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GATE 2014 : Electronics and Communication Engineering

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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 of marks for a 1-mark question and 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- 3 General Aptitude -GA Q. 1 Q. 5 carry one mark each. Q.1 Choose the most appropriate phrase from the options given below to complete the following sentence. The aircraft take off as soon as its flight plan was filed. (A) is allowed to (C) was allowed to Q.2 (B) will be allowed to (D) has been allowed to Read the statements: 20 14 ) All women are entrepreneurs. Some women are doctors. Which of the following conclusions can be logically inferred from the above statements? (A) All women are doctors (C) All entrepreneurs are women Q.3 (B) All doctors are entrepreneurs (D) Some entrepreneurs are doctors Choose the most appropriate word from the options given below to complete the following sentence. Q.4 (B) dispel (C) propel The statistics of runs scored in a series by four batsmen are provided in the following table. Who is the most consistent batsman of these four? Average 31.2 46.0 54.4 17.9 (G Batsman K L M N Standard deviation 5.21 6.35 6.22 5.90 (B) L (C) M 3 (A) K (D) N What is the next number in the series? A0 Q.5 (D) repel AT (A) impel E Many ancient cultures attributed disease to supernatural causes. However, modern science has largely helped _________ such notions. 35 81 173 357 ____ G 12 Q. 6 Q. 10 carry two marks each. Q.6 Find the odd one from the following group: W,E,K,O (A) W,E,K,O GA (B) I,Q,W,A I,Q,W,A F,N,T,X (C) F,N,T,X N,V,B,D (D) N,V,B,D 1/2 GATE 2014 Q.7 SET- 3 General Aptitude -GA For submitting tax returns, all resident males with annual income below Rs 10 lakh should fill up Form P and all resident females with income below Rs 8 lakh should fill up Form Q. All people with incomes above Rs 10 lakh should fill up Form R, except non residents with income above Rs 15 lakhs, who should fill up Form S. All others should fill Form T. An example of a person who should fill Form T is (A) a resident male with annual income Rs 9 lakh (B) a resident female with annual income Rs 9 lakh (C) a non-resident male with annual income Rs 16 lakh (D) a non-resident female with annual income Rs 16 lakh A train that is 280 metres long, travelling at a uniform speed, crosses a platform in 60 seconds and passes a man standing on the platform in 20 seconds. What is the length of the platform in metres? Q.9 The exports and imports (in crores of Rs.) of a country from 2000 to 2007 are given in the following bar chart. If the trade deficit is defined as excess of imports over exports, in which year is the trade deficit 1/5th of the exports? AT 2000 (B) 2004 2002 2003 2004 2005 (C) 2007 2006 2007 (D) 2006 A0 You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is G (A) 1/4 GA 2001 3 (A) 2005 Q.10 Imports E Exports (G 120 110 100 90 80 70 60 50 40 30 20 10 0 20 14 ) Q.8 (B) 1/3 (C) 1/2 (D) 2/3 END OF THE QUESTION PAPER 2/2 GATE 2014 SET1 ELECTRONICS AND COMMUNICATION ENGINEERING EC Q. 1 Q. 25 carry one mark each. Q.4 Q.5 Q.6 is a closed path in the -plane given by | | = 3. The value of the integral (A) 4 (1 + 2) (B) 4 (3 2) (C) 4 (3 + 2) 2 +4 +2 (D) 4 (1 2) is A real (4 4) matrix satisfies the equation 2 = , where is the (4 4) identity matrix. The positive eigen value of is _________. Let X1, X2, and X3 be independent and identically distributed random variables with the uniform distribution on [0, 1]. The probability P{X1 is the largest} is ________ For maximum power transfer between two cascaded sections of an electrical network, the relationship between the output impedance Z1 of the first section to the input impedance Z2 of the second section is (A) 2 = 1 (C) 2 = 1 (B) 2 = 1 (D) 2 = 1 Consider the configuration shown in the figure which is a portion of a larger electrical network EC 01 (G Q.7 In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at random, has a sibling is _____ 4) Q.3 (A)( ) = (B) ( ) = ( ) (C) ( + ) = + (D) = 20 1 Q.2 For matrices of same dimension M, N and scalar c, which one of these properties DOES NOT ALWAYS hold? AT E Q.1 i5 i2 R R i3 R i4 i1 i6 For R = 1 and currents 1 = 2 A, 4 = 1 A, 5 = 4 A, which one of the following is TRUE? Q.8 EC (A) 6 = 5 (B) 3 = 4 (C) Data is sufficient to conclude that the supposed currents are impossible (D) Data is insufficient to identify the currents 2 , 3 , and 6 When the optical power incident on a photodiode is 10 W and the responsivity is 0.8 A/W, the photocurrent generated (in A) is ________. 1/11 GATE 2014 Q.9 SET1 ELECTRONICS AND COMMUNICATION ENGINEERING EC In the figure, assume that the forward voltage drops of the PN diode D1 and Schottky diode D2 are 0.7 V and 0.3 V, respectively. If ON denotes conducting state of the diode and OFF denotes nonconducting state of the diode, then in the circuit, 20 1 k 10 V both D1 and D2 are ON D1 is ON and D2 is OFF both D1 and D2 are OFF D1 is OFF and D2 is ON If fixed positive charges are present in the gate oxide of an n-channel enhancement type MOSFET, it will lead to 20 1 Q.10 (A) a decrease in the threshold voltage (B) channel length modulation (C) an increase in substrate leakage current (D) an increase in accumulation capacitance A good current buffer has (A) (B) (C) (D) In the ac equivalent circuit shown in the figure, if is the input current and is very large, the type of feedback is EC 01 (G Q.12 low input impedance and low output impedance low input impedance and high output impedance high input impedance and low output impedance high input impedance and high output impedance AT E Q.11 D2 4) (A) (B) (C) (D) D1 small signal input iin RD RD vout M2 M1 RF (A) voltage-voltage feedback (B) voltage-current feedback (C) current-voltage feedback (D) current-current feedback EC 2/11 GATE 2014 SET1 ELECTRONICS AND COMMUNICATION ENGINEERING EC In the low-pass filter shown in the figure, for a cut-off frequency of 5 kHz , the value of R 2 (in k ) is _____________. Q.14 In the following circuit employing pass transistor logic, all NMOS transistors are identical with a threshold voltage of 1 V. Ignoring the body-effect, the output voltages at P, Q and R are, 5V 5V P Q.15 4 V, 3 V, 2 V 5 V, 5 V, 5 V 4 V, 4 V, 4 V 5 V, 4 V, 3 V (B) Y EC (D) X+Y (G 01 1 1 EC Q.18 (C) XY Five JK flip-flops are cascaded to form the circuit shown in Figure. Clock pulses at a frequency of 1 MHz are applied as shown. The frequency (in kHz) of the waveform at Q3 is __________ . 1 J4 Q4 clk 1 K4 Q.17 R The Boolean expression (X + Y) (X + Y) + (X Y) + X simplifies to (A) X Q.16 Q AT E (A) (B) (C) (D) 5V 20 1 5V 4) Q.13 J3 Q3 clk K3 1 J2 Q2 clk 1 K2 1 J1 Q1 clk 1 K1 1 1 J0 Q0 clk K0 clock A discrete-time signal [ ] = sin( 2 ) , being an integer, is (A) periodic with period . (C) periodic with period /2. (B) periodic with period 2 . (D) not periodic. Consider two real valued signals, ( ) band-limited to [ 500 Hz, 500 Hz] and ( ) band-limited to [ 1 kHz, 1 kHz]. For ( ) = ( ) ( ), the Nyquist sampling frequency (in kHz) is ______. 3/11 GATE 2014 Q.19 SET1 ELECTRONICS AND COMMUNICATION ENGINEERING EC A continuous, linear time-invariant filter has an impulse response ( ) described by ( ) = 3 for 0 3 0 otherwise When a constant input of value 5 is applied to this filter, the steady state output is _____. Q.20 The forward path transfer function of a unity negative feedback system is given by ( ) = ( + 2)( 1) Consider the feedback system shown in the figure. The Nyquist plot of ( ) is also shown. Which one of the following conclusions is correct? (A) (B) (C) (D) AT E 20 1 Q.21 4) The value of which will place both the poles of the closed-loop system at the same location, is ______ . ( ) is an all-pass filter ( ) is a strictly proper transfer function ( ) is a stable and minimum-phase transfer function The closed-loop system is unstable for sufficiently large and positive In a code-division multiple access (CDMA) system with N = 8 chips, the maximum number of users who can be assigned mutually orthogonal signature sequences is ________ Q.23 The capacity of a Binary Symmetric Channel (BSC) with cross-over probability 0.5 is ________ Q.24 A two-port network has scattering parameters given by [ S ] = 01 (G Q.22 s11 s21 s12 . If the port-2 of the twos22 port is short circuited, the s11 parameter for the resultant one-port network is EC s11 s11s22 + s12 s21 1 + s22 s +s s +s s (C) 11 11 22 12 21 1 s22 (A) Q.25 The force on a point charge + kept at a distance from the surface of an infinite grounded metal plate in a medium of permittivity is 2 (A) 0 2 (C) 16 2 towards the plate EC s11 + s11s22 s12 s21 1 + s22 s s s +s s (D) 11 11 22 12 21 1 s22 (B) (B) 16 2 away from the plate 2 (D) 4 2 towards the plate 4/11 GATE 2014 SET1 ELECTRONICS AND COMMUNICATION ENGINEERING EC Q. 26 Q. 55 carry two marks each. The Taylor series expansion of 3 sin + 2 cos is 3 2 (B) 2 3 + 2 3 2 (D) 2 3 2 + 3 2 (C) 2 + 3 + 2 + Q.27 3 2 + . . . .. + .. + ..... + ..... + For a function ( ), it is given that ( ) = 2 for any real value . + If ( ) = ( ) , then ( ) is (A) 0 (C) (D) 2 2 The volume under the surface ( , ) = + and above the triangle in the x-y plane defined by {0 and 0 12} is _________. Consider the matrix 0 0 0 6 = 0 0 1 (G Q.29 (B) AT E Q.28 2 4) (A) 2 + 3 2 20 1 Q.26 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 A Y-network has resistances of 10 each in two of its arms, while the third arm has a resistance of 11 . In the equivalent -network, the lowest value (in ) among the three resistances is ________. EC Q.30 01 which is obtained by reversing the order of the columns of the identity matrix 6 . Let = 6 + 6 , where is a non-negative real number. The value of for which det( ) = 0 is ________. Q.31 A 230 V rms source supplies power to two loads connected in parallel. The first load draws 10 kW at 0.8 leading power factor and the second one draws 10 kVA at 0.8 lagging power factor. The complex power delivered by the source is (A) (18 + j 1.5) kVA (C) (20 + j 1.5) kVA EC (B) (18 j 1.5) kVA (D) (20 j 1.5) kVA 5/11 GATE 2014 SET1 ELECTRONICS AND COMMUNICATION ENGINEERING EC A periodic variable x is shown in the figure as a function of time. The root-mean-square (rms) value of x is _________. Q.33 In the circuit shown in the figure, the value of capacitor C (in mF) needed to have critically damped response i(t) is________. 40 4H + - 20 1 i(t) C 4) Q.32 Vo A BJT is biased in forward active mode. Assume VBE = 0.7 V, kT/q = 25 mV and reverse saturation current IS = 10-13 A. The transconductance of the BJT (in mA/V) is __________. Q.35 The doping concentrations on the p-side and n-side of a silicon diode are 1 1016 cm-3 and 1 1017 cm-3, respectively. A forward bias of 0.3 V is applied to the diode. At T = 300 K, the = 26 mV. The electron intrinsic carrier concentration of silicon ni = 1.5 1010 cm-3 and AT E Q.34 concentration at the edge of the depletion region on the p-side is A depletion type N-channel MOSFET is biased in its linear region for use as a voltage controlled resistor. Assume threshold voltage VTH = -0.5 V, VGS = 2.0 V, VDS = 5 V, W/L = 100, Cox = 10-8 F/cm2 and n = 800 cm2/V-s. The value of the resistance of the voltage controlled resistor (in ) is __________. EC Q.36 01 (G (A) 2.3 109 cm-3 (B) 1 1016 cm-3 (C) 1 1017 cm-3 (D) 2.25 106 cm-3 EC 6/11 GATE 2014 Q.37 SET1 ELECTRONICS AND COMMUNICATION ENGINEERING EC In the voltage regulator circuit shown in the figure, the op-amp is ideal. The BJT has VBE = 0.7 V and = 100, and the zener voltage is 4.7 V. For a regulated output of 9 V, the value of R (in ) is _______. VI = 12 V VO = 9 V + 1 k 1 k VZ = 4.7 V Q.38 20 1 4) R In the circuit shown, the op-amp has finite input impedance, infinite voltage gain and zero input offset voltage. The output voltage Vout is R1 AT E R2 I1 Vout (G I2 EC 01 (A 2 ( 1 + 2 ) (B) 2 2 (C)) 1 2 (D) 1 ( 1 + 2 ) EC 7/11 GATE 2014 Q.39 SET1 ELECTRONICS AND COMMUNICATION ENGINEERING EC For the amplifier shown in the figure, the BJT parameters are VBE = 0.7 V, = 200, and thermal voltage VT = 25 mV. The voltage gain (vo/vi) of the amplifier is _______ . VCC = +12 V R1 33 k 1 F vo 1 F R2 11 k RS 10 The output in the digital logic circuit shown in the figure is AT E Q.40 CE 1 mF 20 1 RE 1 k 4) vi RC 5 k XOR X AND Y F (G Z XNOR = = = = + + + + EC 01 (A) (B) (C) (D) Q.41 Consider the Boolean function, ( , , , ) = + + + + + . Which one of the following is the complete set of essential prime implicants? (A) (B) (C) (D) EC , , , , , , , , 8/11 GATE 2014 Q.42 SET1 ELECTRONICS AND COMMUNICATION ENGINEERING EC The digital logic shown in the figure satisfies the given state diagram when Q1 is connected to input A of the XOR gate. S=0 S=1 00 A 01 S=0 D1 Q1 D2 Q2 S=1 S=1 S=0 S 11 10 S=1 Q2 Q1 CLK S=0 4) Suppose the XOR gate is replaced by an XNOR gate. Which one of the following options preserves the state diagram? 1 1 (A) is | | > 9 . 1 1 (C) is 3 > | | > 9 . Consider a discrete time periodic signal [ ] = 5 . Let be the complex Fourier series coefficients of [ ]. The coefficients { } are non-zero when = 1, where is any integer. The value of is______. A system is described by the following differential equation, where ( ) is the input to the system and ( ) is the output of the system. 01 Q.45 1 (B) is | | < 3 . (D) does not exist. (G Q.44 1 Let [ ] = ( ) ( 1). The Region of Convergence (ROC) of the z9 3 transform of [ ] AT E Q.43 20 1 (A) Input A is connected to 2 (B) Input A is connected to 2 (C) Input A is connected to 1 and S is complemented (D) Input A is connected to 1 ( ) + 5 ( ) = ( ) When (0) = 1 and ( ) is a unit step function, ( ) is EC (A) 0.2 + 0.8 5 Q.46 (B) 0.2 0.2 5 (C) 0.8 + 0.2 5 Consider the state space model of a system, as given below 1 1 1 0 1 0 2 = 0 1 0 2 + 4 ; = [1 3 0 0 2 3 0 The system is (D) 0.8 0.8 5 1 1 1] 2 . 3 (A) controllable and observable (B) uncontrollable and observable (C) uncontrollable and unobservable (D) controllable and unobservable EC 9/11 GATE 2014 ELECTRONICS AND COMMUNICATION ENGINEERING EC The phase margin in degrees of ( ) = plot is ________. Q.48 10 ( +0.1)( +1)( +10) calculated using the asymptotic Bode 1 For the following feedback system ( ) = ( +1)( +2) . The 2%-settling time of the step response is required to be less than 2 seconds. Which one of the following compensators ( ) achieves this? (B) 5(0.03 + 1) (C) 2( + 4) (D) 4 Let be a real-valued random variable with [ ] and [ 2 ] denoting the mean values of and 2 , respectively. The relation which always holds true is (A) ( [ ])2 > [ 2 ] (B) [ 2 ] ( [ ])2 (C) [ 2 ] = ( [ ])2 (D) [ 2 ] > ( [ ])2 Consider a random process ( ) = 2sin(2 + ), where the random phase is uniformly distributed in the interval [0,2 ]. The auto-correlation [ ( 1 ) ( 2 )] is (G Q.50 +8 +3 AT E Q.49 1 +5 20 1 (A 3 4) Q.47 SET1 (A) cos 2 ( 1 + 2 ) 01 (B) sin 2 ( 1 2 ) (C) sin 2 ( 1 + 2 ) EC (D) cos 2 ( 1 2 ) EC 10/11 GATE 2014 Q.51 SET1 ELECTRONICS AND COMMUNICATION ENGINEERING EC Let ( ) be the BER of a BPSK system over an AWGN channel with two-sided noise power spectral density 0 2. The parameter is a function of bit energy and noise power spectral density. A system with two independent and identical AWGN channels with noise power spectral density 0 2 is shown in the figure. The BPSK demodulator receives the sum of outputs of both the channels. AWGN Channel 1 BPSK Demodulator BPSK Modulator 20 1 AWGN Channel 2 0 /1 4) 0 /1 If the BER of this system is ( ), then the value of is _____. A fair coin is tossed repeatedly until a Head appears for the first time. Let L be the number of tosses to get this first Head . The entropy H(L) in bits is ________. Q.53 In spherical coordinates, let , denote unit vectors along the , directions. AT E Q.52 = and = 100 sin cos( ) / 0.265 sin cos( ) / (G represent the electric and magnetic field components of the EM wave at large distances from a dipole antenna, in free space. The average power (W) crossing the hemispherical shell located at = 1 , 0 /2 is ________ For a parallel plate transmission line, let be the speed of propagation and be the characteristic impedance. Neglecting fringe effects, a reduction of the spacing between the plates by a factor of two results in 01 Q.54 halving of and no change in no changes in and halving of no change in both and halving of both and EC (A) (B) (C) (D) Q.55 The input impedance of a section of a lossless transmission line of characteristic impedance 8 R + jX ) . If X is 50 is found to be real when the other end is terminated by a load Z L ( = 30 , the value of R ( in ) is _______ END OF THE QUESTION PAPER EC 11/11 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. 3. Any useful data required for your paper can be viewed by clicking on the Useful Common Data button that appears on the screen. 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. 6. The Question Palette displayed on the right side of screen will show the status of each question using one of the following symbols: 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 : 7. To answer a question, do the following: a. Click on the question number in the Question Palette to go to that question directly. 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. 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. You can view all the questions by clicking on the Question Paper button. This feature is provided, so that if you want you can just see the entire question paper at a glance. Answering a Question : 8. Procedure for answering a multiple choice (MCQ) type question: a. Choose one answer from the 4 options (A,B,C,D) given below the question, click on the bubble placed before the chosen option. b. To deselect your chosen answer, click on the bubble of the chosen option again or click on the Clear Response button. c. To change your chosen answer, click on the bubble of another option. d. To save your answer, you MUST click on the Save & Next button. 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. c. To clear your answer, click on the Clear Response button. d. To save your answer, you MUST click on the Save & Next button 10. To mark a question for review, click on the Mark for Review & Next button. If an answer is selected (for MCQ) or entered (for numerical answer type) for a question that is Marked for Review, that answer will be considered in the evaluation unless the status is modified by the candidate. 11. To change your answer to a question that has already been answered, first select that question for answering and then follow the procedure for answering that type of question. 12. Note that ONLY Questions for which answers are saved or marked for review after answering will be considered for evaluation. Choosing a Section : 13. Sections in this question paper are displayed on the top bar of the screen. Questions in a Section can be viewed by clicking on the name of that Section. The Section you are currently viewing will be highlighted. 14. A checkbox is displayed for every optional Section, if any, in the Question Paper. To select the optional Section for answering, click on the checkbox for that Section. 15. If the checkbox for an optional Section is not selected, the Save & Next button and the Mark for Review & Next button will NOT be enabled for that Section. You will only be able to see questions in this Section, but you will not be able to answer questions in the Section. 16. After clicking the Save & Next button for the last question in a Section, you will automatically be taken to the first question of the next Section in sequence. 17. You can move the mouse cursor over the name of a Section to view the answering status for that Section. Changing the Optional Section : 18. After answering the chosen optional Section, partially or completely, you can change the optional Section by selecting the checkbox for a new Section that you want to attempt. A warning message will appear along with a table showing the number of questions answered in each of the previously chosen optional Sections and a checkbox against each of these Sections. Click on a checkbox against a Section that you want to reset and then click on the RESET button. Note that RESETTING a Section will DELETE all the answers for questions in that Section. Hence, if you think that you may want to select this Section again later, you will have to note down your answers for questions in that Section. If you do not want to reset the Section and want to continue answering the previously chosen optional Section, then click on the BACK button. 19. If you deselect the checkbox for an optional Section in the top bar, the following warning message will appear: "Deselecting the checkbox will DELETE all the answers for questions in this Section. Do you want to deselect this Section? If you want to deselect, click on the RESET button. If you do not want to deselect, click on the BACK button. 20. You can shuffle between different Sections or change the optional Sections any number of times. 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 of marks for a 1-mark question and 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- 4 General Aptitude -GA Q. 1 Q. 5 carry one mark each. Q.1 Choose the most appropriate word from the options given below to complete the following sentence. Communication and interpersonal skills are (A) each Q.2 important in their own ways. (B) both (C) all (D) either Which of the options given below best completes the following sentence? She will feel much better if she ________________. Q.3 (B) gets some rest (D) is getting some rest 20 14 ) (A) will get some rest (C) will be getting some rest Choose the most appropriate pair of words from the options given below to complete the following sentence. She could not _____ the thought of _________ the election to her bitter rival. (A) bear, loosing (D) bare, losing E A regular die has six sides with numbers 1 to 6 marked on its sides. If a very large number of throws show the following frequencies of occurrence: 1 0.167; 2 0.167; 3 0.152; 4 0.166; 5 0.168; 6 0.180. We call this die (A) irregular Q.5 (C) bear, losing (B) biased (C) Gaussian AT Q.4 (B) bare, loosing (D) insufficient Fill in the missing number in the series. 3 6 15 157.5 630 (G 2 Find the odd one in the following group A0 Q.6 4 Q. 6 Q. 10 carry two marks each. Q,W,Z,B (A) Q,W,Z,B W,C,G,J (C) W,C,G,J M,S,V,X (D) M,S,V,X Lights of four colors (red, blue, green, yellow) are hung on a ladder. On every step of the ladder there are two lights. If one of the lights is red, the other light on that step will always be blue. If one of the lights on a step is green, the other light on that step will always be yellow. Which of the following statements is not necessarily correct? G Q.7 (B) B,H,K,M B,H,K,M (A) The number of red lights is equal to the number of blue lights (B) The number of green lights is equal to the number of yellow lights (C) The sum of the red and green lights is equal to the sum of the yellow and blue lights (D) The sum of the red and blue lights is equal to the sum of the green and yellow lights Q.8 GA The sum of eight consecutive odd numbers is 656. The average of four consecutive even numbers is 87. What is the sum of the smallest odd number and second largest even number? 1/2 GATE 2014 Q.9 SET- 4 General Aptitude -GA The total exports and revenues from the exports of a country are given in the two charts shown below. The pie chart for exports shows the quantity of each item exported as a percentage of the total quantity of exports. The pie chart for the revenues shows the percentage of the total revenue generated through export of each item. The total quantity of exports of all the items is 500 thousand tonnes and the total revenues are 250 crore rupees. Which item among the following has generated the maximum revenue per kg? Revenues Exports Item 1 11% Item 6 19% Item 5 12% Item 2 20% Item 3 19% Item 4 22% Item 4 6% (C) Item 6 Item 3 23% (D) Item 5 It takes 30 minutes to empty a half-full tank by draining it at a constant rate. It is decided to simultaneously pump water into the half-full tank while draining it. What is the rate at which water has to be pumped in so that it gets fully filled in 10 minutes? AT Q.10 (B) Item 3 Item 2 20% Item 5 20% E (A) Item 2 Item 1 12% 20 14 ) Item 6 16% (B) 3 times the draining rate (D) 2 times the draining rate (G (A) 4 times the draining rate (C) 2.5 times the draining rate G A0 4 END OF THE QUESTION PAPER GA 2/2 GATE 2014 SET2 ELECTRONICS AND COMMUNICATION ENGINEERING EC Q. 1 Q. 25 carry one mark each. Q.1 Q.3 Let X be a random variable which is uniformly chosen from the set of positive odd numbers less than 100. The expectation, [ ], is __________. Q.4 (A) = log 4 For 0 < , the maximum value of the function ( ) = 2 2 occurs at is (A) 2 Q.5 (C) = 0 1 lim 1 + (B) 1.0 (C) (D) = log 8 4) The value of (B) = log 2 20 1 Q.2 The determinant of matrix is 5 and the determinant of matrix is 40. The determinant of matrix is ________. (D) If the characteristic equation of the differential equation AT E 2 +2 + =0 2 has two equal roots, then the values of are (A) 1 (C) j (D) 1/2 Norton s theorem states that a complex network connected to a load can be replaced with an equivalent impedance (G Q.6 (B) 0,0 In the figure shown, the ideal switch has been open for a long time. If it is closed at = 0, then the magnitude of the current (in mA) through the 4 k resistor at = 0+ is _______. EC Q.7 02 (A) in series with a current source (B) in parallel with a voltage source (C) in series with a voltage source (D) in parallel with a current source Q.8 A silicon bar is doped with donor impurities ND = 2.25 x 1015 atoms / cm3. Given the intrinsic carrier concentration of silicon at T = 300 K is ni = 1.5 x 1010 cm-3. Assuming complete impurity ionization, the equilibrium electron and hole concentrations are (A) (B) (C) (D) EC n0 = 1.5 x 1016 cm-3, p0 = 1.5 x 105 cm-3 n0 = 1.5 x 1010 cm-3, p0= 1.5 x 1015 cm-3 n0 = 2.25 x 1015 cm-3, p0 = 1.5 x 1010 cm-3 n0 = 2.25 x 1015 cm-3, p0 = 1 x 105 cm-3 1/12 GATE 2014 Q.9 SET2 ELECTRONICS AND COMMUNICATION ENGINEERING EC An increase in the base recombination of a BJT will increase (A) the common emitter dc current gain (B) the breakdown voltage BVCEO (C) the unity-gain cut-off frequency fT (D) the transconductance gm Q.10 In CMOS technology, shallow P-well or N-well regions can be formed using The feedback topology in the amplifier circuit ( the base bias circuit is not shown for simplicity) in the figure is (G AT E 20 1 Q.11 4) (A) low pressure chemical vapour deposition (B) low energy sputtering (C) low temperature dry oxidation (D) low energy ion-implantation EC 02 (A) Voltage shunt feedback (B) Current series feedback (C) Current shunt feedback (D) Voltage series feedback EC 2/12 GATE 2014 Q.13 ELECTRONICS AND COMMUNICATION ENGINEERING EC 4) In the differential amplifier shown in the figure, the magnitudes of the common-mode and differential-mode gains are and , respectively. If the resistance RE is increased, then (A) increases (C) increases (B) common-mode rejection ratio increases (D) common-mode rejection ratio decreases 20 1 Q.12 SET2 A cascade connection of two voltage amplifiers A1 and A2 is shown in the figure. The open-loop gain Av0 , input resistance R in , and output resistance R o for A1 and A2 are as follows: A1: Av0 = 10, R in = 10 k , R o = 1 k . A2: Av0 = 5, R in = 5 k , R o = 200 . Q.14 (G AT E The approximate overall voltage gain vout/vin is __________. For an n-variable Boolean function, the maximum number of prime implicants is (A) 2(n-1) (B) n/2 (C) 2n (D) 2(n-1) The number of bytes required to represent the decimal number 1856357 in packed BCD (Binary Coded Decimal) form is __________ . Q.16 In a half-subtractor circuit with X and Y as inputs, the Borrow (M) and Difference (N = X - Y) are given by EC 02 Q.15 (A) (B) (C) (D) Q.17 = = = = , = , = , = , = An FIR system is described by the system function The system is (A) maximum phase EC 7 3 ( ) = 1 + z 1 + z 2 2 2 (B) minimum phase (C) mixed phase (D) zero phase 3/12 GATE 2014 Q.18 SET2 Let [ ] = [ ]. Let ( ) be the -transform of [ ]. If 0.5 + 0.25 is a zero of ( ), which one of the following must also be a zero of ( ). (A) 0.5 0.25 (B) 1/(0.5 + 0.25) (C) 1/(0.5 0.25) (D) 2+ 4 Consider the periodic square wave in the figure shown. 4) Q.19 ELECTRONICS AND COMMUNICATION ENGINEERING EC 20 1 The ratio of the power in the 7th harmonic to the power in the 5th harmonic for this waveform is closest in value to _______. Q.20 The natural frequency of an undamped second-order system is 40 rad/s. If the system is damped with a damping ratio 0.3, the damped natural frequency in rad/s is ________. Q.21 For the following system, AT E X2 (s) + X1 (s) (G - when 1 ( ) = 0, the transfer function (B) 1 +1 ( ) 2 ( ) 1 s Y(s) is (C) +2 ( +1) (D) +1 ( +2) The capacity of a band-limited additive white Gaussian noise (AWGN) channel is given by = log 2 1 + 2 bits per second (bps), where is the channel bandwidth, is the average power received and 2 is the one-sided power spectral density of the AWGN. EC Q.22 +1 2 02 (A) + s s+1 + For a fixed 2 = 1000, the channel capacity (in kbps) with infinite bandwidth ( ) is approximately (A) 1.44 Q.23 EC (B) 1.08 (C) 0.72 (D) 0.36 Consider sinusoidal modulation in an AM system. Assuming no overmodulation, the modulation index ( ) when the maximum and minimum values of the envelope, respectively, are 3 V and 1 V, is ________. 4/12 GATE 2014 Q.24 SET2 ELECTRONICS AND COMMUNICATION ENGINEERING EC To maximize power transfer, a lossless transmission line is to be matched to a resistive load impedance via a /4 transformer as shown. lossless transmission line /4 transformer ZL = 100 Zin =50 Which one of the following field patterns represents a TEM wave travelling in the positive direction? 20 1 Q.25 4) The characteristic impedance (in ) of the /4 transformer is _________. (A) = +8 , = 4 (C) = +2 , = +2 (B) = 2 , = 3 (D) = 3 , = +4 Q.26 The system of linear equations 2 1 3 0 1 2 3 5 1 = 4 has 5 14 02 The real part of an analytic function ( ) where = + is given by cos( ). The imaginary part of ( ) is Q.28 (A) cos( ) Q.29 If EC (B) sin( ) (C) sin( ) (D) sin( ) The maximum value of the determinant among all 2 2 real symmetric matrices with trace 14 is ________. EC Q.30 (G (A) a unique solution (B) infinitely many solutions (C) no solution (D) exactly two solutions Q.27 AT E Q. 26 Q. 55 carry two marks each. x + ya y + za z and r r = xa = r, then div 2 (ln ) = ______ . A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1 H, 1 F and 1 , respectively, the operating angular frequency (in rad/s) is ________. 5/12 GATE 2014 Q.31 SET2 ELECTRONICS AND COMMUNICATION ENGINEERING EC In the h-parameter model of the 2-port network given in the figure shown, the value of 22 (in S) is ______ . 3 3 1 2 2 1' 2' 2 4) 2 In the figure shown, the capacitor is initially uncharged. Which one of the following expressions describes the current I(t) (in mA) for > 0? 20 1 Q.32 3 Q.33 (C) I( ) = 5 1 / , 3 5 1 / , 3 = 2 3 msec = 3 msec 5 1 / , 2 5 1 / , 2 (D) I( ) = = 2 3 msec = 3 msec In the magnetically coupled circuit shown in the figure, 56 % of the total flux emanating from one coil links the other coil. The value of the mutual inductance (in H) is ______ . M (G 10 4H 5H (1/16) F 02 60cos(4t + 300 ) V Assume electronic charge q = 1.6 10-19 C, kT/q = 25 mV and electron mobility n = 1000 cm2/V-s. If the concentration gradient of electrons injected into a P-type silicon sample is 1 1021/cm4, the magnitude of electron diffusion current density (in A/cm2) is _________. EC Q.34 (B) I( ) = AT E (A) I( ) = Q.35 EC Consider an abrupt PN junction (at T = 300 K) shown in the figure. The depletion region width Xn on the N-side of the junction is 0.2 m and the permittivity of silicon ( si) is 1.044 10-12 F/cm. At the junction, the approximate value of the peak electric field (in kV/cm) is _________. 6/12 GATE 2014 Q.36 ELECTRONICS AND COMMUNICATION ENGINEERING EC When a silicon diode having a doping concentration of NA = 9 1016 cm-3 on p-side and ND = 1 1016 cm-3 on n-side is reverse biased, the total depletion width is found to be 3 m. Given that the permittivity of silicon is 1.04 10 12 F/cm, the depletion width on the p-side and the maximum electric field in the depletion region, respectively, are (A) (B) (C) (D) 2.7 m 0.3 m 0.3 m 2.1 m and 2.3 105 V/cm and 4.15 105 V/cm and 0.42 105 V/cm and 0.42 105 V/cm The diode in the circuit shown has Von = 0.7 Volts but is ideal otherwise. If Vi = 5 sin( )Volts, the minimum and maximum values of Vo (in Volts) are, respectively, 20 1 4) Q.37 SET2 AT E (B) 2.7 and 5 (D) 1.3 and 5 For the n-channel MOS transistor shown in the figure, the threshold voltage VTh is 0.8 V. Neglect channel length modulation effects. When the drain voltage VD = 1.6 V, the drain current ID was found to be 0.5 mA. If VD is adjusted to be 2 V by changing the values of R and VDD , the new value of ID (in mA) is 02 (G Q.38 (A) 5 and 2.7 (C) 5 and 3.85 EC (A) 0.625 EC (B) 0.75 (C) 1.125 (D) 1.5 7/12 GATE 2014 Q.39 SET2 ELECTRONICS AND COMMUNICATION ENGINEERING EC For the MOSFETs shown in the figure, the threshold voltage |Vt| = 2 V and K= 1 W Cox 2 L 2 = 0.1 mA/V . The value of ID (in mA) is _______ . VDD = +12 V R1 10 k ID 20 1 4) R2 10 k VSS = 5 V In the circuit shown, choose the correct timing diagram of the output (y) from the given waveforms W1, W2, W3 and W4. EC 02 (G AT E Q.40 (A) W1 EC (B) W2 (C) W3 (D) W4 8/12 GATE 2014 Q.41 SET2 ELECTRONICS AND COMMUNICATION ENGINEERING EC The outputs of the two flip-flops Q1, Q2 in the figure shown are initialized to 0, 0. The sequence generated at Q1 upon application of clock signal is Q1 J1 Q1 J2 Q2 K1 Q1 K2 Q2 A2 A1 A0 AT E For the 8085 microprocessor, the interfacing circuit to input 8-bit digital data (DI0 DI7) from an external device is shown in the figure. The instruction for correct data transfer is 3-to-8 7 Decoder 6 C 5 4 B 3 2 A 1 0 G 2A G 2B G1 IO/M RD Digital Inputs DI0 DI7 DS1 DO0 DO7 Data Bus (D0 D7) DS2 A8 A9 A10 A11 A12 02 A3 A4 A5 A6 A7 I/O Device (G Q.42 01110 01010 00110 01100 20 1 (A) (B) (C) (D) 4) CLK A13 A14 EC (A) MVI A, F8H Q.43 Q.44 A15 (B) IN F8H (C) OUT F8H (D) LDA F8F8H Consider a discrete-time signal [ ] = for 0 10 . 0 otherwise If [ ] is the convolution of [ ] with itself, the value of [4] is _________. The input-output relationship of a causal stable LTI system is given as [ ] = [ 1] + [ ] If the impulse response [ ] of this system satisfies the condition =0 [ ] = 2, the relationship between and is EC (A) = 1 /2 (B) = 1 + /2 (C) = 2 (D) = 2 9/12 GATE 2014 Q.45 Q.46 SET2 ELECTRONICS AND COMMUNICATION ENGINEERING EC The value of the integral sinc 2 (5 ) is ________. An unforced linear time invariant (LTI) system is represented by 1 1 0 1 = 2 0 2 2 If the initial conditions are 1 (0) = 1 and 2 (0) = 1, the solution of the state equation is 20 1 The Bode asymptotic magnitude plot of a minimum phase system is shown in the figure. AT E Q.47 1 ( ) = 1, 2 ( ) = 2 1 ( ) = , 2 ( ) = 2 1 ( ) = , 2 ( ) = 2 1 ( ) = , 2 ( ) = 2 4) (A) (B) (C) (D) Consider the state space system expressed by the signal flow diagram shown in the figure. EC 02 Q.48 (G If the system is connected in a unity negative feedback configuration, the steady state error of the closed loop system, to a unit ramp input, is_________. The corresponding system is (A) always controllable (C) always stable EC (B) always observable (D) always unstable 10/12 GATE 2014 SET2 ELECTRONICS AND COMMUNICATION ENGINEERING EC Q.49 The input to a 1-bit quantizer is a random variable with pdf ( ) = 2 2 for 0 and ( ) = 0 for < 0. For outputs to be of equal probability, the quantizer threshold should be _____. Q.50 Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol waveforms 1 ( ) = cos 2 1 and 2 ( ) = cos 2 2 , where = 4 mV. Assume an AWGN channel with two-sided noise power spectral density 0 = 0.5 10 12 W/Hz. Using an optimal 2 500 kbps is (A) (2) (B) 2 2 (C) (4) (D) 4 2 The power spectral density of a real stationary random process ( ) is given by ( ) = 1 , 0, The value of the expectation ( ) | | 1 4 | | > . is_________. In the figure, ( ) is the Fourier transform of the message signal ( ) where A = 100 Hz and B = 40 Hz. Given ( ) = cos(2 ) and ( ) = cos(2 ( + ) ), where > . The cutoff frequencies of both the filters are . AT E Q.52 , the bit error probability for a data rate of 20 1 Q.51 2 1 2 2 4) receiver and the relation ( ) = M(f) (G 1 -A m(t) -B B A Low Pass Filter 02 High Pass Filter v(t) f s(t) w(t) EC The bandwidth of the signal at the output of the modulator (in Hz) is _____. Q.53 If the electric field of a plane wave is ( , ) = 3cos( + 30 ) 4sin( + 45 ) (mV/m), the polarization state of the plane wave is (A) left elliptical (B) left circular (C) right elliptical (D) right circular EC 11/12 GATE 2014 SET2 ELECTRONICS AND COMMUNICATION ENGINEERING EC In the transmission line shown, the impedance Zin (in ohms) between node A and the ground is _________. Q.55 For a rectangular waveguide of internal dimensions ( > ), the cut-off frequency for the TE11 mode is the arithmetic mean of the cut-off frequencies for TE10 mode and TE20 mode. If 20 1 = 5 cm, the value of (in cm) is _____. 4) Q.54 EC 02 (G AT E END OF THE QUESTION PAPER EC 12/12 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. 3. Any useful data required for your paper can be viewed by clicking on the Useful Common Data button that appears on the screen. 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. 6. The Question Palette displayed on the right side of screen will show the status of each question using one of the following symbols: 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 : 7. To answer a question, do the following: a. Click on the question number in the Question Palette to go to that question directly. 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. 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. You can view all the questions by clicking on the Question Paper button. This feature is provided, so that if you want you can just see the entire question paper at a glance. Answering a Question : 8. Procedure for answering a multiple choice (MCQ) type question: a. Choose one answer from the 4 options (A,B,C,D) given below the question, click on the bubble placed before the chosen option. b. To deselect your chosen answer, click on the bubble of the chosen option again or click on the Clear Response button. c. To change your chosen answer, click on the bubble of another option. d. To save your answer, you MUST click on the Save & Next button. 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. c. To clear your answer, click on the Clear Response button. d. To save your answer, you MUST click on the Save & Next button 10. To mark a question for review, click on the Mark for Review & Next button. If an answer is selected (for MCQ) or entered (for numerical answer type) for a question that is Marked for Review, that answer will be considered in the evaluation unless the status is modified by the candidate. 11. To change your answer to a question that has already been answered, first select that question for answering and then follow the procedure for answering that type of question. 12. Note that ONLY Questions for which answers are saved or marked for review after answering will be considered for evaluation. Choosing a Section : 13. Sections in this question paper are displayed on the top bar of the screen. Questions in a Section can be viewed by clicking on the name of that Section. The Section you are currently viewing will be highlighted. 14. A checkbox is displayed for every optional Section, if any, in the Question Paper. To select the optional Section for answering, click on the checkbox for that Section. 15. If the checkbox for an optional Section is not selected, the Save & Next button and the Mark for Review & Next button will NOT be enabled for that Section. You will only be able to see questions in this Section, but you will not be able to answer questions in the Section. 16. After clicking the Save & Next button for the last question in a Section, you will automatically be taken to the first question of the next Section in sequence. 17. You can move the mouse cursor over the name of a Section to view the answering status for that Section. Changing the Optional Section : 18. After answering the chosen optional Section, partially or completely, you can change the optional Section by selecting the checkbox for a new Section that you want to attempt. A warning message will appear along with a table showing the number of questions answered in each of the previously chosen optional Sections and a checkbox against each of these Sections. Click on a checkbox against a Section that you want to reset and then click on the RESET button. Note that RESETTING a Section will DELETE all the answers for questions in that Section. Hence, if you think that you may want to select this Section again later, you will have to note down your answers for questions in that Section. If you do not want to reset the Section and want to continue answering the previously chosen optional Section, then click on the BACK button. 19. If you deselect the checkbox for an optional Section in the top bar, the following warning message will appear: "Deselecting the checkbox will DELETE all the answers for questions in this Section. Do you want to deselect this Section? If you want to deselect, click on the RESET button. If you do not want to deselect, click on the BACK button. 20. You can shuffle between different Sections or change the optional Sections any number of times. 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 of marks for a 1-mark question and 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- 5 General Aptitude -GA Q. 1 Q. 5 carry one mark each. Q.1 India is a country of rich heritage and cultural diversity. Which one of the following facts best supports the claim made in the above sentence? (A) India is a union of 28 states and 7 union territories. (B) India has a population of over 1.1 billion. (C) India is home to 22 official languages and thousands of dialects. (D) The Indian cricket team draws players from over ten states. The value of one U.S. dollar is 65 Indian Rupees today, compared to 60 last year. The Indian Rupee has ____________. (A) depressed Q.3 (B) depreciated 20 14 ) Q.2 (C) appreciated (D) stabilized (C) an adjective (D) both a verb and a noun 'Advice' is ________________. (A) a verb (B) a noun The next term in the series 81, 54, 36, 24, is ________ Q.5 In which of the following options will the expression P < M be definitely true? (B) M > S < P < F (C) Q < M < F = P AT (A) M < R > P > S E Q.4 (D) P = A < R < M Q. 6 Q. 10 carry two marks each. Find the next term in the sequence: 7G, 11K, 13M, ___ (B) 17Q (C) 15P (D) 17P G A0 5 (A) 15Q (G Q.6 GA 1/3 GATE 2014 General Aptitude -GA The multi-level hierarchical pie chart shows the population of animals in a reserve forest. The correct conclusions from this information are: AT E 20 14 ) Q.7 SET- 5 (G (i) Butterflies are birds (ii) There are more tigers in this forest than red ants (iii) All reptiles in this forest are either snakes or crocodiles (iv) Elephants are the largest mammals in this forest (A) (i) and (ii) only (C) (i), (iii) and (iv) only A man can row at 8 km per hour in still water. If it takes him thrice as long to row upstream, as to row downstream, then find the stream velocity in km per hour. G A0 5 Q.8 (B) (i), (ii), (iii) and (iv) (D) (i), (ii) and (iii) only GA 2/3 GATE 2014 SET- 5 General Aptitude -GA 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%. If the company registered a profit of Rs. 10 lakhs in 2012, at what price (in Rs.) was each air purifier sold? Q.10 A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch is rejected if even one of the bulbs is defective. A batch typically has five defective bulbs. The probability that the current batch is accepted is (G AT E 20 14 ) Q.9 G A0 5 END OF THE QUESTION PAPER GA 3/3 GATE 2014 SET3 ELECTRONICS AND COMMUNICATION ENGINEERING EC Q. 1 Q. 25 carry one mark each. Q.1 The maximum value of the function ( ) = (1 + ) (where > 1) occurs at =______. Q.2 Which ONE of the following is a linear non-homogeneous differential equation, where x and y are the independent and dependent variables respectively? (C) (D) Q.3 + = + = 0 + = 4) (B) + = 0 20 1 (A) Match the application to appropriate numerical method. Application Numerical |Method P1: P2: P3: P4: M1: M2: M3: M4: Newton-Raphson Method Runge-Kutta Method Simpson s 1/3-rule Gauss Elimination Method AT E Numerical integration Solution to a transcendental equation Solution to a system of linear equations Solution to a differential equation An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is 03 Q.4 (G (A) P1 M3, P2 M2, P3 M4, P4 M1 (B) P1 M3, P2 M1, P3 M4, P4 M2 (C) P1 M4, P2 M1, P3 M3, P4 M2 (D) P1 M2, P2 M1, P3 M3, P4 M4 (A) 0.067 z z +y = 0 x y z z (C) x =y x y (A) x EC (C) 0.082 (D) 0.091 If z = xy ln( xy ), then EC Q.5 (B) 0.073 z z =x x y z z (D) y +x = 0 x y (B) y 1/14 GATE 2014 Q.6 SET3 ELECTRONICS AND COMMUNICATION ENGINEERING EC A series RC circuit is connected to a DC voltage source at time t = 0. The relation between the source voltage VS, the resistance R, the capacitance C, and the current i(t) is given below: 1 = ( ) + ( ) . Which one of the following represents the current i(t)? (A) (B) i(t) 0 0 t (D) t AT E (C) i(t) (G i(t) 0 0 t 03 t In the figure shown, the value of the current I (in Amperes) is __________. EC Q.7 20 1 4) i(t) Q.8 In MOSFET fabrication, the channel length is defined during the process of (A) isolation oxide growth (B) channel stop implantation (C) poly-silicon gate patterning (D) lithography step leading to the contact pads EC 2/14 GATE 2014 Q.9 SET3 ELECTRONICS AND COMMUNICATION ENGINEERING EC A thin P-type silicon sample is uniformly illuminated with light which generates excess carriers. The recombination rate is directly proportional to (A) the minority carrier mobility (B) the minority carrier recombination lifetime (C) the majority carrier concentration (D) the excess minority carrier concentration At T = 300 K, the hole mobility of a semiconductor = 500 cm2 /V-s and hole diffusion constant in cm2 /s is ________ The desirable characteristics of a transconductance amplifier are (A) (B) (C) (D) In the circuit shown, the PNP transistor has | | = 0.7 Vand = 50. Assume that = 100 . For V0 to be 5 V, the value of (in ) is _______ AT E Q.12 high input resistance and high output resistance high input resistance and low output resistance low input resistance and high output resistance low input resistance and low output resistance = 26 mV. The 20 1 Q.11 4) Q.10 RC (G V0 The figure shows a half-wave rectifier. The diode D is ideal. The average steady-state current (in Amperes) through the diode is approximately ____________. EC Q.13 V EE = 10 V 03 RB Q.14 EC An analog voltage in the range 0 to 8 V is divided in 16 equal intervals for conversion to 4-bit digital output. The maximum quantization error (in V) is _________ 3/14 GATE 2014 Q.15 SET3 ELECTRONICS AND COMMUNICATION ENGINEERING EC The circuit shown in the figure is a D Q Q D Latch En D Latch Q En Q Clk 20 1 Q.16 4) (A) Toggle Flip Flop (B) JK Flip Flop (C) SR Latch (D) Master-Slave D Flip Flop Consider the multiplexer based logic circuit shown in the figure. 0 MUX 1 0 MUX 1 F AT E W S1 S2 Which one of the following Boolean functions is realized by the circuit? 1 2 1 + 2 + 1 2 + 1 + 2 1 2 Let ( ) = cos(10 ) + cos(30 ) be sampled at 20 Hz and reconstructed using an ideal low-pass filter with cut-off frequency of 20 Hz. The frequency/frequencies present in the reconstructed signal is/are 03 Q.17 = = = = (G (A) (B) (C) (D) EC (A) 5 Hz and 15 Hz only (C) 5 Hz, 10 Hz and 15 Hz only Q.18 For an all-pass system ( ) = ( 1 ) (1 1 ) If Re( ) 0, Im( ) 0, then b equals (A) EC (B) (B) 10 Hz and 15 Hz only (D) 5 Hz only , where = 1, for all . (C) 1/ (D) 1/ 4/14 GATE 2014 SET3 ELECTRONICS AND COMMUNICATION ENGINEERING EC A modulated signal is ( ) = ( ) cos(40000 ), where the baseband signal ( ) has frequency components less than 5 kHz only. The minimum required rate (in kHz) at which ( ) should be sampled to recover ( ) is _______. Q.20 Consider the following block diagram in the figure. 2 1 2 1 (A)1+ ( ) ( ) 20 1 The transfer function 4) Q.19 is (B) 1 2 + 1 + 1 (C) 1 2 + 2 + 1 (D)1+ 1 AT E 1 2 The input 3e2 ( ), where ( ) is the unit step function, is applied to a system with transfer 2 function +3. If the initial value of the output is 2, then the value of the output at steady state is _______. Q.22 The phase response of a passband waveform at the receiver is given by (G Q.21 ( ) = 2 ( ) 2 03 where is the centre frequency, and and are positive constants. The actual signal propagation delay from the transmitter to receiver is + EC (A) Q.23 Q.24 EC (B) + (C) (D) Consider an FM signal ( ) = cos[2 + 1 sin 2 1 + 2 sin 2 2 ]. The maximum deviation of the instantaneous frequency from the carrier frequency is (A) 1 1 + 2 2 (C) 1 + 2 (B) 1 2 + 2 1 (D) 1 + 2 Consider an air filled rectangular waveguide with a cross-section of 5 cm 3 cm. For this waveguide, the cut-off frequency (in MHz) of TE21 mode is _________. 5/14 GATE 2014 Q.25 SET3 ELECTRONICS AND COMMUNICATION ENGINEERING EC In the following figure, the transmitter Tx sends a wideband modulated RF signal via a coaxial cable to the receiver Rx. The output impedance ZT of Tx, the characteristic impedance Z0 of the cable and the input impedance ZR of Rx are all real. The signal gets distorted if ZR Z0, irrespective of the value of ZT The signal gets distorted if ZT Z0, irrespective of the value of ZR Signal distortion implies impedance mismatch at both ends: ZT Z0 and ZR Z0 Impedance mismatches do NOT result in signal distortion but reduce power transfer efficiency Q. 26 Q. 55 carry two marks each. Q.28 Which one of the following statements is NOT true for a square matrix ? (A) If is upper triangular, the eigenvalues of are the diagonal elements of it (B) If is real symmetric, the eigenvalues of are always real and positive (C) If is real, the eigenvalues of and are always the same (D) If all the principal minors of are positive, all the eigenvalues of are also positive A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is ______ . Let X1, X2, and X3 be independent and identically distributed random variables with the uniform distribution on [0, 1]. The probability P{X1+ X2 X3} is ________. EC 03 Q.29 AT E Q.27 The maximum value of ( ) = 2 3 9 2 + 12 3 in the interval 0 3 is _______. (G Q.26 20 1 (A) (B) (C) (D) 4) Which one of the following statements is TRUE about the distortion of the received signal due to impedance mismatch? EC 6/14 GATE 2014 Q.30 SET3 ELECTRONICS AND COMMUNICATION ENGINEERING EC Consider the building block called Network N shown in the figure. Let C = 100 F and R = 10 k . Network N + V1(s) + C V2(s) R - - V1(s) C R N Network - The transfer function - 2 V3(s) - 2 2+ (C) 1+ (D) (C) 22 j 2 V (D) 2 j 22 V In the circuit shown in the figure, the value of node voltage 2 is 03 (G Q.31 Network N of the cascaded network is (B) 1+3 + 2 + AT E (A) 1+ 3 ( ) 1 ( ) + 20 1 + 4) Two such blocks are connected in cascade, as shown in the figure. (B) 2 + j 22 V EC (A) 22 + j 2 V Q.32 EC In the circuit shown in the figure, the angular frequency (in rad/s), at which the Norton equivalent impedance as seen from terminals b-b is purely resistive, is _________. 7/14 GATE 2014 Q.33 SET3 ELECTRONICS AND COMMUNICATION ENGINEERING EC For the Y-network shown in the figure, the value of R1 (in ) in the equivalent -network is ____. R1 5 Q.34 20 1 4) 7.5 3 The donor and accepter impurities in an abrupt junction silicon diode are 1 x 1016 cm-3 and 5 x 1018 cm-3, respectively. Assume that the intrinsic carrier concentration in silicon ni = 1.5 x 1010 cm-3 at = 26 mV and the permittivity of silicon = 1.04 10 12 F/cm. The built-in potential 300 K, (A) (B) (C) (D) The slope of the vs. curve of an n-channel MOSFET in linear regime is 10 3 1 at = 0.1 V. For the same device, neglecting channel length modulation, the slope of the vs. curve (in A/V) under saturation regime is approximately _________. An ideal MOS capacitor has boron doping-concentration of 1015 cm-3 in the substrate. When a gate voltage is applied, a depletion region of width 0.5 m is formed with a surface (channel) potential of 0.2 V. Given that 0 = 8.854 10-14 F/cm and the relative permittivities of silicon and silicon dioxide are 12 and 4, respectively, the peak electric field (in V/ m) in the oxide region is _____________. EC 03 Q.36 0.7 V and 1 x 10-4 cm 0.86 V and 1 x 10-4 cm 0.7 V and 3.3 x 10-5 cm 0.86 V and 3.3 x 10-5 cm (G Q.35 AT E and the depletion width of the diode under thermal equilibrium conditions, respectively, are EC 8/14 GATE 2014 In the circuit shown, the silicon BJT has = 50. Assume VBE = 0.7 V and VCE(sat) = 0.2 V. Which one of the following statements is correct? 5 V 2 1 3 2 4) AT E Assuming that the Op-amp in the circuit shown is ideal, Vo is given by (A) Q.39 For RC = 1 k , the BJT operates in the saturation region For RC = 3 k , the BJT operates in the saturation region For RC =20 k , the BJT operates in the cut-off region For RC =20 k , the BJT operates in the linear region 20 1 (A) (B) (C) (D) Q.38 ELECTRONICS AND COMMUNICATION ENGINEERING EC 5 3V2 7 2 (B) 2V1 2 V2 (C) V1 + V2 (D) 3V1 + (G Q.37 SET3 11 V 2 2 For the MOSFET M1 shown in the figure, assume W/L = 2, VDD = 2.0 V, = 100 A/V 2 and VTH = 0.5 V. The transistor M1 switches from saturation region to linear region when Vin (in Volts) is__________. EC 03 VDD EC R= 10 k Vout Vin M1 9/14 GATE 2014 ELECTRONICS AND COMMUNICATION ENGINEERING EC If WL is the Word Line and BL the Bit Line, an SRAM cell is shown in (B) (C) (D) Q.41 AT E 20 1 (A) 4) Q.40 SET3 In the circuit shown, and are MSBs of the control inputs. The output is given by 4:1 MUX I0 I0 I1 I1 (G 4:1 MUX EC 03 VCC (A) (B) (C) (D) EC = = = = I2 Q I3 W F Q I2 I3 X Y Z + + + + + + ) ( 10/14 GATE 2014 ELECTRONICS AND COMMUNICATION ENGINEERING EC If X and Y are inputs and the Difference (D = X Y) and the Borrow (B) are the outputs, which one of the following diagrams implements a half-subtractor? (A) (B) I1 2:1 MUX X I1 S S X I0 Y I1 2:1 MUX I0 I1 2:1 MUX I0 I1 X B I0 Y 2:1 MUX B 2:1 MUX B S S Y X D I0 I1 2:1 MUX D AT E I1 2:1 MUX I0 I1 S S X Let 1 ( ) = (1 1 ) 1 , 2 ( ) = (1 1 ) 1 , ( ) = 1 ( ) + 2 ( ). The quantities , , 1 1 are real numbers. Consider = , = , | | < 1. If the zero of ( ) lies on the unit circle, 2 4 then = ________ (G Q.44 X B D S S (D) Y 2:1 MUX Y (C) Q.43 I0 D 4) I0 Y 20 1 Q.42 SET3 Let ( ) denote the impulse response of a causal system with transfer function following three statements. 1 . +1 Consider the S1: The system is stable. ( +1) S2: is independent of for > 0. 03 ( ) S3: A non-causal system with the same transfer function is stable. For the above system, EC (A) only S1 and S2 are true (C) only S1 and S3 are true Q.45 1 The z-transform of the sequence [ ] is given by X( ) = (1 2 1 )2 , with the region of convergence | | > 2. Then, [2] is ________. EC (B) only S2 and S3 are true (D) S1, S2 and S3 are true 11/14 GATE 2014 SET3 ELECTRONICS AND COMMUNICATION ENGINEERING EC Q.46 The steady state error of the system shown in the figure for a unit step input is _______. 1 For 0 = , 1 ( ) = ( ), 2 ( ) = 2 . + 2 2 (B) 11 8 2 11 + 16 2 (D) 5 3 2 5 + 6 AT E 3 When 0 = , ( ) is 5 In the root locus plot shown in the figure, the pole/zero marks and the arrows have been removed. Which one of the following transfer functions has this root locus? 03 (G Q.48 (0) = 0 0 ( ) = and for 0 = , 1 + 11 2 (A) 8 8 22 2 2 (C) 3 5 2 3 + 10 4) The state equation of a second-order linear system is given by 20 1 Q.47 +1 ( +2)( +4)( +7) +7 ( +1)( +2)( +4) EC (A) (C) Q.49 (D) +4 ( +1)( +2)( +7) ( +1)( +2) ( +7)( +4) Let ( ) be a wide sense stationary (WSS) random process with power spectral density ( ). If ( ) is the process defined as ( ) = (2 1), the power spectral density ( ) is (A) ( ) = (C) ( ) = EC (B) 1 2 1 2 2 2 (B) (D) ( ) = ( ) = 1 2 1 2 2 /2 2 2 12/14 GATE 2014 Q.50 SET3 ELECTRONICS AND COMMUNICATION ENGINEERING EC A real band-limited random process ( ) has two-sided power spectral density ( ) = 10 0 6 (3000 | |) Watts/Hz for | | 3 kHz otherwise where is the frequency expressed in Hz. The signal ( ) modulates a carrier cos 16000 and the resultant signal is passed through an ideal band-pass filter of unity gain with centre frequency of 8 kHz and band-width of 2 kHz. The output power (in Watts) is _______. In a PCM system, the signal ( ) = {sin(100 ) + cos(100 )} V is sampled at the Nyquist rate. The samples are processed by a uniform quantizer with step size 0.75 V. The minimum data rate of the PCM system in bits per second is _____. Q.52 A binary random variable takes the value of 1 with probability 1 3. is input to a cascade of 2 independent identical binary symmetric channels (BSCs) each with crossover probability 1 2. The output of BSCs are the random variables 1 and 2 as shown in the figure. X Y2 BSC AT E Q.54 The value of ( 1 ) + ( 2 ) in bits is _____. Y1 Given the vector = (cos )(sin ) + (sin )(cos ) , where , denote unit vectors along x,y directions, respectively. The magnitude of curl of is ________ A region shown below contains a perfect conducting half-space and air. The surface current on field in the air = 2 amperes per meter. The tangential the surface of the perfect conductor is just above the perfect conductor is (G Q.53 BSC 20 1 4) Q.51 EC 03 y Air x Perfect conductor (A) ( + )2 amperes per meter (B) 2 amperes per meter (C) 2 amperes per meter (D) 2 amperes per meter EC 13/14 GATE 2014 Q.55 SET3 ELECTRONICS AND COMMUNICATION ENGINEERING EC y V/m is Assume that a plane wave in air with an electric field = E 10 cos t 3 x 3 z a ( ) incident on a non-magnetic dielectric slab of relative permittivity 3 which covers the region z > 0 . The angle of transmission in the dielectric slab is ________ degrees. EC 03 (G AT E 20 1 4) END OF THE QUESTION PAPER EC 14/14 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. 3. Any useful data required for your paper can be viewed by clicking on the Useful Common Data button that appears on the screen. 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. 6. The Question Palette displayed on the right side of screen will show the status of each question using one of the following symbols: 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 : 7. To answer a question, do the following: a. Click on the question number in the Question Palette to go to that question directly. 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. 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. You can view all the questions by clicking on the Question Paper button. This feature is provided, so that if you want you can just see the entire question paper at a glance. Answering a Question : 8. Procedure for answering a multiple choice (MCQ) type question: a. Choose one answer from the 4 options (A,B,C,D) given below the question, click on the bubble placed before the chosen option. b. To deselect your chosen answer, click on the bubble of the chosen option again or click on the Clear Response button. c. To change your chosen answer, click on the bubble of another option. d. To save your answer, you MUST click on the Save & Next button. 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. c. To clear your answer, click on the Clear Response button. d. To save your answer, you MUST click on the Save & Next button 10. To mark a question for review, click on the Mark for Review & Next button. If an answer is selected (for MCQ) or entered (for numerical answer type) for a question that is Marked for Review, that answer will be considered in the evaluation unless the status is modified by the candidate. 11. To change your answer to a question that has already been answered, first select that question for answering and then follow the procedure for answering that type of question. 12. Note that ONLY Questions for which answers are saved or marked for review after answering will be considered for evaluation. Choosing a Section : 13. Sections in this question paper are displayed on the top bar of the screen. Questions in a Section can be viewed by clicking on the name of that Section. The Section you are currently viewing will be highlighted. 14. A checkbox is displayed for every optional Section, if any, in the Question Paper. To select the optional Section for answering, click on the checkbox for that Section. 15. If the checkbox for an optional Section is not selected, the Save & Next button and the Mark for Review & Next button will NOT be enabled for that Section. You will only be able to see questions in this Section, but you will not be able to answer questions in the Section. 16. After clicking the Save & Next button for the last question in a Section, you will automatically be taken to the first question of the next Section in sequence. 17. You can move the mouse cursor over the name of a Section to view the answering status for that Section. Changing the Optional Section : 18. After answering the chosen optional Section, partially or completely, you can change the optional Section by selecting the checkbox for a new Section that you want to attempt. A warning message will appear along with a table showing the number of questions answered in each of the previously chosen optional Sections and a checkbox against each of these Sections. Click on a checkbox against a Section that you want to reset and then click on the RESET button. Note that RESETTING a Section will DELETE all the answers for questions in that Section. Hence, if you think that you may want to select this Section again later, you will have to note down your answers for questions in that Section. If you do not want to reset the Section and want to continue answering the previously chosen optional Section, then click on the BACK button. 19. If you deselect the checkbox for an optional Section in the top bar, the following warning message will appear: "Deselecting the checkbox will DELETE all the answers for questions in this Section. Do you want to deselect this Section? If you want to deselect, click on the RESET button. If you do not want to deselect, click on the BACK button. 20. You can shuffle between different Sections or change the optional Sections any number of times. 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 of marks for a 1-mark question and 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 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) get back to him (C) move in reverse (D) retreat 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 Let ( , ) = = . If x is doubled and y is halved, the new value of f is (B) 2 (C) 2( ) Q. 6 Q. 10 carry two marks each. E Q.4 (D) decadent After the discussion, Tom said to me, 'Please revert!'. He expects me to _________. (A) retract Q.3 (C) decent 20 14 ) Q.2 (B) descent AT Q.6 Find the next term in the sequence: 13M, 17Q, 19S, ___ (A) 21W Q.7 (B) 21V (C) 23W (D) 23V If KCLFTSB stands for best of luck and SHSWDG stands for good wishes , which of the following indicates ace the exam ? (B) MXHTC 6 (A) MCHTX (C) XMHCT (D) XMHTC 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. A0 Q.8 (D) 2( ) 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? (G Q.5 (A) 2 (B) 7.2 (C) 10.0 (D) 12.2 G (A) 5.6 GA 1/2 GATE 2014 SET- 6 General Aptitude -GA 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? AT E 20 14 ) Q.9 (B) 6666600 (C) 6666666 (D) 6666606 (G (A) 6666660 G A0 6 END OF THE QUESTION PAPER GA 2/2 GATE 2014 SET4 ELECTRONICS AND COMMUNICATION ENGINEERING EC Q. 1 Q. 25 carry one mark each. Q.4 Q.5 (D) The magnitude of the gradient for the function ( , , ) = 2 + 3 2 + 3 at the point (1,1,1) is _________. Let be a zero mean unit variance Gaussian random variable. [| |] is equal to _____ If and are constants, the most general solution of the differential equation 2 +2 + = 0 is 2 (A) (B) + The directional derivative of f ( = x, y ) angle of Q.6 (C) 2 (B) 2 4 (C) + 4) Q.3 (A) 2 ln 2 (D) 2 20 1 Q.2 1 The series =0 ! converges to xy ( x + y ) at (1, 1) in the direction of the unit vector at an 2 with y-axis, is given by ______ . AT E Q.1 The circuit shown in the figure represents a AIIi R 04 (G Ii EC (A) voltage controlled voltage source (B) voltage controlled current source (C) current controlled current source (D) current controlled voltage source Q.7 EC The magnitude of current (in mA) through the resistor R2 in the figure shown is_______. 1/13 GATE 2014 Q.8 SET4 ELECTRONICS AND COMMUNICATION ENGINEERING EC 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 ( C) 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 m < C < 0.87 m (C) 1.42 m < C < 1.62 m Q.9 (B) 0.87 m < C < 1.42 m (D) 1.62 m < C < 6.62 m In the figure, ln ( i) is plotted as a function of 1/T, where i is the intrinsic resistivity of silicon, T is the temperature, and the plot is almost linear. 20 1 4) ln ( i) 1/T The slope of the line can be used to estimate AT E (A) band gap energy of silicon (Eg) (B) sum of electron and hole mobility in silicon ( n + p) (C) reciprocal of the sum of electron and hole mobility in silicon ( n + p) -1 (D) intrinsic carrier concentration of silicon (ni) The cut-off wavelength (in m) 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 (G Q.10 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 for which the output voltage = , is EC Q.12 04 (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 Vi R D1 VO -1 V (A) 0.3 (B) 0.3 (C) 1.0 (D) 1.7 EC < < < < < < < < D2 2V 1.3 2 2.0 2.7 2/13 GATE 2014 Q.13 SET4 ELECTRONICS AND COMMUNICATION ENGINEERING EC The circuit shown represents vi C2 +12 V vo + R2 12 V R1 2 V C1 For a given sample-and-hold circuit, if the value of the hold capacitor is increased, then (A) (B) (C) (D) In the circuit shown in the figure, if = 0, the expression for is (G AT E Q.15 droop rate decreases and acquisition time decreases droop rate decreases and acquisition time increases droop rate increases and acquisition time decreases droop rate increases and acquisition time increases 20 1 Q.14 (B) a voltage controlled oscillator (D) a monostable multivibrator 4) (A) a bandpass filter (C) an amplitude modulator (B) = + (C) = + (D) = EC 04 (A) = + EC 3/13 GATE 2014 Q.16 SET4 ELECTRONICS AND COMMUNICATION ENGINEERING EC The output (Y) of the circuit shown in the figure is VDD A B C Output (Y) 4) A 20 1 B A Fourier transform pair is given by 04 Q.17 A+B+C A + B C + A C A+B+ C A B C (G (A) (B) (C) (D) AT E C 2 6 [ + 3] 2 3 1 3 2 EC where [ ] denotes the unit step sequence. The values of is _________. Q.18 A real-valued signal ( ) limited to the frequency band | | invariant system whose frequency response is ( ) = The output of the system is (A) ( + 4) EC (B) ( 4) 4 , 0, 2 2 | | > 2 | | (C) ( + 2) is passed through a linear time . (D) ( 2) 4/13 GATE 2014 SET4 ELECTRONICS AND COMMUNICATION ENGINEERING EC Q.19 The sequence [ ] = 0.5 [ ] , where [ ] is the unit step sequence, is convolved with itself to obtain [ ]. Then + = [ ] 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 (D) +80 dB/decade For the second order closed-loop system shown in the figure, the natural frequency (in rad/s) is U(s) + 20 1 (B) 4 (C) 2 (D) 1 AT E (A) 16 Y(s) 4 s(s+4) - Q.22 (C) +40 dB/decade 4) Q.21 (B) 40 dB/decade 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 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 120 , the magnitude of average 04 (G Q.23 power density due to this antenna at a distance of 2 km from the antenna (in nW/m2 ) is ____. Match column A with column B. EC Q.25 Column A 1. Point electromagnetic source 2. Dish antenna 3. Yagi-Uda antenna (A) 1 2 3 EC (B) Column B P. Highly directional Q. End fire R. Isotropic (C) 1 2 3 (D) 1 2 3 1 2 3 5/13 GATE 2014 SET4 ELECTRONICS AND COMMUNICATION ENGINEERING EC Q. 26 Q. 55 carry two marks each. Q.26 With initial values (0) = (0) = 1, the solution of the differential equation 2 +4 + 4 = 0 2 at = 1 is _____. Parcels from sender S to receiver R pass sequentially through two post-offices. Each post-office has 1 a probability of losing an incoming parcel, independently of all other parcels. Given that a parcel 5 is lost, the probability that it was lost by the second post-office is_________. Q.28 The unilateral Laplace transform of ( ) is Laplace transform of ( ) = ( )? (2 +1) (A)( 2 + +1)2 (B)( 2 + +1)2 2 +1 (C)( 2 + +1)2 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 R C y(t) C EC 04 sin( t) (A) Q.31 (D) 45o The steady state output of the circuit shown in the figure is given by ( ) = ( ) sin( + ( )). If the amplitude | ( )| = 0.25 , then the frequency is (G Q.30 (D)( 2 + +1)2 AT E Q.29 Which one of the following is the unilateral 20 1 1 . 2 + +1 4) Q.27 1 3 (B) C 2 3 (C) 1 (D) 2 In the circuit shown in the figure, the value of v0 (t) (in Volts) for t is ______. ix 2H 10 u(t) A + - 2ix 5 EC 5 + vo (t) - 6/13 GATE 2014 Q.34 The value of R e /R is ________ (A) 6 24 42 9 (B) 9 8 8 24 4) For the two-port network shown in the figure, the impedance (Z) matrix (in ) is (C) 9 6 6 24 (D) 42 6 6 60 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 ______. Consider two BJTs biased at the same collector current with area A1 = 0.2 m 0.2 m and A2 = 300 m 300 m. 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 _____. EC 04 (G Q.35 The equivalent resistance in the infinite ladder network shown in the figure, is Re. 20 1 Q.33 ELECTRONICS AND COMMUNICATION ENGINEERING EC AT E Q.32 SET4 EC 7/13 GATE 2014 Q.36 SET4 ELECTRONICS AND COMMUNICATION ENGINEERING EC 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? (B) 4) (A) EC EC EF EF (C) (D) EC EF EV 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, and 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 R E ? EC 04 (G Q.37 EC EF AT E EV 20 1 EV EV Q.38 EC (A) R E 1 (B) IC R E VT (C) 1 (D) VBE VT A BJT in a common-base configuration is used to amplify a signal received by a 50 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________. 8/13 GATE 2014 Q.39 SET4 ELECTRONICS AND COMMUNICATION ENGINEERING EC For the common collector amplifier shown in the figure, the BJT has high , negligible VCE(sat), and VBE = 0.7 V. The maximum undistorted peak-to-peak output voltage vo (in Volts) is _______. VCC = +12 V R1 5 k 1 F vi 1 F vo RE 1 k An 8-to-1 multiplexer is used to implement a logical function as shown in the figure. The output is given by A0 B0 FA0 S0 Q.42 = + = + C0 A1 B1 FA1 S1 A14 B14 C1 FA14 S14 A15 B15 C14 FA15 C15 S15 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 (C) 1FH, 1FH, 12H, 12H EC (B) (D) 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 __________. EC Q.41 = + = + 04 (A) (C) (G AT E Q.40 20 1 4) R2 10 k (B) 1FH, FEH, 1FH, FFH, 12H (D) 1FH, 1FH, 12H, 20H, 12H 9/13 GATE 2014 ELECTRONICS AND COMMUNICATION ENGINEERING EC 1 A stable linear time invariant (LTI) system has a transfer function ( ) = 2 + 6. To make this system causal it needs to be cascaded with another LTI system having a transfer function 1 ( ). A correct choice for 1 ( ) among the following options is (A) + 3 Q.44 (B) 2 (C) 6 (D) + 1 A causal LTI system has zero initial conditions and impulse response ( ). Its input ( ) and output ( ) are related through the linear constant-coefficient differential equation ( ) 2 ( ) + + 2 ( ) = ( ). 2 2 ( ) = ( ) + If ( ) is the Laplace transform of ( ), then the number of poles of ( ) is _____. The -point DFT of a sequence [ ], 0 1 is given by 1 AT E Q.45 0 ( ) + ( ). 20 1 Let another signal ( ) be defined as 4) Q.43 SET4 [ ] = 1 [ ] =0 2 , 0 1. Denote this relation as = ( ). For = 4, which one of the following sequences satisfies ( ( )) = ? (G 1 1 0 EC (A) Q.47 (B) = [1 2 3 2] (D) = [1 2 2 3] 0 1 1 The state transition matrix (t) of a system 1 = is 2 0 0 2 04 Q.46 (A) = [1 2 3 4] (C) = [1 3 2 2] (B) 1 0 1 Consider a transfer function ( ) = (C) 2 +3 2 0 1 1 2 +(3+ ) +(2 ) (D) 1 0 1 with a positive real parameter. The maximum value of until which remains stable is ________. EC 10/13 GATE 2014 Q.48 SET4 ELECTRONICS AND COMMUNICATION ENGINEERING EC The characteristic equation of a unity negative feedback system is 1 + ( ) = 0. The open loop transfer function ( ) has one pole at 0 and two poles at -1. The root locus of the system for varying K is shown in the figure. j =0.5 AT E 20 1 1 (0,0) 1/3 O 4) A Consider a communication scheme where the binary valued signal X satisfies { = +1} = 0.75 and { = 1} = 0.25. The received signal Y = X + Z, where Z is a Gaussian random variable with zero mean and variance 2 . The received signal Y is fed to the threshold detector. The output is: of the threshold detector 04 Q.49 (G The constant damping ratio line, for =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 at point A is ________ . = +1, 1, > . EC , the threshold should be To achieve a minimum probability of error (A) strictly positive (B) zero (C) strictly negative (D) strictly positive, zero, or strictly negative depending on the nonzero value of 2 EC 11/13 GATE 2014 Q.50 SET4 ELECTRONICS AND COMMUNICATION ENGINEERING EC Consider the Z-channel given in the figure. The input is 0 or 1 with equal probability. 1.0 0 INPUT 0 OUTPUT 0.25 1 1 0.75 4) If the output is 0, the probability that the input is also 0 equals ______________ 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 raisedcosine spectrum with 100% excess bandwidth. The minimum value of M is ________. Q.52 Consider a discrete-time channel = + , where the additive noise is signal-dependent. In particular, given the transmitted symbol { , + } at any instant, the noise sample is chosen independently from a Gaussian distribution with mean and unit variance. Assume a threshold detector with zero threshold at the receiver. 20 1 Q.51 AT E When = 0, the BER was found to be ( ) = 1 10 8 . 2 2 ( ( ) = 1 2 , and for > 1, use ( ) 2 ) 2 When = 0.3, the BER is closest to (A) 10 7 (D) 10 2 (G (C) 10 4 The electric field (assumed to be one-dimensional) between two points A and B is shown. Let and be the electrostatic potentials at A and B, respectively. The value of in Volts is ________. EC 04 Q.53 (B) 10 6 Q.54 x + xa y + ya z . If S represents the portion of the sphere x + y + z = 1 for z 0 , Given F = za then EC 2 2 2 is______________. 12/13 GATE 2014 Q.55 SET4 ELECTRONICS AND COMMUNICATION ENGINEERING EC If = (2 3 3 2 ) (6 2 3 2 ) + (6 ) is the electric field in a source free region, a valid expression for the electrostatic potential is (A) 3 2 (B) 2 3 2 (C) 3 + 2 (D) 2 3 3 2 EC 04 (G AT E 20 1 4) END OF THE QUESTION PAPER EC 13/13

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