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Partial Derivatives And Euler's Equation NAT - Physics MCQ


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10 Questions MCQ Test - Partial Derivatives And Euler's Equation NAT

Partial Derivatives And Euler's Equation NAT for Physics 2024 is part of Physics preparation. The Partial Derivatives And Euler's Equation NAT questions and answers have been prepared according to the Physics exam syllabus.The Partial Derivatives And Euler's Equation NAT MCQs are made for Physics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Partial Derivatives And Euler's Equation NAT below.
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*Answer can only contain numeric values
Partial Derivatives And Euler's Equation NAT - Question 1

  then the value of x2fxx + 2xyfxy + y2fyy =


Detailed Solution for Partial Derivatives And Euler's Equation NAT - Question 1




The correct answer is: 0

*Answer can only contain numeric values
Partial Derivatives And Euler's Equation NAT - Question 2

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


Detailed Solution for Partial Derivatives And Euler's Equation NAT - Question 2

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

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*Answer can only contain numeric values
Partial Derivatives And Euler's Equation NAT - Question 3

Let f = yx, what is  at x = 2, y = 1


Detailed Solution for Partial Derivatives And Euler's Equation NAT - Question 3

f = yx

The correct answer is: 1

*Answer can only contain numeric values
Partial Derivatives And Euler's Equation NAT - Question 4

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


Detailed Solution for Partial Derivatives And Euler's Equation NAT - Question 4

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
Partial Derivatives And Euler's Equation NAT - Question 5


Detailed Solution for Partial Derivatives And Euler's Equation NAT - Question 5

v is homogeneous function of degree 3

The correct answer is: 3

*Answer can only contain numeric values
Partial Derivatives And Euler's Equation NAT - Question 6

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


Detailed Solution for Partial Derivatives And Euler's Equation NAT - Question 6





The correct answer is: 2

*Answer can only contain numeric values
Partial Derivatives And Euler's Equation NAT - Question 7

If  f(x, y) = x3y – xy3  then 


Detailed Solution for Partial Derivatives And Euler's Equation NAT - Question 7

1 – 12 = –11

The correct answer is: 0

*Answer can only contain numeric values
Partial Derivatives And Euler's Equation NAT - Question 8

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


Detailed Solution for Partial Derivatives And Euler's Equation NAT - Question 8

We have 

= 1 - 0 = 1

a + b = 1

The correct answer is: 1

*Answer can only contain numeric values
Partial Derivatives And Euler's Equation NAT - Question 9

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


Detailed Solution for Partial Derivatives And Euler's Equation NAT - Question 9

The correct answer is: 0

*Answer can only contain numeric values
Partial Derivatives And Euler's Equation NAT - Question 10

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


Detailed Solution for Partial Derivatives And Euler's Equation NAT - Question 10

= 2abz

The correct answer is: 2

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