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QUESTION: 1

**Q.1 – Q.5 Carry One Mark Each**

Which of the following is CORRECT with respect to grammar and usage?

Mount Everest is ______

Solution:

Before superlative article ‘the’ has to be used. ‘one of ’ the expression should take plural noun and so option ‘C’ and ‘D’ can’t be the answer.

QUESTION: 2

The policeman asked the victim of a theft, “What did you ______?”

Solution:

lose’ is verb.

QUESTION: 3

Despite the new medicine’s ___________ in treating diabetes, it is not ______ widely

Solution:

‘effectiveness’ is noun and ‘prescribed’ is verb. These words are apt and befitting with the word ‘medicine.’

QUESTION: 4

In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% are unripe fruits,

Of the unripe fruits, 45% are apples, Of the ripe ones, 66% are oranges. If the pile contains a total

of 5692000 fruits, how many of them are apples?

Solution:

QUESTION: 5

Michael lives 10 km way from where I live. Ahmed lives 5km away and Susan lives 7 km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information provided here, what is one possible distance (in km) at which I live from Arun’s place?

Solution:

From given data, the following diagram is possible

AH = Ahmed lives; M = Michael lives

S = Susan lives; A= Arun lives

→ Arun lives farthes away than Ahmed means more than 5 km but closer than Susan means less than 7 km, from given alternatives, option ‘C’ only possible.

QUESTION: 6

**Q.6 – Q.10 Carry two marks each**

**Q.**

**A person moving through a tuberculosis prone zone has a 50% probability of becoming infected.
However, only 30% of infected people develop the disease. What percentage of people moving
through a tuberculosis prone zone remains infected but does not shows symptoms of disease?**

Solution:

QUESTION: 7

In a world filled with uncertainty, he was glad to have many good friends. He had always assisted

them in times of need and was confident that they would reciprocate. However, the events of the

last week proved him wrong.

Which of the following interference(s) is/are logically valid and can be inferred from the above

passage?

(i) His friends were always asking him to help them

(ii) He felt that when in need of help, his friends would let him down.

(iii) He was sure that his friends would help him when in need.

(iv) His friends did not help him last week.

Solution:

The words ‘was confident that they would reciprocate’ and ‘last week proved him wrong’ lead to statements iii and iv as logically valid inferences.

QUESTION: 8

Leela is older than her cousin Pavithra, pavithra’s brother Shiva is older than Leela. When Pavithra

and shiva are visiting Leela, all three like to play chess. Pavithra wins more often than Leela does.

Which one of the following statements must be TRUE based on the above?

Solution:

From given data, the following arrangement is possible

Shiva

Leela

Pavithra

Among four alternatives, option D is TRUE.

QUESTION: 9

Solution:

QUESTION: 10

P,Q,R and S are working on a project. Q can finish the taks in 25 days, working alone for 12 hours a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a day but took sick leave in the beginning for two days. R worked 18 hours a day on all days. What is the ratio of work done by Q and R after 7 days from the start of the project?

Solution:

QUESTION: 11

**Q.11 – Q.35 Carry one mark each.**

**Q. **Let M4 = I (where I denotes the identity matrix)and M ? I, M2 ? I and M3 ? I. Then, for any

natural number k, M–1 equals:

Solution:

M^{4} = I

M^{8} = M^{4} = I M^{7} = M^{-1}

M^{12} = M^{8} = I M^{11} = M^{-1}

M^{16} = M^{12} = I M^{15} = M^{-1}

…………………..

M^{-1} = M^{4K+ 3}, K is a natural number

*Answer can only contain numeric values

QUESTION: 12

The second moment of a Poisson-distributed random variables is 2. The mean of the random variable is _____.

Solution:

QUESTION: 13

Given the following statements about a function f: R→R, select the right option:

P : If f(x) is continuous at x = x0, then it is also differentiable at x = x_{0}

Q : If f(x) is continuous at x = x0, then it may not be differentiable at x = x_{0}

R : If f(x) is continuous at x = x0, then it is also different at x = x_{0}

Solution:

Since continuous function may not be differentiable. But differentiable function is always continuous.

QUESTION: 14

Which one of the following is a property of the solutions to the Laplace equation :

Solution:

QUESTION: 15

Consider the plot of f(x) versus x as shown below

Suppose which one of the following is a graph of F(x)?

Solution:

integration of ramp is parabolic, integration of step is ramp.

QUESTION: 16

Which one of the following is an eigen function of the class of all continuous-time, linear, timeinvariant

systems (u(t) denotes the unit-step function) ?

Solution:

If the input to a system is its eigen signal, the response has the same form as the eigen signal

QUESTION: 17

A continuous –time function x(t) is periodic with period T. The function is sampled uniformly with

a sampling period Ts. In which one of the following cases is the sampled signal periodic ?

Solution:

A discrete time signal is said to be periodic if is a rational number

QUESTION: 18

Consider the sequence x[n] = a^{n} u[n] +b^{n} u[n], where u[n] denotes the until-step sequence and 0 <

|a| < |b| <1. The region of convergence (ROC) of the z-transform of x[n] is

Solution:

QUESTION: 19

Consider a two-port network with the transmission matrix : If the network is

reciprocal, then

Solution:

A two port network is reciprocal in transmission parameters if AD – BC = 1

i.e Determinant(T) = 1

*Answer can only contain numeric values

QUESTION: 20

A continuous-time sinusoid of frequency 33 Hz is multiplie with a periodic Dirac impulse train of

frequency 46 Hz. The resulting signal is passed through an ideal analog low-pass filter with a

cutoff frequency of 23Hz. The functional frequency (in Hz) of the output is _____.

Solution:

f_{m} = 33Hz, f_{s} = 46Hz

The frequency in sampled signal are = 33, 13, 79, 59, 125 …… The above frequencies are passed

to a LPF of cutoff frequency 23Hz. The output frequency are = 13Hz.

QUESTION: 21

A small percentage of impurity is added to intrinsic semiconductor at 300 K. Which one of the

following statements is true for the energy band diagram shown in the following figure?

Solution:

Donor energy level close to conduction band.

QUESTION: 22

Consider the following statements for a metal oxide semiconductor field after effect transistor

(MOSFET):

P : As channel length reduces, OFF-state current increases

Q : As channel length reduces, output resistance increases

R : As channel length reduces, threshold voltage remains constant

S: As channel reduces, ON current increases.

Which of the above statements are INCORRECT?

Solution:

P: TRUE

Q: FALSE, As channel length reduces, output resistance reduces

R: FALSE: As channel length reduces, threshold voltage reduces

S: TRUE

QUESTION: 23

Consider the constant current source shown in the figure below. Let ? represent the current gain of

the transistor

The load current I0 through R_{L} is

Solution:

*Answer can only contain numeric values

QUESTION: 24

The following signal Vi of peak voltage 8V is applied to the non-inverting terminal of an ideal

Opamp. The transistor has V_{BE} = 0.7 V, β = 100; V_{LED} = 1.5V, V_{CC} = 10V and –V_{CC} = – 10V.

The number of times the LED glows is –––––

Solution:

V_{i }crosses 2V, 3times

Therefore the LED glows 3 times

QUESTION: 25

Consider the oscillator circuit shown in the figure. The function of the network (shown in dotted

lines) consisting of the 100 k? resistor in series with the two diodes connected back-to-back is to:

Solution:

The circuit shown is a wein bridge oscillator. The amplitude of oscillations can be determined and stabilized by using a nonlinear control network. As the oscillations grow, the diodes start to conduct causing the effective resistance in the feedback to decrease. Equilibrium will be reached at the output amplitude that causes the loop gain to be exactly unity.

QUESTION: 26

The block diagram of a frequency synthesizer consisting of Phase Locked Loop (PLL) and a

divide-by-N counter (comprising /2, /4, /8, /16 outputs) is sketched below. The synthesizer is

excited with a 5 kHz signal (Input 1). The free-running frequency of the PLL is set to 20kHz.

Assume that the commutator switch makes contacts repeatedly in the order 1-2-3-4.

The corresponding frequencies synthesized are:

Solution:

QUESTION: 27

The output of the combinational circuit given below is

Solution:

QUESTION: 28

What is the voltage V_{out} in the following circuit?

Solution:

QUESTION: 29

Match the inferences X, Y, and Z, about a system, to the corresponding properties of the elements

of first column in Routh’s Table of the system characteristic equation.

X: The system is stable ….. P: … When all elements are positive

Y: The system is unstable … Q: … When any on element is zero

Z: The test breaks down …. R: … When there is a change in sign of coefficients

Solution:

X - P, Y - R, Z -Q

QUESTION: 30

A closed-loop control system is stable if the Nyquist plot of the corresponding open-loop transfer

function

Solution:

For closed loop stability Z = 0, N = P

(-1, j0) should be encircled in Counter clock wise direction equaling P poles in RHP.

*Answer can only contain numeric values

QUESTION: 31

Consider binary data transmission at a rate of 56 kbps using baseband binary pulse amplitude

modulation (PAM) that is designed to have a raised-cosine spectrum. The transmission bandwidth

(in kHz) required for a roll-off factor of 0.25 is –––––.

Solution:

*Answer can only contain numeric values

QUESTION: 32

A superheterodyne receiver operates in the frequency range of 58 MHz-68MHz. The intermediate frequency f1F and local oscillator frequency f_{LO} are chosen such that f_{1F} f_{LO}. It is required that the image frequencies fall outside the 59 MHz – 68 MHz band. The minimum required f_{1F} (in MHz) is

Solution:

f_{s} = 58 MHz– 68 MHz

When fs = 58 MHz

f_{si} = f_{s} + 21F > 68 MHz

21F > 10 MHz

1F ? 5 MHz

*Answer can only contain numeric values

QUESTION: 33

The amplitude of a sinusoidal carrier is modulated by a single sinusoid to obtain the amplitude

modulated signal s(t) = 5 cos 1600?t + 20 cos 1800 ?t + 5 cos 2000?t. The value of the modulation

index is –––––––.

Solution:

*Answer can only contain numeric values

QUESTION: 34

Concentric spherical shells of radii 2m, 4m, and 8m carry uniform surface charge densities of 20

nC/m^{2}, –4 nC/m^{2} and ρs, respectively. The value of ρs (nC/m^{2}) required to ensure that the electric

flux density D = 0 at radius 10 m is –––––.

Solution:

QUESTION: 35

The propagation constant of a lossy transmission line is (2 +j5) m^{-1} and its characteristic

impedance is (50 + j0) ? at ω = 10^{6} rad S^{-1}. The values of the line constants L,C,R,G are,

respectively,

Solution:

Therefore line constants L, C, R & G are respectively L = 250 μH/m, C = 0.1 μF/m, R = 100 ?/m, G = 0.04 s/m

*Answer can only contain numeric values

QUESTION: 36

Solution:

Converting to polar coordinates, we get

*Answer can only contain numeric values

QUESTION: 37

A sequence x[n] is specified as

The initial conditions are x[0] = 1, x[1] = 1 and x[n] = 0 for n < 0. The value of x[12] is ––––

Solution:

From the above values we can write the recursive relation as

x(n) = x(n–1) + x(n –2)

x(2) = x(1) + x(0) = 1 +1 = 2

x(3) = x(2) + x(1) = 2 +1 = 3

x(4) = x(3) + x(2) = 3 + 2 = 5

x(5) = x(4) + x(3) = 5 + 3 = 8

x(6) = x(5) + x(4) = 8 + 5 = 13

x(7) = x(6) + x(5) = 13+ 8 = 21

x(8) = x(7) + x(6) = 21 + 13 = 34

x(9) = x(8) + x(7) = 34 + 21 = 55

x(10) = x(9) + x(8) = 55 + 34 = 89

x(11) = 89 + 55 = 144

x(12) = 144 + 89 = 233

*Answer can only contain numeric values

QUESTION: 38

In the following integral, the contour C encloses the points 2πj and –2πj . The value of the integral

Solution:

*Answer can only contain numeric values

QUESTION: 39

The region specified by in cylindrical coordinates has volume of –––––.

Solution:

QUESTION: 40

The Laplace transform of the causal periodic square wave of period T shown in the figure below

is

Solution:

QUESTION: 41

A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor (C)

elements, connected all in series or all in parallel, is excited with a source of the form

The source has nonzero impedance. Which one of the

following is a possible form of the output measured across a resistor in the network?

Solution:

Consider a series RLC-Circuit with voltage source

Here

QUESTION: 42

A first-order low-pass filter of time constant T is excited with different input signals (with zero

initial conditions up to t = 0 ). Match the excitation signals X,Y, Z with the corresponding time

responses for t 0:

X: Impulse P: 1 – e^{-t/T}

Y: Unit step Q: t – T(1 – e^{-t/T})

Z: Ramp R: e^{-t/T}

Solution:

*Answer can only contain numeric values

QUESTION: 43

An AC voltage source V = 10 sin (t) volts is applied to the following network. Assume that

R1 = 3 k?, R2 = 6k? and R3 = 9k?, and that the diode is ideal.

Rms current I_{rms} (in mA) through the diode is _____

Solution:

We can join nodes that are at same Potential so network becomes

*Answer can only contain numeric values

QUESTION: 44

In the circuit shown in the figure, the maximum power (in watt) delivered to the resistor R is ––––.

Solution:

*Answer can only contain numeric values

QUESTION: 45

Consider the signal x[n] =6δ[n +2] +3δ[n +1]+8δ[n]+7δ[n – 1] +4δ[n – 2].

If X(e^{jω}) is the discrete-time Fourier transform of x[n], then

Solution:

Plancheral’s relation is

*Answer can only contain numeric values

QUESTION: 46

Consider a silicon p-n junction with a uniform acceptor doping concentration of 1017 cm-3 on the pside

and a uniform donor doping concentration of 1016 cm-3 on the n-side. No external voltage is

applied to the diode. Given:

and q= 1.6 x 10^{-19}c

The charge per unit junction area (nC cm^{-2}) in the depletion region on the p-side is –––––.

Solution:

*Answer can only contain numeric values

QUESTION: 47

Consider an n-channel metal oxide semiconductor field effect transistor (MOSFET) with a gate-tosource

voltage of 1.8V. Assume that W /L =4, μ_{N}C_{ox} = 70 X10^{-6}AV^{-2}, the threshold voltage is 0.3V,

and the channel length modulation parameter is 0.09 V^{-1}, In the saturation region, the drain

conductance (in micro siemens)is –––––.

Solution:

*Answer can only contain numeric values

QUESTION: 48

The figure below shows the doping distribution in a P-type semiconductor in log scale.

The magnitude of the electric field (in kV/cm) in the semiconductor due to non uniform doping is

Solution:

QUESTION: 49

Consider a silicon sample at T = 300 K, with a uniform donor density N_{d} = 5x1016 cm^{-3}

illuminated uniformly such that the optical generation rate is G_{opt} = 1.5 x10^{20} cm^{-3}s^{-1} through out

the sample. The incident radiation is turned off at t = 0. Assume low-level injection to be valid and

ignore surface effects. The carrier lifetimes are _{po} = 0.1 and _{no} = 0.5 ?s.

The hole concentration at t = 0 and the hole concentration at t = 0.3 μs, respectively, are

Solution:

*Answer can only contain numeric values

QUESTION: 50

An ideal opamp has voltage source V_{1}, V_{2}, V_{3}, V_{5}, …. , V_{N–1} connected to the non-inverting input

and V_{2}, V_{4}, V_{6} ….V_{N} connected to the inverting input as shown in the figure below (+V_{CC }= 15

volt, –V_{CC} = –15 volt). The voltage V_{1}, V_{2}, V_{3}, V_{5}, V_{6} …. are 1, –1/2, 1/3,–1/4, 1/5, –1/6, …..

volt, respectively. As N approaches infinity, the output voltage (in volt) is ________

Solution:

*Answer can only contain numeric values

QUESTION: 51

A p-i-n photo diode of responsivity 0.8A/W is connected to the inverting input of an ideal opamp

as shown in the figure, +Vcc = 15V, –Vcc = –15V,Load resistor RL = 10 k?. If 10μW

of power is incident on the photodiode, then the value of the photocurrent (in μA) through the

load is _____.

Solution:

The photo diode with Responsivity 0.8A/W

Diode current = 0.8A/W[10μW]

= 8 x 10^{-6}A

V_{0} = –8μ (1M) = –8V

Therefore the value of photo current throughput the load is –800 μA

QUESTION: 52

Identify the circuit below.

Solution:

(No Answer) if considering OP_{6} → IP_{5}, OP_{7} →IP_{4}

Thus it is a Binary to Gray code converter

QUESTION: 53

The functionally implemented by the circuit below is

Solution:

Hence it is a “4 to 1 multiplexer”

QUESTION: 54

In a 8085 system, a PUSH operation requires more clock cycles than a POP operation, which one

of the following options is the correct reason for this?

Solution:

Push takes 12T states due to pre decrement and pop takes 10T states.

*Answer can only contain numeric values

QUESTION: 55

The open-loop transfer function of a unity-feedback control system is

The value of K at the breakaway point of the feedback control system’s root-locus plot is ____

Solution:

Break away point dk/ds=0

*Answer can only contain numeric values

QUESTION: 56

The open-loop transfer function of a unity-feedback control system is given by

For the peak overshoot of the closed-loop system to a until step input to be 10% , the value of K is

Solution:

*Answer can only contain numeric values

QUESTION: 57

The transfer function of a linear time invariant systems is given by H(s) = 2s^{4}–5s^{3}+5s–2

The number of zeros in the right half of the s-plane is _____.

Solution:

TF H(s) 2s^{4} – 5s^{3}+5s–2

RH – Criteria

3 Sign Changes

3 Roots (Zeros) in the RH -S-Plane.

*Answer can only contain numeric values

QUESTION: 58

Consider a discreet memoryless source with alphabet S = {s0, s1, s2, s3, s4 …..} and respective

probabilities of occurrence

The entropy of the source (in bits ) is _____.

Solution:

*Answer can only contain numeric values

QUESTION: 59

A digital communication system uses a repetition code for channel encoding/decoding. During

transmission, each bit is repeated three times (0 is transmitted as 000, and 1 is transmitted as 111).

It is assumed that the source puts out symbols independently and with equal probability . The

decoder operates as follows: In a block of three received bits, if the number of zeros exceeds the

number of ones, the decoder decides in favor of a 0, and if the number of ones exceeds the number

of zeros, the decoder decides in favor of a 1,Assuming a binary symmetric channel with crossover

probability p = 0.1, the average probability of error is ________.

Solution:

P_{e} = P^{3} + 3P^{2} (1 –P)

P = 0.1

P_{e} = (0.1)^{3} + 3 x (0.1)^{2} (1–0.1) = 0.001 + 3 x 0.01 x 0.9 = 0.001 + 0.027 = 0.028

QUESTION: 60

An analog pulse s(t) is transmitted over an additive white Gaussian (AWGN) channel. The

received signal is r(t) = s(t) + n(t), where n(t) is additive white Gaussian noise with power spectral

density N_{0}/2 . The received signal is passed through a filter with impulse response h(t). Let E_{s} and

En denote the energies of the pulse s(t) and the filter h(t), respectively. When the signal-to-noise

ratio (SNR) is maximized at the output of the filter (SNR_{max}), which of the following holds?

Solution:

The impulse response of the filter is same on the signal so E_{s} = E_{h}

QUESTION: 61

The current density in a medium is given by

The total current and the average current density flowing through the portion of a spherical

surface are given, respectively, by

Solution:

correct option is not given

current passing through the portion of sphere of radius r = 0.8 m is given by

The average current density through the given sphere surface is

QUESTION: 62

An antenna pointing in a certain direction has a noise temperature of 50K. The ambient

temperature is 290K. The antenna is connected to pre-amplifier that has a noise figure of 2dB and

an available gain of 40 dB over an effective bandwidth of 12 MHz. The effective input noise

temperature Te for the amplifier and the noise power Pao at the output of the preamplifier,

respectively, are

Solution:

*Answer can only contain numeric values

QUESTION: 63

Two lossless X-band horn antennas are separated by a distance of 200?. The amplitude reflection

coefficients at the terminals of the transmitting and receiving antennas are 0.15 and 0.18,

respectively. The maximum directivities of the transmitting and receiving antennas (over the

isotropic antenna) are 18dB and 22dB, respectively. Assuming that the input power in the lossless

transmission line connected to the antenna is 2 W, and that the antennas are perfectly aligned and

polarization matched, the power (in mW) delivered to the load at the receiver is ____

Solution:

Given

Lossless horn antennas

ηT = ηR = 1

Power Gain = Directivity

Directivity of Txing antenna, DT = 18 dB

10 logD_{T} = 18

GT (or) D_{T} = 63.09

Directivity of Rxing antenna, D_{R} = 22 dB

10logD_{R} = 22

GR(or) D_{R} = 158.48

input power Pin = 2 W

Spacing, r = 200 λ

= 3.1 x10^{–3}

As there is a reflection at the terminals of Rxing antenna power delivered to the load in given by

QUESTION: 64

The electric filed of a uniform plane wave travelling along the negative z direction is given by the

following equation:

This wave is incident upon a receiving antenna placed at the origin and whose radiated electric

field towards the incident wave is given by the following equation:

The polarization of the incident wave, the polarization of the antenna and losses due to the

polarization mismatch are, respectively,

Solution:

Given

As a tip of electric field intensity is tracing a circle when time varies, hence the wave is said to be circularly polarized in clockwise direction (or) RHCP. Polarizing vector of incident wave is given

by,

As both x & y components are in-phase, hence the wave is said to be linear polarized. Polarizing vector of radiated field is

polarizing mismatch; The polarizing mismatch is said to

have, if the polarization of receiving antenna is not same on the polarization of the incident wave.

The polarization loss factor (PLF) characterizes the loss of EM power due to polarization mismatch.

QUESTION: 65

The far-zone power density radiated by a helical antenna is approximated as:

The radiated power density is symmetrical with respect to ? and exists only in the upper

hemisphere: is a constant. The power radiated by the antenna (in watts)

and the maximum directivity of the antenna, respectively, are

Solution:

Given

Power density radiated by the antenna

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