Test: Application of Derivatives- Case Based Type Questions- 2 - JEE MCQ

# Test: Application of Derivatives- Case Based Type Questions- 2 - JEE MCQ

Test Description

## 15 Questions MCQ Test Mathematics (Maths) Class 12 - Test: Application of Derivatives- Case Based Type Questions- 2

Test: Application of Derivatives- Case Based Type Questions- 2 for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The Test: Application of Derivatives- Case Based Type Questions- 2 questions and answers have been prepared according to the JEE exam syllabus.The Test: Application of Derivatives- Case Based Type Questions- 2 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Application of Derivatives- Case Based Type Questions- 2 below.
Solutions of Test: Application of Derivatives- Case Based Type Questions- 2 questions in English are available as part of our Mathematics (Maths) Class 12 for JEE & Test: Application of Derivatives- Case Based Type Questions- 2 solutions in Hindi for Mathematics (Maths) Class 12 course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt Test: Application of Derivatives- Case Based Type Questions- 2 | 15 questions in 30 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mathematics (Maths) Class 12 for JEE Exam | Download free PDF with solutions
Test: Application of Derivatives- Case Based Type Questions- 2 - Question 1

### Read the following text and answer the following questions on the basis of the same:P(x) = –5x2 + 125x + 37500 is the total profit function of a company, where x is the production of the company.What will be the maximum profit?

Detailed Solution for Test: Application of Derivatives- Case Based Type Questions- 2 - Question 1

Maximum profit

= P(12.5)

= - 5(12.5)2 + 125 x 12.5 + 37500

= -781.25 + 1562.5 + 37500

= 38,281.25

Test: Application of Derivatives- Case Based Type Questions- 2 - Question 2

### Read the following text and answer the following questions, on the basis of the same:An architect designs a building for a multi-national company. The floor consists of a rectangular region with semicircular ends having a perimeter of 200 m as shown below:The area of the rectangular region A expressed as a function of x is :

Detailed Solution for Test: Application of Derivatives- Case Based Type Questions- 2 - Question 2

 1 Crore+ students have signed up on EduRev. Have you?
Test: Application of Derivatives- Case Based Type Questions- 2 - Question 3

### Read the following text and answer the following questions, on the basis of the same: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 – 1/2x2. where x is the number of days exposed to sunlight.What is the number of days it will take for the plant to grow to the maximum height?

Detailed Solution for Test: Application of Derivatives- Case Based Type Questions- 2 - Question 3

The number of days it will take for the plant to grow to the maximum height,

Test: Application of Derivatives- Case Based Type Questions- 2 - Question 4

Read the following text and answer the following questions on the basis of the same:

A right circular cylinder is inscribed in a cone.

S = Curved Surface Area of Cylinder.

Find the value of d2S/dh2 ?

Detailed Solution for Test: Application of Derivatives- Case Based Type Questions- 2 - Question 4

Test: Application of Derivatives- Case Based Type Questions- 2 - Question 5

Read the following text and answer the following questions. On the basis of the same:

An open box is to be made out of a piece of cardboard measuring (24 cm × 24 cm) by cutting of equal squares from the corners and turning up the sides.

Find the value of d2V/dx2 ?

Detailed Solution for Test: Application of Derivatives- Case Based Type Questions- 2 - Question 5

Test: Application of Derivatives- Case Based Type Questions- 2 - Question 6

Read the following text and answer the following questions on the basis of the same:

P(x) = –5x2 + 125x + 37500 is the total profit function of a company, where x is the production of the company.

When the production is 2 units what will be the profit of the company?

Detailed Solution for Test: Application of Derivatives- Case Based Type Questions- 2 - Question 6

When production is 2 units, then profit of company = P(2)

= -5 x 22 + 125 x 2 + 37500

= -20 + 250 + 37500

= 37,730

Test: Application of Derivatives- Case Based Type Questions- 2 - Question 7

Read the following text and answer the following questions on the basis of the same:

A right circular cylinder is inscribed in a cone.

S = Curved Surface Area of Cylinder.

Find the value of ‘S’ ?

Detailed Solution for Test: Application of Derivatives- Case Based Type Questions- 2 - Question 7

Curved surface area of cylinder,

Test: Application of Derivatives- Case Based Type Questions- 2 - Question 8

Read the following text and answer the following questions, on the basis of the same:

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 – 1/2x2. where x is the number of days exposed to sunlight.

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

Detailed Solution for Test: Application of Derivatives- Case Based Type Questions- 2 - Question 8

We will take x = 1, because it will take 4 days for the plant to grow to the maximum height i.e. 8 cm and 7/2 cm is not maximum height so, it will take less than 4 days. i.e., 1 Day.

Test: Application of Derivatives- Case Based Type Questions- 2 - Question 9

Read the following text and answer the following questions on the basis of the same: The shape of a toy is given as f(x) = 6(2x4 – x2). To make the toy beautiful 2 sticks which are perpendicular to each other were placed at a point (2, 3), above the toy.

Find the slope of the normal based on the position of the stick.

Detailed Solution for Test: Application of Derivatives- Case Based Type Questions- 2 - Question 9

Slope of the normal based on the position of the stick

Test: Application of Derivatives- Case Based Type Questions- 2 - Question 10

Read the following text and answer the following questions. On the basis of the same:

An open box is to be made out of a piece of cardboard measuring (24 cm × 24 cm) by cutting of equal squares from the corners and turning up the sides.

Find the volume of that open box ?

Detailed Solution for Test: Application of Derivatives- Case Based Type Questions- 2 - Question 10

Volume of open box =length * breadth * height

=( 24 - 2x ) * (24 -2x) * x

= 4x3 – 96x2 + 576x

Test: Application of Derivatives- Case Based Type Questions- 2 - Question 11

Read the following text and answer the following questions, on the basis of the same:

An architect designs a building for a multi-national company. The floor consists of a rectangular region with semicircular ends having a perimeter of 200 m as shown below:

The extra area generated if the area of the whole floor is maximized is :

Detailed Solution for Test: Application of Derivatives- Case Based Type Questions- 2 - Question 11

Test: Application of Derivatives- Case Based Type Questions- 2 - Question 12

Read the following text and answer the following questions on the basis of the same:

P(x) = –5x2 + 125x + 37500 is the total profit function of a company, where x is the production of the company.

What will be production of the company when the profit is ₹ 38,250?

Detailed Solution for Test: Application of Derivatives- Case Based Type Questions- 2 - Question 12

Hence, production of company is 10 units when the profit is ₹38250.

Test: Application of Derivatives- Case Based Type Questions- 2 - Question 13

Read the following text and answer the following questions on the basis of the same: The shape of a toy is given as f(x) = 6(2x4 – x2). To make the toy beautiful 2 sticks which are perpendicular to each other were placed at a point (2, 3), above the toy.

What will be the equation of the tangent at the critical point if it passes through (2, 3)?

Detailed Solution for Test: Application of Derivatives- Case Based Type Questions- 2 - Question 13

Test: Application of Derivatives- Case Based Type Questions- 2 - Question 14

Read the following text and answer the following questions, on the basis of the same:

An architect designs a building for a multi-national company. The floor consists of a rectangular region with semicircular ends having a perimeter of 200 m as shown below:

The CEO of the multi-national company is interested in maximizing the area of the whole floor including the semi-circular ends. For this to happen the value of x should be

Detailed Solution for Test: Application of Derivatives- Case Based Type Questions- 2 - Question 14

Test: Application of Derivatives- Case Based Type Questions- 2 - Question 15

Read the following text and answer the following questions on the basis of the same:

A right circular cylinder is inscribed in a cone.

S = Curved Surface Area of Cylinder.

What is the relation between r1 and r ?

Detailed Solution for Test: Application of Derivatives- Case Based Type Questions- 2 - Question 15

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests
Information about Test: Application of Derivatives- Case Based Type Questions- 2 Page
In this test you can find the Exam questions for Test: Application of Derivatives- Case Based Type Questions- 2 solved & explained in the simplest way possible. Besides giving Questions and answers for Test: Application of Derivatives- Case Based Type Questions- 2, EduRev gives you an ample number of Online tests for practice

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests