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# Vector Calculus MCQ Level - 2

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

Description
This mock test of Vector Calculus MCQ Level - 2 for IIT JAM helps you for every IIT JAM entrance exam. This contains 10 Multiple Choice Questions for IIT JAM Vector Calculus MCQ Level - 2 (mcq) to study with solutions a complete question bank. The solved questions answers in this Vector Calculus MCQ Level - 2 quiz give you a good mix of easy questions and tough questions. IIT JAM students definitely take this Vector Calculus MCQ Level - 2 exercise for a better result in the exam. You can find other Vector Calculus MCQ Level - 2 extra questions, long questions & short questions for IIT JAM on EduRev as well by searching above.
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 :

Solution:

By Green's theorem, we have,

QUESTION: 2

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

Solution:

By Stoke’s Theorem,

where C : x2 + y2 = 1, z = 0

QUESTION: 3

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

Solution:

We have,

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

QUESTION: 4

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

Solution:

u = x + y + z

= 0

QUESTION: 5

The potential function for the vector field  will be :

Solution:

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.

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 :

Solution:

The given surface is z + y2 = 9

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}

Solution:

By Gauss Divergence Theorem,

QUESTION: 8

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

Solution:

By Stokes theorem,

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

QUESTION: 9

is equal to :

Solution:

Consider,