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Test: Order & Degree of Differential Equations - JEE MCQ


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10 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Order & Degree of Differential Equations

Test: Order & Degree of Differential Equations for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Order & Degree of Differential Equations questions and answers have been prepared according to the JEE exam syllabus.The Test: Order & Degree of Differential Equations MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Order & Degree of Differential Equations below.
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Test: Order & Degree of Differential Equations - Question 1

The differential equation,is a:

Detailed Solution for Test: Order & Degree of Differential Equations - Question 1

To calculate the degree or the order of a differential equation, the powers of derivatives should be an integer.
On squaring both sides, we get a differential equation with the integral power of derivatives.

⇒ Order (the highest derivative) = 2
⇒ Degree (The degree of a differential equation is defined as the power to which the highest order derivative is raised) = 1

Test: Order & Degree of Differential Equations - Question 2

The differential equation for the equation  is :

Detailed Solution for Test: Order & Degree of Differential Equations - Question 2

y = Acos(αx) + Bsin(αx)

dy/dx = -Aαsin(αx) + Bαcos(αx)

d2y/dx2 = -Aα2cos(αx) - Bα2sin(αx)

= -α2(Acos(αx) + Bsin(αx))

= -α2 * y

d2y/dx2 + α2*y = 0

Test: Order & Degree of Differential Equations - Question 3

Formation of the differential equation of the family of curves represented by  y = Ae2x + Be-2x is :

Detailed Solution for Test: Order & Degree of Differential Equations - Question 3

y = Ae2x + Be-2x 
dy/dx = 2Ae2x – 2Be-2x
d2y/dx2 = 4Ae2x + 4Be-2x
= 4*y
d2y/dx2 – 4y = 0

Test: Order & Degree of Differential Equations - Question 4

The degree of the differential equation 

Detailed Solution for Test: Order & Degree of Differential Equations - Question 4

Given equation is : 

(dy/dx)2 + 1/(dy/dx) = 1

((dy/dx)3 + 1)/(dy/dx) = 1

(dy/dx)3 +1 = dy/dx

So, final equation is

(dy/dx)3 - dy/dx + 1 = 0

So, degree = 3

Test: Order & Degree of Differential Equations - Question 5

Differential equation representing the family of curves given by y = ax + x2 is:

Detailed Solution for Test: Order & Degree of Differential Equations - Question 5

The answer is C. We eliminate constants.

We have

y=ax+x2

Differentiating with respect to x,

Test: Order & Degree of Differential Equations - Question 6

The order of the differential equation: 

Detailed Solution for Test: Order & Degree of Differential Equations - Question 6


Order of the D.E. is 3
Order of a differential equation is the order of the highest derivative present in the equation.

Test: Order & Degree of Differential Equations - Question 7

Formation of the differential equation corresponding to the ellipse major axis 2a and minor axis 2b is:

Detailed Solution for Test: Order & Degree of Differential Equations - Question 7

Equation of ellipse :

 x2/a2 + y2/b2 = 1

Differentiation by x,

2x/a2 + (dy/dx)*(2y/b2) = 0

dy/dx = -(b2/a2)(x/y)

-(b2/a^2) = (dy/dx)*(y/x) ----- eqn 1

Again differentiating by x,

d2y/dx2 = -(b2/a2)*((y-x(dy/dx))/y2)

Substituting value of -b2/a2 from eqn 1

d2y/dx2 = (dy/dx)*(y/x)*((y-x(dy/dx))/y2)

d2y/dx2 = (dy/dx)*((y-x*(dy/dx))/xy)

(xy)*(d2y/dx2) = y*(dy/dx) - x*(dy/dx)2

(xy)*(d2y/dx2) + x*(dy/dx)2- y*(dy/dx) = 0

Test: Order & Degree of Differential Equations - Question 8

The differential equation  is a solution of the equation:

Detailed Solution for Test: Order & Degree of Differential Equations - Question 8

Solving second order differential equation with variable coefficients becomes a bit lengthy and complicated. So, its better to check by options.

On checking option A :

y = A/x + B

dy/dx = -A/x2

d2y/dx= (2A)/x3

So,

 d2y/dx2 + (2/x)*(dy/dx) = 0

(2A)/x3 + (2/x)*((-A)/x2) = 0

(2A - 2A)/x3 = 0

0 = 0

LHS = RHS

Test: Order & Degree of Differential Equations - Question 9

The differential equation  is a:

Detailed Solution for Test: Order & Degree of Differential Equations - Question 9

3*(d2y/dx2) = [1+(dy/dx)2]3/2
On squaring both side,
9*(d2y/dx2)2 = [1+(dy/dx)2]3
The order of the equation is 2. The power of the term determining the order determines the degree.
So, the degree is also 2.

Test: Order & Degree of Differential Equations - Question 10

The order and degree of the differential equation: (y”)2 + (y”)3 + (y’)4 + y5 = 0 is:​

Detailed Solution for Test: Order & Degree of Differential Equations - Question 10

The highest order derivative here is y’’. Therefore the order of the differential equation=2.
The highest power of the highest order derivative here is 3. Therefore the order of the differential equation=3.

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