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# Vector Calculus MCQ Level - 1

## 10 Questions MCQ Test Basic Physics for IIT JAM | Vector Calculus MCQ Level - 1

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

### The angle between the  x2 + y2 + z2 = 9  and  z = x2 + y2 – 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 x2 + y2 + z2 = 9 at (2, -1, 2) is

A normal to z = x2 + y2 - 36 at (2, -1, 2) is

We know that,  is the required angle

QUESTION: 2

### For  where C is the square in xy–plane projected from the cube x = 0, x = 2, y = 0, y = 2, z = 0, z = 2 above xy–plane, will be equal to :

Solution:

By Stoke’s theorem,

∴  we need to evaluate

= –4

QUESTION: 3

### If  and C is the curve  y = x3  from the point (1, 1) to (2, 8), then will be :

Solution:

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 :

QUESTION: 5

Using Gauss Divergence theorem, find the value of   over the entire surface of the sphere x2 + y2 + z2 = 1 equal to :

Solution:

Comparing

where  (normal to the surface) =
we get,

By Gauss Divergence Theorem,

[∵ 3x2y is an odd function of y and x is an odd function of x]

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:

By Green’s Theorem,

The correct answer is: -28(e2 - 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,

QUESTION: 8

If   and  then (a, b) =

Solution:

which is given to be
Hence,

for b = 2 and a being any value.

The correct answer is: (1, 2)

QUESTION: 9

is equal to :

Solution:

QUESTION: 10

The value of  where C is the intersection of  z = x + 4 with x2 + y2 = 4  will be :

Solution:

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