Vector Calculus MCQ Level - 2 - IIT JAM MCQ

# Vector Calculus MCQ Level - 2 - IIT JAM MCQ

Test Description

## 10 Questions MCQ Test - Vector Calculus MCQ Level - 2

Vector Calculus MCQ Level - 2 for IIT JAM 2024 is part of IIT JAM preparation. The Vector Calculus MCQ Level - 2 questions and answers have been prepared according to the IIT JAM exam syllabus.The Vector Calculus MCQ Level - 2 MCQs are made for IIT JAM 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Vector Calculus MCQ Level - 2 below.
Solutions of Vector Calculus MCQ Level - 2 questions in English are available as part of our course for IIT JAM & Vector Calculus MCQ Level - 2 solutions in Hindi for IIT JAM course. Download more important topics, notes, lectures and mock test series for IIT JAM Exam by signing up for free. Attempt Vector Calculus MCQ Level - 2 | 10 questions in 45 minutes | Mock test for IIT JAM preparation | Free important questions MCQ to study for IIT JAM Exam | Download free PDF with solutions
 1 Crore+ students have signed up on EduRev. Have you?
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,