Vector Calculus MCQ Level - 1 - Physics MCQ

# Vector Calculus MCQ Level - 1 - Physics MCQ

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## 10 Questions MCQ Test Topic wise Tests for IIT JAM Physics - Vector Calculus MCQ Level - 1

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

### The angle between the  x2 + y2 + z2 = 9  and  z = x2 + y2 – 3  at the point (2, –1, 2) is :

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

The angle between the surfaces at point is the angle between the normals to the surfaces at the point.

A normal to z = x2 + y2 - 3 at (2, -1, 2) is

A normal to x2 + y2 + z2 = 9 at (2, -1, 2) is

Let angle between surfaces ϕ1 and ϕ2 is θ.

Vector Calculus MCQ Level - 1 - 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 :

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

By Stoke’s theorem,

∴  we need to evaluate

= –4

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Vector Calculus MCQ Level - 1 - Question 3

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

Detailed Solution for Vector Calculus MCQ Level - 1 - Question 3

Now y = x3
Differentiating both sides,
dy = 3xdx
Now, r = x Î + y Ĵ
Differentiating both sides,
Now, dr = dx Î + dy Ĵ
Now F.dr = (5xy - 6x²)dx + (2y - 4x) dy
Substituting dy = 3xdx and y = x3 in the above equation

Vector Calculus MCQ Level - 1 - Question 4

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

Detailed Solution for Vector Calculus MCQ Level - 1 - Question 4

Normal to the surface  = constant will be :

Vector Calculus MCQ Level - 1 - Question 5

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

Detailed Solution for Vector Calculus MCQ Level - 1 - Question 5

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.

Vector Calculus MCQ Level - 1 - 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 :

Detailed Solution for Vector Calculus MCQ Level - 1 - Question 6

By Green’s Theorem,

Explanation : ∫3x2ey dx + ey dy

= ∫∫-3x2ey dxdy

= -3*4 ∫(1 to 2) x2 dx ∫(1 to 2) ey dy

= 12[x3/3](1 to 2) [ey](1 to 2)

= -4(8-1)(e2-e)

= -28(e2-e)

Vector Calculus MCQ Level - 1 - 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 :

Detailed Solution for Vector Calculus MCQ Level - 1 - Question 7

By Gauss Divergence Theorem,

Vector Calculus MCQ Level - 1 - Question 8

If   and  then (a, b) =

Detailed Solution for Vector Calculus MCQ Level - 1 - Question 8

which is given to be
Hence,

for b = 2 and a being any value.

The correct answer is: (1, 2)

Vector Calculus MCQ Level - 1 - Question 9

is equal to :

Detailed Solution for Vector Calculus MCQ Level - 1 - Question 9

Vector Calculus MCQ Level - 1 - Question 10

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

Detailed Solution for Vector Calculus MCQ Level - 1 - Question 10

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

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