Vector Calculus NAT Level - 1


10 Questions MCQ Test Topic wise Tests for IIT JAM Physics | Vector Calculus NAT Level - 1


Description
This mock test of Vector Calculus NAT Level - 1 for Physics helps you for every Physics entrance exam. This contains 10 Multiple Choice Questions for Physics Vector Calculus NAT Level - 1 (mcq) to study with solutions a complete question bank. The solved questions answers in this Vector Calculus NAT Level - 1 quiz give you a good mix of easy questions and tough questions. Physics students definitely take this Vector Calculus NAT Level - 1 exercise for a better result in the exam. You can find other Vector Calculus NAT Level - 1 extra questions, long questions & short questions for Physics on EduRev as well by searching above.
*Answer can only contain numeric values
QUESTION: 1

  Evaluate the line integral    from (0, 0, 0) to (1, 1, 1) along the curve x = t, y = t2, z = t3


Solution:

x = t, y = t2, z = t3
dx = dt, dy = 2t dt, dz = 3t2dt

= 5
The correct answer is: 5

*Answer can only contain numeric values
QUESTION: 2

Compute the flux of  across the cone   (upto three decimal places)


Solution:


The correct answer is: 4.187

*Answer can only contain numeric values
QUESTION: 3


Solution:



= –0.858
The correct answer is: -0.858

*Answer can only contain numeric values
QUESTION: 4

 is a conservative field and potential any curve C in the path from (0, 0, 1) to  evaluate  upto three decimal places.


Solution:

The conservative field vector 

The correct answer is: 4.141

*Answer can only contain numeric values
QUESTION: 5

If V = x2y2z the Laplacian of the field V at point  is :


Solution:

The correct answer is: 24

*Answer can only contain numeric values
QUESTION: 6

Div grad rm = m(m + 1)rm-α. Find the value of α.


Solution:




= m(m + 1)rm-2
Hence value of  α = 2.

The correct answer is: 2

*Answer can only contain numeric values
QUESTION: 7

are unit vectors satisfying  then 


Solution:



⇒ Angle between each pair is 120º

Now,  

= 54 – 10 – 10 – 25 = 9


The correct answer is: 3

*Answer can only contain numeric values
QUESTION: 8

S is the surface of sphere x2 + y2 + z2 = 9, the integral [(x + z) dydz + (y + z)dzdx + (x + y)dxdy] is equal to, (upto three decimal places)


Solution:

By Gauss divergence theorem

The correct answer is: 226.194

*Answer can only contain numeric values
QUESTION: 9

 Evaluate  around any closed path C. (Ans. upto three decimal places)


Solution:

The correct answer is: 6.282

*Answer can only contain numeric values
QUESTION: 10

If T(x, y, z) = x2 + y2 + 2z2 defines the temperature at any location (x, y, z) then the magnitude of the temperature gradient point P(1, 1, 1), (upto three decimal places)


Solution:


Magnitude of temperature gradient

The correct answer is: 4.898

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