Vector Calculus - 8


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


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This mock test of Vector Calculus - 8 for Mathematics helps you for every Mathematics entrance exam. This contains 20 Multiple Choice Questions for Mathematics Vector Calculus - 8 (mcq) to study with solutions a complete question bank. The solved questions answers in this Vector Calculus - 8 quiz give you a good mix of easy questions and tough questions. Mathematics students definitely take this Vector Calculus - 8 exercise for a better result in the exam. You can find other Vector Calculus - 8 extra questions, long questions & short questions for Mathematics on EduRev as well by searching above.
QUESTION: 1

If  then div curl  is equal to

Solution:
QUESTION: 2

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

Solution:
QUESTION: 3

If  then is

Solution:
QUESTION: 4

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

Solution:
QUESTION: 5

The value of  is

Solution:
QUESTION: 6

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

Solution:
QUESTION: 7

If  and  are two vectors then the value of will be

Solution:
QUESTION: 8

The value of div grad Φ is

Solution:
QUESTION: 9

The value of  is

Solution:
QUESTION: 10

Gauss’s divergence theorem is

Solution:
QUESTION: 11

If   then the value of div  will be

Solution:
QUESTION: 12

If S denotes the surface of the cube bounded by the planes x = 0, x = a, y = 0, y = a, z = 0, z = a then by Gauss divergence theorem the value of  is

Solution:
QUESTION: 13

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

Solution:
QUESTION: 14

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

Solution:

Given that

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

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

Solution:

Grad f=

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

Solution:

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

QUESTION: 17

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

Solution:

By Gauss divergence theorem,

QUESTION: 18

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

Solution:

By Gauss divergence theorem,

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

QUESTION: 19

 A vector normal to  is

Solution:


We take, 

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

QUESTION: 20

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

Solution:

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, 

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