Gate questions ec04 2014 praveen someh

GATE 2014: General Instructions during Examination
1. Total duration of the GATE examination is 180 minutes.
2. The clock will be set at the server. The countdown timer at the top right corner of screen will display the remaining time available for you to complete the examination. When the timer reaches zero, the examination will end by itself. You need not terminate the examination or submit your paper.
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4. Use the scribble pad provided to you for any rough work. Submit the scribble pad at the end of the examination.
5. You are allowed to use a non-programmable type calculator, however, sharing of calculators is not allowed.
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The Marked for Review status for a question simply indicates that you would like to look at that question again. If a question is answered, but marked for review, then the answer will be considered for evaluation unless the status is modified by the candidate.
Navigating to a Question :
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b. Select an answer for a multiple choice type question by clicking on the bubble placed before the 4 choices, namely A, B, C and D. Use the virtual numeric keypad to enter a number as answer for a numerical type question.
c. Click on Save & Next to save your answer for the current question and then go to the next question.
d. Click on Mark for Review & Next to save your answer for the current question and also mark it for review, and then go to the next question. www.jntuworld.com || www.android.jntuworld.com || www.jwjobs.net || www.android.jwjobs.net
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Caution: Note that your answer for the current question will not be saved, if you navigate to another question directly by clicking on a question number without saving the answer to the previous question.
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9. Procedure for answering a numerical answer type question:
a. To enter a number as your answer, use the virtual numerical keypad.
b. A fraction (e.g. -0.3 or -.3) can be entered as an answer with or without '0' before the decimal point. As many as four decimal points, e.g. 12.5435 or 0.003 or -932.6711 or 12.82 can be entered.
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only be able to see questions in this Section, but you will not be able to answer questions in the Section.
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Changing the Optional Section :
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GATE 2014 Examination
EC: Electronics & Communications Engineering
Duration: 180 minutes Maximum Marks: 100
Read the following instructions carefully.
1. To login, enter your Registration Number and password provided to you. Kindly go through the various symbols used in the test and understand their meaning before you start the examination.
2. Once you login and after the start of the examination, you can view all the questions in the question paper, by clicking on the View All Questions button in the screen.
3. This question paper consists of 2 sections, General Aptitude (GA) for 15 marks and the subject specific GATE paper for 85 marks. Both these sections are compulsory.
The GA section consists of 10 questions. Question numbers 1 to 5 are of 1-mark each, while question numbers 6 to 10 are of 2-mark each.
The subject specific GATE paper section consists of 55 questions, out of which question numbers 1 to 25 are of 1-mark each, while question numbers 26 to 55 are of 2-mark each.
4. Depending upon the GATE paper, there may be useful common data that may be required for answering the questions. If the paper has such useful data, the same can be viewed by clicking on the Useful Common Data button that appears at the top, right hand side of the screen.
5. The computer allotted to you at the examination center runs specialized software that permits only one answer to be selected for multiple-choice questions using a mouse and to enter a suitable number for the numerical answer type questions using the virtual keyboard and mouse.
6. Your answers shall be updated and saved on a server periodically and also at the end of the examination. The examination will stop automatically at the end of 180 minutes.
7. In each paper a candidate can answer a total of 65 questions carrying 100 marks.
8. The question paper may consist of questions of multiple choice type (MCQ) and numerical answer type.
9. Multiple choice type questions will have four choices against A, B, C, D, out of which only ONE is the correct answer. The candidate has to choose the correct answer by clicking on the bubble (⃝) placed before the choice.
10. For numerical answer type questions, each question will have a numerical answer and there will not be any choices. For these questions, the answer should be enteredby using the virtual keyboard that appears on the monitor and the mouse.
11. All questions that are not attempted will result in zero marks. However, wrong answers for multiple choice type questions (MCQ) will result in NEGATIVE marks. For all MCQ questions a wrong answer will result in deduction of⅓ marks for a 1-mark question and ⅔ marks for a 2-mark question.
12. There is NO NEGATIVE MARKING for questions of NUMERICAL ANSWER TYPE.
13. Non-programmable type Calculator is allowed. Charts, graph sheets, and mathematical tables are NOT allowed in the Examination Hall. You must use the Scribble pad provided to you at the examination centre for all your rough work. The Scribble Pad has to be returned at the end of the examination.
Declaration by the candidate:
“I have read and understood all the above instructions. I have also read and understood clearly the instructions given on the admit card and shall follow the same. I also understand that in case I am found to violate any of these instructions, my candidature is liable to be cancelled. I also confirm that at the start of the examination all the computer hardware allotted to me are in proper working condition”.

GATE 2014 SET- 6 General Aptitude -GA
GA 1/2
Q. 1 – Q. 5 carry one mark each.
Q.1
Which of the following options is the closest in meaning to the word underlined in the sentence below? In a democracy, everybody has the freedom to disagree with the government.
(A) dissent
(B) descent
(C) decent
(D) decadent
Q.2
After the discussion, Tom said to me, 'Please revert!'. He expects me to _________.
(A) retract
(B) get back to him
(C) move in reverse
(D) retreat
Q.3
While receiving the award, the scientist said, "I feel vindicated". Which of the following is closest in meaning to the word ‘vindicated’?
(A) punished
(B) substantiated
(C) appreciated
(D) chastened
Q.4
Let 푓푓(푥푥,푦푦)= 푥푥푛푛 푦푦푚푚 =푃푃. If x is doubled and y is halved, the new value of f is
(A) 2푛푛−푚푚푃푃
(B) 2푚푚−푛푛푃푃
(C) 2(푛푛−푚푚)푃푃
(D) 2(푚푚−푛푛)푃푃
Q.5
In a sequence of 12 consecutive odd numbers, the sum of the first 5 numbers is 425. What is the sum of the last 5 numbers in the sequence?
Q. 6 – Q. 10 carry two marks each.
Q.6
Find the next term in the sequence: 13M, 17Q, 19S, ___
(A) 21W
(B) 21V
(C) 23W
(D) 23V
Q.7
If ‘KCLFTSB’ stands for ‘best of luck’ and ‘SHSWDG’ stands for ‘good wishes’, which of the following indicates ‘ace the exam’?
(A) MCHTX
(B) MXHTC
(C) XMHCT
(D) XMHTC
Q.8
Industrial consumption of power doubled from 2000-2001 to 2010-2011. Find the annual rate of increase in percent assuming it to be uniform over the years.
(A) 5.6
(B) 7.2
(C) 10.0
(D) 12.2
GA06 (GATE 2014)

GATE 2014 SET- 6 General Aptitude -GA
GA 2/2
Q.9
A firm producing air purifiers sold 200 units in 2012. The following pie chart presents the share of raw material, labour, energy, plant & machinery, and transportation costs in the total manufacturing cost of the firm in 2012. The expenditure on labour in 2012 is Rs. 4,50,000. In 2013, the raw material expenses increased by 30% and all other expenses increased by 20%. What is the percentage increase in total cost for the company in 2013?
Q.10
A five digit number is formed using the digits 1,3,5,7 and 9 without repeating any of them. What is the sum of all such possible five digit numbers?
(A) 6666660
(B) 6666600
(C) 6666666
(D) 6666606
END OF THE QUESTION PAPER
GA06 (GATE 2014)

GATE 2014 SET4 ELECTRONICS AND COMMUNICATION ENGINEERING – EC
EC 1/13
Q. 1 – Q. 25 carry one mark each.
Q.1
The series Σ1 푛푛! ∞푛푛 =0 converges to
(A) 2 ln2
(B) √2
(C) 2
(D) 푒푒
Q.2
The magnitude of the gradient for the function 푓푓(푥푥,푦푦,푧푧)= 푥푥2+ 3푦푦2+푧푧3 at the point (1,1,1) is _________.
Q.3
Let 푋푋 be a zero mean unit variance Gaussian random variable. 퐸퐸[|푋푋|] is equal to _____
Q.4
If 푎푎 and 푏푏 are constants, the most general solution of the differential equation 푑푑2푥푥 푑푑푡푡2+2 푑푑푑푑푑푑+푥푥=0 is
(A) 푎푎푒푒−푡푡
(B) 푎푎푒푒−푡푡+푏푏푏푒푒−푡푡
(C) 푎푎푎푡푡+푏푏푏−푡푡
(D) 푎푎푎−2푡푡
Q.5
The directional derivative of ()(,) 2xyfxyxy=+ at (1, 1) in the direction of the unit vector at an angle of 4 π with y-axis, is given by ______ .
Q.6
The circuit shown in the figure represents a
(A) voltage controlled voltage source
(B) voltage controlled current source
(C) current controlled current source
(D) current controlled voltage source
Q.7
The magnitude of current (in mA) through the resistor R2 in the figure shown is_______.
Ii
R
AIIi
EC04 (GATE 2014)

EC 2/13
Q.8
At T = 300 K, the band gap and the intrinsic carrier concentration of GaAs are 1.42 eV and 106 cm-3, respectively. In order to generate electron hole pairs in GaAs, which one of the wavelength (λC) ranges of incident radiation, is most suitable? (Given that: Plank’s constant is 6.62 × 10-34 J-s, velocity of light is 3 × 1010 cm/s and charge of electron is 1.6 × 10-19 C)
(A) 0.42 μm < λC < 0.87 μm
(B) 0.87 μm < λC < 1.42 μm
(C) 1.42 μm < λC < 1.62 μm
(D) 1.62 μm < λC < 6.62 μm
Q.9
In the figure, ln (ρi) is plotted as a function of 1/T, where ρi is the intrinsic resistivity of silicon, T is the temperature, and the plot is almost linear. ln (ρi) 1 / T The slope of the line can be used to estimate
(A) band gap energy of silicon (Eg)
(B) sum of electron and hole mobility in silicon (μn + μp)
(C) reciprocal of the sum of electron and hole mobility in silicon (μn + μp) -1
(D) intrinsic carrier concentration of silicon (ni)
Q.10
The cut-off wavelength (in μm) of light that can be used for intrinsic excitation of a semiconductor material of bandgap Eg= 1.1 eV is ________
Q.11
If the emitter resistance in a common-emitter voltage amplifier is not bypassed, it will
(A) reduce both the voltage gain and the input impedance
(B) reduce the voltage gain and increase the input impedance
(C) increase the voltage gain and reduce the input impedance
(D) increase both the voltage gain and the input impedance
Q.12
Two silicon diodes, with a forward voltage drop of 0.7 V, are used in the circuit shown in the figure. The range of input voltage 푉푉푖푖 for which the output voltage 푉푉표표=푉푉푖푖, is
(A) −0.3 푉푉 < 푉푉푖푖< 1.3 푉푉
(B) −0.3 푉푉 < 푉푉푖푖< 2 푉푉
(C) −1.0 푉푉 < 푉푉푖푖< 2.0 푉푉
(D) −1.7 푉푉 < 푉푉푖푖< 2.7 푉푉
VO
R
D1
D2
-1 V
2 V
Vi
EC04 (GATE 2014)

EC 3/13
Q.13
The circuit shown represents vi –12 V vo R2 C2 C1 R1 – + +12 V –2 V
(A) a bandpass filter
(B) a voltage controlled oscillator
(C) an amplitude modulator
(D) a monostable multivibrator
Q.14
For a given sample-and-hold circuit, if the value of the hold capacitor is increased, then
(A) droop rate decreases and acquisition time decreases
(B) droop rate decreases and acquisition time increases
(C) droop rate increases and acquisition time decreases
(D) droop rate increases and acquisition time increases
Q.15
In the circuit shown in the figure, if 퐶퐶=0, the expression for 푌푌 is
(A) 푌푌=퐴퐴 퐵퐵ത +퐴퐴̅ 퐵퐵
(B) 푌푌=퐴퐴+퐵퐵
(C) 푌푌= 퐴퐴̅+퐵퐵ത
(D) 푌푌=퐴퐴 퐵퐵
EC04 (GATE 2014)

EC 4/13
Q.16
The output (Y) of the circuit shown in the figure is
(A) CBA++
(B) CACBA⋅+⋅+
(C) CBA++
(D) CBA⋅⋅
Q.17
A Fourier transform pair is given by ൬ 23 ൰ 푛푛 푢푢[푛푛+3] 퐹퐹퐹퐹 ⇔ 퐴퐴 푒푒−푗푗6휋휋휋1−ቀ23ቁ 푒푒−푗푗2휋휋휋
where 푢푢[푛푛] denotes the unit step sequence. The values of 퐴퐴 is _________.
Q.18
A real-valued signal 푥푥(푡푡) limited to the frequency band |푓푓|≤푊푊 2 is passed through a linear time invariant system whose frequency response is 퐻퐻(푓푓)= ൞ 푒푒−푗푗4휋휋휋, |푓푓|≤ 푊푊 2 0, |푓푓|> 푊푊 2 . The output of the system is
(A) 푥푥(푡푡+ 4)
(B) 푥푥(푡푡 − 4)
(C) 푥푥(푡푡 + 2)
(D) 푥푥(푡푡 − 2)
A
B
C
A
B
C
Output (Y)
VDD
EC04 (GATE 2014)

EC 5/13
Q.19
The sequence 푥푥[푛푛]=0.5푛푛 푢푢[푛푛] , where 푢푢[푛푛] is the unit step sequence, is convolved with itself to obtain 푦푦[푛푛]. Then Σ푦푦[푛푛] + ∞ 푛푛= − ∞is _______.
Q.20
In a Bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a 4th order all-pole system?
(A) – 80 dB/decade
(B) – 40 dB/decade
(C) +40 dB/decade
(D) +80 dB/decade
Q.21
For the second order closed-loop system shown in the figure, the natural frequency (in rad/s) is
(A) 16
(B) 4
(C) 2
(D) 1
Q.22
If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival of earlier or future calls, the probability distribution function of the total number of calls in a fixed time interval will be
(A) Poisson
(B) Gaussian
(C) Exponential
(D) Gamma
Q.23
In a double side-band (DSB) full carrier AM transmission system, if the modulation index is doubled, then the ratio of total sideband power to the carrier power increases by a factor of ______.
Q.24
For an antenna radiating in free space, the electric field at a distance of 1 km is found to be 12 mV/m. Given that intrinsic impedance of the free space is 120πΩ, the magnitude of average power density due to this antenna at a distance of 2 km from the antenna (in nW/m2 ) is ____.
Q.25
Match column A with column B.
Column A
Column B
1. Point electromagnetic source
P. Highly directional
2. Dish antenna
Q. End fire
3. Yagi-Uda antenna
R. Isotropic
(A)
1→푃푃
2→푄푄
3→푅푅
(B)
1→푅푅
2→푃푃
3→푄푄
(C)
1→푄푄
2→푃푃
3→푅푅
(D)
1→푅푅
2→푄푄
3→푃푃
U(s)
Y(s)
4s(s+4)
-
+
EC04 (GATE 2014)

EC 6/13
Q. 26 – Q. 55 carry two marks each.
Q.26
With initial values 푦푦(0)=푦푦′(0)=1, the solution of the differential equation 푑푑2푦푦 푑푑푥푥2+4 푑푑푑푑푑푑+4푦푦=0
at 푥푥=1 is _____.
Q.27
Parcels from sender S to receiver R pass sequentially through two post-offices. Each post-office has a probability 15 of losing an incoming parcel, independently of all other parcels. Given that a parcel is lost, the probability that it was lost by the second post-office is_________.
Q.28
The unilateral Laplace transform of 푓푓(푡푡) is 1 푠푠2+푠푠+1. Which one of the following is the unilateral Laplace transform of 푔푔(푡푡)=푡푡∙푓푓(푡푡)?
(A)− 푠푠 (푠푠2+푠푠+1)2
(B)−(2푠푠+1) (푠푠2+푠푠+1)2
(C)푠푠 (푠푠2+푠푠+1)2
(D)2푠푠+1(푠푠2+푠푠+1)2
Q.29
For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the angle between the hypotenuse and the side is
(A) 12o
(B) 36o
(C) 60o
(D) 45o
Q.30
The steady state output of the circuit shown in the figure is given by
푦푦(푡푡)=퐴퐴(휔휔)sin(휔휔휔+휙휙(휔휔)). If the amplitude | 퐴퐴(휔휔)|=0.25 , then the frequency 휔휔 is
(A) 1√3 푅푅 퐶퐶
(B) 2√3 푅푅 퐶퐶
(C) 1 푅푅 퐶퐶
(D) 2 푅푅 퐶퐶
Q.31
In the circuit shown in the figure, the value of v0(t) (in Volts) for t→∞ is ______. 5 Ω5 Ω2 H10 u(t) Axi+ - +- v (t)o2ix
R
C
C
C
sin(ωt)
y(t)
EC04 (GATE 2014)

EC 7/13
Q.32
The equivalent resistance in the infinite ladder network shown in the figure, is Re.
The value of Re/R is ________
Q.33
For the two-port network shown in the figure, the impedance (Z) matrix (in Ω) is
(A) ቂ624429ቃ
(B) ቂ98824ቃ
(C) ቂ96624ቃ
(D) ቂ426660ቃ
Q.34
Consider a silicon sample doped with ND = 1×1015/cm3 donor atoms. Assume that the intrinsic carrier concentration ni = 1.5×1010/cm3. If the sample is additionally doped with NA = 1×1018/cm3 acceptor atoms, the approximate number of electrons/cm3 in the sample, at T=300 K, will be ______.
Q.35
Consider two BJTs biased at the same collector current with area A1 = 0.2 μm × 0.2 μm and A2 = 300 μm × 300 μm. Assuming that all other device parameters are identical, kT/q = 26 mV, the intrinsic carrier concentration is 1 × 1010 cm-3, and q = 1.6 × 10-19 C, the difference between the base-emitter voltages (in mV) of the two BJTs (i.e., VBE1 – VBE2) is _____. EC04 (GATE 2014)

EC 8/13
Q.36
An N-type semiconductor having uniform doping is biased as shown in the figure. If EC is the lowest energy level of the conduction band, EV is the highest energy level of the valance band and EF is the Fermi level, which one of the following represents the energy band diagram for the biased N-type semiconductor?
(A) ECEVEF
(B) ECEVEF
(C) ECEVEF
(D) ECEVEF
Q.37
Consider the common-collector amplifier in the figure (bias circuitry ensures that the transistor operates in forward active region, but has been omitted for simplicity). Let IC be the collector current, VBE be the base-emitter voltage and VT be the thermal voltage. Also, 푔푔푚푚 and 푟푟표표 are the small-signal transconductance and output resistance of the transistor, respectively. Which one of the following conditions ensures a nearly constant small signal voltage gain for a wide range of values of RE?
(A) 푔푔푚푚RE≪1
(B) ICRE≫VT
(C) 푔푔푚푚푟푟표표≫1
(D) VBE≫VT
Q.38
A BJT in a common-base configuration is used to amplify a signal received by a 50 Ω antenna. Assume kT/q = 25 mV. The value of the collector bias current (in mA) required to match the input impedance of the amplifier to the impedance of the antenna is________. EC04 (GATE 2014)

EC 9/13
Q.39
For the common collector amplifier shown in the figure, the BJT has high β, negligible VCE(sat), and VBE = 0.7 V. The maximum undistorted peak-to-peak output voltage vo (in Volts) is _______. vi vo RE 1 kΩ VCC = +12 V R1 5 kΩ • R2 10 kΩ 1 μF 1 μF
Q.40
An 8-to-1 multiplexer is used to implement a logical function 푌푌 as shown in the figure. The output 푌푌 is given by
(A) 푌푌 = 퐴퐴 퐵퐵ത 퐶퐶 + 퐴퐴 퐶퐶̅ 퐷퐷
(B) 푌푌 = 퐴퐴̅ 퐵퐵 퐶퐶 + 퐴퐴 퐵퐵ത 퐷퐷
(C) 푌푌 = 퐴퐴 퐵퐵 퐶퐶̅ + 퐴퐴̅ 퐶퐶 퐷퐷
(D) 푌푌 = 퐴퐴̅ 퐵퐵ത 퐷퐷 +퐴퐴 퐵퐵ത 퐶퐶
Q.41
A 16-bit ripple carry adder is realized using 16 identical full adders (FA) as shown in the figure. The carry-propagation delay of each FA is 12 ns and the sum-propagation delay of each FA is 15 ns. The worst case delay (in ns) of this 16-bit adder will be __________. FA0S0C0A0B0FA1S1A1B1C1FA14S14C14A14B14FA15S15A15B15C15
Q.42
An 8085 microprocessor executes “STA 1234H” with starting address location 1FFEH (STA copies the contents of the Accumulator to the 16-bit address location). While the instruction is fetched and executed, the sequence of values written at the address pins A15−A8 is
(A) 1FH, 1FH, 20H, 12H
(B) 1FH, FEH, 1FH, FFH, 12H
(C) 1FH, 1FH, 12H, 12H
(D) 1FH, 1FH, 12H, 20H, 12H
EC04 (GATE 2014)

EC 10/13
Q.43
A stable linear time invariant (LTI) system has a transfer function 퐻퐻(푠푠) = 1 푠푠2+푠푠−6. To make this system causal it needs to be cascaded with another LTI system having a transfer function 퐻퐻1(푠푠). A correct choice for 퐻퐻1(푠푠) among the following options is
(A) 푠푠+3
(B) 푠푠−2
(C) 푠푠−6
(D) 푠푠+1
Q.44
A causal LTI system has zero initial conditions and impulse response ℎ(푡푡). Its input 푥푥(푡푡) and output 푦푦(푡푡) are related through the linear constant-coefficient differential equation 푑푑2푦푦(푡푡) 푑푑푡푡2+훼훼 푑푑푑(푡푡) 푑푑푑+훼훼2푦푦(푡푡)=푥푥(푡푡).
Let another signal 푔푔(푡푡) be defined as 푔푔(푡푡)=훼훼2නℎ(휏휏)푑푑푑푡푡 0+ 푑푑ℎ(푡푡) 푑푑푑+훼훼ℎ(푡푡).
If 퐺퐺(푠푠) is the Laplace transform of 푔푔(푡푡), then the number of poles of 퐺퐺(푠푠) is _____.
Q.45
The 푁푁-point DFT 푋푋 of a sequence 푥푥[푛푛],0 ≤푛푛 ≤푁푁−1 is given by 푋푋[푘푘]= 1√푁푁 ෍푥푥[푛푛]푒푒−푗푗 2휋휋 푁푁푛푛푛,0 ≤푘푘 ≤푁푁−1. 푁푁−1 푛푛=0
Denote this relation as 푋푋=퐷퐷퐷(푥푥). For 푁푁=4, which one of the following sequences satisfies 퐷퐷퐷(퐷퐷퐷(푥푥)) = 푥푥 ?
(A) 푥푥=[1 2 3 4]
(B) 푥푥=[1 2 3 2]
(C) 푥푥=[1 3 2 2]
(D) 푥푥=[1 2 2 3]
Q.46
The state transition matrix 휙휙(t) of a system ൤ 푥푥̇1 푥푥̇2 ൨=ቂ0100ቃቂ 푥푥1 푥푥2 ቃ is
(A) ቂ푡푡110 ቃ
(B) ቂ10 푡푡1 ቃ
(C) ቂ011푡푡 ቃ
(D) ቂ1푡푡 01 ቃ
Q.47
Consider a transfer function 퐺퐺푝푝(푠푠)= 푝푝푠푠2+3푝푝푝−2 푠푠2+(3+푝푝)푠푠+(2−푝푝) with 푝푝 a positive real parameter. The maximum value of 푝푝 until which 퐺퐺푝푝 remains stable is ________.
EC04 (GATE 2014)

EC 11/13
Q.48
The characteristic equation of a unity negative feedback system is 1+퐾퐾퐾(푠푠)=0. The open loop transfer function 퐺퐺(푠푠) has one pole at 0 and two poles at -1. The root locus of the system for varying K is shown in the figure. OAξ=0.5σω(0,0) −1−1/3j
The constant damping ratio line, for ξ=0.5, intersects the root locus at point A. The distance from the origin to point A is given as 0.5. The value of 퐾퐾 at point A is ________ .
Q.49
Consider a communication scheme where the binary valued signal X satisfies 푃푃{푋푋= +1}=0.75 and 푃푃{푋푋=−1}=0.25. The received signal Y = X + Z, where Z is a Gaussian random variable with zero mean and variance 휎휎2. The received signal Y is fed to the threshold detector. The output of the threshold detector 푋푋෠ is: 푋푋෠ =ቄ+1, 푌푌휏휏 −1,푌푌≤휏휏.
To achieve a minimum probability of error 푃푃൛푋푋෠ ≠푋푋ൟ, the threshold τ should be
(A) strictly positive
(B) zero
(C) strictly negative
(D) strictly positive, zero, or strictly negative depending on the nonzero value of 휎휎2
EC04 (GATE 2014)

EC 12/13
Q.50
Consider the Z-channel given in the figure. The input is 0 or 1 with equal probability.
If the output is 0, the probability that the input is also 0 equals ______________
Q.51
An M-level PSK modulation scheme is used to transmit independent binary digits over a band-pass channel with bandwidth 100 kHz. The bit rate is 200 kbps and the system characteristic is a raised- cosine spectrum with 100% excess bandwidth. The minimum value of M is ________.
Q.52
Consider a discrete-time channel 푌푌 = 푋푋+ 푍푍, where the additive noise 푍푍 is signal-dependent.
In particular, given the transmitted symbol 푋푋∈{−푎푎,+푎푎} at any instant, the noise sample 푍푍 is chosen independently from a Gaussian distribution with mean 훽훽푋푋 and unit variance. Assume a threshold detector with zero threshold at the receiver.
When 훽훽=0, the BER was found to be 푄푄(푎푎)=1 × 10−8.
(푄푄(푣푣)=1√2휋휋∫푒푒−푢푢22⁄∞ 푣푣푑푑푑, and for 푣푣1, use 푄푄(푣푣)≈ 푒푒−푣푣22⁄ )
When 훽훽=−0.3, the BER is closest to
(A) 10−7
(B) 10−6
(C) 10−4
(D) 10−2
Q.53
The electric field (assumed to be one-dimensional) between two points A and B is shown. Let 휓휓퐴퐴 and 휓휓퐵퐵 be the electrostatic potentials at A and B, respectively. The value of 휓휓퐵퐵–휓휓퐴퐴 in Volts is ________.
Q.54
GivenˆˆˆxyzFzaxaya=++  . If Srepresents the portion of the sphere 2221xyz++=for 0z≥, then ∫∇×퐹퐹∙ሬሬሬሬ⃗ 푠푠 푑푑푑ሬሬሬሬ⃗ is______________.
INPUT0101OUTPUT1.00.250.75
EC04 (GATE 2014)

EC 13/13
Q.55
If 퐸퐸ሬ⃗= −(2푦푦3−3푦푦푧푧2)푥푥ො−(6푥푥푥2−3푥푥푧푧2)푦푦ො+(6푥푥푥)푧푧̂ is the electric field in a source free region, a valid expression for the electrostatic potential is
(A) 푥푥푦푦3−푦푦푧푧2
(B) 2푥푥푦푦3−푥푥푥푧푧2
(C) 푦푦3+푥푥푥푧푧2
(D) 2푥푥푦푦3−3푥푥푥푧푧2
END OF THE QUESTION PAPER
EC04 (GATE 2014)

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