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# Vector Calculus - 8

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

Description
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

Solution:
QUESTION: 2

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,  