Vector Calculus - 8


Test Description

20 Questions MCQ Test Topic-wise Tests & Solved Examples for IIT JAM Mathematics | Vector Calculus - 8

Vector Calculus - 8 for Mathematics 2023 is part of Topic-wise Tests & Solved Examples for IIT JAM Mathematics preparation. The Vector Calculus - 8 questions and answers have been prepared according to the Mathematics exam syllabus.The Vector Calculus - 8 MCQs are made for Mathematics 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Vector Calculus - 8 below.
Solutions of Vector Calculus - 8 questions in English are available as part of our Topic-wise Tests & Solved Examples for IIT JAM Mathematics for Mathematics & Vector Calculus - 8 solutions in Hindi for Topic-wise Tests & Solved Examples for IIT JAM Mathematics course. Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free. Attempt Vector Calculus - 8 | 20 questions in 60 minutes | Mock test for Mathematics preparation | Free important questions MCQ to study Topic-wise Tests & Solved Examples for IIT JAM Mathematics for Mathematics Exam | Download free PDF with solutions
1 Crore+ students have signed up on EduRev. Have you?
Vector Calculus - 8 - Question 1

If  then div curl  is equal to

Vector Calculus - 8 - Question 2

If Φ is a differentiable scalar function, then div grad Φ is equal to

Vector Calculus - 8 - Question 3

If  then is

Detailed Solution for Vector Calculus - 8 - Question 3

Correct Answer :- a

Explanation : curl F = ∇ × F

= (∂/∂x, ∂/∂y, ∂/∂z) × (F1, F2, F3)

(∂F3/∂y − ∂F2/∂z , ∂F1/∂z − ∂F3/∂x , ∂F2/∂x − ∂F1/∂y)

= (∂z/∂y − ∂y/∂z , ∂x/∂z − ∂z/∂x, ∂y/∂x − ∂x/∂y)

= (0, 0, 0)

Note that since this curl is 0, the radial vector field

F(x, y, z) = (x, y, z) is irrotational.

Vector Calculus - 8 - Question 4

The value of  along the circle x2 + y2 = 1 is  

Vector Calculus - 8 - Question 5

The value of  is

Vector Calculus - 8 - Question 6

Directional derivative of ψ(x,y,z) = xy2 + 4xyz + z2 at the point (1, 2, 3) in the direction of  is 

Vector Calculus - 8 - Question 7

If  and  are two vectors then the value of will be

Vector Calculus - 8 - Question 8

The value of div grad Φ is

Vector Calculus - 8 - Question 9

The value of  is

Vector Calculus - 8 - Question 10

Gauss’s divergence theorem is

Vector Calculus - 8 - Question 11

If   then the value of div  will be

Vector Calculus - 8 - Question 12

Let W be the region bounded by the planes x = 0, y = 0, y = 3, z = 0 and x + 2z = 6. Let S be the boundary of this region. Using gauss’ divergence theorem, evaluate, where and ň is the outward unit normal vector to S. 

Detailed Solution for Vector Calculus - 8 - Question 12

By gauss divergence theorem



 

Vector Calculus - 8 - Question 13

If  is a differentiable vector point function, then the value of div curl  is 

Vector Calculus - 8 - Question 14

Let  and 
Q. The unit vector perpendicular to the plane containing  and  is

Detailed Solution for Vector Calculus - 8 - Question 14

Given that

and 
Therefore, The unit vector perpendicular to the plane containing vector and is

Vector Calculus - 8 - Question 15

Let us consider the scalar point function f(x y, z) =x2 + y2 + z2
Q. The grad of f(x, y, z) is

Detailed Solution for Vector Calculus - 8 - Question 15

Grad f=

Vector Calculus - 8 - Question 16

Let us consider the scalar point function f(x y, z) =x2 + y2 + z2
Q. The directional derivative of f(x, y, z) at the point P(1, 1, 1) along  is

Detailed Solution for Vector Calculus - 8 - Question 16

(Grad f)(1,1,1)
Now, the directional derivative o f f at P(1,1,1) along  is

Vector Calculus - 8 - Question 17

Let where a, b and c are constants and S is the surface of unit sphere.
Q. The value of is

Detailed Solution for Vector Calculus - 8 - Question 17

By Gauss divergence theorem,

Vector Calculus - 8 - Question 18

Let where a, b and c are constants and S is the surface of unit sphere.
Q. The value of is

Detailed Solution for Vector Calculus - 8 - Question 18

By Gauss divergence theorem,

Since, V is enclosed by a sphere of unit radius. Thereofore
a + b + c = 1
and 

Vector Calculus - 8 - Question 19

 A vector normal to  is

Detailed Solution for Vector Calculus - 8 - Question 19


We take, 

= 1 - 2 + 1 = 0
So, B is normal to A.

Vector Calculus - 8 - Question 20

If  and curve C is the arc of the curve y = x3 from (0,0) to (2,8), then the value of 

Detailed Solution for Vector Calculus - 8 - Question 20

Since, C is the curve y = x3 from (0,0) to (2,8)
So, let x = t ⇒ y = t3
If is the position vector of any point on C, then

or 
or 
At (0, 0) ⇒ t = x = 0 and at (2, 8) ⇒ t = 2
So, 

Use Code STAYHOME200 and get INR 200 additional OFF
Use Coupon Code
Information about Vector Calculus - 8 Page
In this test you can find the Exam questions for Vector Calculus - 8 solved & explained in the simplest way possible. Besides giving Questions and answers for Vector Calculus - 8, EduRev gives you an ample number of Online tests for practice