Partial Derivatives And Euler's Equation MCQ Level - 1

Partial Derivatives And Euler's Equation MCQ Level - 1

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Partial Derivatives And Euler's Equation MCQ Level - 1 for Physics 2023 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 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Partial Derivatives And Euler's Equation MCQ Level - 1 below.
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Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 1

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

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

The correct answer is: z

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

If  then the value of

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

f(xy) 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

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

If   then  equal to

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

The correct answer is

Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 6

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

The correct answers are:

Partial Derivatives And Euler's Equation MCQ Level - 1 - Question 7

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

Find a function w = f(xy) 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

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

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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