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GATE 2014 : Instrumentation Engineering

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GATE 2014 Examination IN: Instrumentation 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- 2 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. A person suffering from Alzheimer s disease (A) experienced (C) is experiencing Q.2 short-term memory loss. (B) has experienced (D) experiences Choose the most appropriate word from the options given below to complete the following sentence. (A) Contentment Q.3 (B) Ambition 20 14 ) ____________ is the key to their happiness; they are satisfied with what they have. (C) Perseverance (D) Hunger Which of the following options is the closest in meaning to the sentence below? As a woman, I have no country. E (A) Women have no country. (B) Women are not citizens of any country. (C) Women s solidarity knows no national boundaries. (D) Women of all countries have equal legal rights. In any given year, the probability of an earthquake greater than Magnitude 6 occurring in the Garhwal Himalayas is 0.04. The average time between successive occurrences of such earthquakes is ____ years. Q.5 The population of a new city is 5 million and is growing at 20% annually. How many years would it take to double at this growth rate? (B) 4-5 years (C) 5-6 years (D) 6-7 years 02 (A) 3-4 years (G AT Q.4 Q. 6 Q. 10 carry two marks each. In a group of four children, Som is younger to Riaz. Shiv is elder to Ansu. Ansu is youngest in the group. Which of the following statements is/are required to find the eldest child in the group? Statements 1. Shiv is younger to Riaz. 2. Shiv is elder to Som. G A Q.6 (A) Statement 1by itself determines the eldest child. (B) Statement 2 by itself determines the eldest child. (C) Statements 1 and 2 are both required to determine the eldest child. (D) Statements 1 and 2 are not sufficient to determine the eldest child. GA 1/2 GATE 2014 Q.7 SET- 2 General Aptitude -GA Moving into a world of big data will require us to change our thinking about the merits of exactitude. To apply the conventional mindset of measurement to the digital, connected world of the twenty-first century is to miss a crucial point. As mentioned earlier, the obsession with exactness is an artefact of the information-deprived analog era. When data was sparse, every data point was critical, and thus great care was taken to avoid letting any point bias the analysis. From BIG DATA Viktor Mayer-Schonberger and Kenneth Cukier The main point of the paragraph is: Q.8 20 14 ) (A) The twenty-first century is a digital world (B) Big data is obsessed with exactness (C) Exactitude is not critical in dealing with big data (D) Sparse data leads to a bias in the analysis The total exports and revenues from the exports of a country are given in the two pie charts below. The pie chart for exports shows the quantity of each item 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 5 lakh tonnes and the total revenues are 250 crore rupees. What is the ratio of the revenue generated through export of Item 1 per kilogram to the revenue generated through export of Item 4 per kilogram? Exports Item 5 12% (A) 1:2 E Item 3 19% (B) 2:1 Item 6 19% Item 1 12% Item 2 20% Item 5 20% Item 4 6% (C) 1:4 Item 3 23% (D) 4:1 A X is 1 km northeast of Y. Y is 1 km southeast of Z. W is 1 km west of Z. P is 1 km south of W. Q is 1 km east of P. What is the distance between X and Q in km? (A) 1 (B) 2 (C) 3 (D) 2 10% of the population in a town is HIV+. A new diagnostic kit for HIV detection is available; this kit correctly identifies HIV+ individuals 95% of the time, and HIV individuals 89% of the time. A particular patient is tested using this kit and is found to be positive. The probability that the individual is actually positive is _______ G Q.10 Item 2 20% 02 Item 4 22% Q.9 Item 1 11% (G AT Item 6 16% Revenues END OF THE QUESTION PAPER GA 2/2 GATE 2014 INSTRUMENTATION - IN Q. 1 Q. 25 carry one mark each. Q.1 Given ( ) = 3 sin(1000 )and ( ) = 5 cos 1000 + 4 The x-yplot will be (C)a hyperbola Q.2 (B)a multi-loop closed curve (D)an ellipse Given that x is a random variable in the range[0, ]with a probability densityfunction 2 , the value of the constant K is___________. The figure shows the plot of y as a function of x (G AT E Q.3 20 14 ) (A) a circle IN The function shown is the solution of the differential equation (assuming all initial conditions to be zero) is : (A) Q.4 d2y =1 dx 2 (B) dy =x dx (C) dy = x dx (D) dy = x dx A vector is defined as f = y i + x j + zk are unit vectors in Cartesian (x,y,z) coordinate system. where i, j and k The surface integral . over the closed surface S of a cube with vertices having the following coordinates: (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1), (1,1,1), (0,1,1) is ___________. IN 1/15 GATE 2014 Q.5 INSTRUMENTATION - IN The figure shows the schematic of a production process with machines A, B and C. An input job needs to be pre-processed either by A or by B before it is fed to C, from which the final finished product comes out. The probabilities of failure of the machines are given as: PA=0.15, PB=0.05, PC=0.1. A C Input job Finished product B Q.6 The circuit shown in figure was at steady state for < 0 with the switch at position A . The switch is thrown to position B at time = 0. The voltage (volts) across the 10 resistor at time = 0+ is___________. 2 V _ 6V (G (C) 1 ( ) lags 2 ( ) by 130o IN 5H Time domain expressions for the voltage 1 ( ) and 2 ( ) are given as 1 ( ) = sin(10 130 )and 2 ( ) = cos(10 + 10 ). Which one of the following statements is TRUE? (A) 1 ( )leads 2 ( ) by 130o Q.9 t=0 The average real power in watts delivered to a load impedance = (4 2) by an ideal current source ( ) = 4 sin( + 20 )A is ___________. IN Q.8 B AT 10 A E + Q.7 20 14 ) Assuming independence of failures of the machines, the probability that a given job is successfully processed (up to the third decimal place) is ___________. (B) 1 ( ) lags 2 ( ) by 130o (D) 1 ( ) leads 2 ( )by 130o A pHelectrode obeys Nernst equation and is being operated at 25 C. The change in the open circuit voltage in millivolts across the electrode for a pH change from 6 to 8 is ___________. 2/15 GATE 2014 Q.10 INSTRUMENTATION - IN The pressure and velocity at the throat of a Venturi tube, measuring the flow of a liquid, are related to the upstream pressure and velocity, respectively, as follows: (A) pressure is lower but velocity is higher (B) pressure is higher but velocity is lower (C) both pressure and velocity are lower (D) pressure and velocity are identical Semiconductor strain gages typically have much higher gage factors than those of metallic strain gages, primarily due to : (A) higher temperature sensitivity (B) higher Poisson s ratio (C) higher piezoresitive coefficient (D) higher magnetostrictive coefficient Q.12 20 14 ) Q.11 For a rotameter, which one of the following statements is TRUE? (A) the weight of the float is balanced by the buoyancy and the drag force acting on the float E (B) the velocity of the fluid remains constant for all positions of the float AT (C) the measurement of volume flow rate of gas is not possible (D) the volume flow rate is insensitive to changes in density of the fluid For the op-amp shown in the figure, the bias currents are Ib1= 450 nA and Ib2=350 nA. The values of the input bias current (IB) and the input offset current (If) are: IN (G Q.13 (A) IB= 800 nA, If=50 nA (C) IB= 400 nA, If=50nA IN (B) IB= 800 nA, If=100nA (D) IB= 400 nA, If=100nA 3/15 GATE 2014 Q.14 INSTRUMENTATION - IN The amplifier in the figure has gain of 10 and input resistance of 50 k . The values of Ri and Rfare: Rf Ri Vin V0 + (B) Ri= 50 k , Rf = 500 k 20 14 ) (A) Ri= 500 k , Rf = 50 k (C) Ri= 5 k , Rf = 10 k (D) Ri= 50 k , Rf = 200 k For the circuit shown in the figure assume ideal diodes with zero forward resistance and zero forward voltage drop. The current through the diode D2 in mAis ___________. Q.16 The system function of an LTI system is given by IN (G AT E Q.15 1 1 1 3 ( ) = 1 1 1 4 The above system can have stable inverse if the region of convergence of H(z)is defined as 1 (A) | | < 4 IN 1 (B) | | < 12 1 (C) | | > 4 1 (D) | | < 3 4/15 GATE 2014 The figure is a logic circuit with inputs A and B and output Y.Vss = + 5 V. The circuit is of type (C) OR (D) NAND The impulse response of an LTI system is given as : c n=0 h [ n] = sin c n n 0 n It represents an ideal AT Q.18 (B) AND E (A) NOR 20 14 ) Q.17 INSTRUMENTATION - IN (C) non-causal, high-pass filter (D) causal, high-pass filter A discrete-time signal [ ] is obtained by sampling an analog signal at 10 kHz. The signal [ ]is filtered by a system with impulse response [ ] = 0.5{ [ ] + [ 1]}. The 3dB cutoff frequency of the filter is: IN Q.19 (B) causal, low-pass filter (G (A)non-causal, low-pass filter (A) 1.25 kHz Q.20 (C) 4 .00 kHz (D) 5.00 kHz A full duplex binary FSK transmission is made through a channel of bandwidth 10 kHz. In each direction of transmission the two carriers used for the two states are separated by 2 kHz. The maximum baud rate for this transmission is: (A) 2000 bps IN (B) 2.50 kHz (B) 3000 bps (C) 5000 bps (D) 10000 bps 5/15 GATE 2014 A loop transfer function is given by : ( + 2) + 10) The point of intersection of the asymptotes of ( ) ( )on the real axis in the -plane is at ( ) ( ) = ___________. Q.22 2 ( The resistance and inductance of an inductive coil are measured using an AC bridge as shown in the figure. The bridge is to be balanced by varying the impedance Z2. 20 14 ) Q.21 INSTRUMENTATION - IN For obtaining balance, Z2 should consist of element(s): Q.23 (B) R and L (C) L and C (D) Only C E (A) R and C A plant has an open-loop transfer function, 20 . ( s + 0.1)( s + 2 )( s + 100 ) AT Gp ( s ) = The approximate model obtained by retaining only one of the above poles, which is closest to the frequency response of the original transfer function at low frequency is (B) 2 s+2 (C) 100 s + 100 (D) 20 s + 0.1 In order to remove respiration related motion artifacts from an ECG signal, the following filter should be used: IN Q.24 0.1 s + 0.1 (G (A) (A) low-pass filter with fc = 0.5 Hz (B) high-pass filter with fc = 0.5 Hz (C)high-pass filter with fc = 49.5 Hz (D)band-pass filter with passband between 0.1 Hz and 0.5 Hz Q.25 IN In a time-of-flight mass spectrometerif is the charge and the mass of the ionized species,then the time of flight is proportional to (A) (B) (C) (D) 6/15 GATE 2014 INSTRUMENTATION - IN Q. 31 Q. 55 carry two marks each. Q.26 A scalar valued function is defined as f ( x ) = xT Ax + bT x + c , where A is a symmetric positive definite matrix with dimension n n ; b and x are vectors of dimension n 1. The minimum value of f ( x ) will occur when x equals ( (A) AT A ) 1 ( (B) AT A b -1 20 14 ) 1 3 N xk ( ) 3 N 1 2 xk + 2 xk 3 1 N 2 xk 2 3 xk E 1 3 N xk ( ) 3 = xk (B) xk +1 = xk +1 = (D) = xk + (C) xk +1 AT For the matrix A satisfying the equation given below, the eigenvaluesare 1 2 3 1 2 3 7 8 9 = 4 5 6 [ A] 4 5 6 7 8 9 (B)(1, 1, 0) (G (A)(1, , ) (C)(1, 1, 1) (D)(1, 0, 0) In the circuit shown in the figure, initially the capacitor is uncharged. The switch S is closed at = 0. Two milliseconds after the switch is closed, the current through the capacitor (in mA) is ___________. IN Q.29 b The iteration step in order to solvefor the cube roots of a given number Nusing the NewtonRaphson s method is (A) xk +1 Q.28 1 A-1 b (D) 2 A b (C) 2 Q.27 ) 2 k S ic (t) t= 0 5V IN 2 k 4 F 7/15 GATE 2014 Q.30 INSTRUMENTATION - IN A capacitor C is to be connected across the terminals A and B as shown in the figure so that the power factor of the parallel combination becomes unity. The value of the capacitance required in F is___________. A 4 60 V 50 Hz 20 14 ) j1 B Q.31 The resistance of a wire is given by the expression = 4 The circuit shown in the figure contains a dependent current source between A and B terminals. The Thevenin s equivalent resistance in k between the terminals C and D is ___________. AT Q.32 E , 2 where, is the resistivity ( -meter),L is the length (meter) and D (meter) is the diameter of the wire. The error in measurement of each of the parameters , L, and D is 1.0% . Assuming that the errors are independent random variables, the percent error in measurement of R is ___________. 5 k A 5 k C + 10 4 Vx (G 10 V _ D IN B vx Q.33 A thermistor has a resistance of 1 k at temperature 298 Kand 465 at temperature 316 K. The temperature sensitivity in K-1[i.e. (1/R)(dR/dT), where R is the resistance at the temperature T(in K)], of this thermistor at 316 K is ___________. Q.34 A barium titanate piezoelectric crystal with d33=150 pC/N, Ccrystal = 25 pF and Rcrystal = 1010 is used to measure the amplitude of a step force. The voltage output is measured using a digital voltmeter with input impedance 1013 connected across the crystal. All other capacitances and resistances may be neglected. A step force of 2 N is applied from direction 3 on the crystal. The time in milliseconds within which the voltmeter should sample the crystal output voltage so that the drop from the peak value is no more than 0.12V is ___________. IN 8/15 GATE 2014 INSTRUMENTATION - IN A thermopile is constructed using 10 junctions of Chromel-Constantan (sensitivity 60 V/ C for each junction) connected in series. The output is fed to an amplifier having an infinite input impedance and a gain of 10. The output from the amplifier is acquired using a 10-bit ADC, with reference voltage of 5 V. The resolution of this system in units of C is ___________. Q.36 A transit time ultrasonic flowmeter uses a pair of ultrasonic transducers placed at 45 angle, as shown in the figure. 20 14 ) Q.35 Assuming an ideal op-amp in linear range of operation, the magnitude of the transfer impedance 0 in M of the current to voltage converter shown in the figure is ___________. IN (G AT Q.37 E The inner diameter of the pipe is 0.5 m. The differential transit time is directly measured using a clock of frequency 5 MHz. The velocity of the fluid is small compared to the velocity of sound in the static fluid, which is 1500 m/s and the size of the crystals is negligible compared to the diameter of the pipe. The minimum change in fluid velocity (m/s) that can be measured using this system is ___________. IN 9/15 GATE 2014 Q.38 INSTRUMENTATION - IN For the circuit shown in the figure, the transistor has = 40, = 0.7 V, and the voltage across the Zener diode is 15 V.The current (in mA) through the Zener diode is ___________. +30 V 330 20 14 ) Q.39 100 In the figure, transistors T1 and T2 have identical characteristics. ( ) of transistor T3 is 0.1 V. The voltage 1 is high enough to put T3 in saturation. Voltage of transistors T1, T2 and T3is 0.7 V. The value of ( 1 2 ) in Vis ___________. 9V V1 T3 E 5 k 3 k AT V2 T2 Q.40 (G T1 The figures show an oscillator circuit having an ideal Schmitt trigger and its input-output vo ( t ) is___________. IN characteristics. The time period (in ms) of IN 10/15 GATE 2014 Q.41 INSTRUMENTATION - IN An N-bit ADC has an analog reference voltage V. Assuming zero mean and uniform distribution of the quantization error, the quantization noise power will be: (A) 2 2 (B) 12(2 1) 12(2 1)2 (C) 12(2 1) A microprocessor accepts external interrupts (Ext INT) through a Programmable Interrupt Controller as shown in the figure. 20 14 ) Q.42 2 (D) 12 E Assuming vectored interrupt, a correct sequence of operations when a single external interrupt (Ext INT1) is received will be : (A) Ext INT1 INTA Data Read INT AT (B) Ext INT1 INT INTA Data Read (C) Ext INT1 INT INTA Address Write IN (G (D) Ext INT1 INT Data Read Address Write IN 11/15 GATE 2014 (A)directly proportional to ref Q.44 (B) inversely proportional to ref (D)directly proportional to clock frequency AT (C)independent of ref 20 14 ) The circuit in the figure represents a counter-based unipolar ADC. When SOC is asserted the counter is reset and clock is enabled so that the counter counts up and the DAC output grows. When the DAC output exceeds the input sample value, the comparator switches from logic 0 to logic 1, disabling the clock and enabling the output buffer by asserting EOC. Assuming all components to be ideal, ref , DAC output and input to be positive, the maximum error in conversion of the analog sample value is: E Q.43 INSTRUMENTATION - IN ( )is the Discrete Fourier Transform of a 6-point real sequence ( ). If (0) = 9 + 0, (2) = 2 + 2, (3) = 3 0, (5) = 1 1, (0) is Q.45 (B) 9 (G (A) 3 (C) 15 The transfer function of a digital system is given by: 1 0 1 + 2 2 ; where 2 is real. IN The transfer function is BIBO stable if the value of 2 is: (A) 1.5 Q.46 (D) 18 (B) 0.75 (C) 0.5 (D) 1.5 The transfer function of a system is given by 500 ( ) = + 500 The input to the system is ( ) = sin 100 . In periodic steady state the output of the system is found to be ( ) = sin(100 ). The phase angle ( ) in degree is ___________. IN 12/15 GATE 2014 Q.47 INSTRUMENTATION - IN In the microprocessor controlled measurement scheme shown in the figure, Rx is the unknown 20 14 ) resistance to be measured, while Rref and Cref are known. Cref is charged from voltage VL to VH (by a constant DC voltage source VS), once through Rref in Tref seconds and then discharged to VL . It isagain charged from voltage VL to VH throughRxin Tx seconds. If Tx = kTref then = (A) Rx kRref 1 VL VH VH VL (B) Rx = kRref ln (D) Rx = Rref ln k (C) Rx = kRref E Frequency of an analog periodic signal in the range of 5kHz - 10kHz is to be measured with a resolution of 100Hz by measuring its period with a counter. Assuming negligible signal and transition delays the minimum clock frequency and minimum number of bits in the counter needed, respectively, are: AT Q.48 (C) 1 MHz, 8-bits Q.49 (B) 10 MHz, 10-bits (D) 10MHz, 8-bits (G (A) 1 MHz, 10-bits The loop transfer function of a feedback control system is given by G (s) H (s) = 1 s ( s + 1)( 9 s + 1) IN Its phase crossover frequency (in rad/s), approximated to two decimal places, is ___________. Q.50 Consider a transport lag process with a transfer function ( ) = . The process is controlled by a purely integral controller with transfer function ( ) = in a unity feedback configuration. The value of for which the closed loop plant has a pole at = 1, is ___________. IN 13/15 GATE 2014 Q.51 INSTRUMENTATION - IN Consider the control system shown in figurewith feedforwardaction for rejection of a measurable disturbance d ( t ) . The value of K, for whichthe disturbance response at the output ( ) is zero (A) 1 (B) 1 20 14 ) mean, is: (C) 2 (D) 2 A mixture contains two mutually inert solutions X and Y in equal volumes. The mixture is examined in a spectrophotometer using a cuvette. It is observed that the transmittance is 0.40. With only the solution X in the same cuvette, the transmittance is 0.20. With only solution Y in the cuvette the transmittance is___________. Q.53 Monochromatic light from a step index (n1 = 1.500; n2 = 1.485), multimode optical fiber of core diameter 100 m is incident through air (n = 1.000) onto a linear photo-detector array placed at 1 mm distance from the tip of the fiber. The tip of the fiber is polished and its exit plane is perpendicular to the axis of the fiber. The detector array is oriented parallel to the exit plane of the tip. The array consists of photo-detector elements each of 5 m diameter. The distance between the edges of two adjacent elements can be assumed to be zero. The number of elements illuminated by the light coming out of the fiber is___________. Q.54 An image of the chest of a patient is taken with an X-ray machine on a photographic film. The Hurter-Driffield (HD) curve of the film is shown in the figure. The highly absorbing parts of the body (e.g. bones), show up as low exposure regions(mapped near A) and the less absorbing parts (e.g. muscles) show up as high exposure regions(mapped near B). IN (G AT E Q.52 If the exposure time is increased 10 times, while keeping the voltages and currents in the X-ray machine constant, in the image, (A)contrast decreases since B moves into the shoulder region (B)contrast decreases since both A and B move into the shoulder region (C)contrast increases sinceA moves into the toe region (D)contrast decreases since both A and B move into the toe region IN 14/15 GATE 2014 INSTRUMENTATION - IN 20 14 ) Q.55 For the given low-pass circuit shown in the figure, the cutoff frequency in Hz will be ___________. IN (G AT E END OF THE QUESTION PAPER IN 15/15

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Additional Info : Solved GATE exam paper, Instrumentation Engineering IN - 2014 paper
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