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QUESTION: 1

If z = xy In (x, y) then

Solution:

QUESTION: 2

Suppose is equal to

Solution:

** u** and

on adding

The correct answer is: *z*

QUESTION: 3

If then the value of

Solution:

*f*(*x*, *y*) is homogeneous function of degree –2

So, using Euler's equation

The correct answer is: 0

QUESTION: 4

If satisfy the equation then

Solution:

Again using the given condition

QUESTION: 5

If then equal to

Solution:

The correct answer is

QUESTION: 6

then

Solution:

** f_{1}** is homogeneous of degree

On adding

The correct answers are:

QUESTION: 7

Solution:

We have

** u** is homogeneous function of degree

Now differentiate partially w.r.t. * x* again

The correct answer is:

QUESTION: 8

Find a function *w* = *f*(*x*, *y*) whose first partial derivatives are and and whose value at point (ln2, 0) is ln2.

Solution:

Integrate both sides w.r.t. *x
*

So, on comparing the above two equation

(on integration)

Now, using (ln2, 0) is ln2, we get

*c* = –2

The correct answer is:

QUESTION: 9

If equal to

Solution:

So, by Euler's theorem

The correct answer is: 2 tan *u*

QUESTION: 10

The contour on xy plane where partial derivative of x^{2} + y^{2} with respect to y is equal to the partial derivative of 6y + 4x w.r.t. x is

Solution:

So,

**2 y = 4**

The correct answer is:

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