**SOLVED PAPERS**

## GATE

**INSTRUMENTATION ENGINEERING (IN)**

**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

### 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.

### 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.

### 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.

### 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).

### contains 11 questions carrying a total of 15 marks: 7 questions carrying 1 mark each

### (sub-total 7 marks), and 4 questions carrying 2 marks each (sub-(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.

**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**

### 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.**

### 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.

**GATE**

**Previous Year Solved Papers**

### 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 of

**⅓**

marks for a 1-mark question and **⅓**

**⅔**

marks for a 2-mark question.
**⅔**

**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”.

**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 short-term memory loss.

(A) experienced (B) has experienced

(C) is experiencing (D) experiences

Q.2 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 (B) Ambition (C) Perseverance (D) Hunger Q.3 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.

Q.7 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?

(A) 1:2 (B) 2:1 (C) 1:4 (D) 4:1

Q.9 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

Q.10 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 **

**Item 1**
**11%**
**Item 2**
**20%**
**Item 3**
**19%**
**Item 4**
**22%**
**Item 5**
**12%**
**Item 6**
**16%**

**Exports**

**Item 1**

**12%**

**Item 2**

**20%**

**Item 3**

**23%**

**Item 4**

**6%**

**Item 5**

**20%**

**Item 6**

**19%**

**Revenues**

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

Q.1 Given
�(�) = 3 sin(1000 ��)and �(�) = 5 cos �1000 �� + �_{4}�
The x-yplot will be

(A) a circle (B)a multi-loop closed curve

(C)a hyperbola (D)an ellipse

Q.2 *Given that x is a random variable in the range[0,∞]with a probability densityfunction *

�−�2

� * , the value of the constant K is___________. *

Q.3 *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)
2
2 1
*d y*
*dx* =
(B) *dy* *x*
*dx* =
(C) *dy* _{x}*dx*= − (D)
*dy*
*x*
*dx*=
Q.4 A vector is defined as

### ˆ

### ˆ

### ˆ

*y*

*x*

*z*

### =

### + +

**f**

**i**

**j**

**k**

where

### ˆ ˆ

**i j**

### , and

**k**

### ˆ

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

Q.5 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.

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___________. }
A _{B}

### +

### _

*V*

### 10

### Ω

### 6 V

### 2

### Ω

### 5 H

### t=0

Q.7 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 ___________.

Q.8 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 (B)�_{1}(�) lags �_{2}(�) by 130o
(C)�1(�) lags �2(�) by −130

o

(D)�1(�) leads�2(�)by −130

o

Q.9 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 ___________.

**A **

**B **

**C **

**Input job ** _{Finished }

Q.10 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

Q.14 The amplifier in the figure has gain of −10 and input resistance of 50 kΩ. The values of Ri and Rfare: +

### R

_{i}

### R

_{f}

### V

_{in}

### V

0 (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 kΩQ.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

### −

1 3### �

−1### 1

### −

14

### �

−1*The above system can have stable inverse if the region of convergence of H(z)is defined as *
(A) |�| <1
4 (B) |�| <
1
12 (C) |�| >
1
4 (D) |�| <
1
3

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 (B) AND (C) OR (D) NAND

Q.18 The impulse response of an LTI system is given as :

### [ ]

0 sin 0*c*

*c*

*n*

*h n*

*n*

*n*

*n*ω π ω π

_{=} =

_{≠} 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

Q.19 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 (B) 2.50 kHz (C) 4 .00 kHz (D) 5.00 kHz

Q.20 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:

Q.21 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 (B) R and L (C) L and C (D) Only C

Q.23 A plant has an open-loop transfer function,

### ( ) (

0.1### )(

202### )(

100### )

*p*

*G*

*s*

*s*

*s*

*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

(A) 0.1
0.1
*s*+ (B)
2
2
*s*+ (C)
100
100
*s*+ (D)
20
0.1
*s*+

Q.24 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) � √�

**Q. 31 – Q. 55 carry two marks each. **

Q.26 A scalar valued function is defined as

### ( )

*T*

*T*

*f* **x** =**x Ax**+**b 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)

### (

**A A**

*T*

### )

−1**b**(B)

**− A A b**

### (

*T*

### )

−1 (C)− �**A**-1

**b**2 � (D)

**A**-1

**b**2

*Q.27 The iteration step in order to solvefor the cube roots of a given number Nusing the *
Newton-Raphson’s method is
(A) _{1}

### 1

### (

3### )

### 3

*k*

*k*

*k*

*x*

_{+}

### =

*x*

### +

*N*

### −

*x*

(B) _{1}2

### 1

### 2

### 3

*k*

*k*

*k*

*N*

*x*

*x*

*x*

+
###

###

### =

_{}

### +

_{}

###

###

(C)_{1}

### 1

### (

3### )

### 3

*k*

*k*

*k*

*x*

_{+}

### =

*x*

### −

*N*

### −

*x*

_{(D)}1 2

### 1

### 2

### 3

*k*

*k*

*k*

*N*

*x*

*x*

*x*

+
###

###

### =

_{}

### −

_{}

###

###

**Q.28 For the matrix A satisfying the equation given below, the eigenvaluesare **

### [ ]

1 2 3 1 2 3 7 8 9 4 5 6 4 5 6 7 8 9 _{=}

**A**(A)(1,−�, �) (B)(1, 1, 0) (C)(1, 1,−1) (D)(1, 0, 0)

Q.29 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 ___________.

### 5 V

### S

### 2 kΩ

### 2 kΩ

### 4

### µF

t= 0### i

c### (t)

Q.30 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___________.

### 4Ω

### j1Ω

### 60 V

### 50 Hz

### A

### B

Q.31 The resistance of a wire is given by the expression

### � =

_{��}4

### ρ

�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 ___________.

A B

### 10 V

### 5 kΩ

### 5 kΩ

C D### +

### _

### v

_{x}### 10

−4### V

_{x}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 = 10
10 _{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 ___________.

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

Q.38 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

330Ω 100Ω

Q.39 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 ___________.

9 V
5 kΩ
3 kΩ
V_{2}
V_{1}
T_{1} T2
T3

Q.40 The figures show an oscillator circuit having an ideal Schmitt trigger and its input-output characteristics. The time period (in ms) of

*v t*

_{o}### ( )

*is___________.*

*Q.41 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 12(2�−1)2 (B) �2 12(2�−1) (C) � 12(2�−1) (D) �2 √12

Q.42 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

Q.43 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:

(A)directly proportional to�ref (B) inversely proportional to �ref

(C)independent of�_{ref} (D)directly proportional to clock frequency

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 (B) 9 (C) 15 (D) 18

Q.45 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 (B) −0.75 (C) 0.5 (D) 1.5

Q.46 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 ___________.

Q.47 In the microprocessor controlled measurement scheme shown in the figure,

*R*

_{x}is the unknown resistance to be measured, while

*R*

_{ref}and

*C*

_{ref}are known.

*C*

_{ref}

*is charged from voltage V*L

*to V*H (by

*a constant DC voltage source VS), once through R*ref

*in T*ref

*seconds and then discharged to V*L . It

*isagain charged from voltage V*L

*to V*H

*throughR*x

*in T*x seconds.

x
If *T* =*kT _{ref}* then
(A) x ref

### 1

*L*

*H*

*V*

*R*

*kR*

*V*

###

###

### =

_{}

### −

_{}

###

###

(B) x ref### ln

*H*

*L*

*V*

*R*

*kR*

*V*

###

###

### =

_{}

_{}

###

_{ }

(C)*R*

_{x}

### =

*kR*

_{ref}(D)

*R*

_{x}

### =

*R*

_{ref}

### ln

*k*

Q.48 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

Q.49 The loop transfer function of a feedback control system is given by

### ( ) ( ) ( )( )

### 1

### 1 9

### 1

*G s H s*

*s s*

*s*

### =

### +

### +

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 ___________.

Q.51 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

Q.55

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

**GATE 2014 - Answer Keys**

**General Aptitude– GA**

**Q. No.**

**Key / Range Q. No.**

**Key / Range Q. No.**

**Key / Range**

1 D 5 A 9 C

2 A 6 A 10 0.48 to 0.49

3 C 7 C

4 25 to 25 8 D

**Instrumentation Engineering - IN**

**Q. No.**

**Key / Range Q. No.**

**Key / Range Q. No.**

**Key / Range**

### 1

### D

### 20

### B

### 39

### 5.5 to 5.8

### 2

### 2 to 2

### 21

### -4 to -4

### 40

### 8.0 to 8.5

### 3

### D

### 22

### B

### 41

### A

### 4

### 1 to 1

### 23

### A

### 42

### B

### 5

### 0.890 to

### 0.899

### 24

### B

### 43

### A

### 6

### -30 to ‐30

### 25

### A

### 44

### A

### 7

### 32 to 32

### 26

### C

### 45

### C

### 8

### A

### 27

### B

### 46

### 67 to 69

### 9

### 117 to 120

### 28

### C

### 47

### C

### 10

### A

### 29

### 1.5 to 1.6

### 48

### C

### 11

### C

### 30

### 186 to 188

### 49

### 0.30 to 0.34

### 12

### A

### 31

### 2.3 to 2.5

### 50

### 0.36 to 0.38

### 13

### D

### 32

### 20 to 20

### 51

### D

### 14

### B

### 33

### -0.042 to

### ‐0.038

### 52

### 0.795 to

### 0.805

### 15

### 10 to 10

### 34

### 2.48 to 2.52

### 53

### 106 to 108

### 16

### C

### 35

### 0.800 to

### 0.833

### 54

### A

### 17

### D

### 36

### 0.45 to 0.45

### 55

### 15 to 16

### 18

### A

### 37

### 0.6 to 0.6

### 19

### B

### 38

### 40 to 43

*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 **

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

Q.1 The dimension of the null space of the matrix

0 1 1 1 1 0 1 0 1 − − − is (A) 0 (B) 1 (C) 2 (D) 3

Q.2 _{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 Two systems with impulse responses *h t*1( ) and *h t*2( ) are connected in cascade. Then the overall

impulse response of the cascaded system is given by

(A) product of *h t*_{1}( ) and *h t*_{2}( ) (B) sum of *h t*_{1}( ) and*h t*_{2}( )

(C) convolution of *h t*_{1}( ) and *h t*_{2}( ) (D) subtraction of *h t*_{2}( ) from *h t*_{1}( )

Q.4 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
(C) ( )
3
*n*
*Im s* ≠ π (D) ( ) (2 1)
2
*n*
*Im s* ≠ + π

Q.5 * For a vector E, which one of the following statements is NOT TRUE? *
(A) If ∇ ⋅

*=0,*

**E**

_{ E is called solenoidal. }(B) If ∇ ×* E* =0,

_{ E is called conservative. }(C) If ∇ ×* E* =0,

_{ E is called irrotational. }(D) If ∇ ⋅* E*=0,

*E is called irrotational.*

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

Q.7 In the transistor circuit as shown below, the value of resistance RE in k is approximately,
**+10 V**
**RE**
**Vout **
**1.5 kΩ**ΩΩΩ
**0.1µF**
**0.1µF**
**I C = 2.0 mA**
**VCE =5.0 V**
**6kΩ**ΩΩΩ
**15k Ω**ΩΩΩ
(A) 1.0 **(B) 1.5 ** (C) 2.0 (D) 2.5

Q.8 A source *v ts*( )=*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 (B) 4 (C) 5 (D) 7

Q.9 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/µs. The input

signal is 0.25sin(ω*t*). The maximum frequency of input in kHz for which there is no distortion in
the output is

Q.11 Assuming zero initial condition, the response *y(t*) of the system given below to a unit step input
)
*(t*
*u* is
(A) *u(t*) (B) *tu(t*) (C) ()
2
2
*t*
*u*
*t* _{(D) }* _{e}*−

*t*

_{u}_{(t}_{)}

Q.12 The transfer function
)
(
)
(
1
2
*s*
*V*
*s*
*V*

of the circuit shown below is

(A)
1
1
5
.
0
+
+
*s*
*s*
(B)
2
6
3
+
+
*s*
*s*
(C)
1
2
+
+
*s*
*s*
(D)
2
1
+
+
*s*
*s*

Q.13 The type of the partial differential equation

2
2
*f* *f*
*t* *x*
∂ ∂
=
∂ ∂ is

(A) Parabolic (B) Elliptic (C) Hyperbolic (D) Nonlinear

Q.14_{ The discrete-time transfer function }

1
1
1 2
1 0.5
*z*
*z*
−
−
−
− is

(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 U : Respiratory volume measurement

Q : Ultrasound Technique V : Ear diagnostics

R : Spirometry W : Echo-cardiography

S : Thermodilution Technique X : Heart volume measurement

(A) P-U, Q-V, R-X, S-W (B) P-V, Q-U, R-X, S-W

(C) P-V, Q-W, R-U, S-X (D) P-V, Q-W, R-X, S-U

Q.16 A continuous random variable X has a probability density function *f*(*x*)=*e*−*x*,0*< x*<∞. Then
}

1
{*X* >

*P* is

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 (B) 12 (C) 15 (D) 20

Q.18 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 (B) 0.18 (C) 0.83 (D) 0.60

Q.19 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 (B) an OR gate (C) an XOR gate (D) a NAND gate

Q.20 The impulse response of a system is *h*(*t*)=*tu*(*t*). For an input *u*(*t*−1), the output is

(A) ()
2
2
*t*
*u*
*t* _{(B) } _{(} _{1}_{)}
2
)
1
(
−
−
*t*
*u*
*t*
*t*
_{(C) } _{(} _{1}_{)}
2
2
)
1
(
−
−
*t*
*u*
*t*
(D) ( 1)
2
1
2
−
−
*t*
*u*
*t*

Q.21 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

R_{B}
R_{C}
R_{b}
R_{a}
R_{c}
R_{A}
*(A) k*2 *(B) k * *(C) 1/k * (D) *k*

Q.22 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 (B) 0 to 9.81 (C) 0 to 11.20 (D) 0 to 52.10

Q.23_{ In the circuit shown below what is the output voltage }_{(} _{)}

out

*V* in Volts if a silicon transistor Q and an
ideal op-amp are used?

Q.24 In the feedback network shown below, if the feedback factor k is increased, then the

### A

0### k

### v

in### v

1### v

out### +

### +

### +

### +

### +

### v

_{f}

### = kv

_{out}

(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)
*s*
8
.
39
(B)
2
8
.
39
*s*
(C)
*s*
32
(D)
2
32
*s*

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

Q.26_{ While numerically solving the differential equation } 2

2 0 ,

*dy*
*xy*

*dx*+ = *y*(0)=1 using Euler’s

*predictor-corrector (improved Euler-Cauchy) method with a step size of 0.2, the value of y after the first step *
is

(A) 1.00 (B) 1.03 (C) 0.97 (D) 0.96

Q.27 One pair of eigenvectors corresponding to the two eigenvalues of the matrix
−
0
1
1
0
is
(A)
−
− , 1
1 *j*
*j* (B)
−
0
1
,
1
0
(C)
1
0
,
1
*j* (D)
1
,
1 *j*
*j*

Q.28 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

**D1**
**Q1** _{D0}**Q0**
Q0
Q1
**clock**
**D-Flip-flop** **D-Flip-flop**
(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

**1:2**
5Ω
5Ω5Ω
5Ω _{5Ω}_{5Ω}_{5Ω}_{5Ω}
2Ω
2Ω
2Ω
2Ω
2Ω
2Ω
2Ω
2Ω **2**
2′
2′2′
2′
**V**_{2}**I**_{2}**1**
1′
1′
1′
1′
**V**_{1}**I**** _{1}**
(A) 1.3 (B) 1.4 (C) 0.5 (D) 2.0

Q.30 The following arrangement consists of an ideal transformer and an attenuator, which attenuates
by a factor of 0.8. An ac voltage*V _{WX}*

_{1}= 100V is applied across WX to get an open circuit voltage

1

*YZ*

*V* across YZ. Next, an ac voltage*V _{YZ}*

_{2}= 100V is applied across YZ to get an open circuit voltage

*V*

_{WX}_{2}across WX. Then,

*V*

_{YZ}_{1}/

*V*

_{WX}_{1},

*V*

_{WX}_{2}/

*V*

_{YZ}_{2}are respectively,

W

X

Y

Z 1:1.25

(A) 125/100 and 80/100 (B) 100/100 and 80/100

(C) 100/100 and 100/100 (D) 80/100 and 80/100

Q.31_{ The open-loop transfer function of a dc motor is given as }

*s*
*s*
*V*
*s*
*a* 1 10
10
)
(
)
(
+
=
ω
. When connected in
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

(A) 1 (B) 5 (C) 10 (D) 100

Q.32 Two magnetically uncoupled inductive coils have Q factors q1* and q*2 at the chosen operating

*frequency. Their respective resistances are R*1* and R*2. When connected in series, the effective

*Q factor of the series combination at the same operating frequency is *

(A) *q*_{1}+*q*_{2} (B) (1/*q*_{1}) (1/+ *q*_{2})

Q.33 For the circuit shown below, the knee current of the ideal Zener diode is 10 mA. To maintain 5 V
across *R _{L}*, the minimum value of the load resistor

*R*in and the minimum power rating of the Zener diode in mW, respectively, are

_{L}

### 100

### I

_{Load}

### V

Z### = 5 V

### 10 V

### R

_{L}

(A) 125 and 125 (B) 125 and 250

(C) 250 and 125 (D) 250 and 250

Q.34 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 (B) 1 (C) 2 (D) 3

Q.35 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 (B) 960 Hz to 1200 Hz

(C) 1080 Hz to 1320 Hz (D) 720 Hz to 1440 Hz

Q.36 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,

C_{3}
C_{1}
C_{2}

(A) 2.8 and 36 (B) 7 and 119

(C) 2.8 and 32 (D) 7 and 80

Q.37 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

Q.38 The Laplace Transform representation of the triangular pulse shown below is
(A) 1_{2}[1 *e* 2*s*]
*s*
−
+ (B) 1_{2}[1 *e* *s* *e* 2*s*]
*s*
−
− _{+}
−
(C) 2
2
1
[1 *e* *s* 2*e* *s*]
*s*
− −
− + (D) 1_{2}[1 2*e* *s* *e* 2*s*]
*s*
−
−
+
−

Q.39* 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

Ω
Ω
Ω
Ω
**V _{S}**

*ΩΩΩ*

**j4 Ω***ΩΩΩ 5Ω5Ω5Ω5Ω 3Ω 3Ω3Ω 3Ω*

**j6 Ω****R**

_{L}=10**10V**

_{L1}

**j40I**

_{2}**I2**

**I1**

**V**(A) 100∠90° (B) 800∠0° (C) 800∠90° (D) 100∠60°

_{L1}Q.40 A signal *V _{i}*(

*t*)=10+10sin100π

*t*+10sin4000π

*t*+10sin100000π

*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

**F**0.1 0.1 0.1 0.1µµµµ

*750Ω 750Ω 750Ω 750Ω 0.10.10.10.1µµµµ*

**V****i****(t)****F**

*1 11 1µµµµ*

**V****0****(t)****F**

**F**0.1 0.1 0.1 0.1µµµµ

**1kΩ**ΩΩΩ

**2kΩ**ΩΩΩ (A) 0 Hz (B) 50 Hz

*(C) 2 kHz*

*(D) 50 kHz*

Q.41 The signal flow graph for a system is given below. The transfer function
)
(
)
(
*s*
*U*
*s*
*Y*

for this system is
given as
(A)
2
6
5
1
2_{+} _{+}
+
*s*
*s*
*s*
(B)
2
6
1
2_{+} _{+}
+
*s*
*s*
*s*
(C)
2
4
1
2
+
+
+
*s*
*s*
*s*
(D)
2
6
5
1
2
+
*+ s*
*s*

Q.42 A voltage ω Volts is applied across YZ. Assuming ideal diodes, the voltage measured across WX in Volts, is 1kΩ _ + 1kΩ W X Z Y

(A) ω _{(B) }_{(sin}

_{ω}

_{t}_{+}

_{sin}

_{ω}

_{t}_{)}

_{/}

_{2}

(C) (sinω*t*− sinω*t* )/2 (D) 0 for all *t*

Q.43 In the circuit shown below the op-amps are ideal. Then V_{out}in Volts is

+15 V – 15 V

### +

+15 V – 15 V### +

1 k 1 k 1 k 1 k 1 k +1 V – 2 V Vout### –

### –

(A) 4 (B) 6 (C) 8 (D) 10### ___________________________________________________________

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 (B) (C) X Y (D) XY

Q.45 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 *
Ω
Ω
Ω
Ω
**mA**
**_**
**+**
Ω
Ω
Ω
Ω
**5V, **
**50Hz**
**10k**
**10k**
**Vo**
(A) 0.45 (B) 0.5 (C) 0.7 (D) 0.9

Q.46 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 (B) 31.66 (C) 33.33 (D) 94.98

Q.47 Two ammeters *A*1 and *A*2 measure the same current and provide readings *I*1 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 :

1 (1 ) 2

*I*=µ*I* + −µ *I*

The value of µwhich gives the lowest standard deviation of *I* is

(A) 2 2 2 2 1 2 σ σ +σ (B) 2 1 2 2 1 2 σ σ +σ (C) 2 1 2 σ σ +σ (D) 1 1 2 σ σ +σ

**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 m*−4 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 J*× −5 /°C

Q.48 The thermal time constant of the hot wire under flowing air condition in ms is

(A) 24.5 (B) 12.25 (C) 6.125 (D) 3.0625

Q.49 At steady state, the resistance of the wire in is

(A) 10.000 (B) 10.144 (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 109*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 mid-band range of measurement, for which the gain amplitude is less than 1.05, approximately is,

(A) 35 (B) 350 (C) 3500 (D) 16 ×103

Q.51 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

**Linked Answer Questions **

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

Consider a plant with the transfer function*G s*

### ( )

=1### (

*s*+1

### )

3. Let*K*and

_{u}*T*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 :

_{u}*K*=0.5

*K*.

_{u}Q.52_{ The values of }

*u*

*K* and *T _{u}*, respectively, are

(A) 2 2and 2π (B) 8 and 2π (C) 8 and 2π 3 (D) 2 2and 2π 3

Q.53 The gain of the transfer function between the plant output and an additive load disturbance input of
frequency 2π *T _{u}* 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 *V _{i}*=2 ,

*V V*

_{0}=3

*mV*, and when

*V*=3 ,

_{i}*V V*

_{0}=4

*mV*.

Fig. (a) Fig. (b)

Q.54 Assuming its differential gain to be 10 and the op-amp to be otherwise ideal, the CMRR is

(A) 102 (B) 103 (C) 104 (D) 105

Q.55 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