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This mock test of Vector Calculus MCQ Level - 1 for IIT JAM helps you for every IIT JAM entrance exam.
This contains 10 Multiple Choice Questions for IIT JAM Vector Calculus MCQ Level - 1 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The angle between the x^{2} + y^{2} + z^{2} = 9 and z = x^{2} + y^{2} – 3 at the point (2, –1, 2) is :

Solution:

The angle between the surface at point is the angle between the normal to the surface at the point.

A normal to *x*^{2} + *y*^{2} + *z*^{2} = 9 at (2, -1, 2) is

A normal to ** z = x^{2} + y^{2} - 36** at (2, -1, 2) is

We know that, is the required angle

The correct answer is:

QUESTION: 2

For where ** C** is the square in xy

Solution:

By Stoke’s theorem,

∴ we need to evaluate

= –4

The correct answer is: –4

QUESTION: 3

If and C is the curve y = x^{3} from the point (1, 1) to (2, 8), then will be :

Solution:

The correct answer is: 35

QUESTION: 4

The value of where and S in the surface of the plane 2x + y + 2z = 6 in the first octant will be

Solution:

Normal to the surface = constant will be :

The correct answer is: 81

QUESTION: 5

A vector field which has a vanishing divergence is called as ____________

Solution:

**By the definition:** A vector field whose divergence comes out to be zero or Vanishes is called as a Solenoidal Vector Field. i.e.

If is a Solenoidal Vector field.

QUESTION: 6

The value of the line integral where, ** C** is the boundary of the region lying between the squares with vertices (1, 1), (–1, 1), (–1, –1) and (1, –1) and (2, 2), (–2, 2), (–2, –2) and (2, -2) will be :

Solution:

**Correct Answer :- c**

By Green’s Theorem,

**Explanation : **∫3x^{2}e^{y} dx + ey dy

= ∫∫-3x^{2}e^{y} dxdy

= -3*4 ∫(1 to 2)x^{2} dx ∫(1 to 2)e^{y} dy

= 12[x^{3}/3](1 to 2) [e^{y}](1 to 2)

= -4(8-1)(e^{2}-e)

= -28(e^{2}-e)

QUESTION: 7

The value of where, and *S* is the surface of the parallelepiped bounded by *x* = 0, *y* = 0, *z* = 0, *x* = 2, *y* = 1, *z* = 3 will be :

Solution:

By Gauss Divergence Theorem,

The correct answer is: 30

QUESTION: 8

If and then (a, b) =

Solution:

which is given to be

Hence,

for ** b** = 2 and

The correct answer is: (1, 2)

QUESTION: 9

is equal to :

Solution:

The correct answer is:

QUESTION: 10

The value of where *C* is the intersection of *z* = *x* + 4 with *x*^{2} + *y*^{2} = 4 will be :

Solution:

Also, the normal to the surface ** z – x** = constant is

The correct answer is: -48π

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