ๐‘ฅ^2 We need to find value of x, when y is maximum Thus, we need to find Maximum value of y Finding Maximum value of y ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 4 โˆ’ x Putting ๐’…๐’š/๐’…๐’™ = 0 4 โˆ’ x = 0 x = 4 Finding sign of (๐’…^๐Ÿ ๐’š)/(๐’…๐’™^๐Ÿ ) (๐’…^๐Ÿ ๐’š)/(๐’…๐’™^๐Ÿ ) = ๐‘‘/๐‘‘๐‘ฅ (๐‘‘๐‘ฆ/๐‘‘๐‘ฅ) = (๐‘‘(4 โˆ’ ๐‘ฅ))/๐‘‘๐‘ฅ = โˆ’1 < 0 Therefore, y is Maximum when x = 4 So, the correct answer is (a) Question 3 What is the maximum height of the plant? (a) 12 cm (b) 10 cm (c) 8 cm (d) 6 cm Putting x = 4 in value of y y = 4๐‘ฅโˆ’1/2 ๐‘ฅ^2 y = 4(4)โˆ’1/2 ร— 4^2 y = 16 โˆ’ 8 y = 8 cm So, the correct answer is (c) Question 4 What will be the height of the plant after 2 days? (a) 4 cm (b) 6 cm (c) 8 cm (d) 10 cm To find Height of plant after 2 days Putting x = 2 in value of y y = 4๐‘ฅโˆ’1/2 ๐‘ฅ^2 y = 4(2)โˆ’1/2 ร— 2^2 y = 8 โˆ’ 2 y = 6 cm So, the correct answer is (b) Question 5 If the height of the plant is 7/2 cm, the number of days it has been exposed to the sunlight is ______ . (a) 2 (b) 3 (c) 4 (d) 1 Putting y = ๐Ÿ•/๐Ÿ in equation of y y = 4๐‘ฅโˆ’1/2 ๐‘ฅ^2 ๐Ÿ•/๐Ÿ = 4๐‘ฅโˆ’1/2 ๐‘ฅ^2 Multiplying both sides by 2 7 = 8x โˆ’ x2 x2 โˆ’ 8x + 7 = 0 x2 โˆ’ 7x โˆ’ x + 7 = 0 x(x โˆ’ 7) โˆ’ 1 (x โˆ’ 7) = 0 (x โˆ’ 1) (x โˆ’ 7) = 0 โˆด x = 1, x = 7 Since x = 1 is option (d) So, the correct answer is (d)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.