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QUESTION: 1

**Q. No. 1 – 5 Carry One Mark Each**

**Q. Choose the grammatically CORRECT sentence:**

Solution:

QUESTION: 2

Statement: You can always give me a ring whenever you need.

Which one of the following is the best inference from the above statement?

Solution:

QUESTION: 3

In the summer of 2012, in New Delhi, the mean temperature of Monday to

Wednesday was 41ºC and of Tuesday to Thursday was 43ºC. If the temperature

on Thursday was 15% higher than that of Monday, then the temperature in ºC on

Thursday was

Solution:

Let the temperature of Monday be T_{M}

Sum of temperatures of Tuesday and Wednesday = T and

Temperature of Thursday =T_{Th}

Now, T_{m} +T = 41x 3 =123

& T_{th+} T= 43x 3= 129

T_{th} -T_{m=} 6, Also T_{th=} 1.15T_{m}

0.15T_{m=} 6 T_{m} =40

Temperature of thursday= 40+ 6= 46^{o} C

QUESTION: 4

Complete the sentence:

Dare ____________ mistakes.

Solution:

QUESTION: 5

They were requested not to quarrel with others.

Which one of the following options is the closest in meaning to the word quarrel?

Solution:

QUESTION: 6

**Q. No. 6 – 10 Carry Two Marks Each**

**Q.**

A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16km in the third quarter. The average speed of the car in km per hour over the entire journey is

Solution:

Average speed = Total distance/Total Time

QUESTION: 7

Find the sum to n terms of the series 10 + 84 + 734 + …

Solution:

Explanations:-Using the answer options, substitute n = 2. The sum should add up to 94

Alternative Solution:

The given series is 10+84+734+………………………..+n terms

QUESTION: 8

Statement: There were different streams of freedom movements in colonial India

carried out by the moderates, liberals, radicals, socialists, and so on.

Which one of the following is the best inference from the above statement?

Solution:

QUESTION: 9

The set of values of p for which the roots of the equation 3x^{2} + 2x + p( p − 1) = 0

are of opposite sign is

Solution:

QUESTION: 10

What is the chance that a leap year, selected at random, will contain 53

Sundays?

Solution:

There are 52 complete weeks in a calendar year 852 × 7 =364days

Number of days in a leap year = 366

Probability of 53 Saturdays 2/7

QUESTION: 11

**Q. No. 11 – 35 Carry One Mark Each**

**Q.**

A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles

Solution:

From Truth Table, it can be verified that Ex-OR logic is implemented

QUESTION: 12

Consider a vector field The closed loop line integral

can be expressed as

Solution:

Stoke’s Theorem: “ The Line Integral of a vector around a closed path L is

equal to the integral of curl of over the open surface S enclosed by the closed

path L”.

QUESTION: 13

In a forward biased pn junction diode, the sequence of events that best describes

the mechanism of current flow is

Solution:

QUESTION: 14

Two systems with impulse responses h_{1}(t) and h_{2}(t) are connected in cascade.

Then the overall impulse response of the cascaded system is given by

Solution:

QUESTION: 15

In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation

(using steam or water vapor) produces

Solution:

QUESTION: 16

The maximum value of q until which the approximation sinθ ≈ θ holds to within 10%

error is

Solution:

Out of all possible options we need to go for max theta below 45° Hence it is

18°

QUESTION: 17

The divergence of the vector field

Solution:

QUESTION: 18

The impulse response of a system is h(t) = tu(t). For an input u(t − 1) , the output is

Solution:

For LTI system, if input gets delayed by one unit, output will also get delayed by

one unit.

QUESTION: 19

The Bode plot of a transfer function G (s) is shown in the figure below

The gain (20 log |G(s)| ) is 32 dB and –8 dB at 1 rad/s and 10 rad/s respectively.

The phase is negative for all ω. The G(s) is

Solution:

Any two paints on same line segment of Bode plot satisfies the equation of

straight line.

QUESTION: 20

In the circuit shown below what is the output voltage ( ) out V if a silicon transistor

Q and an ideal op-amp are used?

Solution:

QUESTION: 21

Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor k, k> 0, the elements of the corresponding star equivalent will be scaled by a factor of

Solution:

Above expression shown that if R_{a} , R_{b} & R_{c} is scaled by k, R_{a} , R_{b} & R_{c} is scaled

by k only.

QUESTION: 22

For 8085 microprocessor, the following program is executed

MVI A, 05H;

MVIB, 05H;

PTR: ADD B;

DCR B;

JNZ PTR;

ADI 03H;

HLT;

At the end of program, accumulator contains

Solution:

Accumulator changes as follows (05 + 05 + 04 +03 +02 +01)H

At the end of Loop accumulator contains = 14H

ADI O3H →A=(14+03)=17H

QUESTION: 23

The bit rate of a digital communication system is R kbits/s. The modulation used is

32-QAM. The minimum bandwidth required for ISI free transmission is

Solution:

Bit rate given = R Kbits/second

Modulation = 32-QAM

No. of bits/symbol = 2 5 [log 32]

Symbol rate =R/5 k symbols / sec ond

Finally we are transmitting symbols.

QUESTION: 24

For a periodic signal v (t) = 30sin100t + 10cos300t + 6 sin(500t + π / 4) , the

fundamental frequency in rad/s

Solution:

ω_{o} =100 rad / sec fundamental

3ω_{o }= 300 rad / sec third harmonic

5ω_{o }= 500 rad / sec fifth harmonic

QUESTION: 25

In a voltage-voltage feedback as shown below, which one of the following

statements is TRUE if the gain k is increased?

Solution:

In voltage-voltage feedback

QUESTION: 26

A band-limited signal with a maximum frequency of 5 kHz is to be sampled.

According to the sampling theorem, the sampling frequency which is not valid is

Solution:

Given: f_{m} = 5kHz

According to sampling frequency

f_{s}2f

f_{s}10 kHz

So, only in option (a) it is less than 10KHz ie., (5KHz)

QUESTION: 27

In a MOSFET operating in the saturation region, the channel length modulation

effect causes

Solution:

No channel length modulation

under the presence of channel length modulation

which is reduced from ∞ to finite value

QUESTION: 28

Which one of the following statements is NOT TRUE for a continuous time causal

and stable LTI system?

Solution:

For an LTI system to be stable and causal all poles or roots of characteristic

equation must lie on LHS of s-plane i.e., left hand side of jω− axis

[Refer Laplace transform].

QUESTION: 29

The minimum Eigen value of the following matrix is

Solution:

So the matrix is singular

Therefore atleast one of the Eigen value is ‘0’

As the choices are non negative, the minimum Eigen value is ‘0’

QUESTION: 30

A polynomial f( x) = a_{4} x^{4} + a_{3} x^{3} + a_{2} x^{2} + a_{1} x − a_{0} with all coefficients positive has

Solution:

Use Routh Hurwitz Criteria to get the condition.

QUESTION: 31

Assuming zero initial condition, the response y(t) of the system given below to a

unit step input u(t) is

Solution:

Integration of unit step function is ramp output

^{}

Writing in time domain

QUESTION: 32

The transfer function V_{2}(s) / V_{1}(s) of the circuit shown below is

Solution:

QUESTION: 33

A source V_{s} (t) = V cos100πt has an internal impedance of (4 + j3)? . If a purely

resistive load connected to this source has to extract the maximum power out of the

source, its value in ? should be

Solution:

For maximum power Transfer

QUESTION: 34

The return loss of a device is found to be 20 dB. The voltage standing wave ratio

(VSWR) and magnitude of reflection coefficient are respectively

Solution:

QUESTION: 35

Let , and h(t) is a filter matched to g(t). If g(t) is applied as input to h(t),

then the Fourier transform of the output is

Solution:

The concept of matched filter assumes that the input signal is of the same form

g(t) as the transmitted signal(except difference in amplitude).this requires that the

shape of the transmitted signal not change on reflection.

QUESTION: 36

**Q. No. 36 – 65 Carry Two Marks Each**

**Q**

Let U and V be two independent zero mean Gaussian random variables of variances1/4 and 1/9 respectively,. The probability P (3V 2U) is

Solution:

QUESTION: 37

Let A be an m x n matrix and B an n x m matrix. It is given that determinant

( I_{m} + AB) = determinant (I_{n} + BA) , where I_{k} is the k × k identity matrix. Using the

above property, the determinant of the matrix given below is

Solution:

QUESTION: 38

In the circuit shown below, if the source voltage V_{s} =10053.13^{o} V then the

Thevenin’s equivalent voltage in Volts as seen by the load resistance R_{L} is

Solution:

QUESTION: 39

The open-loop transfer function of a dc motor is given as when

connected in feedback as shown below, the approximate value of a K that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open-loop system is

Solution:

QUESTION: 40

In the circuit shown below, the knee current of the ideal Zener diode is 10mA. To

maintain 5V across R_{L} , the minimum value of R_{L} in ? and the minimum power

rating of the Zener diode in mW, respectively, are

Solution:

Minimum power rating of Zener should = 50 mA x 5V

= 250 mW

QUESTION: 41

The following arrangement consists of an ideal transformer and an attenuator which attenuates by a factor of 0.8 An ac voltage V_{wx1} = 100V is applied across WX to get an open circuit voltage V_{YZ1} across YZ. Next, an ac voltage V_{YZ2} =100V is applied across YZ to get an open circuit voltage V_{WX2} across WX.

Then, V_{YZ1} / V_{WX1} , V_{WX2} / V_{YZ2} are respectively.

Solution:

The potentiometer gives an attenuation factor of 0.8 over v_{2}

Since potentiometer and transformer are bilateral elements. Hence

QUESTION: 42

Two magnetically uncoupled inductive coils have Q factors q_{1} and q_{2} at the chosen operating frequency. Their respective resistances are R_{1} and R_{2}. When connected in series, their effective Q factor at the same operating frequency is

Solution:

When such two coils are connected in series individual inductances and

resistances are added.

QUESTION: 43

The impulse response of a continuous time system is given by

h(t) = δ (t − 1) + δ (t − 3) . The value of the step response at t = 2 is

Solution:

h(t) =δd (t − 1) + δ (t −)

y(t) =u(t-1)+u(t-3)

y(2)=u(1)+u(-1) =1

QUESTION: 44

The small-signal resistance ( i.e dV_{B/}dI_{D}) in k? offered by the n-channel MOSFET M shown in the figure below, at a bias point of V_{B} = 2 V is (device data for M: device Transconductance parameter k_{N} = μ C_{ox} (W / L0 = 40μA / V^{2 }threshold voltage V_{TN} = 1V, and neglect body effect and channel length

modulation effects)

Solution:

QUESTION: 45

The ac schematic of an NMOS common-source stage is shown in the figure below, where part of the biasing circuits has been omitted for simplicity. For the nchannel MOSFET M, the Transconductance g_{m} = 1mA / V, and body effect and channel length modulation effect are to be neglected. The lower cutoff frequency

in Hz of the circuit is approximately at

Solution:

QUESTION: 46

A system is described by the differential equation

Let x(t) be a rectangular pulse given by

Assuming that y(0)=0 and dy/dt =0 at t = 0, the Laplace transform of y(t) is

Solution:

QUESTION: 47

A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by y(t) for t>0, when the forcing function is x(t) and the initial condition is y(0). If one wishes to modify the system so that the solution becomes -2y(t) for t>0, we need to

Solution:

So if we want −2y (t) as a solution both x(t) and y(0) has to be doubled and

multiplied by –ve sign

x(t) → -2x(t)

y(0) → -2x(0)

QUESTION: 48

Consider two identically distributed zero-mean random variables U and V. Let the

cumulative distribution functions of U and 2V be F(x) and G(x) respectively.

Then, for all values of x

Solution:

F (x) = P{X x}

G (x) = P {2X x}

=P{ X x/2}

For positive value of x,

F (x) − G(x) is always greater than zero

For negative value of x.

F (x) − G(x) is − ve

but . F (x) − G(x) . x 0

QUESTION: 49

The DFT of vector [ a b c d] is the vector[ α β γ δ] . Consider the product

The DFT of the vector [ p q r s] is a scaled version of

Solution:

QUESTION: 50

The signal flow graph for a system is given below. The transfer function Y(s)/U(s) for this system is

Solution:

QUESTION: 51

In the circuit shown below the op-amps are ideal. The V_{out} in Volts is

Solution:

V_{1 }= 1(1+ 1)- 2(-1) =4V

V_{out} =2V_{1=} 8V

QUESTION: 52

In the circuit shown below, Q_{1} has negligible collector-to-emitter saturation

voltage and the diode drops negligible voltage across it under forward bias. If

V_{cc} is + 5V,X and Y are digital signals with 0 V as logic 0 and V_{CC} as logic 1,

then the Boolean expression for Z is

Solution:

QUESTION: 53

A voltage 1000sin ωt Volts is applied across YZ. Assuming ideal diodes, the

voltage measured across WX in Volts, is

Solution:

QUESTION: 54

Three capacitors C_{1} ,C_{2} and C_{3} whose values are 10μF, 5μF, and 2μF respectively, have breakdown voltages of 10V, 5V, and 2V respectively. For the interconnection shown below, the maximum safe voltage in Volts that can be applied across the combination, and the corresponding total charge in μC stored in the effective capacitance across the terminals are respectively.

Solution:

From (3), V 10 Volts

To operate Circuit safe, V should be minimum of those =2.8V

QUESTION: 55

There are four chips each of 1024 bytes connected to a 16 bit address bus as

shown in the figure below. RAMs 1,2,3 and 4 respectively are mapped to

addresses

Solution:

QUESTION: 56

In the circuit shown below, the silicon npn transistor Q has a very high value of

b . The required value of R_{2} in k? to produce I_{C} = 1mA is

Solution:

QUESTION: 57

Let U and V be two independent and identically distributed random variables such

that P(U= 1+) = P(U= -1)=1/2 The entropy H(U + V) in bits is

Solution:

QUESTION: 58

Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the

respective received signals for both bits are as shown below.

**Q.**

**If the detection threshold is 1, the BER will be**

Solution:

QUESTION: 59

Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the

respective received signals for both bits are as shown below.

**Q.**

**The optimum threshold to achieve minimum bit error rate (BER) is**

Solution:

Optimum threshold = The point of intersection of two pdf’s

QUESTION: 60

Consider the following figure

The current I_{S} in Amps in the voltage source, and voltage V_{S} in Volts across the

current source respectively, are

Solution:

I_{s}+8+5 =0

I_{s }=13A

QUESTION: 61

Consider the following figure

**Q.**

**The current in the 1? resistor in Amps is**

Solution:

I ? 10A = we can use principle of superposition to determine the current across 1 ohm resistance.

QUESTION: 62

A monochromatic plane wave of wavelength λ = 600μm is propagating in the direction as shown in the figure below. denote incident, reflected, and transmitted electric field vectors associated with the wave.

The angle of incidence θ_{1} and the expression for are

Solution:

The given oblique incidence is an vertical polarization ie., is parallel to the

plane of incidence, is perpendicular to the plane of incident

QUESTION: 63

A monochromatic plane wave of wavelength l = 600μm is propagating in the direction as shown in the figure below. denote incident, reflected, and transmitted electric field vectors associated with the wave.

**Q.**

The expression for is

Solution:

The reflection co-efficient for parallel polarization is given by

But θ_{r = }θ_{i }since reflected ray and incident ray lies in the same medium by using

snell’s law

QUESTION: 64

The state diagram of a system is shown below. A system is described by the state-variable equations

**Q. The state-variable equations of the system shown in the figure above are**

Solution:

QUESTION: 65

The state diagram of a system is shown below. A system is described by the

state-variable equations

**Q.**

**The state transition matrix e ^{At} of the system shown in the figure above is**

Solution:

### Electronics and Communication Engineering (EC) 2013 GATE Paper (Set B) without solution

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