Applications of Derivatives MCQ Quiz in తెలుగు - Objective Question with Answer for Applications of Derivatives - ముఫ్త్ [PDF] డౌన్‌లోడ్ కరెన్

Last updated on Apr 9, 2025

పొందండి Applications of Derivatives సమాధానాలు మరియు వివరణాత్మక పరిష్కారాలతో బహుళ ఎంపిక ప్రశ్నలు (MCQ క్విజ్). వీటిని ఉచితంగా డౌన్‌లోడ్ చేసుకోండి Applications of Derivatives MCQ క్విజ్ Pdf మరియు బ్యాంకింగ్, SSC, రైల్వే, UPSC, స్టేట్ PSC వంటి మీ రాబోయే పరీక్షల కోసం సిద్ధం చేయండి.

Latest Applications of Derivatives MCQ Objective Questions

Top Applications of Derivatives MCQ Objective Questions

Applications of Derivatives Question 1:

The total revenue in Rupees received from the sale of x units of a product is given by R(x) = 4x2 + 8x + 5. Find the marginal revenue, when x = 5, where by marginal revenue we mean the rate of change of total revenue with respect to the number of items sold at an instant

  1. 48
  2. 40
  3. 45
  4. 50

Answer (Detailed Solution Below)

Option 1 : 48

Applications of Derivatives Question 1 Detailed Solution

Calculation:

Given: Product R(x) = 4x2 + 8x + 5

The marginal revenue  \(\rm {dR(x)\over dx} = {d\over dx}(4x^2 + 8x + 5)\)

⇒ 8x + 8

When x = 5, MR = 8(5) + 8 = 48

Applications of Derivatives Question 2:

A stone is dropped into a quiet lake and waves move in circles at a speed of 5 cm per second. At the instant, when the radius of the circular wave is 15 cm, how fast is the enclosed area increasing? 

  1. 155π
  2. 150π
  3. 100π
  4. 135π

Answer (Detailed Solution Below)

Option 2 : 150π

Applications of Derivatives Question 2 Detailed Solution

Concept;

If y = f(x), then dy/dx denotes the rate of change of y with respect to x.

Decreasing rate is represented by a negative sign whereas the increasing rate is represented by a positive sign.

The area A of a circle with radius r is given by A = πr2

Calculation:

Given: \(\rm \frac {dr}{dt}\) = 5 cm/sec and r = 15

A = πr2

Differentiating with respect to r, we get

⇒ \(\rm \frac{dA}{dt} = π \frac{d(r^2)}{dt}\)

 ⇒ \(\rm \frac{dA}{dt} = 2πr \frac{dr}{dt}\)

⇒ 2π⋅5⋅15

⇒ 150π 

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