GATE Solved Question Papers for Instrumentation [In] by AglaSem.Com

SOLVED PAPERS

GATE INSTRUMENTATION ENGINEERING (IN)

A comprehensive study guide for GATE

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CONTENTS

• • • • • •

Introduction Question Paper Pattern Design of Questions Marking Scheme Syllabus Previous Year Solved Papers o Solved Question Paper 2014 o Answer Key 2014 o Solved Question Paper 2013 o Answer Key 2013 o Solved Question Paper 2012 o Answer Key 2012

Introduction The Graduate Aptitude Test in Engineering (GATE) is the all India level examination conducted by the Indian Institute of Science and seven Indian Institutes of Technology (IITs). A crucial part of GATE preparation is to solve and practice using previous year GATE papers. Solving previous year GATE papers help the candidate in understanding the exam pattern, knowing the level of difficulty of questions, and analyzing preparation. While attempting to solve any previous year GATE paper, it is advisable that it is done in a simulated test environment. This means, that the candidate sets a timer to countdown to test time, makes sure there is no other distraction, and then sits down to take the test as if he / she is in the exam hall. After attempting the paper, check how many questions you could get right in the first attempt. Analyse the strong and weak areas of preparation, and accordingly devise a study schedule or revision pattern. After going through those areas where in the first attempt could not do well, try the next paper. Almost all of the engineering colleges in India take admission in M.Tech courses on the basis of GATE scores. Apart from that, PSUs also recruit students directly on this basis. To score high in this elite examination is tough, but quite achievable.

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Question Paper Pattern In all the papers, there will be a total of 65 questions carrying 100 marks, out of which 10 questions carrying a total of 15 marks are in General Aptitude (GA). In the papers bearing the codes AE, AG, BT, CE, CH, CS, EC, EE, IN, ME, MN, MT, PI, TF and XE, the Engineering Mathematics will carry around 13% of the total marks, the General Aptitude section will carry 15% of the total marks and the remaining percentage of the total marks is devoted to the subject of the paper. In the papers bearing the codes AR, CY, EY, GG, MA, PH and XL, the General Aptitude section will carry 15% of the total marks and the remaining 85% of the total marks is devoted to the subject of the paper. GATE would contain questions of two different types in various papers: (i) Multiple Choice Questions (MCQ) carrying 1 or 2 marks each in all papers and sections. These questions are objective in nature, and each will have a choice of four answers, out of which the candidate has to mark the correct answer(s). (ii) Numerical Answer Questions of 1 or 2 marks each in all papers and sections. For these questions the answer is a real number, to be entered by the candidate using the virtual keypad. No choices will be shown for this type of questions.

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Design of Questions The questions in a paper may be designed to test the following abilities: (i) Recall: These are based on facts, principles, formulae or laws of the discipline of the paper. The candidate is expected to be able to obtain the answer either from his/her memory of the subject or at most from a one-line computation. (ii) Comprehension: These questions will test the candidate's understanding of the basics of his/her field, by requiring him/her to draw simple conclusions from fundamental ideas. (iii) Application: In these questions, the candidate is expected to apply his/her knowledge either through computation or by logical reasoning. (iv) Analysis and Synthesis: In these questions, the candidate is presented with data, diagrams, images etc. that require analysis before a question can be answered. A Synthesis question might require the candidate to compare two or more pieces of information. Questions in this category could, for example, involve candidates in recognising unstated assumptions, or separating useful information from irrelevant information.

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Marking Scheme For 1-mark multiple-choice questions, 1/3 marks will be deducted for a wrong answer. Likewise, for2-marks multiple-choice questions, 2/3 marks will be deducted for a wrong answer. There is no negative marking for numerical answer type questions. General Aptitude (GA) Questions In all papers, GA questions carry a total of 15 marks. The GA section includes 5 questions carrying 1 mark each (sub-total 5 marks) and 5 questions carrying 2 marks each (sub-total 10 marks). Question Papers other than GG, XE and XL These papers would contain 25 questions carrying 1 mark each (sub-total 25 marks) and 30 questions carrying 2 marks each (sub-total 60 marks). The question paper will consist of questions of multiple choice and numerical answer type. For numerical answer questions, choices will not be given. Candidates have to enter the answer (which will be a real number, signed or unsigned, e.g. 25.06, -25.06, 25, -25 etc.) using a virtual keypad. An appropriate range will be considered while evaluating the numerical answer type questions so that the candidate is not penalized due to the usual round-off errors. GG (Geology and Geophysics) Paper Apart from the General Aptitude (GA) section, the GG question paper consists of two parts: Part A and Part B. Part A is common for all candidates. Part B contains two sections: Section 1 (Geology) and Section 2 (Geo-physics). Candidates will have to attempt questions in Part A and either Section 1 or Section 2 in Part B. Part A consists of 25 multiple-choice questions carrying 1-mark each (sub-total 25 marks and some of these may be numerical answer type questions). Each section in Part B (Section 1 and Section 2) consists of 30 multiple choice questions carrying 2 marks each (sub-total 60 marks and some of these may be numerical answer type questions). XE Paper (Engineering Sciences)

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In XE paper, Engineering Mathematics section (Section A) is compulsory. This section contains 11 questions carrying a total of 15 marks: 7 questions carrying 1 mark each (subtotal 7 marks), and 4 questions carrying 2 marks each (sub-total 8 marks). Some questions may be of numerical answer type questions. Each of the other sections of the XE paper (Sections B through G) contains 22 questions carrying a total of 35 marks: 9 questions carrying 1 mark each (sub-total 9 marks) and 13 questions carrying 2 marks each (sub-total 26 marks). Some questions may be of numerical answer type. XL Paper (Life Sciences) In XL paper, Chemistry section (Section H) is compulsory. This section contains 15 questions carrying a total of 25 marks: 5 questions carrying 1 mark each (sub-total 5 marks) and 10 questions carrying 2-marks each (sub-total 20 marks). Some questions may be of numerical answer type. Each of the other sections of the XL paper (Sections I through M) contains 20 questions carrying a total of 30 marks: 10 questions carrying 1 mark each (sub-total 10 marks) and 10 questions carrying 2 marks each (sub-total 20 marks). Some questions may be of numerical answer type. Note on Negative Marking for Wrong Answers For a wrong answer chosen for the multiple choice questions, there would be negative marking. For1-mark multiple choice questions, 1/3 mark will be deducted for a wrong answer. Likewise, for 2-mark multiple choice questions, 2/3 mark will be deducted for a wrong answer. However, there is no negative marking for a wrong answer in numerical answer type questions.

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Syllabus for General Aptitude (GA) Verbal Ability: English grammar, sentence completion, verbal analogies, word groups, instructions, critical reasoning and verbal deduction. Numerical Ability: Numerical computation, numerical estimation, numerical reasoning and data interpretation.

Syllabus for Instrumentation Engineering (IN) ENGINEERING MATHEMATICS Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors. Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems. Differential equations: First order equation (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy’s and Euler’s equations, Initial and boundary value problems, Partial Differential Equations and variable separable method. Complex variables: Analytic functions, Cauchy’s integral theorem and integral formula, Taylor’s and Laurent’ series, Residue theorem, solution integrals. Probability and Statistics: Sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson,Normal and Binomial distribution, Correlation and regression analysis. Numerical Methods: Solutions of non-linear algebraic equations, single and multi-step methods for differential equations. Transform Theory: Fourier transform,Laplace transform, Z-transform. INSTRUMENTATION ENGINEERING Basics of Circuits and Measurement Systems:Kirchoff’s laws, mesh and nodal Analysis. Circuit theorems. One-port and two-port Network Functions. Static and

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dynamic characteristics of Measurement Systems. Error and uncertainty analysis. Statistical analysis of data and curve fitting. Transducers, Mechanical Measurement and Industrial Instrumentation: Resistive, Capacitive, Inductive and piezoelectric transducers and their signal conditioning. Measurement of displacement, velocity and acceleration (translational and rotational), force, torque, vibration and shock. Measurement of pressure, flow, temperature and liquid level.Measurement of pH, conductivity, viscosity and humidity. Analog Electronics: Characteristics of diode, BJT, JFET and MOSFET. Diode circuits. Transistors at low and high frequencies, Amplifiers, single and multi-stage. Feedback amplifiers.

Operational

amplifiers,

characteristics

and

circuit

configurations.

Instrumentation amplifier. Precision rectifier. V-to-I and I-to-V converter. Op-Amp based active filters. Oscillators and signal generators. Digital Electronics: Combinational logic circuits, minimization of Boolean functions. IC families, TTL, MOS and CMOS. Arithmetic circuits. Comparators, Schmitt trigger, timers and mono-stable multi-vibrator. Sequential circuits, flip-flops, counters, shift registers. Multiplexer, S/H circuit.Analog-to-Digital and Digital-to-Analog converters. Basics of number system.Microprocessor applications, memory and input-output interfacing. Microcontrollers. Signals, Systems and Communications: Periodic and aperiodic signals. Impulse response, transfer function and frequency response of first- and second order systems. Convolution, correlation and characteristics of linear time invariant systems. Discrete time system, impulse and frequency response. Pulse transfer function. IIR and FIR filters. Amplitude and frequency modulation and demodulation. Sampling theorem, pulse code modulation. Frequency and time division multiplexing. Amplitude shift keying, frequency shift keying and pulse shift keying for digital modulation. Electrical and Electronic Measurements: Bridges and potentiometers, measurement of R,L and C. Measurements of voltage, current, power, power factor and energy. A.C & D.C current probes. Extension of instrument ranges. Q-meter and waveform analyzer. Digital voltmeter and multi-meter. Time, phase and frequency measurements. Cathode ray oscilloscope. Serial and parallel communication. Shielding and grounding. Control Systems and Process Control: Feedback principles. Signal flow graphs. Transient Response, steady-state-errors. Routh and Nyquist criteria. Bode plot, root loci.

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Time delay systems. Phase and gain margin. State space representation of systems. Mechanical, hydraulic and pneumatic system components. Synchro pair, servo and step motors. On-off, cascade, P, P-I, P-I-D, feed forward and derivative controller, Fuzzy controllers. Analytical, Optical and Biomedical Instrumentation: Mass spectrometry. UV, visible and IR spectrometry. X-ray and nuclear radiation measurements. Optical sources and detectors,

LED,

laser,

Photo-diode,

photo-resistor

and

their

characteristics.

Interferometers, applications in metrology. Basics of fiber optics. Biomedical instruments, EEG, ECG and EMG. Clinical measurements. Ultrasonic transducers and Ultrasonography. Principles of Computer Assisted Tomography.

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GATE Previous Year Solved Papers Instrumentation Engineering - IN

2012 - 14

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GATE 2014 Solved Paper Instrumentation Engineering - IN Duration: 180 minutes

Maximum Marks: 100

Read the following instructions carefully. 1. To login, enter your Registration Number and password provided to you. Kindly go through the various symbols used in the test and understand their meaning before you start the examination. 2. Once you login and after the start of the examination, you can view all the questions in the question paper, by clicking on the View All Questions button in the screen. 3. This question paper consists of 2 sections, General Aptitude (GA) for 15 marks and the subject specific GATE paper for 85 marks. Both these sections are compulsory. The GA section consists of 10 questions. Question numbers 1 to 5 are of 1-mark each, while question numbers 6 to 10 are of 2-mark each. The subject specific GATE paper section consists of 55 questions, out of which question numbers 1 to 25 are of 1-mark each, while question numbers 26 to 55 are of 2-mark each. 4. Depending upon the GATE paper, there may be useful common data that may be required for answering the questions. If the paper has such useful data, the same can be viewed by clicking on the Useful Common Data button that appears at the top, right hand side of the screen. 5. The computer allotted to you at the examination center runs specialized software that permits only one answer to be selected for multiple-choice questions using a mouse and to enter a suitable number for the numerical answer type questions using the virtual keyboard and mouse. 6. Your answers shall be updated and saved on a server periodically and also at the end of the examination. The examination will stop automatically at the end of 180 minutes. 7. In each paper a candidate can answer a total of 65 questions carrying 100 marks. 8. The question paper may consist of questions of multiple choice type (MCQ) and numerical answer type. 9. Multiple choice type questions will have four choices against A, B, C, D, out of which only ONE is the correct answer. The candidate has to choose the correct answer by clicking on the bubble (⃝) placed before the choice. 10. For numerical answer type questions, each question will have a numerical answer and there will not be any choices. For these questions, the answer should be enteredby using the virtual keyboard that appears on the monitor and the mouse. 11. All questions that are not attempted will result in zero marks. However, wrong answers for multiple choice type questions (MCQ) will result in NEGATIVE marks. For all MCQ questions a wrong answer will result in deduction of⅓ marks for a 1-mark question and ⅔ marks for a 2-mark question. 12. There is NO NEGATIVE MARKING for questions of NUMERICAL ANSWER TYPE. 13. Non-programmable type Calculator is allowed. Charts, graph sheets, and mathematical tables are NOT allowed in the Examination Hall. You must use the Scribble pad provided to you at the examination centre for all your rough work. The Scribble Pad has to be returned at the end of the examination. Declaration by the candidate: “I have read and understood all the above instructions. I have also read and understood clearly the instructions given on the admit card and shall follow the same. I also understand that in case I am found to violate any of these instructions, my candidature is liable to be cancelled. I also confirm that at the start of the examination all the computer hardware allotted to me are in proper working condition”.

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GATE 2014

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. ____________ is the key to their happiness; they are satisfied with what they have. (A) Contentment

Q.3

(B) Ambition

(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.” (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.

Q.4

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? (A) 3-4 years

(B) 4-5 years

(C) 5-6 years

(D) 6-7 years

Q. 6 – Q. 10 carry two marks each.

Q.6

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. (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.

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GATE 2014 Q.7

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: (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

Q.8

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 6 16% Item 5 12%

Item 4 22%

(A) 1:2

Q.9

Item 1 11%

Item 6 19% Item 2 20%

Item 2 20%

Item 5 20%

Item 3 19%

(B) 2:1

Item 1 12%

Item 4 6%

(C) 1:4

Item 3 23%

(D) 4:1

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

Q.10

Revenues

(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 _______

END OF THE QUESTION PAPER

GATE Previous Year Solved Papers by

GATE 2014

Instrumentation Engineering - 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

Q.2

(A) a circle

(B)a multi-loop closed curve

(C)a hyperbola

(D)an ellipse

Given that x is a random variable in the range[0,∞]with a probability densityfunction �

− � 2

�

Q.3

, the value of the constant K is___________.

The figure shows the plot of y as a function of x

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 = yˆi + xˆj + zkˆ where ˆi , ˆj and kˆ are unit vectors in Cartesian (x,y,z) coordinate system. 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 ___________.

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GATE 2014 Q.5

Instrumentation Engineering - 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 Assuming independence of failures of the machines, the probability that a given job is successfully processed (up to the third decimal place) is ___________.

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 Ω resistor at time � = 0+ is___________.

2Ω

+ 10 Ω

A

V _

Q.7

Q.8

t=0

5H

6V

The average real power in watts delivered to a load impedance �� = (4 − �2)Ω by an ideal current source �(�) = 4 sin(ω� + 20°)A is ___________. 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

(C)�1 (�) lags �2 (�) by −130o Q.9

B

(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 ___________.

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GATE 2014 Q.10

Instrumentation Engineering - 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

Q.11

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

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 (B) the velocity of the fluid remains constant for all positions of the float (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

Q.13

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:

(A) IB= 800 nA, If=50 nA

(B) IB= 800 nA, If=100nA

(C) IB= 400 nA, If=50nA

(D) IB= 400 nA, If=100nA

GATE Previous Year Solved Papers by

GATE 2014 Q.14

Instrumentation Engineering - IN

The amplifier in the figure has gain of −10 and input resistance of 50 kΩ. The values of Ri and Rfare:

Rf Ri Vin

V0

+

(A) Ri= 500 kΩ, Rf = 50 kΩ

(B) Ri= 50 kΩ, Rf = 500 kΩ

(C) Ri= 5 kΩ, Rf = 10 kΩ

(D) Ri= 50 kΩ, Rf = 200 kΩ

Q.15

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

1 − 13�−1 �(�) = 1 − 14�−1

The above system can have stable inverse if the region of convergence of H(z)is defined as 1

(A) |�| < 4

1

(B) |�| < 12

1

(C) |�| > 4

1

(D) |�| < 3

GATE Previous Year Solved Papers by

GATE 2014 Q.17

The figure is a logic circuit with inputs A and B and output Y.Vss = + 5 V. The circuit is of type

(A) NOR

Q.18

Q.19

(B) AND

(C) OR

(D) NAND

The impulse response of an LTI system is given as :  ωc n=0  π h [ n] =   sin ωc n n ≠ 0  π n It represents an ideal (A)non-causal, low-pass filter

(B) causal, low-pass filter

(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 ℎ[�] = 0.5{�[�] + �[� − 1]}. The 3dB cutoff frequency of the filter is:

(A) 1.25 kHz

Q.20

Instrumentation Engineering - IN

(B) 2.50 kHz

(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

(B) 3000 bps

(C) 5000 bps

(D) 10000 bps

GATE Previous Year Solved Papers by

GATE 2014 Q.21

Instrumentation Engineering - IN

A loop transfer function is given by :

�(� + 2) � 2 (� + 10) The point of intersection of the asymptotes of �(�)�(�)on the real axis in the �-plane is at �(�)�(�) =

___________.

Q.22

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.

For obtaining balance, Z2 should consist of element(s): (A) R and C

Q.23

(B) R and L

(C) L and C

(D) Only C

A plant has an open-loop transfer function,

Gp ( s ) =

20 . ( s + 0.1)( s + 2 )( s + 100 )

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

(A)

Q.24

0.1 s + 0.1

(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: (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 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)

�

√�

GATE Previous Year Solved Papers by

GATE 2014

Instrumentation Engineering - 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

Q.28

b

The iteration step in order to solvefor the cube roots of a given number Nusing the NewtonRaphson’s method is

(A) xk +1

= xk +

1 N − xk3 ) ( 3

(B) xk +1 =

1 N  2 xk + 2  xk  3

(C) xk +1

= xk −

1 N − xk3 ) ( 3

xk +1 = (D)

1 N  2 xk − 2  3 xk 

For the matrix A satisfying the equation given below, the eigenvaluesare 1 2 3 1 2 3 [ A ] 7 8 9  =  4 5 6  4 5 6  7 8 9  (A)(1, −�, �)

(B)(1, 1, 0)

(C)(1, 1, −1) Q.29

−1

A-1 b (D) 2

A b (C)− � � 2 Q.27

)

(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 ___________.

2 kΩ

S ic (t) t= 0

5V

2 kΩ

4 µF

GATE Previous Year Solved Papers by

GATE 2014 Q.30

Instrumentation Engineering - 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 µF is___________.

A 4Ω 60 V 50 Hz j1Ω

B Q.31

The resistance of a wire is given by the expression

�=

4ρ�

, �� 2 where, ρis the resistivity (Ω-meter),L is the length (meter) and D (meter) is the diameter of the wire. The error in measurement of each of the parameters ρ, L, and D is ±1.0% . Assuming that the errors are independent random variables, the percent error in measurement of R is ___________. Q.32

The circuit shown in the figure contains a dependent current source between A and B terminals. The Thevenin’s equivalent resistance in kΩbetween the terminals C and D is ___________.

5 kΩ

A

5 kΩ

C

+ 10 V

10−4 Vx

vx _

B

D

Q.33

A thermistor has a resistance of 1 kΩ at temperature 298 Kand 465 Ω 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 Ω is used to measure the amplitude of a step force. The voltage output is measured using a digital voltmeter with input impedance 1013 Ω 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 ___________.

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Q.35

A thermopile is constructed using 10 junctions of Chromel-Constantan (sensitivity 60µV/°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.

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 ___________. Q.37

Assuming an ideal op-amp in linear range of operation, the magnitude of the transfer impedance �0 in MΩ of the current to voltage converter shown in the figure is ___________. �

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GATE 2014 Q.38

Instrumentation Engineering - IN

For the circuit shown in the figure, the transistor has β = 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 Ω

Q.39

100 Ω

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

5 kΩ 3 kΩ V2 T1

Q.40

T2

The figures show an oscillator circuit having an ideal Schmitt trigger and its input-output characteristics. The time period (in ms) of

vo ( t ) is___________.

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GATE 2014 Q.41

Instrumentation Engineering - 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) Q.42

�2 (D) √12

A microprocessor accepts external interrupts (Ext INT) through a Programmable Interrupt Controller as shown in the figure.

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 (B) Ext INT1→ INT→INTA→Data Read (C) Ext INT1→ INT→INTA→Address Write (D) Ext INT1→ INT→ Data Read→Address Write

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GATE 2014 Q.43

Instrumentation Engineering - IN

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:

(B) inversely proportional to �ref

(A)directly proportional to�ref

(D)directly proportional to clock frequency

(C)independent of�ref Q.44

�(�)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

(A) 3

Q.45

(B) 9

(C) 15

The transfer function of a digital system is given by: �0 −1 1− � + �

2�

−2

; where�2 is real.

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 ___________.

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GATE 2014 Q.47

Instrumentation Engineering - IN

In the microprocessor controlled measurement scheme shown in the figure, Rx is the unknown 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 

(C) Rx = kRref

Q.48

Q.49

(D) Rx = Rref ln k

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: (A) 1 MHz, 10-bits

(B) 10 MHz, 10-bits

(C) 1 MHz, 8-bits

(D) 10MHz, 8-bits

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

G (s) H (s) =

1

s ( s + 1)( 9 s + 1)

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 ___________.

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GATE 2014 Q.51

Instrumentation Engineering - 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 mean, is:

(A) 1

(B)−1

(C) 2

(D) −2

Q.52

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 µm 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 µm 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).

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

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Q.55

For the given low-pass circuit shown in the figure, the cutoff frequency in Hz will be ___________.

END OF THE QUESTION PAPER

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GATE 2014 - Answer Keys General Aptitude– GA Q. No.

Key / Range

Q. No.

Key / Range

Q. No.

Key / Range

1 2 3 4

D A C 25 to 25

5 6 7 8

A A C D

9 10

C 0.48 to 0.49

Instrumentation Engineering - IN Q. No. 1 2 3 4

Q. No. 20 21 22 23

Key / Range B -4 to -4 B A

Q. No. 39 40 41 42

Key / Range 5.5 to 5.8 8.0 to 8.5 A B

5 6 7 8 9 10 11 12 13

Key / Range D 2 to 2 D 1 to 1 0.890 to 0.899 -30 to ‐30 32 to 32 A 117 to 120 A C A D

24 25 26 27 28 29 30 31 32

43 44 45 46 47 48 49 50 51

14 15

B 10 to 10

33 34

52 53

A A C 67 to 69 C C 0.30 to 0.34 0.36 to 0.38 D 0.795 to 0.805 106 to 108

16 17 18 19

C D A B

35 36 37 38

B A C B C 1.5 to 1.6 186 to 188 2.3 to 2.5 20 to 20 -0.042 to ‐0.038 2.48 to 2.52 0.800 to 0.833 0.45 to 0.45 0.6 to 0.6 40 to 43

54 55

A 15 to 16

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Duration: Three Hours

Maximum Marks: 100

Read the following instructions carefully.

1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal and read the instructions printed on the ORS carefully. If you find that either: a. The Question Booklet Code printed at the right hand top corner of this page does not match with the Question Booklet Code at the right hand top corner of the ORS or b. The Question Paper Code preceding the Registration number on the ORS is not IN, then exchange the booklet immediately with a new sealed Question Booklet. 3. On the right hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the appropriate bubble under each digit of your registration number and (ii) write your registration number, your name and name of the examination centre and put your signature at the specified location. 4. This Question Booklet contains 20 pages including blank pages for rough work. After you are permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator. 5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each question has only one correct answer. Questions must be answered on the left hand side of the ORS by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen against the question number. For each question darken the bubble of the correct answer. More than one answer bubbled against a question will be treated as an incorrect response. 6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the bubbles in the ORS very carefully. 7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks questions include two pairs of common data questions and two pairs of linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, then the answer to the second question in the pair will not be evaluated. 8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each. 9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE marks. For all 1 mark questions, mark will be deducted for each wrong answer. For all 2 marks questions, mark will be deducted for each wrong answer. However, in the case of the linked answer question pair, there will be negative marks only for wrong answer to the first question and no negative marks for wrong answer to the second question. 10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the Question Booklet for rough work. 12. Before the start of the examination, write your name and registration number in the space provided below using a black ink ballpoint pen. Name Registration Number

IN

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Q.1 to Q.25 carry one mark each. Q.1

0 1 1 The dimension of the null space of the matrix  1 −1 0  is  −1 0 −1   (A) 0

Q.2

(B) 1

(C) 2

(D) 3

If the A-matrix of the state space model of a SISO linear time invariant system is rank deficient, the transfer function of the system must have (A) a pole with a positive real part (B) a pole with a negative real part (C) a pole with a positive imaginary part (D) a pole at the origin

Q.3

Q.4

Q.5

Two systems with impulse responses h1 (t ) and h2 (t ) are connected in cascade. Then the overall impulse response of the cascaded system is given by (A) product of h1 (t ) and h2 (t )

(B) sum of h1 (t ) and h2 (t )

(C) convolution of h1 (t ) and h2 (t )

(D) subtraction of h2 (t ) from h1 (t )

The complex function tanh ( s ) is analytic over a region of the imaginary axis of the complex s-plane if the following is TRUE everywhere in the region for all integers n (A) Re ( s ) = 0

(B) Im ( s ) ≠ n π

nπ (C) Im ( s ) ≠ 3

(D) Im ( s ) ≠

For a vector E, which one of the following statements is NOT TRUE? (A) If (B) If (C) If (D) If

Q.6

(2n + 1) π 2

∇ ⋅ E = 0, E is called solenoidal. ∇ × E = 0, E is called conservative. ∇ × E = 0, E is called irrotational. ∇ ⋅ E = 0, E is called irrotational.

For a periodic signal v(t ) = 30 sin100 t + 10 cos 300 t + 6 sin (500 t + π / 4) , the fundamental frequency in rad/s is (A) 100

(B) 300

(C) 500

(D) 1500

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Q.7

In the transistor circuit as shown below, the value of resistance RE in k

is approximately,

+10 V

I C = 2.0 mA

1.5 kΩ Ω 15k Ω

0.1µF VCE =5.0 V

0.1µF

6kΩ Ω

Vout RE

(A) 1.0 Q.8

(C) 2.0

(D) 2.5

A source vs (t ) = V cos100π t has an internal impedance of 4 + j3 . If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in should be (A) 3

Q.9

(B) 1.5

(B) 4

(C) 5

(D) 7

Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system? (A) All the poles of the system must lie on the left side of the jω axis. (B) Zeros of the system can lie anywhere in the s-plane. (C) All the poles must lie within s = 1 . (D) All the roots of the characteristic equation must be located on the left side of the jω axis.

Q.10

The operational amplifier shown in the circuit below has a slew rate of 0.8 Volts / µ s . The input signal is 0.25 sin (ω t ) . The maximum frequency of input in kHz for which there is no distortion in the output is

(A) 23.84

(B) 25.0

(C) 50.0

(D) 46.60

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Q.11

Assuming zero initial condition, the response y (t ) of the system given below to a unit step input u (t ) is

(A) u (t ) Q.12

The transfer function

(A)

Q.13

0.5 s + 1 s +1

2

(D) e − t u (t )

V2 ( s) of the circuit shown below is V1 ( s )

(B)

3s + 6 s+2

(B) Elliptic

The discrete-time transfer function

s+2 s +1

(C)

The type of the partial differential equation (A) Parabolic

Q.14

2 (C) t u (t )

(B) t u (t )

∂f ∂t

(D)

s +1 s+2

2

=

∂ f ∂x

2

is

(C) Hyperbolic

(D) Nonlinear

1 − 2 z −1 is 1 − 0.5 z −1

(A) non-minimum phase and unstable. (B) minimum phase and unstable. (C) minimum phase and stable. (D) non-minimum phase and stable. Q.15

Match the following biomedical instrumentation techniques with their applications P : Otoscopy Q : Ultrasound Technique R : Spirometry S : Thermodilution Technique (A) P-U, Q-V, R-X, S-W (C) P-V, Q-W, R-U, S-X

Q.16

U : Respiratory volume measurement V : Ear diagnostics W : Echo-cardiography X : Heart volume measurement (B) P-V, Q-U, R-X, S-W (D) P-V, Q-W, R-X, S-U

A continuous random variable X has a probability density function f ( x) = e − x , 0 < x < ∞ . Then P { X > 1} is

(A) 0.368

(B) 0.5

(C) 0.632

(D) 1.0

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Q.17

A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency in kHz which is not valid is (A) 5

Q.18

(B) 12

(C) 0.83

2

(B) an OR gate

(B)

t (t − 1) 2

(C) an XOR gate

u (t − 1)

(C)

(t − 1) 2 2

Ra

(A) k2

u (t − 1)

RC Rc

(B) k

(D)

t2 −1 2

u (t − 1)

RB

RA

(C) 1/k

(D)

k

An accelerometer has input range of 0 to 10g, natural frequency 30 Hz and mass 0.001 kg. The range of the secondary displacement transducer in mm required to cover the input range is (A) 0 to 2.76

Q.23

(D) a NAND gate

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

Rb

Q.22

(D) 0.60

The impulse response of a system is h(t ) = t u (t ) . For an input u (t − 1) , the output is 2 (A) t u (t )

Q.21

(B) 0.18

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

Q.20

(D) 20

The differential pressure transmitter of a flow meter using a venturi tube reads 2.5 × 105 Pa for a flow rate of 0.5 m3/s. The approximate flow rate in m3/s for a differential pressure 0.9 × 105 Pa is (A) 0.30

Q.19

(C) 15

(B) 0 to 9.81

(C) 0 to 11.20

(D) 0 to 52.10

In the circuit shown below what is the output voltage (Vout ) in Volts if a silicon transistor Q and an ideal op-amp are used?

(A)

15

(B)

0.7

(C)

0.7

(D)

15

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Q.24

In the feedback network shown below, if the feedback factor k is increased, then the

+ v in

v1

+

A0

vf = kvout+

k

+

vout

+

(A) input impedance increases and output impedance decreases (B) input impedance increases and output impedance also increases (C) input impedance decreases and output impedance also decreases (D) input impedance decreases and output impedance increases Q.25

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

The gain (20 log G ( s) ) is 32 dB and –8 dB at 1 rad/s and 10 rad/s respectively. The phase is negative for all ω. Then G (s ) is (A)

39.8 s

(B)

39.8 s2

(C)

32 s

(D)

32 s2

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Q.26 to Q.55 carry two marks each. Q.26

dy + 2 xy 2 = 0 , y (0) = 1 using Euler’s predictordx

While numerically solving the differential equation

corrector (improved Euler-Cauchy) method with a step size of 0.2, the value of y after the first step is (A) 1.00 Q.27

(B) 1.03

(D) 0.96 0 − 1 is 0  

One pair of eigenvectors corresponding to the two eigenvalues of the matrix  1 1   j

(A)   ,   − j  − 1 Q.28

(C) 0.97

0 − 1

1  0

(B)   ,   1  0 

1   j 

(C)   ,    j  1

(D)   ,    j  1 

The digital circuit shown below uses two negative edge-triggered D-flip-flops. Assuming initial condition of Q1 and Q0 as zero, the output Q1Q0 of this circuit is

Q1

D1

D0

D-Flip-flop

Q0

D-Flip-flop Q1

Q0

clock

(A) 00,01,10,11,00 … (B) 00,01,11,10,00 … (C) 00,11,10,01,00 … (D) 00,01,11,11,00 … Q.29

Considering the transformer to be ideal, the transmission parameter ‘A’ of the 2-port network shown in the figure below is

1

2Ω

2

2Ω 1:2

I1 V1

I2 5Ω

5Ω

V2

1′ (A) 1.3

2′ (B) 1.4

(C) 0.5

(D) 2.0

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Q.30

The following arrangement consists of an ideal transformer and an attenuator, which attenuates by a factor of 0.8. An ac voltage VWX 1 = 100V is applied across WX to get an open circuit voltage

VYZ 1 across YZ. Next, an ac voltage VYZ 2 = 100V is applied across YZ to get an open circuit voltage VWX 2 across WX. Then, VYZ 1 / VWX 1 , VWX 2 / VYZ 2 are respectively,

W

1:1.25

Y

X (A) 125/100 and 80/100 (C) 100/100 and 100/100 Q.31

(B) 100/100 and 80/100 (D) 80/100 and 80/100

ω (s) 10 . When connected in = V a ( s ) 1 + 10 s feedback as shown below, the approximate value of K a that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open-loop system is

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

(A) 1 Q.32

Z

(B) 5

(C) 10

(D) 100

Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the chosen operating frequency. Their respective resistances are R1 and R2. When connected in series, the effective Q factor of the series combination at the same operating frequency is (A) q1 + q2

(B) (1/ q1 ) + (1/ q2 )

(C) ( q1 R1 + q2 R2 ) / ( R1 + R2 )

(D) ( q1 R2 + q2 R1 ) / ( R1 + R2 )

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Q.33

For the circuit shown below, the knee current of the ideal Zener diode is 10 mA. To maintain 5 V across RL , the minimum value of the load resistor RL in and the minimum power rating of the Zener diode in mW, respectively, are

100

ILoad

10 V VZ = 5 V

Q.34

(A) 125 and 125

(B) 125 and 250

(C) 250 and 125

(D) 250 and 250

The impulse response of a continuous time system is given by h (t ) = δ (t − 1) + δ (t − 3) . The value of the step response at t = 2 is (A) 0

Q.35

(B) 1

(C) 2

(D) 3

Signals from fifteen thermocouples are multiplexed and each one is sampled once per second with a 16-bit ADC. The digital samples are converted by a parallel to serial converter to generate a serial PCM signal. This PCM signal is frequency modulated with FSK modulator with 1200 Hz as 1 and 960 Hz as 0. The minimum band allocation required for faithful reproduction of the signal by the FSK receiver without considering noise is (A) 840 Hz to 1320 Hz (C) 1080 Hz to 1320 Hz

Q.36

RL

(B) 960 Hz to 1200 Hz (D) 720 Hz to 1440 Hz

Three capacitors C1, C2 and C3 whose values are 10µF, 5µF, and 2µF respectively, have breakdown voltages of 10V, 5V, and 2V respectively. For the interconnection shown below, the maximum safe voltage in Volts that can be applied across the combination, and the corresponding total charge in µC stored in the effective capacitance across the terminals are, respectively,

C2

C3

C1 (A) 2.8 and 36 (C) 2.8 and 32 Q.37

(B) 7 and 119 (D) 7 and 80

The maximum value of the solution y (t ) of the differential equation y (t ) + y (t ) = 0 with initial conditions y (0) = 1 and y (0) = 1 , for t ≥ 0 is (A) 1

(B) 2

(C) π

(D)

2

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Q.38

The Laplace Transform representation of the triangular pulse shown below is

(A) (C) Q.39

1 s

2

1 s2

[1 + e −2 s ]

(B)

[1 − e− s + 2 e− 2 s ]

(D)

1 s2 1

s2

[1 − e − s + e − 2 s ]

[1 − 2 e − s + e − 2 s ]

In the circuit shown below, if the source voltage VS = 100∠53.13° Volts, then the Thevenin’s equivalent voltage in Volts as seen by the load resistance RL is j4 Ω

3Ω

j6 Ω

5Ω

VL1 j40I2

VS I1

(A) 100∠90° Q.40

RL=10 Ω

10VL1 I2

(B) 800∠0°

(C) 800∠90°

(D) 100∠60°

A signal Vi (t ) = 10 + 10 sin 100 π t + 10 sin 4000 π t + 10 sin 100000 π t is supplied to a filter circuit (shown below) made up of ideal op-amps. The least attenuated frequency component in the output will be 0.1µ F

F 1kΩ Ω 0.1µ

F 2kΩ Ω 1µ

F 750Ω 0.1µ

Vi(t)

(A) 0 Hz

V0(t)

(B) 50 Hz

(C) 2 kHz

(D) 50 kHz

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Q.41

The signal flow graph for a system is given below. The transfer function

Y ( s) for this system is U (s)

given as

(A)

(C) Q.42

s +1

(B)

5s2 + 6s + 2 s +1

(D)

2

s + 4s + 2

s +1 s2 + 6 s + 2 1 2

5s + 6s + 2

A voltage ω Volts is applied across YZ. Assuming ideal diodes, the voltage measured across WX in Volts, is 1kΩ

W

Y

X

Z +

(A)

ω

_

(B) (sin ω t + sin ω t ) / 2 (D) 0 for all t

(C) (sin ω t − sin ω t ) / 2 Q.43

1kΩ

In the circuit shown below the op-amps are ideal. Then Vout in Volts is

1k

1k

–2V +15 V +15 V

–

+ –

+

Vout

– 15 V

1k

– 15 V +1 V

1k 1k

(A) 4

(B) 6

(C) 8

(D) 10

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Q.44

In the circuit shown below, Q1 has negligible collector-to-emitter saturation voltage and the diode drops negligible voltage across it under forward bias. If Vcc is +5 V, X and Y are digital signals with 0 V as logic 0 and Vcc as logic 1, then the Boolean expression for Z is

(A) X Y Q.45

(B)

(D) XY

(C) X Y

The circuit below incorporates a permanent magnet moving coil milli-ammeter of range 1 mA having a series resistance of 10 k . Assuming constant diode forward resistance of 50 , a forward diode drop of 0.7 V and infinite reverse diode resistance for each diode, the reading of the meter in mA is _ mA

+ 10k Ω 10k Ω 5V, 50Hz

(A) 0.45 Q.46

(B) 0.5

(C) 0.7

(D) 0.9

Measurement of optical absorption of a solution is disturbed by the additional stray light falling at the photo-detector. For estimation of the error caused by stray light the following data could be obtained from controlled experiments. Photo-detector output without solution and without stray light is 500 µW. Photo-detector output without solution and with stray light is 600 µW. Photo-detector output with solution and with stray light is 200 µW. The percent error in computing absorption coefficient due to stray light is (A) 12.50

Q.47

Vo

(B) 31.66

(C) 33.33

(D) 94.98

Two ammeters A1 and A2 measure the same current and provide readings I1 and I 2 , respectively. The ammeter errors can be characterized as independent zero mean Gaussian random variables of standard deviations σ 1 and σ 2 , respectively. The value of the current is computed as : I = µ I1 + (1 − µ ) I 2 The value of µ which gives the lowest standard deviation of I is (A)

σ 22 + σ 22

σ 12

(B)

σ 12 + σ 22

σ 12

(C)

σ2 σ1 + σ 2

(D)

σ1 σ1 + σ 2

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Common Data Questions Common Data for Questions 48 and 49: A tungsten wire used in a constant current hot wire anemometer has the following parameters : Resistance at 0° C is 10 , Surface area is 10 −4 m 2 , Linear temperature coefficient of resistance of the tungsten wire is 4.8 ×10 −3 /°C, Convective heat transfer coefficient is 25.2 W / m 2 /°C, flowing air temperature is 30°C, wire current is 100 mA, mass-specific heat product is 2.5 ×10 −5 J /°C Q.48

The thermal time constant of the hot wire under flowing air condition in ms is (A) 24.5

Q.49

(B) 12.25

At steady state, the resistance of the wire in (A) 10.000 (B) 10.144

(C) 6.125

(D) 3.0625

is (C) 12.152

(D) 14.128

Common Data for Questions 50 and 51: A piezo-electric force sensor, connected by a cable to a voltage amplifier, has the following parameters : Crystal properties : Stiffness 10 9 N/m, Damping ratio 0.01, Natural frequency 105 rad/s, Force-to-Charge sensitivity 10 −9 C/N, Capacitance 10 −9 F with its loss angle assumed negligible Cable properties : Capacitance 2 × 10 −9 F with its resistance assumed negligible Amplifier properties : Input impedance 1 M , Bandwidth 1MHz , Gain 3 Q.50

The maximum frequency of a force signal in Hz below the natural frequency within its useful midband range of measurement, for which the gain amplitude is less than 1.05, approximately is, (A) 35

Q.51

(B) 350

(C) 3500

(D) 16 ×103

The minimum frequency of a force signal in Hz within its useful mid-band range of measurement, for which the gain amplitude is more than 0.95, approximately is, (A) 16

(B) 160

(C) 1600

(D) 16 ×103

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Linked Answer Questions Statement for Linked Answer Questions 52 and 53: 3

Consider a plant with the transfer function G ( s ) = 1 ( s + 1) . Let K u and Tu be the ultimate gain and ultimate period corresponding to the frequency response based closed loop Ziegler-Nichols cycling method, respectively. The Ziegler-Nichols tuning rule for a P-controller is given as : K = 0.5 K u . Q.52

The values of K u and Tu , respectively, are (A) 2 2 and 2 π

Q.53

(B) 8 and 2 π

(C) 8 and 2 π

3

(D) 2 2 and 2 π

3

The gain of the transfer function between the plant output and an additive load disturbance input of frequency 2π Tu in closed loop with a P-controller designed according to the Ziegler-Nichols tuning rule as given above is (A) –1.0

(B) 0.5

(C) 1.0

(D) 2.0

Statement for Linked Answer Questions 54 and 55: A differential amplifier with signal terminals X,Y,Z is connected as shown in Fig. (a) below for CMRR measurement where the differential amplifier has an additional constant offset voltage in the output. The observations obtained are: when Vi = 2V , V0 = 3 mV , and when Vi = 3V , V0 = 4 mV .

Fig. (a) Q.54

Assuming its differential gain to be 10 and the op-amp to be otherwise ideal, the CMRR is (A) 10 2

Q.55

Fig. (b)

(B) 103

(C) 10 4

(D) 105

The differential amplifier is connected as shown in Fig. (b) above to a single strain gage bridge. Let the strain gage resistance vary around its no-load resistance R by ±1%. Assume the input impedance of the amplifier to be high compared to the equivalent source resistance of the bridge, and the common mode characteristic to be as obtained above. The output voltage in mV varies approximately from (A) +128 to –128

(B) +128 to –122

(C) +122 to –122

(D) +99 to –101

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General Aptitude (GA) Questions Q.56 to Q.60 carry one mark each. Q.56

Statement: You can always give me a ring whenever you need. Which one of the following is the best inference from the above statement? (A) Because I have a nice caller tune. (B) Because I have a better telephone facility. (C) Because a friend in need is a friend indeed. (D) Because you need not pay towards the telephone bills when you give me a ring.

Q.57

Complete the sentence: Dare _______________ mistakes. (A) commit

Q.58

(B) to commit

(C) committed

(D) committing

Choose the grammatically CORRECT sentence: (A) Two and two add four. (B) Two and two become four. (C) Two and two are four. (D) Two and two make four.

Q.59

They were requested not to quarrel with others. Which one of the following options is the closest in meaning to the word quarrel? (A) make out

Q.60

(B) call out

(C) dig out

(D) fall out

In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41°C and of Tuesday to Thursday was 43°C. If the temperature on Thursday was 15% higher than that of Monday, then the temperature in °C on Thursday was (A) 40

(B) 43

(C) 46

(D) 49

Q.61 to Q.65 carry two marks each. Q.61

Find the sum to n terms of the series 10+84+ 734 + ..... (A) (B) (C) (D)

Q.62

(

) +1

(

) +1

(

)+n

(

)+ n

9 9n + 1 10 9 9n − 1 8 n 9 9 −1 8 n 9 9 −1 8

The set of values of p for which the roots of the equation 3x2+2x+p(p–1) = 0 are of opposite sign is (A) (–∞, 0)

Q.63

2

(B) (0, 1)

(C) (1, ∞)

(D) (0, ∞)

A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third quarter. The average speed of the car in km per hour over the entire journey is (A) 30

(B) 36

(C) 40

(D) 24

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Q.64

What is the chance that a leap year, selected at random, will contain 53 Saturdays? (A) 2/7

Q.65

(B) 3/7

(C) 1/7

(D) 5/7

Statement: There were different streams of freedom movements in colonial India carried out by the moderates, liberals, radicals, socialists, and so on. Which one of the following is the best inference from the above statement? (A) The emergence of nationalism in colonial India led to our Independence. (B) Nationalism in India emerged in the context of colonialism. (C) Nationalism in India is homogeneous. (D) Nationalism in India is heterogeneous.

END OF THE QUESTION PAPER

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GATE 2013 - Answer Keys Instrumentation Engineering - IN Q. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Key / Range B D C D D A A C C A B D A D C A A A C C B A

Q. No. 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

Key / Range B A B D Marks to All B A B C C B B D C D D C C A D C B

Q. No. 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Key / Range A B A B D C B C D C B C A D D C D B C A D

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GATE 2012 Solved Paper Instrumentation Engineering - IN

Duration: Three Hours

Maximum Marks: 100

Read the following instructions carefully.

1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal and read the instructions printed on the ORS carefully. 3. On the right half of the ORS, using ONLY a black ink ball point pen, (i) darken the bubble corresponding to your test paper code and the appropriate bubble under each digit of your registration number and (ii) write your registration number, your name and name of the examination centre and put your signature at the specified location. 4. This Question Booklet contains 20 pages including blank pages for rough work. After you are permitted to open the seal, please check all pages and report discrepancies, if any, to the invigilator. 5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each question has only one correct answer. Questions must be answered on the left hand side of the ORS by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ball point pen against the question number. For each question darken the bubble of the correct answer. More than one answer bubbled against a question will be treated as an incorrect response. 6. Since bubbles darkened by the black ink ball point pen cannot be erased, candidates should darken the bubbles in the ORS very carefully. 7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks questions include two pairs of common data questions and two pairs of linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is unattempted, then the answer to the second question in the pair will not be evaluated. 8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each. 9. Unattempted questions will result in zero mark and wrong answers will result in NEGATIVE marks. For all 1 mark questions, ̃ mark will be deducted for each wrong answer. For all 2 marks questions, ̄ mark will be deducted for each wrong answer. However, in the case of the linked answer question pair, there will be negative marks only for wrong answer to the first question and no negative marks for wrong answer to the second question. 10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 11. Rough work can be done on the question paper itself. Blank pages are provided at the end of the question paper for rough work. 12. Before the start of the examination, write your name and registration number in the space provided below using a black ink ball point pen. Name Registration Number

IN

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Instrumentation Engineering - IN

Q. 1 – Q. 25 carry one mark each. Q.1 Q.2

If x   1 , then the value of x x is (C) x (D) 1 (A) e  / 2 (B) e / 2 With initial condition x(1)  0.5 , the solution of the differential equation, dx t  x  t is dt 1 1 t t2 (B) x  t 2  (D) x  (C) x  2 2 2 2 Two independent random variables X and Y are uniformly distributed in the interval [–1, 1]. The probability that max[X, Y] is less than 1 2 is

(A) x  t  Q.3

(A) 3 4 Q.4

(C) 1 4

(D) 2 3

1 . The unilateral Laplace transform of t f (t ) is s  s 1

The unilateral Laplace transform of f (t) is

2

s 2s  1 (B)  2 2 ( s  s  1) 2 ( s  s  1) 2s  1 s (C) (D) 2 2 2 ( s  s  1) ( s  s  1) 2 Given 1 2 . If C is a counterclockwise path in the z-plane such that z  1  1 , the value of f ( z)   z 1 z  3 1 f ( z ) dz is 2 j C

(A) 

Q.5

(B) 9 16

2



Q.6

(A) –2 (B) –1 (C) 1 (D) 2 The average power delivered to an impedance (4  j3) by a current 5cos(100 t  100) A is

Q.7

(A) 44.2 W (B) 50 W (C) 62.5 W In the circuit shown below, the current through the inductor is j1 

1 1 1

0V

-

(B)

1 A 1 j

0V +

-

0A 1

- j1 

2 A 1 j

0A 1

+ 1

(A)

(D) 125 W

(C)

1 A 1 j

(D) 0 A

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Q.8

Instrumentation Engineering - IN

In the following figure, C1 and C2 are ideal capacitors. C1 has been charged to 12 V before the ideal switch S is closed at t = 0. The current i(t) for all t is

t =0

S

C2

C1 i(t)

(A) zero (C) an exponentially decaying function Q.9

(B) a step function (D) an impulse function

The impedance looking into nodes 1 and 2 in the given circuit is ib 1k

99ib

9k 1 100 2

(A) 50  Q.10

(B) 100 

(C) 5 k

(D) 10.1 k

The i-v characteristics of the diode in the circuit given below are  v  0.7 A, v  0.7 V  i   500  0 A, v  0.7 V 

1k i +

+

- 10V

v

-

The current in the circuit is (A) 10 mA Q.11

(B) 9.3 mA

(C) 6.67 mA

(D) 6.2 mA

A system with transfer function G( s) 

( s 2  9 ) ( s  2) ( s  1) ( s  3) ( s  4)

is excited by sin ( t ) . The steady-state output of the system is zero at (A)   1 rad/s (C)   3 rad/s

(B)   2 rad/s (D)   4 rad/s

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Q.12

Instrumentation Engineering - IN

The output Y of a 2-bit comparator is logic 1 whenever the 2-bit input A is greater than the 2-bit input B. The number of combinations for which the output is logic 1, is (A) 4

Q.13

Q.14

(B) 6

(C) 8

In the sum of products function f ( X , Y , Z ) 

(D) 10

(2, 3, 4, 5) , the prime implicants are

(A) X Y , X Y

(B) X Y , X Y Z , X Y Z

(C) X Y Z , X Y Z , X Y

(D) X Y Z , X Y Z , X Y Z , X Y Z

Consider the given circuit. A CLK

B

In this circuit, the race around (A) does not occur (C) occurs when CLK = 1 and A = B = 1 Q.15

If x [n]  (1 / 3) Z-plane will be (A)

Q.16

1 3

n

(B) occurs when CLK = 0 (D) occurs when CLK = 1 and A = B = 0

 (1 / 2) n u[n] , then the region of convergence (ROC) of its Z-transform in the

 z 3

(B)

1 3

 z 

1 2

(C)

1 2

 z 3

(D)

1 3

 z

A capacitive motion transducer circuit is shown. The gap d between the parallel plates of the capacitor is varied as d (t )  103 [1  0.1sin (1000 t )] m . If the value of the capacitance is 2pF at t  0 ms , the output voltage VO at t  2 ms is 1M 5 Volts DC d Capacitive transducer

(A)

Q.17

 2

mV

(C) 2 mV

(B)  mV

VO

(D) 4 mV

A psychrometric chart is used to determine (A) pH (C) CO 2 concentration

(B) Sound velocity in glasses (D) Relative humidity

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Q.18

Instrumentation Engineering - IN

A strain gauge is attached on a cantilever beam as shown. If the base of the cantilever vibrates according to the equation x(t )  sin 1t  sin 2 t , where 2 rad/s  1 , 2  3 rad/s , then the output of the strain gauge is proportional to

x Base

Cantilever beam: Stiffness=8N/m Damping=0.1Ns/m

Mass=0.001Kg

Strain gauge

(A) x Q.19

1 (1  e T s ) s

d 2x dt 2

(D)

d ( x  y) dt

(B)

1 (1  e T s ) 2 s

(C)

1 T s e s

(D)

1 T s e s2

(B) 20 m

(C) 1 m

(D) 50 nm

Light of wavelength 630 nm in vacuum, falling normally on a biological specimen of thickness 10 m, splits into two beams that are polarized at right angles. The refractive index of the tissue for the two polarizations are 1.32 and 1.333. When the two beams emerge, they are out of phase by (A) 0.13

Q.22

(C)

An LED emitting at 1 m with a spectral width of 50 nm is used in a Michelson interferometer. To obtain a sustained interference, the maximum optical path difference between the two arms of the interferometer is (A) 200 m

Q.21

dx dt

The transfer function of a Zero-Order-Hold system with sampling interval T is (A)

Q.20

(B)

y

(B) 74.3

(C) 90.0

(D) 128.6

The responsivity of the PIN photodiode shown is 0.9 A/W. To obtain Vout of –1 V for an incident optical power of 1 mW, the value of R to be used is R +5V Vout -5V

(A) 0.9 

(B) 1.1 

(C) 0.9 k

(D) 1.1 k

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Q.23

Instrumentation Engineering - IN

A periodic voltage waveform observed on an oscilloscope across a load is shown. A permanent magnet moving coil (PMMC) meter connected across the same load reads v(t)

10V 5V 0

10

12

20

time (ms)

-5V

Q.24

(A) 4 V (B) 5 V (C) 8 V (D) 10 V For the circuit shown in the figure, the voltage and current expressions are v(t )  E1 sin ( t )  E3 sin (3 t ) and i (t )  I1 sin ( t  1 )  I 3 sin (3 t  3 )  I 5 sin (5 t ) . The average power measured by the Wattmeter is

i(t) Wattmeter Load

+

v(t)

(A)

1 E1 I 1 cos1 2

(B)

1 [ E1 I 1 cos1  E1 I 3 cos3  E1 I 5 ] 2

1 1 (D) [ E1 I 1 cos1  E3 I 1 cos1 ] [ E1 I 1 cos1  E3 I 3 cos3 ] 2 2 The bridge method commonly used for finding mutual inductance is

(C) Q.25

(A) Heaviside Campbell bridge (C) De Sauty bridge

(B) Schering bridge (D) Wien bridge

Q. 26 to Q. 55 carry two marks each. Q.26

A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is (A) 1/3

Q.27

(B) 1/2

(C) 2/3

(D) 3/4

Given that  5  3 1 0 and I   A , the value of A 3 is   0 2 0 1 

(A) 15 A + 12 I (C) 17 A + 15 I Q.28

(B) 19 A + 30 I (D) 17 A + 21 I

The direction of vector A is radially outward from the origin, with

A  k r n where

r 2  x 2  y 2  z 2 and k is a constant. The value of n for which   A  0 is

(A) –2

(B) 2

(C) 1

(D) 0

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The maximum value of f ( x)  x 3  9 x 2  24 x  5 in the interval [1, 6] is (A) 21

(C) 41

Consider the differential equation d 2 y (t ) dy(t ) 2  y (t )   (t ) with y (t ) 2 dt dt

(A) –2

t 0 

 2 and

dy  0. dt t 0

dy is dt t 0

The numerical value of

Q.31

(D) 46

(B) –1

(C) 0

(D) 1

If VA  VB  6 V, then VC  VD is

R

2

VA

R

VB R R

R R

1

R

10 V

+

Q.30

(B) 25

-

Q.29

Instrumentation Engineering - IN

R VC

+ 5V

(A) –5 V Q.32

VD

2A

(B) 2 V

(C) 3 V

(D) 6 V

Assuming both the voltage sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is 2

R

+

+

- j1 

10 V

3V

-

Circuit A

(A) 0.8  Q.33

Circuit B

(B) 1.4 

(C)

2

(D) 2.8 

The voltage gain Av of the circuit shown below is 13.7 Volts 12k 100k

C

vo

C 10k

vi

(A)

Av  200

(B)

Av  100

(C)

b=100

Av  20

(D)

Av  10

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Q.34

Instrumentation Engineering - IN

The state variable description of an LTI system is given by  x1   0     x 2    0  x   a  3  3

a1 0 0

0   x1   0      a2   x2    0  u 0   x3   1 

 x1    y  1 0 0  x2  x   3

where y is the output and u is the input. The system is controllable for (A) a1  0 , a 2  0 , a3  0 (C) a1  0 , a 2  0 , a3  0

Q.35

(B) a1  0 , a 2  0 , a3  0 (D) a1  0 , a 2  0 , a3  0

The state transition diagram for the logic circuit shown is 2-1 MUX D CLK

Q

X1 Y X0 Select

Q

A A=1 A=1

(A) Q=0

A=0

A=0

Q=0

Q.36

A=1

A=1

A=1

A=1

A=1 A=0

(D) Q=1

Q=1

Q=0

A=0

Q=1

The Fourier transform of a signal h(t) is H ( j )  (2 cos) (sin 2) /  . The value of h(0) is (A) 1/4

Q.37

Q=0

Q=1

A=0 A=1

(B)

A=0

(C)

A=0

A=0

(B) 1/2

(C) 1

(D) 2

Let y[n] denote the convolution of h[n] and g[n], where h [n]  (1 / 2) n u[n] and g[n] is a causal sequence. If y[0] = 1 and y[1] = 1/2, then g[1] equals (A) 0

(B) 1/2

(C) 1

(D) 3/2

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Q.38

Instrumentation Engineering - IN

The feedback system shown below oscillates at 2 rad/s when K ( s  1) s  as 2  2 s  1

R(s) +

Y(s)

3

-

(A) K = 2 and a = 0.75 (C) K = 4 and a = 0.5 Q.39

(B) K = 3 and a = 0.75 (D) K = 2 and a = 0.5

The circuit shown is a R2 C Input

+5V

R1

+

+ Output -

+

-

-5V

1 rad/s ( R1  R2 ) C 1 (B) high pass filter with f3dB = rad/s R1C 1 (C) low pass filter with f3dB = rad/s R1C

(A) low pass filter with f3dB =

(D) high pass filter with f3dB =

1 rad/s ( R1  R2 ) C t

Q.40

The input x(t) and output y(t) of a system are related as y (t ) 

 x( ) cos(3 ) d .

The system is



(A) time-invariant and stable (C) time-invariant and not stable Q.41

A double convex lens is used to couple a laser beam of diameter 5 mm into an optical fiber with a numerical aperture of 0.5. The minimum focal length of the lens that should be used in order to focus the entire beam into the fiber is (A) 1.44 mm

Q.42

(B) 2.50 mm

(C) 4.33 mm

(D) 5.00 mm

An analog voltmeter uses external multiplier settings. With a multiplier setting of 20 kit reads 440 V and with a multiplier setting of 80 kit reads 352 V. For a multiplier setting of 40 k the voltmeter reads (A) 371 V

Q.43

(B) stable and not time-invariant (D) not time-invariant and not stable

(B) 383 V

(C) 394 V

(D) 406 V

The open loop transfer function of a unity negative feedback control system is given by 150 . The gain margin of the system is G( s)  s ( s  9) ( s  25) (A) 10.8 dB

(B) 22.3 dB

(C) 34.1 dB

(D) 45.6 dB

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Q.44

Instrumentation Engineering - IN

A dynamometer arm makes contact with the piezoelectric load cell as shown. The g-constant of the piezoelectric material is 50  103 Vm/N and the surface area of the load cell is 4 cm2. If a torque   20 Nm is applied to the dynamometer, the output voltage VO of the load cell is 0.5 m

Area A=4cm2 Torque τ

d= 1mm Load cell

VO

Dynamometer

(A) 4 V Q.45

(D) 16 V

1 200 5

ms1

(B)

1 75 10

ms1

(C)

1 50 10

ms1

(D)

1 40 5

ms1

A U-tube manometer of tube diameter D is filled with a liquid of zero viscosity. If the volume of the liquid filled is V, the natural frequency of oscillations in the liquid level about its mean position, due to small perturbations, is (A)

Q.47

(C) 10 V

Water (density: 1000 kgm–3) stored in a cylindrical drum of diameter 1 m is emptied through a horizontal pipe of diameter 0.05 m. A pitot-static tube is placed inside the pipe facing the flow. At the time when the difference between the stagnation and static pressures measured by the pitotstatic tube is 10 kPa, the rate of reduction in water level in the drum is, (A)

Q.46

(B) 5 V

D 2 2

g V

(B)

2 2



gV D

2

(C)

gD

1 2  V

1/ 3

(D)

1



g D

The open loop transfer function of a unity gain negative feedback control system is given by s 2  4s  8 . The angle  , at which the root locus approaches the zeros of the system, G( s)  s ( s  2) ( s  8) satisfies 1 (A)     tan1   4  1 (C)    tan1   2 4

(B)   (D)  

3 1  tan1   4  3



1  tan1   4  3

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Instrumentation Engineering - IN

Common Data Questions Common Data for Questions 48 and 49: With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed: (i) 1  connected at port B draws a current of 3 A (ii) 2.5  connected at port B draws a current of 2 A

+ B

A

Q.48

With 10 V dc connected at port A, the current drawn by 7  connected at port B is (A) 3/7 A (B) 5/7 A (C) 1 A (D) 9/7 A

Q.49

For the same network, with 6 V dc connected at port A, 1  connected at port B draws 7/3 A. If 8 V dc is connected to port A, the open circuit voltage at port B is (A) 6 V

(B) 7 V

(C) 8 V

(D) 9 V

Common Data for Questions 50 and 51: The deflection profile y (x ) of a cantilever beam due to application of a point force F (in Newton), as a  x function of distance x from its base, is given by y ( x )  0.001F x 2 1   m . The angular deformation   3 at the end of the cantilever is measured by reflecting a laser beam off a mirror M as shown in the figure. S

90° Laser

Photodetector

θ 3m

y(x) x

Cantilever beam

M F

1m

Q.50

Q.51

The translation S of the spot of laser light on the photodetector when a force of F  1 N is applied to the cantilever is (A) 1 mm (B) 3 mm (C) 6 mm (D) 12 mm 1 1 m and x  m on the 2 4 cantilever to measure the effect of time varying forces, the ratio of their outputs is

If linear variable differential transformers (LVDTs) are mounted at x 

(A) 12/7

(B) 40/11

(C) 176/23

(D) 112/15

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Instrumentation Engineering - IN

Linked Answer Questions Statement for Linked Answer Questions 52 and 53: The transfer function of a compensator is given as

Gc ( s )  Q.52

Gc (s) is a lead compensator if (A) a =1, b = 2 (C) a = –3, b = –1

Q.53

sa . sb (B) a = 3, b = 2 (D) a = 3, b = 1

The phase of the above lead compensator is maximum at (A)

2 rad/s

(B)

3 rad/s

(C)

(D) 1 / 3 rad/s

6 rad/s

Statement for Linked Answer Questions 54 and 55: In the circuit shown, the three voltmeter readings are V1  220 V , V2  122 V , V3  136 V .

I

V2 V1

RL V3

Load

R

X

Q.54

The power factor of the load is (A) 0.45

Q.55

(B) 0.50

(C) 0.55

(D) 0.60

If RL  5  , the approximate power consumption in the load is (A) 700 W

(B) 750 W

(C) 800 W

(D) 850 W

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Instrumentation Engineering - IN

General Aptitude (GA) Questions (Compulsory) Q. 56 – Q. 60 carry one mark each. Q.56

Choose the most appropriate alternative from the options given below to complete the following sentence: If the tired soldier wanted to lie down, he ___ the mattress out on the balcony. (A) (B) (C) (D)

Q.57

should take shall take should have taken will have taken

If (1.001)1259 = 3.52 and (1.001)2062 = 7.85, then (1.001)3321 = (A) 2.23

Q.58

(B) 4.33

(C) 11.37

(D) 27.64

One of the parts (A, B, C, D) in the sentence given below contains an ERROR. Which one of the following is INCORRECT? I requested that he should be given the driving test today instead of tomorrow. (A) requested that (B) should be given (C) the driving test (D) instead of tomorrow

Q.59

Which one of the following options is the closest in meaning to the word given below? Latitude (A) Eligibility

Q.60

(B) Freedom

(C) Coercion

(D) Meticulousness

Choose the most appropriate word from the options given below to complete the following sentence: Given the seriousness of the situation that he had to face, his ___ was impressive. (A) beggary

(B) nomenclature

(C) jealousy

(D) nonchalance

Q. 61 - Q. 65 carry two marks each. Q.61

Raju has 14 currency notes in his pocket consisting of only Rs. 20 notes and Rs. 10 notes. The total money value of the notes is Rs. 230. The number of Rs. 10 notes that Raju has is (A) 5

(B) 6

(C) 9

(D) 10

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Q.62

Instrumentation Engineering - IN

One of the legacies of the Roman legions was discipline. In the legions, military law prevailed and discipline was brutal. Discipline on the battlefield kept units obedient, intact and fighting, even when the odds and conditions were against them. Which one of the following statements best sums up the meaning of the above passage? (A) Thorough regimentation was the main reason for the efficiency of the Roman legions even in adverse circumstances. (B) The legions were treated inhumanly as if the men were animals. (C) Discipline was the armies’ inheritance from their seniors. (D) The harsh discipline to which the legions were subjected to led to the odds and conditions being against them.

Q.63

A and B are friends. They decide to meet between 1 PM and 2 PM on a given day. There is a condition that whoever arrives first will not wait for the other for more than 15 minutes. The probability that they will meet on that day is (A) 1/4

Q.64

(B) 1/16

(C) 7/16

(D) 9/16

The data given in the following table summarizes the monthly budget of an average household. Category Food Clothing Rent Savings Other expenses

Amount (Rs.) 4000 1200 2000 1500 1800

The approximate percentage of the monthly budget NOT spent on savings is (A) 10% Q.65

(B) 14%

(C) 81%

(D) 86%

There are eight bags of rice looking alike, seven of which have equal weight and one is slightly heavier. The weighing balance is of unlimited capacity. Using this balance, the minimum number of weighings required to identify the heavier bag is (A) 2

(B) 3

(C) 4

(D) 8

END OF THE QUESTION PAPER

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GATE 2012 - Answer Keys Electronic & Communication Engineering – EC Q. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Key / Range A D B D C B C D A D C B A A C B D C A B B D

Q. No. 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

Key / Range A C A C B A C D A A D D D C A A B D Marks to All Marks to All C Marks to All

Q. No. 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Key / Range D A D C C C B A A A B A D B B D A A C D A

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