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

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

Description
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
QUESTION: 1

### If z = xy In (x, y) then

Solution:  QUESTION: 2

### Suppose is equal to

Solution: u and v are homogeneous function of degree one on adding  QUESTION: 3

### If then the value of Solution: f(xy) is homogeneous function of degree –2
So, using Euler's equation QUESTION: 4

If  u = sin x/l*sin y/m * sin z/n * cospt  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: f1 is homogeneous of degree 1 and f2 is homogeneous of degree zero  The correct answers are: QUESTION: 7

If then Solution:

We have  u is homogeneous function of degree n Now differentiate partially w.r.t. x again The correct answer is: QUESTION: 8

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

Solution:

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

QUESTION: 9

If u = sin-1 [(x3 + y3 + z3)/(ax + by + cz)] then xdu/dx + ydu/dy + zdu/dz 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 x2 + y2 with respect to y is equal to the partial derivative of 6y + 4x w.r.t. x is

Solution:

So, 2y = 4
y = 2
The correct answer is: y = 2 Use Code STAYHOME200 and get INR 200 additional OFF Use Coupon Code