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IIT JAM Exam  >  IIT JAM Tests  >  Differential Equation NAT Level - 1 - IIT JAM MCQ

Differential Equation NAT Level - 1 - IIT JAM MCQ


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10 Questions MCQ Test - Differential Equation NAT Level - 1

Differential Equation NAT Level - 1 for IIT JAM 2024 is part of IIT JAM preparation. The Differential Equation NAT Level - 1 questions and answers have been prepared according to the IIT JAM exam syllabus.The Differential Equation NAT Level - 1 MCQs are made for IIT JAM 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Differential Equation NAT Level - 1 below.
Solutions of Differential Equation NAT Level - 1 questions in English are available as part of our course for IIT JAM & Differential Equation NAT Level - 1 solutions in Hindi for IIT JAM course. Download more important topics, notes, lectures and mock test series for IIT JAM Exam by signing up for free. Attempt Differential Equation NAT Level - 1 | 10 questions in 30 minutes | Mock test for IIT JAM preparation | Free important questions MCQ to study for IIT JAM Exam | Download free PDF with solutions
*Answer can only contain numeric values
Differential Equation NAT Level - 1 - Question 1
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If the Particular Integral (P.I.) of the differential equation (D3 + 1)y = cos2x. is given by y = 1/65 (cos 2x - β sin 2x). Find the value of β


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




The correct answer is: -0.123

*Answer can only contain numeric values
Differential Equation NAT Level - 1 - Question 2
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I.F of differential equation (y2 + 2x2y)dx + (2x3 – xy)dy = 0 is of the form xαyβ. Then find value of α + β


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

Now, suppose, xh yk is IF then,

At this is exact so,



The correct answer is: -3

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Differential Equation NAT Level - 1 - Question 3
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The IF for the Differential Equation (1 + xy)y + x (1 - xy)dy/dx = 0 is xαyβ. Then find the value of the α + β.


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

Comparing this equation with  

Since, it is a homogeneous differential equation of form

The correct answer is: -4

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Differential Equation NAT Level - 1 - Question 4
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Find the value of f(0) where f(x) is the Particular Integral (P.I.) of the Differential equation (D2 –2D + 1)y = x sin x.

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

Applying the formula, we get 


∴  

The correct answer is: 0.5

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Differential Equation NAT Level - 1 - Question 5
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Solve  In the solution find the value of constant which is in multiplication with cos x only given y(0) = 0.

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

Auxiliary Equation is
m4 – 4m3 + 8m2 – 8m + 4 = 0
 (m2 – 2m + 2)2 = 0
∴  m = 1 ± i, 1 ± i
Hence, sol of equation is

y = 

Now,    y = 0 at x = 0
⇒  c1 = 0
Required constant c1 = 0.
The correct answer is: 0

*Answer can only contain numeric values
Differential Equation NAT Level - 1 - Question 6
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Let y be a function of x satisfying dy/dx = 2x3  y(0) = 0, then find the value of e2y(1).

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




The correct answer is: 0.25

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Differential Equation NAT Level - 1 - Question 7
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Given a differential equation y(0) = 1, y(1) = e4, then y(4) = eα . Find the value of α.

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

∴  Equation becomes 


The correct answer is: 16

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Differential Equation NAT Level - 1 - Question 8
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The Particular Integral (PI) of the differential equation (D2 – 5D + 6)y = x is given as y = mx + c. Find the value of c.

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


y = mx + c
⇒ c = 5/36 = 0.138

The correct answer is: 0.138

*Answer can only contain numeric values
Differential Equation NAT Level - 1 - Question 9
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If the differential equation (3a2y2x2 + bycosx)dx + (2sinx – 4ayx3)dy = 0 is exact then what is the value of   a, b ≠ 0.

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

For Differential equation to be exact


The correct answer is: 0

*Answer can only contain numeric values
Differential Equation NAT Level - 1 - Question 10
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If the Particular Integral (PI) of the Differential equation (D2 + a2)y = cos ax is given by f(x). Then find the value of a2f (π/2a).

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

As, we known, the P.I. of (D2 + a2)y = cos ax is given as  x/2a sin ax
∴  

Now,  


The correct answer is: 0.785

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