SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 3 - Differential Equations [Latest edition]

Chapters Chapter 3: Differential Equations

MCQAnswer the followingAttempt the following questions IAttempt the following questions IIAttempt the following questions III
MCQ

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 3 Differential Equations MCQ

2 Marks

MCQ | Q 1

Select and write the correct alternative from the given option for the question

Solution of the equation x  ("d"y)/("d"x) = y log y is

• y = aex

• y = be2x

• y = be−2x

• y = eax

MCQ | Q 2

Select and write the correct alternative from the given option for the question

Bacterial increases at the rate proportional to the number present. If original number M doubles in 3 hours, then number of bacteria will be 4M in

• 4 hours

• 6 hours

• 8 hours

• 10 hours

MCQ | Q 3

The general solution of ("d"y)/("d"x) = e−x is

• y = ex + c

• y = e–x + c

• y = – e–x + c

• y = e2x + c

MCQ | Q 4

Select and write the correct alternative from the given option for the question

The differential equation of y = Ae5x + Be–5x is

• ("d"^2y)/("d"x^2) = 25y

• ("d"^2y)/("d"x^2) = – 25y

• ("d"^2y)/("d"x^2) = 5y

• y ("d"^2y)/("d"x^2) = – 5y

MCQ | Q 5

Select and write the correct alternative from the given option for the question

Differential equation of the function c + 4yx = 0 is

• xy + ("d"y)/("d"x) = 0

• x  ("d"y)/("d"x) + y = 0

• ("d"y)/("d"x) - 4xy = 0

• x ("d"y)/("d"x) + 1 = 0

MCQ | Q 6

Select and write the correct alternative from the given option for the question

General solution of y - x ("d"y)/("d"x) = 0 is

• 3log x + 7/y = c

• 2logx + 3/y = c

• log x – log y = log c

• 3log y + 2/x = c

MCQ | Q 7

Select and write the correct alternative from the given option for the question

The order and degree of (("d"y)/("d"x))^3 - ("d"^3y)/("d"x^3) + y"e"^x = 0 are respectively

• 3, 1

• 1, 3

• 3, 3

• 1, 1

MCQ | Q 8

Select and write the correct alternative from the given option for the question

The order and degree of (1 + (("d"y)/("d"x))^3)^(2/3) = 8 ("d"^3y)/("d"x^3) are respectively

• 3, 1

• 1, 3

• 3, 3

• 1, 1

MCQ | Q 9

Select and write the correct alternative from the given option for the question

The solution of ("d"y)/("d"x) = 1 is

• x + y = c

• xy = c

• x2 + y2 = c

• y – x = c

MCQ | Q 10

Select and write the correct alternative from the given option for the question

The solutiion of ("d"y)/("d"x) + x^2/y^2 = 0 is

• x3 + y3 = 7

• x2 + y2 = c

• x3 + y3 = c

• x + y = c

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 3 Differential Equations Answer the following

1 Mark

Answer the following | Q 1

Find the differential equation of family of lines making equal intercepts on coordinate axes

Answer the following | Q 2

Find the general solution of ("d"y)/("d"x) = (1 + y^2)/(1 + x^2)

Answer the following | Q 3

Form the differential equation of family of standard circle

Answer the following | Q 4

State the degree of differential equation "e"^(("d"y)/("d"x)) + ("d"y)/("d"x) = x

Attempt the following questions I

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 3 Differential Equations Attempt the following questions I

2 Marks

Attempt the following questions I | Q 1

Form the differential equation of y = (c1 + c2)ex

Attempt the following questions I | Q 2

Solve the differential equation sec2y tan x dy + sec2x tan y dx = 0

Attempt the following questions I | Q 3

Solve the differential equation ("d"y)/("d"x) = e(x+y) + x2ey

Attempt the following questions I | Q 4

Find the differential equation of family of all ellipse whose major axis is twice the minor axis

Attempt the following questions II

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 3 Differential Equations Attempt the following questions II

3 Marks

Attempt the following questions II | Q 1

Solve the differential equation ("d"y)/("d"x) + y = e−x

Attempt the following questions II | Q 2

Solve the differential equation x ("d"y)/("d"x) + 2y = x2logx

Attempt the following questions II | Q 3

Solve ("d"y)/("d"x) = (x + y + 1)/(x + y - 1) when x = 2/3, y = 1/3

Attempt the following questions II | Q 4

Solve the differential equation xdx + 2ydy = 0

Attempt the following questions II | Q 5

Solve the differential equation (x2 – yx2)dy + (y2 + xy2)dx = 0

Attempt the following questions II | Q 6

Solve the following differential equation ("d"y)/("d"x) = x2y + y

Attempt the following questions II | Q 7

Find the differential equation by eliminating arbitrary constants from the relation x2 + y2 = 2ax

Attempt the following questions II | Q 8

Find the differential equation by eliminating arbitrary constants from the relation y = (c1 + c2x)ex

Attempt the following questions II | Q 9

Verify y = log x + c is the solution of differential equation x ("d"^2y)/("d"x^2) + ("d"y)/("d"x) = 0

Attempt the following questions II | Q 10

Solve: ("d"y)/("d"x) + 2/xy = x2

Attempt the following questions III

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 3 Differential Equations Attempt the following questions III

4 Marks

Attempt the following questions III | Q 1

For the differential equation, find the particular solution (x – y2x) dx – (y + x2y) dy = 0 when x = 2, y = 0

Attempt the following questions III | Q 2

Solve the differential equation ("d"y)/("d"x) + (x - 2y)/(2x - y) = 0

Attempt the following questions III | Q 3

Find the differential equation from the relation x2 + 4y2 = 4b2

Attempt the following questions III | Q 4

If the population of a town increases at a rate proportional to the population at that time. If the population increases from 40 thousand to 60 thousand in 40 years, what will be the population in another 20 years? ("Given" sqrt(3/2) = 1.2247)

Attempt the following questions III | Q 5

The rate of growth of bacteria is proportional to the number present. If initially, there were 1000 bacteria and the number doubles in 1 hour, find the number of bacteria after 5/2 hours  ("Given"  sqrt(2) = 1.414)

Attempt the following questions III | Q 6

Solve the following differential equation

yx ("d"y)/("d"x) = x2 + 2y2

Attempt the following questions III | Q 7

Solve the following differential equation y log y = (log  y - x) ("d"y)/("d"x)

Attempt the following questions III | Q 8

For the differential equation, find the particular solution

("d"y)/("d"x) = (4x +y + 1), when y = 1, x = 0

Attempt the following questions III | Q 9

Solve the following differential equation y2dx + (xy + x2) dy = 0

Attempt the following questions III | Q 10

Solve the following differential equation

x^2  ("d"y)/("d"x) = x2 + xy − y2

Chapter 3: Differential Equations

MCQAnswer the followingAttempt the following questions IAttempt the following questions IIAttempt the following questions III SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 3 - Differential Equations

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 3 (Differential Equations) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. SCERT Maharashtra Question Bank textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 3 Differential Equations are Differential Equations, Order and Degree of a Differential Equation, Formation of Differential Equations, Homogeneous Differential Equations, Linear Differential Equations, Application of Differential Equations.

Using SCERT Maharashtra Question Bank 12th Board Exam solutions Differential Equations exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in SCERT Maharashtra Question Bank Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board 12th Board Exam prefer SCERT Maharashtra Question Bank Textbook Solutions to score more in exam.

Get the free view of chapter 3 Differential Equations 12th Board Exam extra questions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 and can use Shaalaa.com to keep it handy for your exam preparation