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# Test: Green’s Theorem

## 10 Questions MCQ Test Electromagnetic Fields Theory | Test: Green’s Theorem

Description
This mock test of Test: Green’s Theorem for Electronics and Communication Engineering (ECE) helps you for every Electronics and Communication Engineering (ECE) entrance exam. This contains 10 Multiple Choice Questions for Electronics and Communication Engineering (ECE) Test: Green’s Theorem (mcq) to study with solutions a complete question bank. The solved questions answers in this Test: Green’s Theorem quiz give you a good mix of easy questions and tough questions. Electronics and Communication Engineering (ECE) students definitely take this Test: Green’s Theorem exercise for a better result in the exam. You can find other Test: Green’s Theorem extra questions, long questions & short questions for Electronics and Communication Engineering (ECE) on EduRev as well by searching above.
QUESTION: 1

### Mathematically, the functions in Green’s theorem will be

Solution:

Explanation: The Green’s theorem states that if L and M are functions of (x,y) in an open region containing D and having continuous partial derivatives then,
∫ (F dx + G dy) = ∫∫(dG/dx – dF/dy)dx dy, with path taken anticlockwise.

QUESTION: 2

### Find the value of Green’s theorem for F = x2 and G = y2 is

Solution:

Explanation: ∫∫(dG/dx – dF/dy)dx dy = ∫∫(0 – 0)dx dy = 0. The value of Green’s theorem gives zero for the functions given.

QUESTION: 3

### Which of the following is not an application of Green’s theorem?

Solution:

Explanation: In physics, Green’s theorem is used to find the two dimensional flow integrals. In plane geometry, it is used to find the area and centroid of plane figures.

QUESTION: 4

The path traversal in calculating the Green’s theorem is

Solution:

Explanation: The Green’s theorem calculates the area traversed by the functions in the region in the anticlockwise direction. This converts the line integral to surface integral.

QUESTION: 5

Calculate the Green’s value for the functions F = y2 and G = x2 for the region x = 1 and y = 2 from origin.

Solution:

Explanation: ∫∫(dG/dx – dF/dy)dx dy = ∫∫(2x – 2y)dx dy. On integrating for x = 0->1 and y = 0->2, we get Green’s value as -2.

QUESTION: 6

If two functions A and B are discrete, their Green’s value for a region of circle of radius a in the positive quadrant is

Solution:

Explanation: Green’s theorem is valid only for continuous functions. Since the given functions are discrete, the theorem is invalid or does not exist.

QUESTION: 7

Applications of Green’s theorem are meant to be in

Solution:

Explanation: Since Green’s theorem converts line integral to surface integral, we get the value as two dimensional. In other words the functions are variable with respect to x,y, which is two dimensional.

QUESTION: 8

The Green’s theorem can be related to which of the following theorems mathematically?

Solution:

Explanation: The Green’s theorem is a special case of the Kelvin- Stokes theorem, when applied to a region in the x-y plane. It is a widely used theorem in mathematics and physics.

QUESTION: 9

he Shoelace formula is a shortcut for the Green’s theorem. State True/False.

Solution: