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Differential Equation MCQ Level - 1 - Physics MCQ


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10 Questions MCQ Test Topic wise Tests for IIT JAM Physics - Differential Equation MCQ Level - 1

Differential Equation MCQ Level - 1 for Physics 2024 is part of Topic wise Tests for IIT JAM Physics preparation. The Differential Equation MCQ Level - 1 questions and answers have been prepared according to the Physics exam syllabus.The Differential Equation MCQ Level - 1 MCQs are made for Physics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Differential Equation MCQ Level - 1 below.
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Differential Equation MCQ Level - 1 - Question 1

The integrating factor of the differential equation,   would be :

Detailed Solution for Differential Equation MCQ Level - 1 - Question 1

The given differential equation is homogeneous
Consider,

Comparing it with the equation

We have,  

Also, the equation is homogeneous &

∴  The integrating factor would be given by

The correct answer is: x

Differential Equation MCQ Level - 1 - Question 2

The curve r = a(secθ + tanθ) is orthogonal to :

Detailed Solution for Differential Equation MCQ Level - 1 - Question 2

Given,

Replacing   to get the orthogonal curve,

Integrating both sides

The correct answer is: 

Differential Equation MCQ Level - 1 - Question 3

Solution to the differential equation 

Detailed Solution for Differential Equation MCQ Level - 1 - Question 3

which is a linear equation

The required solution will be given by

The correct answer is:
5y = x4 + ax–1

Differential Equation MCQ Level - 1 - Question 4

What would be the order and degree of the given differential equation 

Detailed Solution for Differential Equation MCQ Level - 1 - Question 4

Consider the differential equation,

Cubing both sides,

∴  according to definition, degree of the above differential equation is 3 and order is 2.

The correct answer is: Order–2 & Degree–3

Differential Equation MCQ Level - 1 - Question 5

The general solution of the differential equation,  will be given by.

Detailed Solution for Differential Equation MCQ Level - 1 - Question 5

We have 

Putting   the above equations becomes

Auxiliary equation : 





Hence, 

The correct answer is: 

Differential Equation MCQ Level - 1 - Question 6

The general solution of the differential equation,

 will be given by :

Detailed Solution for Differential Equation MCQ Level - 1 - Question 6

Since y = ex is an integral, we take y = ve

 

The given equation becomes




Hence y = vex = (c1 log x + c2)ex is the complete solution.

The correct answer is: (C1 log x + C2)ex

Differential Equation MCQ Level - 1 - Question 7

The particular integral of the differential equation,


 will be

Detailed Solution for Differential Equation MCQ Level - 1 - Question 7

Multiplying the given equation by x2 we obtain

Then the equation, on putting   becomes

The correct answer is: 

Differential Equation MCQ Level - 1 - Question 8

The solution of 

Detailed Solution for Differential Equation MCQ Level - 1 - Question 8


Comparing it with the equation,
Mdx + Ndy = 0
We have,
         M = y cos x + sin y + y    &     N = sin x + x cos y + x

Hence, the given differential equation is exact.
∴  The required solution will be given by,

The correct answer is: y sin x + (sin y + yx = c

Differential Equation MCQ Level - 1 - Question 9

The differential equation,   can be reduced into which of the following linear equation?

Detailed Solution for Differential Equation MCQ Level - 1 - Question 9

We have P + Qx = –x2 + x2 = 0 and so y x is an integral.

Let y = vx so that  

Now the given equation reduces to


Differential Equation MCQ Level - 1 - Question 10

Which of the following function form the solution of the differential equation, [x2D2 – xD + 2]y = x logx ?

Detailed Solution for Differential Equation MCQ Level - 1 - Question 10

On putting    the given equation becomes

The auxiliary equation is  


Hence,   is the solution: 

The correct answer is:

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