# Multiple choice question for engineering

## Set 1

1. The wavelength of a line with a phase constant of 6.28 units is

a) 2

b) 1

c) 0.5

d) 3.14

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2. The wavelength of a wave with a frequency of 6 GHz in air is

a) 50

b) 5

c) 0.5

d) 0.05

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^{8}/6×10

^{9}= 0.05 units.

3. The phase constant of a wave with a wavelength of 2 units is given by

a) 2

b) 3.14

c) 6.28

d) 1

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4. The frequency of a wave travelling in a transmission line with velocity 4 x 108 and wavelength 3 units is

a) 0.75 GHz

b) 0.133 GHz

c) 7.5 GHz

d) 1.33 GHz

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^{8}/3 = 0.133 GHz.

5. The velocity and phase constant relation is given by

a) V = ω/β

b) V = ωβ

c) V = β/ω

d) Vωβ = 1

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6. Find the phase constant of a wave travelling with a velocity of 1.2 x 108 and a frequency of 7.5 giga radian/sec

a) 62.5

b) 26.5

c) 56.2

d) 52.6

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^{9}and v = 1.2 x 10

^{8}, we get the phase constant β = 7.5 x 10

^{9}/1.2 x 10

^{8}= 62.5 units.

7. The electrical length in a transmission line refers to the

a) Product of attenuation constant and length

b) Ratio of attenuation constant and length

c) Product of phase constant and length

d) Ratio of phase constant and length

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8. The unit of attenuation constant is

a) Decibel

b) Bel

c) Neper

d) No unit

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9. The attenuation constant causes phase distortion and the phase constant causes frequency distortion. State True/False.

a) True

b) False

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10. The propagation constant of a wave with attenuation and phase constant given by 2 and 3 respectively is

a) 2 – 3j

b) 3 – 2j

c) 2 + 3j

d) 3 + 2j

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11. The velocity of wave in the air medium is

a) 1 x 10^{8}

b) 1.5 x 10^{8}

c) 3 x 10^{8}

d) 1 x 10^{9}

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^{8}.

12. Identify the secondary parameter from the options given below.

a) Resistance

b) Conductance

c) Phase constant

d) Capacitance

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## Set 2

1. For time varying currents, the field or waves will be

a) Electrostatic

b) Magneto static

c) Electromagnetic

d) Electrical

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2. According to Faraday’s law, EMF stands for

a) Electromagnetic field

b) Electromagnetic force

c) Electromagnetic friction

d) Electromotive force

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3. Calculate the emf when the flux is given by 3sin t + 5cos t

a) 3cos t – 5sin t

b) -3cos t + 5sin t

c) -3sin t – 5cos t

d) 3cos t + 5sin t

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4. The induced voltage will oppose the flux producing it. State True/False.

a) True

b) False

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5. Calculate the emf when a coil of 100 turns is subjected to a flux rate of 0.3 tesla/sec.

a) 3

b) 30

c) -30

d) -300

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6. Find the displacement current when the flux density is given by t^{3} at 2 seconds.

a) 3

b) 6

c) 12

d) 27

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^{2}. At time t = 2, we get Jd = 3(2)

^{2}= 12A.

7. Find the force due to a current element of length 2cm and flux density of 12 tesla. The current through the element will be 5A.

a) 1 N

b) 1.2 N

c) 1.4 N

d) 1.6 N

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8. Which of the following statements is true?

a) E is the cross product of v and B

b) B is the cross product of v and E

c) E is the dot product of v and B

d) B is the dot product of v and E

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9. The time varying electric field E is conservative. State True/False.

a) True

b) False

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10. When the conduction current density and displacement current density are same, the dissipation factor will be

a) Zero

b) Minimum

c) Maximum

d) Unity

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## Set 3

1. Gauss theorem uses which of the following operations?

a) Gradient

b) Curl

c) Divergence

d) Laplacian

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2. Evaluate the surface integral ∫∫ (3x i + 2y j). dS, where S is the sphere given by x^{2} + y^{2} + z^{2} = 9.

a) 120π

b) 180π

c) 240π

d) 300π

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^{3}/3 and r = 3units.Thus we get 180π.

3. The Gauss divergence theorem converts

a) line to surface integral

b) line to volume integral

c) surface to line integral

d) surface to volume integral

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4. The divergence theorem for a surface consisting of a sphere is computed in which coordinate system?

a) Cartesian

b) Cylindrical

c) Spherical

d) Depends on the function

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5. Find the Gauss value for a position vector in Cartesian system from the origin to one unit in three dimensions.

a) 0

b) 3

c) -3

d) 1

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6. The divergence theorem value for the function x^{2} + y^{2} + z^{2} at a distance of one unit from the origin is

a) 0

b) 1

c) 2

d) 3

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7. If a function is described by F = (3x + z, y^{2} − sin x^{2}z, xz + ye^{x5}), then the divergence theorem value in the region 0<x<1, 0<y<3 and 0<z<2 will be

a) 13

b) 26

c) 39

d) 51

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8. Find the divergence theorem value for the function given by (e^{z}, sin x, y^{2})

a) 1

b) 0

c) -1

d) 2

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9. For a function given by F = 4x i + 7y j +z k, the divergence theorem evaluates to which of the values given, if the surface considered is a cone of radius 1/2π m and height 4π^{2} m.

a) 1

b) 2

c) 3

d) 4

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^{3}h/3, where r = 1/2π m and h = 4π

^{2}m. On substituting the radius and height in the triple integral, we get 2 units.

10. Divergence theorem computes to zero for a solenoidal function. State True/False.

a) True

b) False

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## Set 4

1. Divergence theorem is based on

a) Gauss law

b) Stoke’s law

c) Ampere law

d) Lenz law

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2. The Gaussian surface for a line charge will be

a) Sphere

b) Cylinder

c) Cube

d) Cuboid

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3. The Gaussian surface for a point charge will be

a) Cube

b) Cylinder

c) Sphere

d) Cuboid

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4. A circular disc of radius 5m with a surface charge density ρs = 10sinφ is enclosed by surface. What is the net flux crossing the surface?

a) 3

b) 2

c) 1

d) 0

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5. The total charge of a surface with densities 1,2,…,10 is

a) 11

b) 33

c) 55

d) 77

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6. The work done by a charge of 10μC with a potential 4.386 is (in μJ)

a) 32.86

b) 43.86

c) 54.68

d) 65.68

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^{-6}X 4.386 = 43.86 X 10

^{-6}joule.

7. The potential of a coaxial cylinder with charge density 1 unit , inner radius 1m and outer cylinder 2m is (in 10^{9})

a) 12.74

b) 13.47

c) 12.47

d) 13.74

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^{9}volts.

8. Find the potential due to a charged ring of density 2 units with radius 2m and the point at which potential is measured is at a distance of 1m from the ring.

a) 18π

b) 24π

c) 36π

d) 72π

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9. Gauss law cannot be used to find which of the following quantity?

a) Electric field intensity

b) Electric flux density

c) Charge

d) Permittivity

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10. Gauss law for magnetic fields is given by

a) Div(E) = 0

b) Div(B) = 0

c) Div(H) = 0

d) Div(D) = 0

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## Set 5

1. Gauss law can be used to compute which of the following?

a) Permittivity

b) Permeability

c) Radius of Gaussian surface

d) Electric potential

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2. Three charged cylindrical sheets are present in three spaces with σ = 5 at R = 2m, σ = -2 at R = 4m and σ = -3 at R = 5m. Find the flux density at R = 1m.

a) 0

b) 1

c) 2

d) 3

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3. Three charged cylindrical sheets are present in three spaces with σ = 5 at R = 2m, σ = -2 at R = 4m and σ = -3 at R = 5m. Find the flux density at R = 3m.

a) 3

b) 10/3

c) 11/3

d) 4

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4. Three charged cylindrical sheets are present in three spaces with σ = 5 at R = 2m, σ = -2 at R = 4m and σ =-3 at R = 5m. Find the flux density at R = 4.5m.

a) 4/4.5

b) 3/4.5

c) 2/4.5

d) 1/4.5

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5. Three charged cylindrical sheets are present in three spaces with σ = 5 at R = 2m, σ = -2 at R = 4m and σ = -3 at R = 5m. Find the flux density at R = 6m.

a) 17/6

b) -17/6

c) 13/6

d) -13/6

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6. Gauss law can be evaluated in which coordinate system?

a) Cartesian

b) Cylinder

c) Spherical

d) Depends on the Gaussian surface

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7. Gauss law cannot be expressed in which of the following forms?

a) Differential

b) Integral

c) Point

d) Stokes theorem

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8. The tangential component of electric field intensity is always continuous at the interface. State True/False.

a) True

b) False

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9. The normal component of the electric flux density is always discontinuous at the interface. State True/False.

a) True

b) False

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10. With Gauss law as reference which of the following law can be derived?

a) Ampere law

b) Faraday’s law

c) Coulomb’s law

d) Ohm’s law