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Test: Differential Equations- 1


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25 Questions MCQ Test Mathematics (Maths) Class 12 | Test: Differential Equations- 1

Test: Differential Equations- 1 for JEE 2022 is part of Mathematics (Maths) Class 12 preparation. The Test: Differential Equations- 1 questions and answers have been prepared according to the JEE exam syllabus.The Test: Differential Equations- 1 MCQs are made for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Differential Equations- 1 below.
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Test: Differential Equations- 1 - Question 1

Differential equations are equations containing functions y = f(x), g(x) and

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Differential equations are equations containing functions y = f(x), g(x) and derivatives of y with respect to x.

Test: Differential Equations- 1 - Question 2

General solution of a given differential equation

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General solution of a given differential equation contains arbitrary constants depending on the order of the differential equation.

Test: Differential Equations- 1 - Question 3

Find a particular solution of cos 

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Test: Differential Equations- 1 - Question 4

Differential equation of the family of circles touching the y-axis at origin is

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Test: Differential Equations- 1 - Question 5

Which of the following is a homogeneous differential equation?

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y2dx + (x2− xy − y2) dy = 0 is a homogeneous differential equation ,because the degree of each individual term is same i.e. 2.

Test: Differential Equations- 1 - Question 6

Order of a differential equation is defined as

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Order of a differential equation is defined asthe order of the highest order derivative ofthe dependent variable.

Test: Differential Equations- 1 - Question 7

Particular solution of a given differential equation

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Particular solution of a given differential equationdoes not contain arbitrary constants i.e. a,b ,c etc.

Test: Differential Equations- 1 - Question 8

Find a particular solution of   = y tanx; y = 1 when x = 0

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Test: Differential Equations- 1 - Question 9

Differential equation of the family of parabolas having vertex at origin and axis along positive y-axis is

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Test: Differential Equations- 1 - Question 10

A first order linear differential equation. Is a differential equation of the form

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A first order linear differential equation. Is a differential equation of the form  + Py = Q or  + Px = Q

Test: Differential Equations- 1 - Question 11

Degree of a differential equation, when the equation is polynomial equation in y′ is

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Degree of a differential equation, when the equation is polynomial equation in y′ isHighest power (positive integral index) of the highest order derivative in the given differential equation.

Test: Differential Equations- 1 - Question 12

The number of arbitrary constants in the general solution of a differential equation of fourth order are:

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4 , because the no. of arbitrary constants is equal to order of the differential equation.

Test: Differential Equations- 1 - Question 13

For the differential equation xy  = (x+2) (y+2) find the solution curve passing through the point (1, –1).

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Test: Differential Equations- 1 - Question 14

Differential equation of the family of ellipses having foci on y-axis and centre at origin is

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Test: Differential Equations- 1 - Question 15

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Test: Differential Equations- 1 - Question 16

The order of the equation 

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2

Test: Differential Equations- 1 - Question 17

The number of arbitrary constants in the particular solution of a differential equation of third order are:

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0 , because the particular solution is free from arbitrary constants.

Test: Differential Equations- 1 - Question 18

Find the particular solution of the differential equation log  = 3x+4y, given that y = 0 and x = 0.

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Test: Differential Equations- 1 - Question 19

Find the equation of a curve passing through the point (0, 0) and whose differential equation is y′ = ex sin x.

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Test: Differential Equations- 1 - Question 20

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Test: Differential Equations- 1 - Question 21

The order of the equation 

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3

Test: Differential Equations- 1 - Question 22

General solution of 

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Test: Differential Equations- 1 - Question 23

In a bank, principal increases continuously at the rate of r% per year. Find the value of r if Rs 100 double itself in 10 years (loge2 = 0.6931).

Detailed Solution for Test: Differential Equations- 1 - Question 23

Let P be the principal at any time t. then,





When P = 100 and t = 0., then, c = 100, therefore, we have:

Now, let t = T, when P = 100., then;

Test: Differential Equations- 1 - Question 24

Find the equation of a curve passing through the point (0, –2) given that at any point (x, y) on the curve, the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.

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When x= 0 and y = - 2 ,we have : c = 2,

Test: Differential Equations- 1 - Question 25

Solution of (x – y) dy – (x + y) dx = 0 is

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