#### Online Mock Tests

#### Chapters

Chapter 1.2: Matrics

Chapter 1.3: Trigonometric Functions

Chapter 1.4: Pair of Lines

Chapter 1.5: Vectors and Three Dimensional Geometry

Chapter 1.6: Line and Plane

Chapter 1.7: Linear Programming Problems

Chapter 2.1: Differentiation

Chapter 2.2: Applications of Derivatives

Chapter 2.3: Indefinite Integration

Chapter 2.4: Definite Integration

Chapter 2.5: Application of Definite Integration

Chapter 2.6: Differential Equations

Chapter 2.7: Probability Distributions

Chapter 2.8: Binomial Distribution

## 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 MCQ

#### 2 Marks

**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 = ae

^{x}y = be

^{2x}y = be

^{−2x}y = e

^{ax }

**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

The general solution of `("d"y)/("d"x)` = e^{−x} is

y = e

^{x}+ cy = e

^{–x}+ cy = – e

^{–x}+ cy = e

^{2x}+ c

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

The differential equation of y = Ae^{5x} + 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

**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

**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

**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

**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

**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

x

^{2}+ y^{2}= cy – x = c

**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

x

^{3}+ y^{3}= 7x

^{2}+ y^{2}= cx

^{3}+ y^{3}= cx + 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

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

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

Form the differential equation of family of standard circle

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

### 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

Form the differential equation of y = (c^{1} + c^{2})e^{x}^{ }

Solve the differential equation sec^{2}y tan x dy + sec^{2}x tan y dx = 0

Solve the differential equation `("d"y)/("d"x)` = e^{(x+y)} + x^{2}e^{y}

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

### 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

Solve the differential equation `("d"y)/("d"x) + y` = e^{−x}

Solve the differential equation `x ("d"y)/("d"x) + 2y` = x^{2}logx

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

Solve the differential equation xdx + 2ydy = 0

Solve the differential equation (x^{2} – yx^{2})dy + (y^{2} + xy^{2})dx = 0

Solve the following differential equation `("d"y)/("d"x)` = x^{2}y + y

Find the differential equation by eliminating arbitrary constants from the relation x^{2} + y^{2} = 2ax

Find the differential equation by eliminating arbitrary constants from the relation y = (c_{1} + c_{2}x)e^{x}

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

Solve: `("d"y)/("d"x) + 2/xy` = x^{2}

### 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

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

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

Find the differential equation from the relation x^{2} + 4y^{2} = 4b^{2}

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)`

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)`

Solve the following differential equation

`yx ("d"y)/("d"x)` = x^{2} + 2y^{2}

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

For the differential equation, find the particular solution

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

Solve the following differential equation y^{2}dx + (xy + x^{2}) dy = 0

Solve the following differential equation

`x^2 ("d"y)/("d"x)` = x^{2} + xy − y^{2}

## 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

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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.

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