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This mock test of Vector Calculus - 7 for Mathematics helps you for every Mathematics entrance exam.
This contains 20 Multiple Choice Questions for Mathematics Vector Calculus - 7 (mcq) to study with solutions a complete question bank.
The solved questions answers in this Vector Calculus - 7 quiz give you a good mix of easy questions and tough questions. Mathematics
students definitely take this Vector Calculus - 7 exercise for a better result in the exam. You can find other Vector Calculus - 7 extra questions,
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QUESTION: 1

A vector is said to be irrotational vector, if

Solution:

QUESTION: 2

The plane containing principal, normal and binormal is called

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QUESTION: 3

Maximum value of directional derivative of f= x^{2}yz at the point (1, 4,1) is

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QUESTION: 4

If V is the volume enclosed by surface S and = then is

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QUESTION: 5

The minimum value of the directional derivative is which occurs when θ is

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QUESTION: 6

where P is a vector, is equal to

Solution:

QUESTION: 7

if and be the set of orthonormal unit vectors, then is

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QUESTION: 8

Stoke’s theorem is

Solution:

QUESTION: 9

The relation between the line integral and the surface integral is

Solution:

QUESTION: 10

The divergence of the vector field

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QUESTION: 11

If Φ(x, y, z) = 3x^{2}y - y^{3}z^{2 } then the value of grad Φ at the point (1,- 2 ,- 1 ) is

Solution:

QUESTION: 12

If Φ is a differentiable scalar point function, then the value of curl grad Φ is

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QUESTION: 13

If then is

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QUESTION: 14

A particle moves along the curve Acceleration of the particle in the direction of the motion is

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QUESTION: 15

If C is the curve x^{2} + y^{2} = 1, z = y^{2} then by stoke’s theorem (yz dx + zx dy + xy dz) is

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QUESTION: 16

Gauss’s divergence theorem can be written a

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QUESTION: 17

If = and r^{2} = x^{2} + y^{2} + z^{2}, then-the value of grad will be

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QUESTION: 18

Let be a vector field.

Q. The value of div is

Solution:

Given that

Therefore,

QUESTION: 19

Let be a vector field.

Q. The value of curl is

Solution:

Given that

QUESTION: 20

Let and

Q. The value of is

Solution:

Given that

and

Therefore,

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