Differential Equation NAT Level - 1


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


Description
This mock test of Differential Equation NAT Level - 1 for Physics helps you for every Physics entrance exam. This contains 10 Multiple Choice Questions for Physics Differential Equation NAT Level - 1 (mcq) to study with solutions a complete question bank. The solved questions answers in this Differential Equation NAT Level - 1 quiz give you a good mix of easy questions and tough questions. Physics students definitely take this Differential Equation NAT Level - 1 exercise for a better result in the exam. You can find other Differential Equation NAT Level - 1 extra questions, long questions & short questions for Physics on EduRev as well by searching above.
*Answer can only contain numeric values
QUESTION: 1

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


Solution:




The correct answer is: -0.123

*Answer can only contain numeric values
QUESTION: 2

I.F of differential equation (y2 + 2x2y)dx + (2x3 – xy)dy = 0 is of the form xαyβ. Then find value of α + β


Solution:

Now, suppose, xh yk is IF then,

At this is exact so,



The correct answer is: -3

*Answer can only contain numeric values
QUESTION: 3

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.


Solution:

Comparing this equation with  

Since, it is a homogeneous differential equation of form

The correct answer is: -4

*Answer can only contain numeric values
QUESTION: 4

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.


Solution:

Applying the formula, we get 


∴  

The correct answer is: 0.5

*Answer can only contain numeric values
QUESTION: 5

Solve  In the solution find the value of constant which is in multiplication with cos x only given y(0) = 0.


Solution:

Auxiliary Equation is
m– 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
QUESTION: 6

Let y be a function of x satisfying dy/dx = 2x3  y(0) = 0, then find the value of e2y(1).


Solution:




The correct answer is: 0.25

*Answer can only contain numeric values
QUESTION: 7

Given a differential equation y(0) = 1, y(1) = e4, then y(4) = eα . Find the value of α.


Solution:

∴  Equation becomes 


The correct answer is: 16

*Answer can only contain numeric values
QUESTION: 8

The Particular Integral (PI) of the differential equation (D2 – 5D + 6)y = x is given as y = mx + c. Find the value of c.


Solution:


y = mx + c
⇒ c = 5/36 = 0.138

The correct answer is: 0.138

*Answer can only contain numeric values
QUESTION: 9

If the differential equation (3a2y2x2 + bycosx)dx + (2sinx – 4ayx3)dy = 0 is exact then what is the value of   a, b ≠ 0.


Solution:

For Differential equation to be exact


The correct answer is: 0

*Answer can only contain numeric values
QUESTION: 10

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).


Solution:

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