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Test: Vector Analysis - 1 - Question 1

If φ = xy^{2}z^{3} then match List-I with List-II and select the correct answer using the codes given below the lists:

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Test: Vector Analysis - 1 - Question 2

The unit vector which points from z = h on the z-axis towards (r, φ, 0) in cylindrical co-ordinates as shown below is given by

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Test: Vector Analysis - 1 - Question 3

If the vector V given below is irrotational, then the values of a, b and c will be respectively

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Test: Vector Analysis - 1 - Question 4

Match List-I (Vector Identities) with List-ll. (Equivalent expression) and select the correct answer using the codes given below the lists:

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Test: Vector Analysis - 1 - Question 5

The vector differential operator, in spherical co-ordinate system is given by

Test: Vector Analysis - 1 - Question 6

Assertion (A): Divergence of a vector function at each point gives the rate per unit volume at which the physical entity is issuing from that point.

Reason (R): If some physical entity is generated or absorbed within a certain region of the field, then that region is known as source or sink respectively and if there are no sources or sinks in the field, the net outflow of the incompressible physical entity over any part of the region is zero. However, the net outflow is said to be positive, if the total strength of the sources are greater than the total strength of sink and vice-versa.

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Test: Vector Analysis - 1 - Question 8

The vector directed from (2, - 4,1) to (0, -2,0) in Cartesian coordinates is given by

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Test: Vector Analysis - 1 - Question 9

What is the value of where

Here, s is the surface bounded by x = 0, x = 1, y = o, y = 1, z = 0, z =1 and are unit vectors along x, yand z axes respectively.

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