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The most preferred set of solution books by the students of CBSE board schools are the RD Sharma books. It helps the students prepare well for all their public exams in every subject and chapter. For the students who encounter lots of doubts and confusion while solving Differential Equations, the RD Sharma Class 12th Exercise 21.7 is the rescuer. A good guide is essential for the students who are preparing for their public exams.

Differential Equations exercise 21.7 question 1

Integrating both sides

Differential Equations exercise 21.7 question 2

Integrating both sides

Differential Equations exercise 21.7 question 3

Integrating on both sides

Differential Equations exercise 21.7 question 4 maths

Integrating both sides

Differential Equations exercise 21.7 question 5

Integrating both sides

Differential Equations exercise 21.7 question 6

Integrating both sides

Differential Equations exercise 21.7 question 7

Integrating both sides,

[Integrating by parts]

Differential Equations exercise 21.7 question 8 maths

Differential Equations exercise 21.7 question 9

Integrating on both sides

We get,

Differential Equations exercise 21.7 question 10

Differential Equations exercise 21.7 question 11

Integrating both sides

Using integration by parts

Using identity,

Differential Equations exercise 21.7 question 12 maths

Differential Equations exercise 21.7 question 13

Integrating both sides

Differential Equations exercise 21.7 question 14

Integrating both sides

Differential Equations exercise 21.7 question 15

Integrating both sides

Differential Equations exercise 21.7 question 16 maths

Integrating both sides

Differential Equations exercise 21.7 question 17

Integrating both sides

Put

Similarly,

Hence,

Differential Equations exercise 21.7 question 18

Integrating both sides

Differential Equations exercise 21.7 question 19

Integrating both sides and using integrating by parts

Differential Equations exercise 21.7 question 20 maths

Integrating both sides

Differential Equations exercise 21.7 question 21

Integrating both sides

Put

Differential Equations exercise 21.7 question 22

Integrating both sides

Differential Equations exercise 21.7 question 23

Integrating both sides

Differential Equations exercise 21.7 question 24 maths

Integrating both sides

Differential Equations exercise 21.7 question 25

Integrating both sides

Differential Equations exercise 21.7 question 26

Integrating both sides

Differential Equations exercise 21.7 question 27

We know

Integration of

Similarly Integration of

Differential Equations exercise 21.7 question 28 maths

Integrating both sides

Differential Equations exercise 21.7 question 29

Integrating both sides and also separate the terms

Differential Equations exercise 21.7 question 30

Differential Equations exercise 21.7 question 31

Differential Equations exercise 21.7 question 32 maths

Integrating both sides

Differential Equations exercise 21.7 question 33

Integrating both sides

Differential Equations exercise 21.7 question 34

Integrating both sides

Differential Equations exercise 21.7 question 35

Integrating both sides

Differential Equations exercise 21.7 question 36 maths

Integrating both sides

Differential Equations exercise 21.7 question 37 (i)

Integrating both sides

Differential Equations exercise 21.7 question 37 (ii)

Integrating both sides

{ using integration by parts}

Differential Equations exercise 21.7 question 38 (i)

Integrating both sides

Differential Equations exercise 21.7 question 38 (ii) maths

Integrating both sides

Differential Equations exercise 21.7 question 38 (iii)

Integrating both sides

Put

Differential Equations exercise 21.7 question 38 (iv)

Integrating both sides

Differential Equations exercise 21.7 question 39

Integrating both sides

Differential Equations exercise 21.7 question 40 maths

Integrating both sides

Differential Equations exercise 21.7 question 41

Integrating both sides

....................(1)

Put in (1)

Put in (1), we get

Differential Equations exercise 21.7 question 42

Integrating both sides

..............(1)

Now given that

Put in (1)

Put in (1) we get

Differential Equations exercise 21.7 question 43

Integrating both sides

...............(1)

Given that

Put in (1)

Put in (1) we get

Differential Equations exercise 21.7 question 44 maths

Integrating both sides

...............(1)

Now Given that

Put in (1) we get

Differential Equations exercise 21.7 question 45 (i)

Integrating both sides

...............(1)

Now Given that

Differential Equations exercise 21.7 question 45 (ii)

Integrating both sides

...................(1)

Now given that

Put in (1)

Differential Equations exercise 21.7 question 45 (iii)

Integrating both sides

..............(1)

Given that

Put in (1)

Differential Equations exercise 21.7 question 45 (iv) maths

Integrating both sides

..............(1)

Given that

Put in (1) we get

Differential Equations exercise 21.7 question 45 (v)

Integrating both sides

.............(1)

Given that at

Put in (1) we get

Differential Equations exercise 21.7 question 45 (vi)

Integrating both sides

...............(1)

Given that

Differential Equations exercise 21.7 question 45 (vii)

Integrating both sides

.................(1)

Given that i.e. when

Put in (1)

Differential Equations exercise 21.7 question 45 (viii) maths

Integrating both sides

..............(1)

Given that when

Put in (1) we get

Differential Equations exercise 21.7 question 45 (ix)

Integrating both sides

..............(1)

Given that

Put in (1) we get

Differential Equations exercise 21.7 question 45 (x)

Integrating both sides

Given that

Put in (1)

Differential Equations exercise 21.7 question 46

Integrating both sides

...............(1)

Now, when

Put in (1)

Differential Equations exercise 21.7 question 47

Integrating both sides

................(1)

Given that

Put in (1) we get

Differential Equations exercise 21.7 question 48 maths

Integrating both sides

[?Integration by parts]

...........(1)

Given that

Put in (1)

Differential Equations exercise 21.7 question 49

Integrating both sides

[Integration by parts]

..............(1)

Now when

Put in (1)

Differential Equations exercise 21.7 question 50

Integrating both sides

..............(1)

When

Put in (1) we get

Differential Equations exercise 21.7 question 51

Integrating both sides

...............(1)

Now when

Put in (1)

Differential Equations exercise 21.7 question 52 maths

**Solution: **

Integrating both sides

.................(*)

..............(1)

The curve passes through (0,0) [∴ of given]

Differential Equations exercise 21.7 question 53

Integrating both sides

..............(1)

It passes through pt(-1,1)

Put in (1) we get

Differential Equations exercise 21.7 question 54

Now it is being inflated changes at a constant rate

where k is any constant ……………….(*)

New volume of spherical balloon, r is radius

Integrating both sides

...........(1)

Now given conditions are:

When and when

We have to find r at

Put in (1) we get

?By(1)

..................(2)

Now at

Put in (2)

which is our required radius.

Differential Equations exercise 21.7 question 55

As principal increases at the rate of r% w.r.t time i.e. per year.

Integrating both sides

..................(1)

Suppose initially

Put in (1)

..............(2)

According to given

When

By (2)

Differential Equations exercise 21.7 question 56 maths

An amount of Rs.1000 is deposited with this bank, how much will it worth after 10 years.(e0.5 =1.648)

As Principal increases at the rate of 5% w.r.t t

Integrating both sides

................(1)

Now initially P

By (1)

Principal after 10 years = 1648

Differential Equations exercise 21.7 question 57

As the rate of growth of bacteria is proportional to the no. present

Integrating both sides

.................(1)

Initially

By (1)

Put in (1) we get

...................(2)

According to given

When

....................(3)

Now we have to find in how many hours i.e t

By (3)

Differential Equations exercise 21.7 question 58

Integrating both sides

..........(1)

According to given:

Put in (1)

.............(2)

Now we have to find i.e. value of y at

Put in (2)

Differential Equations exercise 21.7 question 59

Integrating both sides

Put

Now,

Put

Put the values in (*) we get

................(1)

Now according to given when

Put in (1) we get

The Differential Equation chapter 21 in mathematics of class 12 has about eleven exercises. The seventh exercise, ex 21.7, has 72 questions, with some of them having subparts in the textbook. RD Sharma solutions The concept of these questions revolves around solving the differential equations, initial value problems, equations in variable separable form and word problems using differentiation. This exercise has questions only in the Level 1 category. Yet, the importance of RD Sharma Class 12 Chapter 21 Exercise 21.7 solution book has not been reduced.

As the RD Sharma books follow the NCERT pattern, the CBSE school students benefit from it. The previous exercises before ex 21.7 had sums wherein differentiation can be done directly. While in this exercise, the students must find the equation from the word problem and then solve it. Therefore, the RD Sharma Class 12th Exercise 21.7 reference material lends a helping hand to the students. All solutions are given in the exact order as present in the textbook for the convenience of the students.

The Class 12 RD Sharma Chapter 21 Exercise 21.7 Solution book has an abundance of additional practice questions that help them work out the concept more and understand it deeply. Each answer provided is the work of experts who have committed their time to create the best solution book for the class 12 students.

Moreover, no student needs to pay even a single penny to purchase the RD Sharma Class 12 Solutions Differential Equation Exercise 21.7 reference book. It can be downloaded in the form of a PDF for free of cost from the Career 350 website. This applies to the other RD Sharma solution books too. Students can download the RD Sharma Class 12th Exercise 21.7 book's PDF for free; anyone accessing the website can download the best solution books.

Students who prepare for their public exam with the RD Sharma Class 12 Solutions Chapter 21 Ex 21.7 book are gradually getting ready to face their exams confidently. These best solutions books make the students cross their benchmark score and achieve more in their tests and exams.

- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

1. Is there any best solution book to refer to the concepts given in Class 12, mathematics chapter 21, ex 21.7?

The RD Sharma Class 12th Exercise 21.7 serves the purpose of the students looking for the best solution book on this concept.

2. Which website provides the best solution books for the class 12 students to refer to?

The Career 360 website provides RD Sharma solutions for the class 12 students to clarify their doubts and prepare for their exams

3. Where can I find the RD Sharma solution books for free?

The Career 360 website gives access to everyone to download the RD Sharma Solution books for free of cost.

4. How can I download the RD Sharma solution from the Career 360 website?

Visit the Career 360 site and look out for the solutions you need, or type the book's name. For example, RD Sharma Class 12th Exercise 21.7 search query will provide you with the book, and you can download it by tapping the Download button.

5. Do many students use the RD Sharma solution books?

Most of the students of CBSE Schools use the RD Sharma book to help them with their homework, assignments, and exam preparation.

Mar 22, 2023

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