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This mock test of Vector Analysis - MCQ Test for Railways helps you for every Railways entrance exam.
This contains 20 Multiple Choice Questions for Railways Vector Analysis - MCQ Test (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The two vector are R_{AM} = 20u_{x} + 18u_{y} - 10u_{z }and R_{AN} = -10u_{x} + 8u_{y} + 15u_{z}. The u of the triangle that bisects the interior angle at A is

Solution:

The non-unit vector in the required direction is

QUESTION: 2

Two points in cylindrical coordinates are A(ρ = 5, Ø = 70^{0 }, z = -3) and B(ρ = 2, Ø = 30^{0 }, z = 1) A unit vector at A towards B is

Solution:

In cartesian coordinates

QUESTION: 3

A field in cartesian form is given as

In cylindrical form it will be

Solution:

QUESTION: 4

The surface ρ = 2, ρ = 4, Ø = 100^{0} ,Ø = 130^{0} ,z = 3 and z = 4.5 define a closed surface. The enclosed volume is

Solution:

QUESTION: 5

The surface ρ = 2, ρ = 4, Ø = 45^{0} ,Ø = 135^{0} ,z = 3 and z = 4 define a closed surface. The total area of the enclosing surface is

Solution:

Area is

QUESTION: 6

The surface ρ = 3, ρ = 5, Ø = 100^{0} ,Ø = 130^{0} ,z = 3 and z = 4.5 define a closed surface. The length of the longest straight line that lies entirely within the volume is

Solution:

QUESTION: 7

A vector field H is

Solution:

QUESTION: 8

A vector is A = yu_{x} +(x+z)u_{y} .At point P(-2, 6, 3) A in cylindrical coordinate is

Solution:

QUESTION: 9

The directional derivative of function φ = xy + yz + zx at point P(3, -3, -3) in the directiontoward point Q(4, -1, -1) is

Solution:

QUESTION: 10

The temperature in a auditorium is given by T = 2x^{2} +y^{2} - 2z^{2} . A mosquito located at (2, 2, 1) in the auditorium desires to fly in such a direction that it will get warm as soon as possible. The direction, in that it must fly is

Solution:

QUESTION: 11

The angle between the normal to the surface x^{2}y + z = 3 and x ln z - y^{2} = -4 at the point of intersection (-1, 2, 1) is

Solution:

QUESTION: 12

The divergence of vector A = yzu_{x} + 4xyu_{y} + yu_{z} at point P(1, -2, 3) is

Solution:

QUESTION: 13

The divergence of the vector at point P(1, 30^{0} , 60^{0} ) is

Solution:

QUESTION: 14

Which of the quantities is nearest to the value of

Solution:

QUESTION: 15

The flux of over the closed surface of the cylinder 0 ≤ z ≤ 3 , ρ = 3 is

Solution:

By divergence theorem

QUESTION: 16

The curl of vector is

Solution:

QUESTION: 17

The curl of vector field

Solution:

QUESTION: 18

The curl of vector field

Solution:

QUESTION: 19

the value is

Solution:

QUESTION: 20

Solution:

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