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Physics Exam  >  Physics Tests  >  Topic wise Tests for IIT JAM Physics  >  Partial Derivatives And Euler's Equation NAT - Physics MCQ

Partial Derivatives And Euler's Equation NAT - Physics MCQ


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

Partial Derivatives And Euler's Equation NAT for Physics 2024 is part of Topic wise Tests for IIT JAM 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.
Solutions of Partial Derivatives And Euler's Equation NAT questions in English are available as part of our Topic wise Tests for IIT JAM Physics for Physics & Partial Derivatives And Euler's Equation NAT solutions in Hindi for Topic wise Tests for IIT JAM Physics course. Download more important topics, notes, lectures and mock test series for Physics Exam by signing up for free. 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
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Partial Derivatives And Euler's Equation NAT - Question 1
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  then the value of x2fxx + 2xyfxy + y2fyy =


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




The correct answer is: 0

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Partial Derivatives And Euler's Equation NAT - Question 2
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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

uxx=α2eαx+ βy , uyy=β2eαx+ βy

uxy= αβeαx+ βy

put these values in the given relation, we get

uxx-7uxy+12uyy=0

eαx+ βy[α2-7αβ+12β2]=0

eαx+ β ≠0=> α2-7αβ+12β2=0

The correct answer is: 0

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Partial Derivatives And Euler's Equation NAT - Question 3
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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

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Partial Derivatives And Euler's Equation NAT - Question 4
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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/dx2 + d2z/dx2 = 4a2 - 2 + 4b2 - 2

=> 4(a2+b2) - 4

As we know that a2 + b2 = 1

=> 4(1) - 4

=> 0

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

v is homogeneous function of degree 3

The correct answer is: 3

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Partial Derivatives And Euler's Equation NAT - Question 6
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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

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Partial Derivatives And Euler's Equation NAT - Question 7
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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

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Partial Derivatives And Euler's Equation NAT - Question 8
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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

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Partial Derivatives And Euler's Equation NAT - Question 9
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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

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Partial Derivatives And Euler's Equation NAT - Question 10
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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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