Partial Derivatives And Euler's Equation NAT


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


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Attempt Partial Derivatives And Euler's Equation NAT | 10 questions in 30 minutes | Mock test for Physics preparation | Free important questions MCQ to study Topic wise Tests for IIT JAM Physics for Physics Exam | Download free PDF with solutions
*Answer can only contain numeric values
QUESTION: 1

  then the value of x2fxx + 2xyfxy + y2fyy =


Solution:




The correct answer is: 0

*Answer can only contain numeric values
QUESTION: 2

If u(x, y) = eαx+βy satisfy the condition uxx - 7uxy + 12uyy = 0. α2 - 7αβ + β2 = ____


Solution:

We are given with u(x,y)=eαx+ βy

ux=αeαx+ βy , uy= βeαx+ βy

uxx2eαx+ βy , uyy2eαx+ βy

uxy= αβeαx+ βy

put these values in the given relation, we get

uxx-7uxy+12uyy=0

eαx+ βy2-7αβ+12β2]=0

eαx+ β ≠0=> α2-7αβ+12β2=0

The correct answer is: 0

*Answer can only contain numeric values
QUESTION: 3

Let f = yx, what is  at x = 2, y = 1


Solution:

f = yx

The correct answer is: 1

*Answer can only contain numeric values
QUESTION: 4

If  z = 2(ax + by)2 – (x2 + y2)  and  a2 + b2 = 1 then find the value of 


Solution:

Correct Answer :- 0

Explanation : dz/dx = 4a(ax+by) - 2x

d2z/dx2 = 4a2 - 2

dz/dy = 4b(ax+by) - 2y

d2z/dy2 = 4b2 - 2

d2z/dx+ d2z/dx2 = 4a2 - 2 + 4b2 - 2

=> 4(a2+b2) - 4

As we know that a2 + b2 = 1

=> 4(1) - 4

=> 0

*Answer can only contain numeric values
QUESTION: 5


Solution:

v is homogeneous function of degree 3

The correct answer is: 3

*Answer can only contain numeric values
QUESTION: 6

If u = log(tan x + tan y + tan z), then (sin 2x) ux + (sin 2y)uy + sin 2z)uz is equal to


Solution:





The correct answer is: 2

*Answer can only contain numeric values
QUESTION: 7

If  f(x, y) = x3y – xy3  then 


Solution:

1 – 12 = –11

The correct answer is: 0

*Answer can only contain numeric values
QUESTION: 8

If w = x2cos xy, then  Find the value of a + b.


Solution:

We have 

= 1 - 0 = 1

a + b = 1

The correct answer is: 1

*Answer can only contain numeric values
QUESTION: 9

If v = log(x2 + y2) then vxx + vyy equal to


Solution:

The correct answer is: 0

*Answer can only contain numeric values
QUESTION: 10

If  z = eax+by f(ax - by) then the value of  The value of n is


Solution:

= 2abz

The correct answer is: 2

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