# Multiple choice question for engineering

## Set 1

1. Gradient of a function is a constant. State True/False.

a) True

b) False

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2. The mathematical perception of the gradient is said to be

a) Tangent

b) Chord

c) Slope

d) Arc

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3. Divergence of gradient of a vector function is equivalent to

a) Laplacian operation

b) Curl operation

c) Double gradient operation

d) Null vector

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^{2}V, which is the Laplacian operation. A function is said to be harmonic in nature, when its Laplacian tends to zero.

4. The gradient of xi + yj + zk is

a) 0

b) 1

c) 2

d) 3

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5. Find the gradient of t = x^{2}y+ e^{z} at the point p(1,5,-2)

a) i + 10j + 0.135k

b) 10i + j + 0.135k

c) i + 0.135j + 10k

d) 10i + 0.135j + k

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^{2}j + e

^{z}k. On substituting p(1,5,-2), we get 10i + j + 0.135k.

6. Curl of gradient of a vector is

a) Unity

b) Zero

c) Null vector

d) Depends on the constants of the vector

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7. Find the gradient of the function given by, x^{2} + y^{2} + z^{2} at (1,1,1)

a) i + j + k

b) 2i + 2j + 2k

c) 2xi + 2yj + 2zk

d) 4xi + 2yj + 4zk

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^{2}+y

^{2}+z

^{2}) = 2xi + 2yj + 2zk. Put x=1, y=1, z=1, the gradient will be 2i + 2j + 2k.

8. The gradient can be replaced by which of the following?

a) Maxwell equation

b) Volume integral

c) Differential equation

d) Surface integral

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9. When gradient of a function is zero, the function lies parallel to the x-axis. State True/False.

a) True

b) False

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10. Find the gradient of the function sin x + cos y.

a) cos x i – sin y j

b) cos x i + sin y j

c) sin x i – cos y j

d) sin x i + cos y j

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## Set 2

1. Mathematically, the functions in Green’s theorem will be

a) Continuous derivatives

b) Discrete derivatives

c) Continuous partial derivatives

d) Discrete partial derivatives

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2. Find the value of Green’s theorem for F = x^{2} and G = y^{2} is

a) 0

b) 1

c) 2

d) 3

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3. Which of the following is not an application of Green’s theorem?

a) Solving two dimensional flow integrals

b) Area surveying

c) Volume of plane figures

d) Centroid of plane figures

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4. The path traversal in calculating the Green’s theorem is

a) Clockwise

b) Anticlockwise

c) Inwards

d) Outwards

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5. Calculate the Green’s value for the functions F = y^{2} and G = x^{2} for the region x = 1 and y = 2 from origin.

a) 0

b) 2

c) -2

d) 1

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6. If two functions A and B are discrete, their Green’s value for a region of circle of radius a in the positive quadrant is

a) ∞

b) -∞

c) 0

d) Does not exist

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7. Applications of Green’s theorem are meant to be in

a) One dimensional

b) Two dimensional

c) Three dimensional

d) Four dimensional

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8. The Green’s theorem can be related to which of the following theorems mathematically?

a) Gauss divergence theorem

b) Stoke’s theorem

c) Euler’s theorem

d) Leibnitz’s theorem

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9. The Shoelace formula is a shortcut for the Green’s theorem. State True/False.

a) True

b) False

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10. Find the area of a right angled triangle with sides of 90 degree unit and the functions described by L = cos y and M = sin x.

a) 0

b) 45

c) 90

d) 180

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## Set 3

1. Calculate the emf of a coil with turns 100 and flux rate 5 units.

a) 20

b) -20

c) 500

d) -500

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2. The equivalent inductances of two coils 2H and 5H in series aiding flux with mutual inductance of 3H is

a) 10

b) 30

c) 1

d) 13

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3. The expression for the inductance in terms of turns, flux and current is given by

a) L = N dφ/di

b) L = -N dφ/di

c) L = Niφ

d) L = Nφ/i

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4. The equivalent inductance of two coils with series opposing flux having inductances 7H and 2H with a mutual inductance of 1H.

a) 10

b) 7

c) 11

d) 13

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5. A coil is said to be loosely coupled with which of the following conditions?

a) K>1

b) K<1

c) K>0.5

d) K<0.5

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6. With unity coupling, the mutual inductance will be

a) L1 x L2

b) L1/L2

c) √(L1 x L2)

d) L2/L1

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7. The inductance is proportional to the ratio of flux to current. State True/False.

a) True

b) False

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8. Calculate the mutual inductance of two tightly coupled coils with inductances 49H and 9H.

a) 21

b) 58

c) 40

d) 49/9

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9. Find the inductance of a coil with turns 50, flux 3 units and a current of 0.5A

a) 150

b) 300

c) 450

d) 75

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10. The inductance of a coaxial cable with inner radius a and outer radius b, from a distance d, is given by

a) L = μd ln(b/a)/2π

b) L = 2π μd ln(b/a)

c) L = πd/ln(b/a)

d) L = 0

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## Set 4

1. The characteristic impedance of a quarter wave transformer with load and input impedances given by 30 and 75 respectively is

a) 47.43

b) 37.34

c) 73.23

d) 67.45

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^{2}= Z

_{IN}Z

_{L}. On substituting for Z

_{IN}= 75 and Z

_{L}= 30, we get the characteristic impedance as 47.43 units.

2. The input impedance of a quarter wave line 50 ohm and load impedance of 20 ohm is

a) 50

b) 20

c) 1000

d) 125

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^{2}= Zin ZL. On substituting for Zo = 50 and ZL = 20, we get the input impedance as 50

^{2}/20 = 125 ohm.

3. For a matched line, the input impedance will be equal to

a) Load impedance

b) Characteristic impedance

c) Output impedance

d) Zero

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4. The reflection coefficient lies in the range of

a) 0 < τ < 1

b) -1 < τ < 1

c) 1 < τ < ∞

d) 0 < τ < ∞

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5. When the ratio of load voltage to input voltage is 5, the ratio of the characteristic impedance to the input impedance is

a) 1/5

b) 5

c) 10

d) 25

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6. The power of the transmitter with a radiation resistance of 12 ohm and an antenna current of 3.5A is

a) 147

b) 741

c) 174

d) 471

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^{2}Rrad. On substituting Irad = 3.5 and Rrad =12, we get Prad = 3.5

^{2}x 12 = 147 units.

7. The group delay of the wave with phase constant of 62.5 units and frequency of 4.5 radian/sec is

a) 13.88

b) 31.88

c) 88.13

d) 88.31

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8. The maximum impedance of a transmission line 50 ohm and the standing wave ratio of 2.5 is

a) 20

b) 125

c) 200

d) 75

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9. The minimum impedance of a transmission line 75 ohm with a standing wave ratio of 4 is

a) 75

b) 300

c) 18.75

d) 150

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10. The average power in an electromagnetic wave is given by

a) propagation constant

b) poynting vector

c) phase constant

d) attenuation constant

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11. The characteristic impedance of a transmission line is normally chosen to be

a) 50

b) 75

c) 50 or 75

d) 100

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12. Identify the material which is not present in a transmission line setup.

a) waveguides

b) cavity resonator

c) antenna

d) oscillator

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## Set 5

1. An electric field is given as E = 6y^{2}z i + 12xyz j + 6xy^{2} k. An incremental path is given by dl = -3 i + 5 j – 2 k mm. The work done in moving a 2mC charge along the path if the location of the path is at p(0,2,5) is (in Joule)

a) 0.64

b) 0.72

c) 0.78

d) 0.80

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^{-3}X (6y

^{2}z i + 12xyz j + 6xy

^{2}k) . (-3 i + 5 j -2 k) At p(0,2,5), W = -2(-18.22.5) X 10

^{-3}= 0.72 J.

2. The integral form of potential and field relation is given by line integral. State True/False

a) True

b) False

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3. If V = 2x^{2}y – 5z, find its electric field at point (-4,3,6)

a) 47.905

b) 57.905

c) 67.905

d) 77.905

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4. Find the potential between two points p(1,-1,0) and q(2,1,3) with E = 40xy i + 20x^{2} j + 2 k

a) 104

b) 105

c) 106

d) 107

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^{2}dy + 2 dz) , from q to p. On integrating, we get 106 volts.

5. Find the potential between a(-7,2,1) and b(4,1,2). Given E = (-6y/x^{2} )i + ( 6/x) j + 5 k.

a) -8.014

b) -8.114

c) -8.214

d) -8.314

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6. The potential of a uniformly charged line with density λ is given by,

λ/(2πε) ln(b/a). State True/False.

a) True

b) False

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7. A field in which a test charge around any closed surface in static path is zero is called

a) Solenoidal

b) Rotational

c) Irrotational

d) Conservative

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8. The potential in a lamellar field is

a) 1

b) 0

c) -1

d) ∞

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9. Line integral is used to calculate

a) Force

b) Area

c) Volume

d) Length

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10. The energy stored in the inductor 100mH with a current of 2A is

a) 0.2

b) 0.4

c) 0.6

d) 0.8

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^{2}= 0.5 X 0.1 X 2

^{2}= 0.2 Joule.