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QUESTION: 1

The Canadian constitution requires that equal importance be given to English and French. Last year, Air Canada lost a lawsuit, and had to pay a six-figure fine to a French-speaking couple after they filed complaints about formal in-flight announcements in English lasting 15 seconds, as opposed to informal 5 second messages in French.

The French-speaking couple were upset at _________ .

Solution:

QUESTION: 2

A superadditive function f(.) satisfies the following property

f(x_{1 }+ x_{2}) > f{x_{1}) +f(x_{2})

Which of the following functions is a superadditive function for x > 1?

Solution:

Verify with options

Option (a):

0.2 > 0.8 which is wrong.

Option (b)

√ 5 > 1.414 + 1.732

2.23 > 3.146 which is wrong.

Option c: e^{x1} + ^{x2} > e^{x1} + e^{x2}

e^{1 + 2} > e^{1} + e^{2}

20.085 > 2.718 + 7.389 Satisfying.

QUESTION: 3

Select the word that fits the analogy:

Explicit : Implicit : : Express : ________

Solution:

QUESTION: 4

The following figure shows the data of students enrolled in 5 years (2014 to 2018) for two schools P and Q. During this period, the ratio of the average number of the students enrolled in school P to the average of the difference of the number of students enrolled in schools P and Q is ________ .

Solution:

Average number of students in school,

Average number of students in school,

Difference of the number of students enrolled in school P and Q

Ratio of the average number of the students enrolled in school P to the average of the difference of the number of students enrolled in schools P and Q is = 23 : 8

QUESTION: 5

a, b, c are real numbers. The quadratic equation ax^{2}- bx + c = 0 has equal roots, which is β, then

Solution:

QUESTION: 6

The untimely loss of life is a cause of serious global concern as thousands of people get killed ______ accidents every year while many other die _______ diseases like cardio vascular disease, cancer, etc.

Solution:

QUESTION: 7

It is quarter past three in your watch. The angle between the hour hand and the minute hand is _________.

Solution:

QUESTION: 8

A circle with centre O is shown in the figure. A rectangle PQRS of maximum possible area is inscribed in the circle. If the radius of the circle is a, then the area of the shaded portion is _________ .

Solution:

Area of shaded portion = Area of circle - area of rectangle

Maximum possible area of rectangle inscribed in the circle = 2a^{2}

So, Required shaded area = πa^{2} - 2a^{2}

QUESTION: 9

The global financial crisis in 2008 is considered to be the most serious world-wide financial crisis, which started with the sub-prime lending crisis in USA in 2007. The subprime lending crisis led to the banking crisis in 2008 with the collapse of Lehman Brothers in 2008. The sub-prime lending refers to the provision of loans to those borrowers who may have difficulties in repaying loans, and it arises because of excess liquidity following the East Asian crisis.

Which one of the following sequences shows the correct precedence as per the given passage?

Solution:

QUESTION: 10

He was not only accused of theft_______of conspiracy.

Solution:

*Answer can only contain numeric values

QUESTION: 11

The current in the RL-circuit shown below is i(t) = 10 cos ( 5t - π/4)A The value of the inductor (rounded off to two decimal places) is ________ H.

Solution:

x_{L} = 10√2

ωL = 10√2

*Answer can only contain numeric values

QUESTION: 12

In the given circuit, the two-port network has the impedance matrix [Z] =

The value of Z_{L} for which maximum power is transferred to the load is Ω.

Solution:

From maximum power transfer theorem

Z_{L} = Z_{th}

For given data,

Z_{L} = 48Ω

QUESTION: 13

If v_{1}, v_{2}, v_{6} are six vectors in R^{4}, which one of the following statements is False?

Solution:

*Answer can only contain numeric values

QUESTION: 14

The loop transfer function of a negative feedback system is

The value of K, for which the system is marginally stable, is__________.

Solution:

Characteristic equation q(s) for the given open loop system will be

q(s) = s^{3} + 10s^{2} + 16s + Ks + 11K = 0

Using R-H criteria,

For system to be marginally stabled

160 + 10 K - 11 K = 0

K = 160

QUESTION: 15

The partial derivative of the function

with respect to x at the point (1, 0, e) is

Solution:

Given

f(x, y, z) =

= e°(0 - 1) + e . e^{-1/(1 + 0)}

= - 1 + 1 = 0

*Answer can only contain numeric values

QUESTION: 16

The random variable

and W(t) is a real white Gaussian noise process with two-sided power spectral density S_{w}(f) = 3 W/Hz, for all f. The variance of Y is _________.

Solution:

Given:

S_{ω}(f) = 3 Watts/Hz

R_{ω}(τ) = 38(τ) = 38(t_{1} - t_{2})

Var[y] = E [y^{2}] - { E [y]^{2}

{E[W(t)]}^{2} = DC power = Area under PSD at f = 0

{E[W(t)]}^{2 }= 0

E[W(t)] = 0

= 3 x 2 = 6

Var[y] = 6 - 0 = 6

Detailed explanations for:

Above integration exists provided

t_{1 }= t_{2 }= t

= 3 x 1 x Energy [φ(t)]

E[y^{2}] = 6

QUESTION: 17

For a vector field which one of the following is False?

Solution:

*Answer can only contain numeric values

QUESTION: 18

A transmission line of length 3λ/4 and having a characteristic impedance of 50 Q is terminated with a load of 400 Ω. The impedance (rounded off to two decimal places) seen at the input end of the transmission line is _________ Ω.

Solution:

Z_{in} for (l = λ/4) =

*Answer can only contain numeric values

QUESTION: 19

A 10-bit D/A converter is calibrated over the full range from 0 to 10 V. If the input to the D/A converter is 13A (in hex), the output (rounded off to three decimal places) is ________ V.

Solution:

Given, n = 10

V_{FS} = 10 V

Input voltage = (13A)_{16} = (314)_{10}

Output voltage = Resolution x Decimal equivalent of input

QUESTION: 20

The pole-zero map of a rational function G(s) is shown below. When the closed counter r is mapped into the G(s)-plane, then the mapping encircles.

Solution:

s-plane contour is encircling 2-poles and 3-zeros in clockwise direction hence the corresponding G(s) plane contour encircles origin 2-times in anti-clockwise direction and 3-times in clockwise direction.

∴ Effectively once in clockwise direction.

*Answer can only contain numeric values

QUESTION: 21

In the circuit shown below, all the components are ideal. If V/. is +2 V, the current I_{0} sourced by the op-amp is _________mA.

Solution:

V_{0} = (1 + 1) x 2 = 4 V

(KCL at node V_{0})

-2 + I_{0} - 4 = 0

⇒ I_{0} = 6 mA

*Answer can only contain numeric values

QUESTION: 22

The two sides of a fair coin are labelled as 0 and 1. The coin is tossed two times independently. Let M and N denote the labels corresponding to the outcomes of those tosses. For a random variable X, defined as X = min{M, N), the expected value E(X) (rounded off to two decimal places) is ________ .

Solution:

s = {( H, H), (H, T), (T, H), (T, T)}

Now, X = Min {M, N}

∴ X = Min {H, H} = Min{(1, 1)} = 1

X = Min {H, T} = Min{1, 0} = 0

X = Min{T, H} = Min{0, 1} = 0

X = Min{T, T} = Min{0, 0} = 0

∴

We know that, E(X) =

QUESTION: 23

A single crystal intrinsic semiconductor is at a temperature of 300 K with effective density of states for holes twice that of electrons. The thermal voltage is 26 mV. The intrinsic Fermi level is shifted from mid-bandgap energy level by

Solution:

QUESTION: 24

The output y[n] of a discrete-time system for an input x[n] is

The unit impulse response of the system is

Solution:

*Answer can only contain numeric values

QUESTION: 25

A binary random variable X takes the value +2 or -2. The probability P{X = +2) = α.

The value of α (rounded off to one decimal place), for which the entropy of X is maximum, is _________.

Solution:

Given that P{X = 2) = α

Entropy will be maximum; provided probabilities are equal,

i.e.

*Answer can only contain numeric values

QUESTION: 26

In the circuit shown below, all the components are ideal and the input voltage is sinusoidal. The magnitude of the steady-state output V_{0} (rounded off to two decimal places) is ________ V.

Solution:

Voltage doubles, V_{0} = 2 V_{m} = 2 x 230√2 ≌ 650.4 V

QUESTION: 27

Consider the recombination process via bulk traps in a forward biased pn homojunction diode. The maximum recombination rate is U_{max}. If the electron and the hole capture cross-section are equal, which one of the following is False?

Solution:

QUESTION: 28

The general solution of is

Solution:

Taking d/dx = D

Given, D^{2} - 6D + 9 = 0

(D - 3)^{2 }= 0

D = 3, 3

So, solution of the given differential equation

y = (c_{1} + c_{2} x) e^{3x}

*Answer can only contain numeric values

QUESTION: 29

In an 8085 microprocessor, the number of address lines required to access a 16 K byte memory bank is _________.

Solution:

2_{n} = N

n → Number of address lines

N → Number of Memory locations

∴ 2_{n} = 16 kB

= 2^{4}(2^{10}) [∵ 1 kB = 2^{10}]

= 2^{14}

n = 14

QUESTION: 30

The impedances Z = jX, for all X in the range (-∞,∞), map to the Smith chart as

Solution:

For given impedance Normalized impedance is

Z = jX

⇒ Z = 0 + jX

Normalized resistance = 0 ⇒ r = 0

X = -∞ to ∞

r = 0 and X from to -∞ to ∞ is a unit circle (radius 1) and centre (0, 0) on a complex reflection coefficient plane:

QUESTION: 31

A digital communication system transmits a block of N bits. The probability of error in decoding a bit is a. The error event of each bit is independent of the error events of the other bits. The received block is declared erroneous if at least one of the its bits is decoded wrongly. The probability that the received block is erroneous is

Solution:

Probability of error in decoding single bit = α

Then probability of no error will be 1 - a.

Total A/-bits transmitted, so that probability of no error in received block

= (1 - α) (1 - α) ... N times

= (1 - α )^{N}

The probability of received block is erroneous is = 1 - (1 - α)^{N}

QUESTION: 32

The figure below shows a multiplexer where S_{1} and S_{0} are the select lines. I_{0} to I_{3} are the input data lines, EN is the enable line, and F(P, Q, R) is the output. F is

Solution:

Output,

QUESTION: 33

In the circuit shown below, the Thevenin voltage V_{Th} is

Solution:

By applying source transformation

V_{th} = 3.6 V

QUESTION: 34

Which one of the following pole-zero corresponds to the transfer function of an LTI system characterized by the input-output difference equation given below?

Solution:

= x{n) - x{n - 1) + x(n - 2) - x{n - 3)

⇒ Y(z) = X(z) - z -* 1 X(z) + 2T~2 X(z) - z - 3 X(z)

⇒

Pole zero plot:

QUESTION: 35

The components in the circuit shown below are ideal. If the op-amp is in positive feedback and the input voltage V_{i}. is a sine wave of amplitude 1 V, the output voltage V_{0} is

Solution:

Given circuit is a Schmitt trigger of non-inverting type.

V0 = ± 5 V

Let, V0 = -5 V,

V_{0} can change from - 5 V to +5 V if V^{+} > 0 i.e. => V_{i} > 5 V.

Similarly V_{0} can change from +5 V to -5 V if V_{i} < -5 V

But given input has peak value 1 V. Hence output cannot change from +5 V to -5 V or -5 V to +5 V.

∴ Output remain constant at +5 V or -5 V.

Correct answer is option (d)

QUESTION: 36

An enhancement MOSFET of threshold voltage 3 V is being used in the sample and hold circuit given below. Assume that the substrate of the MOS device is connected to -10 V_{i} If the input voltage V. lies between ±10 V. the minimum and the maximum values of V_{G} required for proper sampling and holding respectively, are

Solution:

for holding MOSFET should be OFF.

V_{1 min }→ - 10 V

V_{G} - V_{1 min} < 3

V_{G} < 3 - 10 V ⇒ -7 V

For sampling,V_{G }- V_{imax} > 3

V_{G} - 3 + V_{i max}

V_{G} > 3 + V_{i} max

V_{G} > 13

QUESTION: 37

P, Q, and R are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1’s complement, and 2’s complement representations, respectively. The 6-bit 2’s complement representation of (P + Q + R) is

Solution:

Given, binary number 1100

1's complement of 1100 = -3

Sign magnitude of 1100 = -4

2's complement of 1100 = -4

∴ P + Q + R = - 4 - 3 - 4 = - 11

The 6 digit 2’s complement of (-11) = 110101

QUESTION: 38

The band diagram of a p-type semiconductor with a band-gap of 1 eV is shown. Using this semiconductor, a MOS capacitor having V_{Th} of -0.16 V, C'_{0x} of 100 nF/crm^{2} and a metal work function of 3.87 eV is fabricated. There is no charge within the oxide. If the voltage across the capacitor is 1/Th. the magnitude of depletion charge per unit area (in C/cm^{2}) is

Solution:

MOS capacitance

φ_{m} = 3.87, φ_{S} = 4.8, φ_{ms} = -0-93

φ_{Fp} = E_{i} - E_{F} = 0.5 - 0.2 = 0.3

= 0.6 + 0.16 - 0.93 = -0.17

Q_{b} = -0.17 x C_{ox} = -0.17 x 100 x 10^{-9} = -1.7 x 10^{-8} C/cm^{2}

*Answer can only contain numeric values

QUESTION: 39

For the solid S shown below, the value of (rounded off to two decimal places) is _____ .

Solution:

x : 0 to 3

y : 0 to 1

z : 0 to 1 - y

*Answer can only contain numeric values

QUESTION: 40

S_{PM}(t) and S_{FM}(t) as defined below, are the phase modulated and the frequency modulated waveforms, respectively, corresponding to the message signal m(t) shown in the figure.

S_{PM}(t) = cos(1000πt + K_{p} m(t))

and

where K_{p} is the phase deviation constant in radians/volt and K_{f }is the frequency deviation constant in radians/second/volt. If the highest instantaneous frequencies of S_{PM}(t) and S_{FM}(t) are same, then the value of the ratio K_{p}/K_{f }is __________ Seconds.

Solution:

S(t)_{pm} = A_{c} cos[2π f_{c} t + k_{p} m(t)]

Instantaneous frequency are equal

Given that,

5 k_{p} = 10 k_{f}

K_{p}/K_{f }= 2

QUESTION: 41

Which one of the following options contains two solutions of the differential equation

Solution:

Given differential equation:

By variable separable method:

and the second solution is for y = 1.

*Answer can only contain numeric values

QUESTION: 42

In the voltage regulator shown below, V_{t} is the unregulated at 15 V. Assume V_{BE} = 0.7 V and the base current is negligible for both the BJTs. If the regulated output V_{0} is 9 V, the value of R_{2} is _______ Ω.

Solution:

9R_{2} = 4R_{2} + 4 kΩ

5R_{2} =4K

QUESTION: 43

For the modulated signal x(t) = m(t) cos{2nf_{c}t), the message signal m(t) = 4cos(1000πt) and the carrier frequency f_{c} is 1 MHz. The signal x(t) is passed through a demodulator, as shown in the figure below. The output y(t) of the demodulator is

Solution:

Output of multiplier

= x(t) cos2π(f_{c} + 40)t = m(t) cos2πf_{c}t.cos2π(f_{c} + 40)t

Given, m(t) = 4cos1000πt

So, output of multiplier = = cos2π(2f_{c} + 540)t + cos2π(2f_{c}-460)t + cos2π(540)t+ cos2π(460)t

Output of Low pass filter

= cos [2π(460)]t

= cos 920 πt

QUESTION: 44

For the given circuit, which one of the following is the corre ct state equation?

Solution:

From source transformation,

KVL in loop 1,

(i)

KCL at node (a),

(ii)

QUESTION: 45

The state diagram of a sequence detector is shown below. State S0 is the initial state of the sequence detector. If the output is 1, then

Solution:

The sequence detected is 01010.

*Answer can only contain numeric values

QUESTION: 46

For a 2-port network consisting of an ideal lossless transformer, the parameter S_{21 }(rounded off to two decimal places) for a reference impedance of 10 Ω, is ____ .

Solution:

For ideal transformer of n : 1, the scattering matrix is

QUESTION: 47

The characteristic equation of a system is

s^{3} + 3s^{2} + (K + 2)s + 3K = 0

In the root locus plot for the given system, as K varies from 0 to ∞ the break-away or break-in point(s) lie within

Solution:

Q(s) = 1 + G(s) H(s) = 0

s^{3} + 3s^{2} + 2s + ks + 3k = 0

3s^{3} + 6s^{2} + 2s + 9s^{2} + 18s + 6 - s^{3} - 3s^{2} - 2s = 0

2s^{3} + 12 s^{2} + 18s + 6 = 0

s = -0.46, -3.87, -1.65

∴ Break-away point lies between (0, -1), i.e. (-1, 0).

QUESTION: 48

The base of an npn BJT T1 has a linear doping profile N_{B}(x) as shown below. The base of another npn BJT T2 has a uniform doping N_{B} of 10^{17} cm^{-3}. All other parameters are identical for both the devices. Assuming that the hole density profile is the same as that of doping, the common-emitter current gain of T2 is

Solution:

β_{2} = 0.5β_{1}

Hence no option is matching.

QUESTION: 49

Consider the following system of linear equation.

x_{1} + 2x_{2} = b_{1} ; 2x_{1} + 4x_{2} = b_{2} ; 3x_{1} + 7x_{2} = b_{3} ; 3x_{1} + 9x_{2} = b_{4}

Which one of the following conditions ensures that a solution exists for the above system?

Solution:

Given:

x_{1} + 2 x_{2} = b_{1} ...(i)

2x_{1} + 4x_{2 }= b_{2} ...(ii)

3x_{1} t 7x_{2} = b_{3} ...(iii)

3x_{1} + 9x_{2} = b_{4 } ....(iv)

From equations (ii]I and (i)

We can write,

b_{2} = 2[x_{1} + 2x_{2}] =- 2 b_{1}

From option (b):

3b_{1} - 3b_{3} + b_{4} = 3[x_{1 }+ 7x^{2}] + 3x_{1} + 9x_{2} ≠ 0

From option (c)

b_{2 }= 2b_{1}

and b_{1 }- 3b_{3} + b_{4} = [6x_{1} + 2x_{2}] - 3[3x_{1} + 7x_{2}] + [3x_{1} + 9x_{2}] = 0

6b_{1} - 3b_{3} + b_{4} = 0

Hence, answer is option (c).

QUESTION: 50

For the BJT in the amplifier shown below. V_{BE} = 0.7 V, kT/q = 26 mV. Assume the BJT output resistance (r_{0}) is very high and the base current is negligible. The capacitors are also assumed to be short circuited at signal frequencies. The input vt is direct coupled. The low frequency gain v_{0}/ v_{i} of the amplifier is

Solution:

QUESTION: 51

For an infinitesimally small dipole in free space, the electric field Eθ in the far field is proportional to (e-^{jkr}/r)sinθ, where k = 2π/λ. A vertical infinitesimally small electric dipole (δl < < λ is placed at a distance h(h > 0) above an infinite ideal conducting plane, as shown in the figure. The minimum value of h, for which one of the maxima in the far field radiation pattern occurs at 0 = 60°. is

Solution:

cosθ is maximum, whenever θ = nπ; n = 0, 1, 2 ...

⇒ For n = 1, h_{min} = λ

QUESTION: 52

The current 7 in the given network is

Solution:

I=-[I_{1} +I_{2}]

I= 2.38 ∠143.7°

*Answer can only contain numeric values

QUESTION: 53

A system with transfer function is subjected an input 5 cos 3t.

The steady state output of the system is The value of a is________.

Solution:

Given that ,

G (jω) = ;

According to question,

⇒

⇒

α^{2} + 9 = 25

α^{2} = 16

α = 4

QUESTION: 54

A finite duration discrete-time signal x[n] is obtained by sampling the continuous-time signal x(t) = cos(200πt) at sampling instants t = n/400, n = 0,1, ... , 7. The 8-point discrete Fourier transform (DFT) of x[n] is defined as

Which one of the following statements is true?

Solution:

x(t) = cos 200πt

Suppose,

Now, as we know,

If for {a, b , c, d} { A B, C, D}

Then for {a, 0, b, 0, c, 0, d, 0} { A B, C, D, A, B, C, D}

Similarly, for y ( n ) = {1, - 1 , 1 , - 1 } Y(k) = {0, 0, 4, 0}

Here, for x{n) = {1, 0, -1, 0, 1, 0, -1, 0}

QUESTION: 55

The com ponents in the circuit given below are ideal. If R = 2 kΩ and C = 1 μF, the -3 dB cut-off frequency of the circuit in Hz is

Solution:

Op-amp active filter (LPF) inverting type 3 dB cut-off frequency,

QUESTION: 56

A one-sided abrupt pn junction diode has a depletion capacitance C_{D}of 50 pF at a reverse bias of 0.2 V. The plot of versus the applied voltage I/for this diode is a straight line as shown in the figure below. The slope of the plot is _______ x10^{20} F^{-2} V^{-1}.

Solution:

Depletion or transition capacitance is,

For one-sided PN junction (Ex : P^{+} N junction)

where l/is anode to cathode applied potential.

⇒

⇒

becomes zero at V = V_{bi}

From above graph, y = at x_{1} = V_{bi}

And

∵ V_{bi} is not provided, slope cannot be found.

QUESTION: 57

A pn junction solar cell of area 1.0 cm^{2}, illuminated uniformly with 100 mW cm^{-2}, has the following parameters:E fficiency = 15%, open circuit voltage = 0.7 V, fill factor = 0.8, and thickness = 200 pm, The charge of an electron is 1.6 x 10^{-19} C. The average optical generation rate (in cm^{-3} S^{-1}) is

Solution:

⇒

*Answer can only contain numeric values

QUESTION: 58

In a digital communication system, a symbol S randomly chosen from the set (s_{1}, s_{2}, s_{3}, s_{4}) is transmitted. It is given that s_{1} = -3, s_{2} = -1, s_{3} = +1 and s_{4} = +2. The received symbol is Y = S W/. W is a zero-mean unit-variance Gaussian random variable and is independent of S. P_{i} is the conditional probability of symbol error for the maximum likelihood (ML) decoding when the transmitted symbol S = s_{i}. The index i for which the conditional symbol error probability P_{i} is the highest is _____ .

Solution:

Since the noise variable is Gaussian with zero mean and ML decoding is used, the decision boundary between two adjacent signal points will be their arithmetic mean. In the following graphs, the shaded area indicates the conditional probability of decoding a symbol correctly when it is transmitted.

By comparing the above graphs, we can conclude that P_{3} is larger among the four.

QUESTION: 59

Using the incremental low frequency small-signal model of the MOS device, the Norton equivalent resistance of the following circuit is

Solution:

vπ = -Vx

V_{x} = (I_{x} - g_{m} V_{x}) r_{ds} + I_{x}R

V_{x}(1 + g_{m} r_{ds}) = (r_{ds} + R)I_{x
}

*Answer can only contain numeric values

QUESTION: 60

Consider the following closed loop control system

where If the steady state error for a unit ramp input is 0.1, then the value of K is ______ .

Solution:

Open loop transfer function for the system = C(s) x G(s) =

Since the system is type-1 so far a given unit ramp input steady state

where, K_{v} =

So,

Given that, e_{ss} = 0.1

So,

*Answer can only contain numeric values

QUESTION: 61

Xis a random variable with uniform probability density function in the interval [-2,10], For Y = 2X- 6, the conditional probability P(Y__<__ 7 I X __>__ 5) (rounded off to three decimal places) is ____ .

Solution:

x follows uniform distribution over [-2, 10]

∴

Given: y = 2x - 6

⇒

For y = 7

*Answer can only contain numeric values

QUESTION: 62

X(ω) is the Fourier transform of x (t) shown below. The value of (rounded off to two decimal places) is___________.

Solution:

*Answer can only contain numeric values

QUESTION: 63

The transfer function of a stable discrete-tim e LTI system is H(z) where K and α are real numbers. The value of a (rounded off to one decimal place) with for which the magnitude response of the system is constant over all frequencies, is ____ .

Solution:

System is all-pass filter.

For digital all-pass filter, condition is

...(1)

By given transfer function,

Zero = α

Pole = -0.5

Using condition (i),

*Answer can only contain numeric values

QUESTION: 64

For the com ponents in the sequential circuit shown below, t_{pd} is the propagation delay, t_{setup} is the setup time, and t_{hold} the holcl time.The maximum clock frequency (rounded off to the nearest integer), at which the given circu it can operate reliably, is ____ MHz.

Solution:

Total propagation delay = (t_{pd} + t_{set-up})max = 8ns + 5 ns = 13 ns

∴ Frequency of operations =

*Answer can only contain numeric values

QUESTION: 65

The magnetic field of a uniform plane wave in vacuum is given by

The value of b is ____ .

Solution:

For uniform plane wave

is unit vector in magnetic field direction is unit vector in power flow direction

-3 + 2 + b = 0

b = 1

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