Vector Calculus MCQ Level - 2 - Physics MCQ

# Vector Calculus MCQ Level - 2 - Physics MCQ

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## 10 Questions MCQ Test Topic wise Tests for IIT JAM Physics - Vector Calculus MCQ Level - 2

Vector Calculus MCQ Level - 2 for Physics 2024 is part of Topic wise Tests for IIT JAM Physics preparation. The Vector Calculus MCQ Level - 2 questions and answers have been prepared according to the Physics exam syllabus.The Vector Calculus MCQ Level - 2 MCQs are made for Physics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Vector Calculus MCQ Level - 2 below.
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Vector Calculus MCQ Level - 2 - Question 1

### The line integral  taken along the closed path formed by y = x and x2 = y3 in the first quadrant will be valuated to :

Detailed Solution for Vector Calculus MCQ Level - 2 - Question 1

By Green's theorem, we have,

Vector Calculus MCQ Level - 2 - Question 2

### where S : x2 + y2 + z2 = 1, z ≥ 0 and  will have the value :

Detailed Solution for Vector Calculus MCQ Level - 2 - Question 2

By Stoke’s Theorem,

where C : x2 + y2 = 1, z = 0

Vector Calculus MCQ Level - 2 - Question 3

### The line integral of the vector field  along the helix defined by x = cos t, y = sin t,   is equal to :

Detailed Solution for Vector Calculus MCQ Level - 2 - Question 3

We have,

Hence, the line integral of the given vector field will be,

Vector Calculus MCQ Level - 2 - Question 4

If  u = x + y + z, v = x2 + y2 + z2  and w = yz = zx + xy then  is equal to :

Detailed Solution for Vector Calculus MCQ Level - 2 - Question 4

u = x + y + z

= 0

Vector Calculus MCQ Level - 2 - Question 5

The potential function for the vector field  will be :

Detailed Solution for Vector Calculus MCQ Level - 2 - Question 5

Compare the given vector field with the gradient of some function, say φ, i.e.,

⇒ The potential function for the given vector field would be x2y3z4.

Vector Calculus MCQ Level - 2 - Question 6

The value of the surface integral  where S is the closed surface of the solid bounded by the graphs of x = 4 and z = 9 – y2 and coordinate planes &  will be given by :

Detailed Solution for Vector Calculus MCQ Level - 2 - Question 6

The given surface is z + y2 = 9

Vector Calculus MCQ Level - 2 - Question 7

The value of the integral   where  and where S is the entire surface of the  paraboloid z = 1 - x2 - y2 with z = 0 together with the disk {(x, y) : x2 + y2 < 1}

Detailed Solution for Vector Calculus MCQ Level - 2 - Question 7

By Gauss Divergence Theorem,

Vector Calculus MCQ Level - 2 - Question 8

The value of    where  and S is the surface of the paraboloid z = 4 – (x2 + y2) above the xy-plane will be :

Detailed Solution for Vector Calculus MCQ Level - 2 - Question 8

By Stokes theorem,

Here, the boundary curve C of the surface will be given by x2 + y2 = 4, z = 0, or

Vector Calculus MCQ Level - 2 - Question 9

is equal to :

Detailed Solution for Vector Calculus MCQ Level - 2 - Question 9

Consider,

Vector Calculus MCQ Level - 2 - Question 10

is equivalent to :

Detailed Solution for Vector Calculus MCQ Level - 2 - Question 10

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