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Partial Derivatives And Euler's Equation MCQ Level - 1 - Physics MCQ


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

Partial Derivatives And Euler's Equation MCQ Level - 1 for Physics 2024 is part of Topic wise Tests for IIT JAM Physics preparation. The Partial Derivatives And Euler's Equation MCQ Level - 1 questions and answers have been prepared according to the Physics exam syllabus.The Partial Derivatives And Euler's Equation MCQ Level - 1 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 MCQ Level - 1 below.
Solutions of Partial Derivatives And Euler's Equation MCQ Level - 1 questions in English are available as part of our Topic wise Tests for IIT JAM Physics for Physics & Partial Derivatives And Euler's Equation MCQ Level - 1 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 MCQ Level - 1 | 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
Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 1
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If z = xy In (x, y) then

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


Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 2
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Suppose  is equal to

Detailed Solution for Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 2

u and v are homogeneous function of degree one

on adding  

The correct answer is: z

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Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 3
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If  then the value of 

Detailed Solution for Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 3


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

The correct answer is: 0

Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 4
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If  u = sin x/l*sin y/m * sin z/n * cospt  satisfy the equation  then
Detailed Solution for Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 4




Again using the given condition

Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 5
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If   then  equal to
Detailed Solution for Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 5

Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 6
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 then 
Detailed Solution for Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 6

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

On adding

The correct answers are:  

Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 7
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If  then 
Detailed Solution for Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 7

We have 

u is homogeneous function of degree n

Now differentiate partially w.r.t. x again

The correct answer is: 

Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 8
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Find a function w = f(x, y) whose first partial derivatives are    and  and whose value at point (ln2, 0) is ln2.
Detailed Solution for Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 8

We σw/σx=1+excos y

Integrate both w.r.t.x

w(x,y)  =x+ex cosy+f(y)

σw/σy=0-exsiny+f’(y)

Given =-exsiny+2y

So,on comparing the above two equation

f’(y)=2y

f(y)=y2+c(on integration)

so, w(x,y)=x+excos y+y2+c

Now, using (In2,0)is In2,we get

C=-2

Hence, w(x,y)=x+y2+excosy-2

The correct answer is, option C; w=x+y2+excosy-2

Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 9
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If u = sin-1 [(x3 + y3 + z3)/(ax + by + cz)] then xdu/dx + ydu/dy + zdu/dz equal to
Detailed Solution for Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 9

So, by Euler's theorem

The correct answer is: 2 tan u

Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 10
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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
Detailed Solution for Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 10

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

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