Partial Derivatives And Euler's Equation MCQ Level - 1


10 Questions MCQ Test Topic wise Tests for IIT JAM Physics | Partial Derivatives And Euler's Equation MCQ Level - 1


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QUESTION: 1

If z = xy In (x, y) then

Solution:


QUESTION: 2

Suppose  is equal to

Solution:

u and v are homogeneous function of degree one

on adding  

The correct answer is: z

QUESTION: 3

If  then the value of 

Solution:


f(xy) is homogeneous function of degree –2
So, using Euler's equation

The correct answer is: 0

QUESTION: 4

If  satisfy the equation  then

Solution:




Again using the given condition

QUESTION: 5

If   then  equal to

Solution:

The correct answer is 

QUESTION: 6

 then 

Solution:

f1 is homogeneous of degree 1 and f2 is homogeneous of degree zero

On adding

The correct answers are:  

QUESTION: 7

Solution:

We have 

u is homogeneous function of degree n

Now differentiate partially w.r.t. x again

The correct answer is: 

QUESTION: 8

Find a function w = f(xy) whose first partial derivatives are    and  and whose value at point (ln2, 0) is ln2.

Solution:

Integrate both sides w.r.t. x

So, on comparing the above two equation

  (on integration)

Now, using (ln2, 0) is ln2, we get
c = –2

The correct answer is: 

QUESTION: 9

If  equal to

Solution:

So, by Euler's theorem

The correct answer is: 2 tan u

QUESTION: 10

The contour on xy plane where partial derivative of x2 + y2 with respect to y is equal to the partial derivative of 6y + 4x w.r.t. x is

Solution:

So, 
2y = 4
y = 2
The correct answer is: y = 2