GATE IN 2013: Instrumentation Engineering
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SESSION - 1
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2013 Question Booklet Code
A
IN : INSTRUMENTATION ENGINEERING
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, ⅓ mark will be deducted for each wrong answer. For all 2 marks
questions, ⅔ 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
IN-A 1/20
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2013 INSTRUMENTATION ENGG. - IN
Q.1 to Q.25 carry one mark each.
0 1 1
Q.1 The dimension of the null space of the matrix 1 −1 0 is
−1 0 −1
(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 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 )
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
nπ (2n + 1) π
(C) Im ( s ) ≠ (D) Im ( s ) ≠
3 2
Q.5 For a vector E, which one of the following statements is NOT TRUE?
(A) If ∇ ⋅ E = 0, 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 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
IN-A 2/20
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2013 INSTRUMENTATION ENGG. - IN
Q.7 In the transistor circuit as shown below, the value of resistance RE in kΩ is approximately,
+10 V
1.5 kΩ I C = 2.0 mA
15k Ω
0.1µF
VCE =5.0 V
0.1µF
6kΩ Vout
RE
(A) 1.0 (B) 1.5 (C) 2.0 (D) 2.5
Q.8 A source vs (t ) = V cos100π t has an internal impedance of 4 + j3 Ω. If a purely resistive load
connected to this source has to extract the maximum power out of the source, its value in Ω 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 / 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
IN-A 3/20
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2013 INSTRUMENTATION ENGG. - IN
Q.11 Assuming zero initial condition, the response y (t ) of the system given below to a unit step input
u (t ) is
2
(A) u (t ) (B) t u (t ) (C) t u (t ) (D) e − t u (t )
2
V2 ( s)
Q.12 The transfer function of the circuit shown below is
V1 ( s )
0.5 s + 1 3s + 6 s+2 s +1
(A) (B) (C) (D)
s +1 s+2 s +1 s+2
2
∂f ∂ f
Q.13 The type of the partial differential equation = 2
is
∂t ∂x
(A) Parabolic (B) Elliptic (C) Hyperbolic (D) Nonlinear
Q.14 1 − 2 z −1
The discrete-time transfer function 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 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
P { X > 1} is
(A) 0.368 (B) 0.5 (C) 0.632 (D) 1.0
IN-A 4/20
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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 (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 ) = t u (t ) . For an input u (t − 1) , the output is
2 t (t − 1)
(A) t u (t ) (B) u (t − 1) (t − 1) 2 t2 −1
2 2 (C) u (t − 1) (D) u (t − 1)
2 2
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
Ra RC RB
Rb Rc
RA
(A) k2 (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 (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
IN-A 5/20
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2013 INSTRUMENTATION ENGG. - IN
Q.24 In the feedback network shown below, if the feedback factor k is increased, then the
+ v + + vout
in v1 A0 –
– –
vf = kvout+ k +
– –
(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.
Gain (dB)
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
39.8 39.8 32 32
(A) (B) (C) (D)
s s2 s s2
IN-A 6/20
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Q.26 to Q.55 carry two marks each.
dy
Q.26 While numerically solving the differential equation + 2 xy 2 = 0 , y (0) = 1 using Euler’s predictor-
dx
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
0 − 1
Q.27 One pair of eigenvectors corresponding to the two eigenvalues of the matrix is
1 0
1 j 0 − 1 1 0 1 j
(A) , (B) , (C) , (D) ,
− j − 1 1
0 j 1 j 1
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
Q1 D0 Q0
D1
D-Flip-flop 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 2Ω 2
1:2
I1 I2
V1 5Ω 5Ω V2
1′ 2′
(A) 1.3 (B) 1.4 (C) 0.5 (D) 2.0
IN-A 7/20
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2013 INSTRUMENTATION ENGG. - IN
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 Z
(A) 125/100 and 80/100 (B) 100/100 and 80/100
(C) 100/100 and 100/100 (D) 80/100 and 80/100
ω (s) 10
Q.31 The open-loop transfer function of a dc motor is given as = . 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
(A) 1 (B) 5 (C) 10 (D) 100
Q.32 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 )
IN-A 8/20
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2013 INSTRUMENTATION ENGG. - IN
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 Ω and the minimum power rating of the
Zener diode in mW, respectively, are
100 Ω
10 V ILoad
VZ = 5 V RL
(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,
C2 C3
C1
(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
(A) 1 (B) 2 (C) π (D) 2
IN-A 9/20
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Q.38 The Laplace Transform representation of the triangular pulse shown below is
1 1
(A) 2
[1 + e −2 s ] (B) [1 − e − s + e − 2 s ]
s s2
1 1
(C) [1 − e− s + 2 e− 2 s ] (D) [1 − 2 e − s + e − 2 s ]
s2 s2
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
3Ω j4 Ω j6 Ω 5Ω
VL1
VS j40I2 10VL1 RL=10 Ω
I1 I2
(A) 100∠90° (B) 800∠0° (C) 800∠90° (D) 100∠60°
Q.40 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 2kΩ 1µ
F
1kΩ 0.1µ
F
750Ω 0.1
µF
Vi(t) V0(t)
(A) 0 Hz (B) 50 Hz (C) 2 kHz (D) 50 kHz
IN-A 10/20
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Y ( s)
Q.41 The signal flow graph for a system is given below. The transfer function for this system is
U (s)
given as
s +1 s +1
(A) (B)
5s2 + 6s + 2 s2 + 6 s + 2
s +1 1
(C) (D)
s + 4s + 2
2
5s + 6s + 2
2
Q.42 A voltage 1000 sin ω t Volts is applied across YZ. Assuming ideal diodes, the voltage measured
across WX in Volts, is
1kΩ
W Y X
Z
+ 1kΩ _
(A) sin ω t (B) (sin ω t + sin ω t ) / 2
(C) (sin ω t − sin ω t ) / 2 (D) 0 for all t
Q.43 In the circuit shown below the op-amps are ideal. Then Vout in Volts is
1 kΩ 1 kΩ
–2V
+15 V
+15 V
–
+ Vout
+
–
1 kΩ – 15 V
– 15 V
+1 V 1 kΩ
1 kΩ
(A) 4 (B) 6 (C) 8 (D) 10
IN-A 11/20
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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 (B) X Y (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 kΩ. Assuming constant diode forward resistance of 50 Ω, 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 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 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
σ 22 σ 12 σ2 σ1
(A) (B) (C) (D)
σ 1 + σ 22
2
σ 1 + σ 22
2
σ1 + σ 2 σ1 + σ 2
IN-A 12/20
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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 10Ω, 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 (B) 12.25 (C) 6.125 (D) 3.0625
Q.49 At steady state, the resistance of the wire in Ω 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 MΩ, 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
IN-A 13/20
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Linked Answer Questions
Statement for Linked Answer Questions 52 and 53:
Consider a plant with the transfer function G ( s ) = 1 ( s + 1) . Let K u and Tu be the ultimate gain and
3
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 (B) 8 and 2 π (C) 8 and 2 π 3 (D) 2 2 and 2 π 3
Q.53 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) Fig. (b)
Q.54 Assuming its differential gain to be 10 and the op-amp to be otherwise ideal, the CMRR is
(A) 10 2 (B) 103 (C) 10 4 (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
IN-A 14/20
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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 (B) to commit (C) committed (D) committing
Q.58 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 (B) call out (C) dig out (D) fall out
Q.60 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)
(
9 9n + 1 )
+1
10
(B)
(
9 9n − 1 )
+1
8
(C)
(
9 9n −1 )
+n
8
(D)
(
9 9n − 1 )
+ n2
8
Q.62 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) (B) (0, 1) (C) (1, ∞) (D) (0, ∞)
Q.63 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
IN-A 15/20
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Q.64 What is the chance that a leap year, selected at random, will contain 53 Saturdays?
(A) 2/7 (B) 3/7 (C) 1/7 (D) 5/7
Q.65 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
IN-A 16/20
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SESSION - 2
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2013 Question Booklet Code
B
IN : INSTRUMENTATION ENGINEERING
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, ⅓ mark will be deducted for each wrong answer. For all 2 marks
questions, ⅔ 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
IN-B 1/20
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Q.1 to Q.25 carry one mark each.
Q.1 1 − 2 z −1
The discrete-time transfer function 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.
2
∂f ∂ f
Q.2 The type of the partial differential equation = 2
is
∂t ∂x
(A) Parabolic (B) Elliptic (C) Hyperbolic (D) Nonlinear
Q.3 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.4 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
Q.5 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.6 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.7 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.8 The impulse response of a system is h(t ) = t u (t ) . For an input u (t − 1) , the output is
2 t (t − 1)
(A) t u (t ) (B) u (t − 1) (t − 1) 2 t2 −1
2 2 (C) u (t − 1) (D) u (t − 1)
2 2
IN-B 2/20
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Q.9 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
Ra RC RB
Rb Rc
RA
(A) k2 (B) k (C) 1/k (D) k
Q.10 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.11 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
Q.12 The Bode plot of a transfer function G (s ) is shown in the figure below.
Gain (dB)
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
39.8 39.8 32 32
(A) (B) (C) (D)
s s2 s s2
IN-B 3/20
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Q.13 In the feedback network shown below, if the feedback factor k is increased, then the
(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
0 1 1
Q.14 The dimension of the null space of the matrix 1 −1 0 is
−1 0 −1
(A) 0 (B) 1 (C) 2 (D) 3
Q.15 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.16 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 )
Q.17 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 (2n + 1) π
(C) Im ( s ) ≠ (D) Im ( s ) ≠
3 2
Q.18 For a vector E, which one of the following statements is NOT TRUE?
(A) If ∇ ⋅ E = 0, 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.
IN-B 4/20
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Q.19 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
Q.20 In the transistor circuit as shown below, the value of resistance RE in kΩ is approximately,
+10 V
1.5 kΩ I C = 2.0 mA
15k Ω
0.1µF
VCE =5.0 V
0.1µF
6kΩ Vout
RE
(A) 1.0 (B) 1.5 (C) 2.0 (D) 2.5
Q.21 A source vs (t ) = V cos100π t has an internal impedance of 4 + j3 Ω. If a purely resistive load
connected to this source has to extract the maximum power out of the source, its value in Ω should be
(A) 3 (B) 4 (C) 5 (D) 7
Q.22 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.
IN-B 5/20
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Q.23 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
Q.24 Assuming zero initial condition, the response y (t ) of the system given below to a unit step input
u (t ) is
2
(A) u (t ) (B) t u (t ) (C) t u (t ) (D) e − t u (t )
2
V2 ( s)
Q.25 The transfer function of the circuit shown below is
V1 ( s )
0.5 s + 1 3s + 6 s+2 s +1
(A) (B) (C) (D)
s +1 s+2 s +1 s+2
IN-B 6/20
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Q.26 to Q.55 carry two marks each.
Q.26 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
Q.27 The Laplace Transform representation of the triangular pulse shown below is
1 1
(A) [1 + e −2 s ] (B) [1 − e − s + e − 2 s ]
s2 s2
1 1
(C) [1 − e− s + 2 e − 2 s ] (D) [1 − 2 e − s + e − 2 s ]
s2 s2
Q.28 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
3Ω j4 Ω j6 Ω 5Ω
VL1
VS j40I2 10VL1 RL=10 Ω
I1 I2
(A) 100∠90° (B) 800∠0° (C) 800∠90° (D) 100∠60°
IN-B 7/20
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Q.29 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 2kΩ 1µ
F
1kΩ 0.1µ
F
0.1µ F
750Ω
Vi(t) V0(t)
(A) 0 Hz (B) 50 Hz (C) 2 kHz (D) 50 kHz
Y ( s)
Q.30 The signal flow graph for a system is given below. The transfer function for this system is
U (s)
given as
s +1 s +1
(A) (B)
5s2 + 6s + 2 s2 + 6 s + 2
s +1 1
(C) (D)
s2 + 4 s + 2 5s2 + 6s + 2
IN-B 8/20
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Q.31 A voltage 1000 sin ω t Volts is applied across YZ. Assuming ideal diodes, the voltage measured
across WX in Volts, is
1kΩ
W Y X
Z
+ 1kΩ _
(A) sin ω t (B) (sin ω t + sin ω t ) / 2
(C) (sin ω t − sin ω t ) / 2 (D) 0 for all t
Q.32 In the circuit shown below the op-amps are ideal. Then Vout in Volts is
(A) 4 (B) 6 (C) 8 (D) 10
Q.33 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) X Y (C) X Y (D) XY
IN-B 9/20
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Q.34 The circuit below incorporates a permanent magnet moving coil milli-ammeter of range 1 mA
having a series resistance of 10 kΩ. Assuming constant diode forward resistance of 50 Ω, 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 Vo
(A) 0.45 (B) 0.5 (C) 0.7 (D) 0.9
Q.35 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
σ 22 σ 12 σ2 σ1
(A) (B) (C) (D)
σ 12 + σ 22 σ 12 + σ 22 σ1 + σ 2 σ1 + σ 2
Q.36 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
0 − 1
Q.37 One pair of eigenvectors corresponding to the two eigenvalues of the matrix is
1 0
1 j 0 − 1 1 0 1 j
(A) , (B) , (C) , (D) ,
− j − 1 1 0 j 1 j 1
IN-B 10/20
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dy
Q.38 While numerically solving the differential equation + 2 xy 2 = 0, y (0) = 1 using Euler’s predictor-
dx
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.39 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 D0 Q0
D1
D-Flip-flop 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.40 Considering the transformer to be ideal, the transmission parameter ‘A’ of the 2-port network
shown in the figure below is
1 2Ω 2Ω 2
1:2
I1 I2
V1 5Ω 5Ω V2
1′ 2′
(A) 1.3 (B) 1.4 (C) 0.5 (D) 2.0
IN-B 11/20
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Q.41 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 Z
(A) 125/100 and 80/100 (B) 100/100 and 80/100
(C) 100/100 and 100/100 (D) 80/100 and 80/100
ω (s) 10
Q.42 The open-loop transfer function of a dc motor is given as = . When connected in
Va ( 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
(A) 1 (B) 5 (C) 10 (D) 100
Q.43 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 )
Q.44 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 Ω and the minimum power rating of the
Zener diode in mW, respectively, are
(A) 125 and 125 (B) 125 and 250
(C) 250 and 125 (D) 250 and 250
Q.45 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
IN-B 12/20
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Q.46 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.47 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 (B) 7 and 119
(C) 2.8 and 32 (D) 7 and 80
Common Data Questions
Common Data for Questions 48 and 49:
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 MΩ, Bandwidth 1MHz , Gain 3
Q.48 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.49 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
Common Data for Questions 50 and 51:
A tungsten wire used in a constant current hot wire anemometer has the following parameters :
Resistance at 0° C is 10Ω, 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.50 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.51 At steady state, the resistance of the wire in Ω is
(A) 10.000 (B) 10.144 (C) 12.152 (D) 14.128
IN-B 13/20
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2013 INSTRUMENTATION ENGG. - IN
Linked Answer Questions
Statement for Linked Answer Questions 52 and 53:
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) Fig. (b)
Q.52 Assuming its differential gain to be 10 and the op-amp to be otherwise ideal, the CMRR is
(A) 10 2 (B) 103 (C) 10 4 (D) 105
Q.53 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
Statement for Linked Answer Questions 54 and 55:
Consider a plant with the transfer function G ( s ) = 1 ( s + 1) . Let K u and Tu be the ultimate gain and
3
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.54 The values of K u and Tu , respectively, are
(A) 2 2 and 2 π (B) 8 and 2 π (C) 8 and 2 π 3 (D) 2 2 and 2 π 3
Q.55 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
IN-B 14/20
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General Aptitude (GA) Questions
Q.56 to Q.60 carry one mark each.
Q.56 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.57 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.58 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.59 Complete the sentence:
Dare _______________ mistakes.
(A) commit (B) to commit (C) committed (D) committing
Q.60 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 (B) call out (C) dig out (D) fall out
Q.61 to Q.65 carry two marks each.
Q.61 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
Q.62 Find the sum to n terms of the series 10+84+ 734 + .....
(A)
(
9 9n + 1 )
+1
10
(B)
(
9 9n − 1 )
+1
8
(C)
(
9 9n −1 )
+n
8
(D)
(
9 9n − 1 )
+ n2
8
IN-B 15/20
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Q.63 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.
Q.64 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) (B) (0, 1) (C) (1, ∞) (D) (0, ∞)
Q.65 What is the chance that a leap year, selected at random, will contain 53 Saturdays?
(A) 2/7 (B) 3/7 (C) 1/7 (D) 5/7
END OF THE QUESTION PAPER
IN-B 16/20
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SESSION - 3
Text of page 36
2013 Question Booklet Code
C
IN : INSTRUMENTATION ENGINEERING
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, ⅓ mark will be deducted for each wrong answer. For all 2 marks
questions, ⅔ 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
IN-C 1/20
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Q.1 to Q.25 carry one mark each.
V2 ( s)
Q.1 The transfer function of the circuit shown below is
V1 ( s )
0.5 s + 1 3s + 6 s+2 s +1
(A) (B) (C) (D)
s +1 s+2 s +1 s+2
Q.2 Assuming zero initial condition, the response y (t ) of the system given below to a unit step input
u (t ) is
2
(A) u (t ) (B) t u (t ) (C) t u (t ) (D) e − t u (t )
2
Q.3 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.4 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.5 A source vs (t ) = V cos100π t has an internal impedance of 4 + j3 Ω. If a purely resistive load
connected to this source has to extract the maximum power out of the source, its value in Ω should be
(A) 3 (B) 4 (C) 5 (D) 7
Q.6 In the transistor circuit as shown below, the value of resistance RE in kΩ is approximately,
+10 V
1.5 kΩ I C = 2.0 mA
15k Ω
0.1µF
VCE =5.0 V
0.1µF
6kΩ Vout
RE
(A) 1.0 (B) 1.5 (C) 2.0 (D) 2.5
Q.7 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
Q.8 For a vector E, which one of the following statements is NOT TRUE?
(A) If ∇ ⋅ E = 0, 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.9 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 (2n + 1) π
(C) Im ( s ) ≠ (D) Im ( s ) ≠
3 2
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Q.10 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 )
Q.11 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
0 1 1
Q.12 The dimension of the null space of the matrix 1 −1 0 is
−1 0 −1
(A) 0 (B) 1 (C) 2 (D) 3
Q.13 The Bode plot of a transfer function G (s ) is shown in the figure below.
Gain (dB)
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
39.8 39.8 32 32
(A) (B) (C) (D)
s s 2 s s2
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Q.14 In the feedback network shown below, if the feedback factor k is increased, then the
(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.15 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
Q.16 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.17 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
Ra RC RB
Rb Rc
RA
(A) k2 (B) k (C) 1/k (D) k
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Q.18 The impulse response of a system is h(t ) = t u (t ) . For an input u (t − 1) , the output is
2 t (t − 1)
(A) t u (t ) (B) u (t − 1) (t − 1) 2 t2 −1
2 2 (C) u (t − 1) (D) u (t − 1)
2 2
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 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.21 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.22 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
Q.23 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.24 1 − 2 z −1
The discrete-time transfer function 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.
2
∂f ∂ f
Q.25 The type of the partial differential equation = 2
is
∂t ∂x
(A) Parabolic (B) Elliptic (C) Hyperbolic (D) Nonlinear
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Q.26 to Q.55 carry two marks each.
Q.26 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 (B) 7 and 119
(C) 2.8 and 32 (D) 7 and 80
Q.27 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.28 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.29 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 Ω and the minimum power rating of the
Zener diode in mW, respectively, are
100 Ω
10 V ILoad
VZ = 5 V RL
(A) 125 and 125 (B) 125 and 250
(C) 250 and 125 (D) 250 and 250
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Q.30 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 )
ω (s)
10
Q.31 The open-loop transfer function of a dc motor is given as = . 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
(A) 1 (B) 5 (C) 10 (D) 100
Q.32 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 Z
(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.33 Considering the transformer to be ideal, the transmission parameter ‘A’ of the 2-port network
shown in the figure below is
1 2Ω 2Ω 2
1:2
I1 I2
V1 5Ω 5Ω V2
1′ 2′
(A) 1.3 (B) 1.4 (C) 0.5 (D) 2.0
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Q.34 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 D0 Q0
D1
D-Flip-flop 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 …
dy
Q.35 While numerically solving the differential equation + 2 xy 2 = 0, y (0) = 1 using Euler’s predictor-
dx
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
0 − 1
Q.36 One pair of eigenvectors corresponding to the two eigenvalues of the matrix is
1 0
1 j 0 − 1 1 0 1 j
(A) , (B) , (C) , (D) ,
− j − 1 1 0 j 1 j 1
Q.37 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.38 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
σ 22 σ 12 σ2 σ1
(A) (B) (C) (D)
σ 1 + σ 22
2
σ 1 + σ 22
2 σ1 + σ 2 σ1 + σ 2
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Q.39 The circuit below incorporates a permanent magnet moving coil milli-ammeter of range 1 mA
having a series resistance of 10 kΩ. Assuming constant diode forward resistance of 50 Ω, 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 Vo
(A) 0.45 (B) 0.5 (C) 0.7 (D) 0.9
Q.40 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) X Y (C) X Y (D) XY
Q.41 In the circuit shown below the op-amps are ideal. Then Vout in Volts is
(A) 4 (B) 6 (C) 8 (D) 10
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Q.42 A voltage 1000 sin ω t Volts is applied across YZ. Assuming ideal diodes, the voltage measured
across WX in Volts, is
1kΩ
W Y X
Z
+ 1kΩ _
(A) sin ω t (B) (sin ω t + sin ω t ) / 2
(C) (sin ω t − sin ω t ) / 2 (D) 0 for all t
Y ( s)
Q.43 The signal flow graph for a system is given below. The transfer function for this system is
U (s)
given as
s +1 s +1
(A) (B)
5s + 6s + 2
2
s + 6s + 2
2
s +1 1
(C) (D)
s2 + 4 s + 2 5s2 + 6s + 2
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Q.44 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 2kΩ 1µ
F
1kΩ 0.1µ
F
750Ω 0.1µ
F
Vi(t) V0(t)
(A) 0 Hz (B) 50 Hz (C) 2 kHz (D) 50 kHz
Q.45 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
3Ω j4 Ω j6 Ω 5Ω
VL1
VS j40I2 10VL1 RL=10 Ω
I1 I2
(A) 100∠90° (B) 800∠0° (C) 800∠90° (D) 100∠60°
Q.46 The Laplace Transform representation of the triangular pulse shown below is
1 1
(A) 2
[1 + e −2 s ] (B) [1 − e − s + e − 2 s ]
s s2
1 1
(C) [1 − e− s + 2 e− 2 s ] (D) [1 − 2 e − s + e − 2 s ]
s2 s2
Q.47 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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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 10Ω, 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 At steady state, the resistance of the wire in Ω is
(A) 10.000 (B) 10.144 (C) 12.152 (D) 14.128
Q.49 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
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 MΩ, Bandwidth 1MHz , Gain 3
Q.50 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
Q.51 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
IN-C 13/20
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Linked Answer Questions
Statement for Linked Answer Questions 52 and 53:
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) Fig. (b)
Q.52 Assuming its differential gain to be 10 and the op-amp to be otherwise ideal, the CMRR is
(A) 10 2 (B) 103 (C) 10 4 (D) 105
Q.53 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
Statement for Linked Answer Questions 54 and 55:
Consider a plant with the transfer function G ( s ) = 1 ( s + 1) . Let K u and Tu be the ultimate gain and
3
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.54 The values of K u and Tu , respectively, are
(A) 2 2 and 2 π (B) 8 and 2 π (C) 8 and 2 π 3 (D) 2 2 and 2 π 3
Q.55 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
IN-C 14/20
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General Aptitude (GA) Questions
Q.56 to Q.60 carry one mark each.
Q.56 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 (B) call out (C) dig out (D) fall out
Q.57 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.58 Complete the sentence:
Dare _______________ mistakes.
(A) commit (B) to commit (C) committed (D) committing
Q.59 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.60 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.61 to Q.65 carry two marks each.
Q.61 What is the chance that a leap year, selected at random, will contain 53 Saturdays?
(A) 2/7 (B) 3/7 (C) 1/7 (D) 5/7
Q.62 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.
Q.63 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) (B) (0, 1) (C) (1, ∞) (D) (0, ∞)
IN-C 15/20
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Q.64 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
Q.65 Find the sum to n terms of the series 10+84+ 734 + .....
(A)
(
9 9n + 1 )
+1
10
(B)
(
9 9n − 1)+1
8
(C)
(
9 9n −1 )+n
8
(D)
(
9 9n − 1 )
+ n2
8
END OF THE QUESTION PAPER
IN-C 16/20
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SESSION - 4
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2013 Question Booklet Code
D
IN : INSTRUMENTATION ENGINEERING
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, ⅓ mark will be deducted for each wrong answer. For all 2 marks
questions, ⅔ 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
IN-D 1/20
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Q.1 to Q.25 carry one mark each.
Q.1 In the feedback network shown below, if the feedback factor k is increased, then the
+ v + + vout
in v1 A0 –
– –
vf = kvout+ k +
– –
(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.2 The Bode plot of a transfer function G (s ) is shown in the figure below.
Gain (dB)
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
39.8 39.8 32 32
(A) (B) (C) (D)
s s 2 s s2
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Q.3 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
Q.4 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.5 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
Ra RC RB
Rb Rc
RA
(A) k2 (B) k (C) 1/k (D) k
Q.6 The impulse response of a system is h(t ) = t u (t ) . For an input u (t − 1) , the output is
2 t (t − 1)
(A) t u (t ) (B) u (t − 1) (t − 1) 2 t2 −1
2 2 (C) u (t − 1) (D) u (t − 1)
2 2
Q.7 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.8 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
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Q.9 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.10 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
Q.11 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
2
∂f ∂ f
Q.12 The type of the partial differential equation = 2
is
∂t ∂x
(A) Parabolic (B) Elliptic (C) Hyperbolic (D) Nonlinear
Q.13 1 − 2 z −1
The discrete-time transfer function 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.
V2 ( s)
Q.14 The transfer function of the circuit shown below is
V1 ( s )
0.5 s + 1 3s + 6 s+2 s +1
(A) (B) (C) (D)
s +1 s+2 s +1 s+2
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Q.15 Assuming zero initial condition, the response y (t ) of the system given below to a unit step input
u (t ) is
2
(A) u (t ) (B) t u (t ) (C) t u (t ) (D) e − t u (t )
2
Q.16 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
Q.17 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.18 A source vs (t ) = V cos100π t has an internal impedance of 4 + j3 Ω. If a purely resistive load
connected to this source has to extract the maximum power out of the source, its value in Ω should be
(A) 3 (B) 4 (C) 5 (D) 7
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Q.19 In the transistor circuit as shown below, the value of resistance RE in kΩ is approximately,
+10 V
1.5 kΩ I C = 2.0 mA
15k Ω
0.1µF
VCE =5.0 V
0.1µF
6kΩ Vout
RE
(A) 1.0 (B) 1.5 (C) 2.0 (D) 2.5
Q.20 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
Q.21 For a vector E, which one of the following statements is NOT TRUE?
(A) If ∇ ⋅ E = 0, 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.22 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 (2n + 1) π
(C) Im ( s ) ≠ (D) Im ( s ) ≠
3 2
Q.23 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 )
Q.24 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
0 1 1
Q.25 The dimension of the null space of the matrix 1 −1 0 is
−1 0 −1
(A) 0 (B) 1 (C) 2 (D) 3
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Q.26 to Q.55 carry two marks each.
Q.26 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.27 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
σ 22 σ 12 σ2 σ1
(A) (B) (C) (D)
σ 12 + σ 22 σ 12 + σ 22 σ1 + σ 2 σ1 + σ 2
Q.28 The circuit below incorporates a permanent magnet moving coil milli-ammeter of range 1 mA
having a series resistance of 10 kΩ. Assuming constant diode forward resistance of 50 Ω, 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 Vo
(A) 0.45 (B) 0.5 (C) 0.7 (D) 0.9
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Q.29 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) X Y (C) X Y (D) XY
Q.30 In the circuit shown below the op-amps are ideal. Then Vout in Volts is
(A) 4 (B) 6 (C) 8 (D) 10
Q.31 A voltage 1000 sin ω t Volts is applied across YZ. Assuming ideal diodes, the voltage measured
across WX in Volts, is
1kΩ
W Y X
Z
+ 1kΩ _
(A) sin ω t (B) (sin ω t + sin ω t ) / 2
(C) (sin ω t − sin ω t ) / 2 (D) 0 for all t
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Y ( s)
Q.32 The signal flow graph for a system is given below. The transfer function for this system is
U (s)
given as
1
U(s) 1 s-1 s-1 1 Y(s)
–4
–2
s +1 s +1
(A) (B)
5s + 6s + 2
2
s + 6s + 2
2
s +1 1
(C) (D)
s + 4s + 2
2
5s + 6s + 2
2
Q.33 A signal Vi (t ) = 10 + 10 sin 100 π t + 10 sin 4000 π t + 10 sin 100000π 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 2kΩ 1µ
F
1kΩ 0.1µ
F
750Ω 0.1
µF
Vi(t) V0(t)
(A) 0 Hz (B) 50 Hz (C) 2 kHz (D) 50 kHz
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Q.34 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
3Ω j4 Ω j6 Ω 5Ω
VL1
VS j40I2 10VL1 RL=10 Ω
I1 I2
(A) 100∠90° (B) 800∠0° (C) 800∠90° (D) 100∠60°
Q.35 The Laplace Transform representation of the triangular pulse shown below is
1 1
(A) 2
[1 + e −2 s ] (B) 2
[1 − e − s + e − 2 s ]
s s
1 1
(C) [1 − e −s
+ 2e −2s
] (D) [1 − 2 e − s + e − 2 s ]
s2 s 2
Q.36 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
Q.37 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 (B) 7 and 119
(C) 2.8 and 32 (D) 7 and 80
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Q.38 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.39 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.40 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 Ω and the minimum power rating of the
Zener diode in mW, respectively, are
(A) 125 and 125 (B) 125 and 250
(C) 250 and 125 (D) 250 and 250
Q.41 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 )
ω (s) 10
Q.42 The open-loop transfer function of a dc motor is given as = . When connected in
Va ( 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
(A) 1 (B) 5 (C) 10 (D) 100
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Q.43 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 Z
(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.44 Considering the transformer to be ideal, the transmission parameter ‘A’ of the 2-port network
shown in the figure below is
1 2Ω 2Ω 2
1:2
I1 I2
V1 5Ω 5Ω V2
1′ 2′
(A) 1.3 (B) 1.4 (C) 0.5 (D) 2.0
Q.45 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 D0 Q0
D1
D-Flip-flop 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 …
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dy
Q.46 While numerically solving the differential equation + 2 xy 2 = 0, y (0) = 1 using Euler’s predictor-
dx
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
0 − 1
Q.47 One pair of eigenvectors corresponding to the two eigenvalues of the matrix is
1 0
1 j 0 − 1 1 0 1 j
(A) , (B) , (C) , (D) ,
− j − 1 1
0 j 1 j 1
Common Data Questions
Common Data for Questions 48 and 49:
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 MΩ, Bandwidth 1MHz , Gain 3
Q.48 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
Q.49 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
Common Data for Questions 50 and 51:
A tungsten wire used in a constant current hot wire anemometer has the following parameters :
Resistance at 0° C is 10Ω, 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.50 At steady state, the resistance of the wire in Ω is
(A) 10.000 (B) 10.144 (C) 12.152 (D) 14.128
Q.51 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
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Linked Answer Questions
Statement for Linked Answer Questions 52 and 53:
Consider a plant with the transfer function G ( s ) = 1 ( s + 1) . Let K u and Tu be the ultimate gain and
3
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 (B) 8 and 2 π (C) 8 and 2 π 3 (D) 2 2 and 2 π 3
Q.53 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) Fig. (b)
Q.54 Assuming its differential gain to be 10 and the op-amp to be otherwise ideal, the CMRR is
(A) 10 2 (B) 103 (C) 10 4 (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
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General Aptitude (GA) Questions
Q.56 to Q.60 carry one mark each.
Q.56 Complete the sentence:
Dare _______________ mistakes.
(A) commit (B) to commit (C) committed (D) committing
Q.57 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 (B) call out (C) dig out (D) fall out
Q.58 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.59 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.60 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.61 to Q.65 carry two marks each.
Q.61 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) (B) (0, 1) (C) (1, ∞) (D) (0, ∞)
Q.62 What is the chance that a leap year, selected at random, will contain 53 Saturdays?
(A) 2/7 (B) 3/7 (C) 1/7 (D) 5/7
Q.63 Find the sum to n terms of the series 10+84+ 734 + .....
(A)
(
9 9n + 1 )
+1
10
(B)
(
9 9n − 1 )
+1
8
(C)
(
9 9n −1 )
+n
8
(D)
(
9 9n − 1 )
+ n2
8
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Q.64 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.
Q.65 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
END OF THE QUESTION PAPER
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Source: GATE. Question paper published by GATE.