GATE IN 2018: Instrumentation Engineering
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GATE 2018 General Aptitude (GA) Set-4
Q. 1 – Q. 5 carry one mark each.
Q.1 “When she fell down the _______, she received many _______ but little help.”
The words that best fill the blanks in the above sentence are
(A) stairs, stares (B) stairs, stairs
(C) stares, stairs (D) stares, stares
Q.2 “In spite of being warned repeatedly, he failed to correct his _________ behaviour.”
The word that best fills the blank in the above sentence is
(A) rational (B) reasonable (C) errant (D) good
Q.3 For 0 ≤ x ≤ 2π, sin x and cos x are both decreasing functions in the interval ________.
π π 3π 3π
(A) (0, 2 ) (B) ( 2 , π) (C) (π, 2 ) (D) ( 2 , 2π)
Q.4 The area of an equilateral triangle is √3. What is the perimeter of the triangle?
(A) 2 (B) 4 (C) 6 (D) 8
Q.5 Arrange the following three-dimensional objects in the descending order of their volumes:
(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm
(ii) A cube of side 8 cm
(iii) A cylinder with base radius 7 cm and height 7 cm
(iv) A sphere of radius 7 cm
(A) (i), (ii), (iii), (iv)
(B) (ii), (i), (iv), (iii)
(C) (iii), (ii), (i), (iv)
(D) (iv), (iii), (ii), (i)
Q. 6 – Q. 10 carry two marks each.
Q.6 An automobile travels from city A to city B and returns to city A by the same route. The
speed of the vehicle during the onward and return journeys were constant at 60 km/h and
90 km/h, respectively. What is the average speed in km/h for the entire journey?
(A) 72 (B) 73 (C) 74 (D) 75
GA 1/2
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GATE 2018 General Aptitude (GA) Set-4
Q.7 A set of 4 parallel lines intersect with another set of 5 parallel lines. How many
parallelograms are formed?
(A) 20 (B) 48 (C) 60 (D) 72
Q.8 To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of
6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000
candidates. Question B was answered correctly by 2,50,000 candidates. Question C was
answered correctly by 2,60,000 candidates. Both questions A and B were answered
correctly by 1,00,000 candidates. Both questions B and C were answered correctly by
90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates.
If the number of students answering all questions correctly is the same as the number
answering none, how many candidates failed to clear the test?
(A) 30,000 (B) 2,70,000 (C) 3,90,000 (D) 4,20,000
1
Q.9 If x 2 + x − 1 = 0 what is the value of x 4 + ?
x4
(A) 1 (B) 5 (C) 7 (D) 9
Q.10 In a detailed study of annual crow births in India, it was found that there was relatively no
growth during the period 2002 to 2004 and a sudden spike from 2004 to 2005. In another
unrelated study, it was found that the revenue from cracker sales in India which remained
fairly flat from 2002 to 2004, saw a sudden spike in 2005 before declining again in 2006.
The solid line in the graph below refers to annual sale of crackers and the dashed line refers
to the annual crow births in India. Choose the most appropriate inference from the above
data.
(A) There is a strong correlation between crow birth and cracker sales.
(B) Cracker usage increases crow birth rate.
(C) If cracker sale declines, crow birth will decline.
(D) Increased birth rate of crows will cause an increase in the sale of crackers.
END OF THE QUESTION PAPER
GA 2/2
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GATE 2018 Instrumentation Engineering
Q. 1 – Q. 25 carry one mark each.
Q.1 Let N be a 3 by 3 matrix with real number entries. The matrix N is such that N 2 = 0. The eigen
values of N are
(A) 0, 0, 0 (B) 0,0,1 (C) 0,1,1 (D) 1,1,1
Q.2 Let f1 (z) = z 2 and f2 (z) = z̅ be two complex variable functions. Here z̅ is the complex
conjugate of z. Choose the correct answer.
(A) Both f1 (z) and f2 (z) are analytic
(B) Only f1 (z) is analytic
(C) Only f2 (z) is analytic
(D) Both f1 (z) and f2 (z) are not analytic
Q.3 X and Y are two independent random variables with variances 1 and 2, respectively.
Let Z = X − Y. The variance of Z is
(A) 0 (B) 1 (C) 2 (D) 3
Q.4 Consider two functions f(x) = (x − 2)2 and g(x) = 2x − 1, where x is real. The smallest
value of x for which f(x) = g(x) is _______.
Q.5 Consider a sequence of tossing of a fair coin where the outcomes of tosses are independent.
The probability of getting the head for the third time in the fifth toss is
5 3 3 9
(A) (B) (C) (D)
16 16 5 16
Q.6 A series R-C circuit is excited by a 10 V sinusoidal ac voltage source. The locus diagram
of the phasor current I= (x + jy) A, when C is varied, while keeping R fixed, is
(A) +jy (B) +jy
x x
(C) +jy (D) +jy
x x
IN 1/14
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GATE 2018 Instrumentation Engineering
Q.7 The Thevenin equivalent circuit representation across terminals p-q of the circuit shown in
the figure is a
100 kΩ
p
100 kΩ
+
4V 100 kΩ
-
q
(A) 1 V source in series with 150 kΩ (B) 1 V source in parallel with 100 kΩ
(C) 2 V source in series with 150 kΩ (D) 2 V source in parallel with 200 kΩ
Q.8 A coil having an impedance of (10 + j100) Ω is connected in parallel to a variable capacitor
as shown in figure. Keeping the excitation frequency unchanged, the value of the capacitor
is changed so that parallel resonance occurs. The impedance across terminals p-q at
resonance (in Ω) is ______.
p
q
Q.9 Two periodic signals x(t) and y(t) have the same fundamental period of 3 seconds. Consider
the signal z(t) = x(−t) + y(2t + 1). The fundamental period of z(t) in seconds is
(A) 1 (B) 1.5 (C) 2 (D) 3
1, |t| ≤ 2
Q.10 Consider signal x(t) = { . Let δ(t) denote the unit impulse (Dirac-delta)
0 |t| > 2
5
function. The value of the integral ∫0 2x(t − 3)δ(t − 4)dt is
(A) 2 (B) 1 (C) 0 (D) 3
IN 2/14
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GATE 2018 Instrumentation Engineering
Q.11 An ideal square wave with period of 20 ms shown in the figure, is passed through an ideal
low pass filter with cut-off frequency 120 Hz. Which of the following is an accurate
description of the output?
(A) Output is zero.
(B) Output consists of both 50 Hz and 100 Hz frequency components.
(C) Output is a pure sinusoid of frequency 50 Hz.
(D) Output is a square wave of fundamental frequency 50 Hz.
s−1
Q.12 An input p(t) = sin(t) is applied to the system G(s) = . The corresponding steady
s+1
state output is y(t) = sin(t + φ), where the phase φ (in degrees), when restricted to
0 ≤ φ ≤ 360, is ______ .
2 −0.01 s
Q.13 The approximate phase response of 100 e is
2 s +0.2 s+ 1002
(A) (B)
(C) (D)
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GATE 2018 Instrumentation Engineering
2
Q.14 Consider the transfer function G(s) = . The phase margin of G(s) in degrees
(s+1)(s+2)
is ____.
Q.15 In the given circuit, assume that the opamp is ideal and the transistor has a of 20. The
current Io (in A) flowing through the load ZL is ____.
Q.16 The diodes given in the circuit are ideal. At t = 60 ms, Vpq (in Volts) is ____.
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GATE 2018 Instrumentation Engineering
Q.17 For the 3-bit binary counter shown in the figure, the output increments at every positive
transition in the clock (CLK). Assume ideal diodes and the starting state of the counter as
000. If output high is 1 V and output low is 0 V, the current I (in mA) flowing through the
50 Ω resistor during the 5th clock cycle is (up to one decimal place) ______.
Q.18 The representation of the decimal number (27.625)10 in base-2 number system is
(A) 11011.110 (B) 11101.101
(C) 11011.101 (D) 10111.110
Q.19 The number of comparators required for implementing an 8-bit flash analog-to-digital
converter is
(A) 8 (B) 128 (C) 255 (D) 256
Q.20 A voltage of 6 cos(100πt) V is fed as y-input to a CRO. The waveform seen on the screen of
the CRO is shown in the figure. The Y and X axes settings for the CRO are respectively
(A) 1 V/div and 1 ms/div (B) 1 V/div and 2 ms/div
(C) 2 V/div and 1 ms/div (D) 2 V/div and 2 ms/div
Q.21 A 300 V, 5A, 0.2 pf low power factor wattmeter is used to measure the power consumed by
a load. The wattmeter scale has 150 divisions and the pointer is on the 100 th division. The
power consumed by the load (in Watts) is _____ .
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GATE 2018 Instrumentation Engineering
Q.22 As shown in the figure, temperature is measured using a K type thermocouple. It has a
sensitivity of 40 V/C. The gain (G) of the ideal instrumentation amplifier is 25. If the
output Vo is 96 mV, then the value of (in C) is ____.
Room
temperature
M
+
N
+
INA
Vo
N G = 25
ref = 0 C +
M
Q.23 A piezoelectric pressure sensor has a bandpass characteristic with cut-off frequencies of
0.1 Hz and 1 MHz, and a sensitivity of 100 mV/kPa. The sensor is subjected to a static
constant pressure of 100 kPa. Its steady-state output will be
(A) 0 V (B) 0.1 V (C) 1 V (D) 10 V
Q.24 An amplitude modulated signal is shown in the figure. The modulation index is (up to one decimal
place) ______.
Q.25 An optical pulse containing 6 × 106 photons is incident on a photodiode and 4.5 × 106
electron-hole pairs are created. The maximum possible quantum efficiency (in %) of the
photodiode is _______ .
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GATE 2018 Instrumentation Engineering
Q. 26 – Q. 55 carry two marks each.
Q.26 Given F⃗ = ( x 2 − 2y) i⃗ − 4yz j⃗ + 4xz 2 ⃗⃗⃗⃗
k, the value of the line integral ∫c F⃗ ⋅ dl⃗ along
the straight line c from (0,0,0) to (1,1,1) is
(A) 3/16 (B) 0 (C) 5/12 (D) 1
Q.27 Two bags A and B have equal number of balls. Bag A has 20% red balls and 80% green
balls. Bag B has 30% red balls, 60% green balls and 10% yellow balls. Contents of Bags A
and B are mixed thoroughly and a ball is randomly picked from the mixture. What is the
chance that the ball picked is red?
(A) 20% (B) 25% (C) 30% (D) 40%
Q.28 Consider the following system of linear equations:
3x + 2ky = −2
kx + 6y = 2
Here x and y are the unknowns and k is a real constant. The value of k for which there are
infinite number of solutions is
(A) 3 (B) 1 (C) −3 (D) −6
Q.29 Consider the following equations
∂V(x, y)
= px 2 + y 2 + 2xy
∂x
∂V(x, y)
= x 2 + qy 2 + 2xy
∂y
where p and q are constants. V(x, y) that satisfies the above equations is
x3 y3 x3 y3
(A) p 3 + q 3 + 2xy + 6 (B) p 3 + q 3 + 5
x3 y3 x3 y3
(C) p 3 + q 3 + x 2 y + xy 2 + xy (D) p 3 + q 3 + x 2 y + xy 2
IN 7/14
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GATE 2018 Instrumentation Engineering
Q.30 In the given circuit, superposition is applied. When V2 is set to 0 V, the current I2 is -6 A.
When V1 is set to 0 V, the current I1 is +6 A. Current I3 (in A) when both sources are applied
will be (up to two decimal places) _____.
3Ω I1 I2 2Ω
I3
V1 V2
6Ω
Q.31 In the figure, an RLC load is supplied by a 230 V, 50 Hz single phase source. The magnitude
of the reactive power (in VAr) supplied by the source is ________.
Q.32 In the given circuit, the mesh currents I1, I2 and I3 are
5V
- +
I2 1Ω
6Ω
2Ω 1Ω
I1 2A
I3
(A) I1 = 1 A, I2 = 2 A and I3 = 3 A (B) I1 = 2 A, I2 = 3 A and I3 = 4 A
(C) I1 = 3 A, I2 = 4 A and I3 = 5 A (D) I1 = 4 A, I2 = 5 A and I3 = 6 A
IN 8/14
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GATE 2018 Instrumentation Engineering
Q.33 The Fourier transform of a signal x(t), denoted by X(j), is shown in the figure.
Let y(t) = x(t) + e jt x(t). The value of Fourier transform of y(t) evaluated at the angular
frequency = 0.5 rad/s is
(A) 0.5 (B) 1 (C) 1.5 (D) 2.5
Q.34 Let y[n] = x[n] ∗ ℎ[n], where ∗ denotes convolution and x[n] and ℎ[n] are two discrete
time sequences. Given that the z-transform of y[n] is Y(z) = 2 + 3z −1 + z −2 , the
z-transform of p[n] = x[n] ∗ ℎ[n − 2] is
(A) 2 + 3z + z −2 (B) 3z + z −2 (C) 2z 2 + 3z + 1 (D) 2z −2 + 3z −3 + z −4
Q.35 fFor the sequence x[n] = {1, −1,1, −1}, with n = 0,1,2,3, the DFT is computed as
2π
X(k) = ∑3n=0 x[n]e −j 4 nk , for k = 0,1,2,3. The value of k for which X(k) is not zero
is
(A) 0 (B) 1 (C) 2 (D) 3
s 2 +0.2s+100
Q.36 Consider the standard negative feedback configuration with G(s) = and
s 2 −0.2s+100
1
H(s) = . The number of clockwise encirclements of (−1,0) in the Nyquist plot of the
2
Loop transfer-function G(s)H(s) is _____
−1 0 1
Q.37 Consider the linear system ẋ = [ ] x , with initial condition x (0) = [ ].
0 −2 1
The solution x(t) for this system is
−t −t
(A) x(t) = [e te −2t ] [1] (B) x(t) = [e 0 ] [1]
0 e −2t 1 0 e 2t 1
−t −t
(C) x(t) = [e −t 2 e −2t ] [1] (D) x(t) = [e 0 1
−2t ] [1]
0 e −2t 1 0 e
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GATE 2018 Instrumentation Engineering
1
Q.38 Consider a standard negative feedback configuration with G(s) = and
(s+1)(s+2)
s+α
H(s) = . For the closed loop system to have poles on the imaginary axis, the value
s
of α should be equal to (up to one decimal place)_____.
Q.39 Unit step response of a linear time invariant (LTI) system is given by
y(t) = (1 − e −2t )u(t). Assuming zero initial condition, the transfer function of the system
is
1 2 1 2
(A) (B) (C) (D)
s+1 (s+1)(s+2) s+2 s+2
Q.40 In the given relaxation oscillator, the opamps and the zener diodes are ideal. The frequency
(in kHz) of the square wave output vo is _____.
Q.41 An opamp that is powered from a 5V supply is used to build a non-inverting amplifier
having a gain of 15. The slew rate of the opamp is 0.5106 V/s. For a sinusoidal input with
amplitude of 0.3 V, the maximum frequency (in kHz) up to which it can be operated without
any distortion is (up to one decimal place) ___.
Q.42 The circuit given uses ideal opamps. The current I (in A) drawn from the source vs is (up
to two decimal places) ____.
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GATE 2018 Instrumentation Engineering
Q.43 The product of sum expression of a Boolean function F(A, B, C) of three variables is given
by
F(A, B, C) = ( A + B + C̅ ) ∙ (A + B̅ + C̅ ) ∙ ( A̅ + B + C ) ∙ ( A̅ + B̅ + C̅ )
The canonical sum of product expression of F(A, B, C) is given by
(A) A̅ B̅ C + A̅ B C + A B̅ C̅ + A B C
(B) A̅ B̅ C̅ + A̅ B C̅ + AB̅ C + A B C̅
(C) A B C̅ + A B̅ C̅ + A̅ B C + A̅ B̅ C̅
(D) A̅ B̅ C̅ + A̅ B C + A B C̅ + A B C
Q.44 A 2-bit synchronous counter using two J-K flip flops is shown. The expressions for the inputs
to the J-K flip flops are also shown in the figure. The output sequence of the counter starting
from Q1Q2 = 00 is
Q1 + Q2 SET Q1 + Q2 SET
J Q J Q
Q1 Q2
Q1 + Q2 K CLR Q K CLR Q
Q1 + Q2
Clock
(A) 00 → 11 → 10 → 01 → 00
(B) 00 → 01 → 10 → 11 → 00
(C) 00 → 01 → 11 → 10 → 00
(D) 00 → 10 → 11 → 01 → 00
Q.45 A portion of an assembly language program written for an 8-bit microprocessor is given
below along with explanations. The code is intended to introduce a software time delay. The
processor is driven by a 5 MHz clock. The time delay (in s) introduced by the program is
_______.
MVI B, 64H ; Move immediate the given byte into register B. Takes 7 clock periods.
LOOP : DCR B ; Decrement register B. Affects Flags. Takes 4 clock periods.
JNZ LOOP ; Jump to address with Label LOOP if zero flag is not set. Takes
10 clock periods when jump is performed and 7 clock periods when
jump is not performed.
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GATE 2018 Instrumentation Engineering
Q.46 The Boolean function F( X, Y) realized by the given circuit is
(A) X̅ Y + X Y̅ (B) ̅X Y̅ + X Y (C) X + Y (D) X̅ ∙ Y̅
Q.47 The voltage and current drawn by a resistive load are measured with a 300 V voltmeter of
accuracy 1% of full scale and a 5 A ammeter of accuracy 0.5% of full scale. The readings
obtained are 200 V and 2.5 A. The limiting error (in %) in computing the load resistance is
(up to two decimal places) ____.
Q.48 A high Q coil having distributed (self) capacitance is tested with a Q-meter. First resonance
at 1 = 106 rad/s is obtained with a capacitance of 990 pF. The second resonance at
2 = 2 106 rad/s is obtained with a 240 pF capacitance. The value of the inductance (in mH)
of the coil is (up to one decimal place) ______.
Q.49 The inductance of a coil is measured using the bridge shown in the figure. Balance (D = 0)
is obtained with C1 = 1 nF, R1 = 2.2 MΩ, R2 = 22.2 kΩ, R4 = 10 kΩ. The value of the
inductance Lx (in mH) is ______.
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GATE 2018 Instrumentation Engineering
Q.50 The average velocity v of flow of clear water in a 100 cm (inner) diameter tube is measured
using the ultrasonic flow meter as shown in the figure. The angle is 45. The measured
transit times are t1 = 0.9950 ms and t2 = 1.0000 ms. The velocity v (in m/s) in the pipe is (up
to one decimal place) ___.
Tx/Rx
v 100 cm
= 45
Tx/Rx
Q.51 A 1000 strain gage (Rg) has a gage factor of 2.5. It is connected in the bridge as shown in
figure. The strain gage is subjected with a positive strain of 400 m/m. The output Vo (in
mV) of the bridge is (up to two decimal places) _____.
Q.52 Assuming ideal opamp, the RMS voltage (in mV) in the output Vo only due to the 230 V, 50
Hz interference is (up to one decimal place) _____.
Q.53 The sampling rate for Compact Discs (CDs) is 44,000 samples/s. If the samples are
quantized to 256 levels and binary coded, the corresponding bit rate (in bits per second)
is _____.
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GATE 2018 Instrumentation Engineering
Q.54 A Michelson Interferometer using a laser source of wavelength λ0 = 500 nm, with both the
mirrors (M1 & M2 ) fixed and positioned equidistant from the splitter/combiner is shown in
the figure. When a dielectric plate of refractive index n = 1.5, of thickness t , is placed in
front of the mirror M2 , a dark fringe is observed on the detector. When the dielectric plate
is removed without changing the position of the mirrors M1 & M2 , a bright fringe is observed
on the detector. The minimum thickness t (in nm) of the dielectric is ________.
Q.55 A multi-mode optical fiber with a large core diameter has a core refractive index n1 = 1.5
and cladding refractive index n2 = 1.4142. The maximum value of θA (in degrees) for which
the incident light from air will be guided in the optical fiber is ______.
END OF THE QUESTION PAPER
IN 14/14
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Q.No. Type Section Key/Range Marks
1 MCQ GA A 1
2 MCQ GA C 1
3 MCQ GA B 1
4 MCQ GA C 1
5 MCQ GA D 1
6 MCQ GA A 2
7 MCQ GA C 2
8 MCQ GA D 2
9 MCQ GA C 2
10 MCQ GA A 2
1 MCQ IN A 1
2 MCQ IN B 1
3 MCQ IN D 1
4 NAT IN 1 to 1 1
5 MCQ IN B 1
6 MCQ IN A 1
7 MCQ IN C 1
8 NAT IN 1009 to 1011 1
9 MCQ IN D 1
10 MCQ IN A 1
11 MCQ IN C 1
90 to 90 (or)
12 NAT IN 1
‐270 to ‐270
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Q.No. Type Section Key/Range Marks
13 MCQ IN A 1
180 to 180 (or)
14 NAT IN 1
‐180 to ‐180
15 NAT IN 0 to 0 1
16 NAT IN 200 to 200 1
17 NAT IN 10 to 10 1
18 MCQ IN C 1
19 MCQ IN C 1
20 MCQ IN D 1
21 NAT IN 200 to 200 1
22 NAT IN 95 to 97 1
23 MCQ IN A 1
24 NAT IN 0.3 to 0.3 1
25 NAT IN 75 to 75 1
26 MCQ IN D 2
27 MCQ IN B 2
28 MCQ IN C 2
29 MCQ IN D 2
30 NAT IN 0.95 to 1.05 2
31 NAT IN 66 to 68 2
32 MCQ IN A 2
33 MCQ IN C 2
34 MCQ IN D 2
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Q.No. Type Section Key/Range Marks 35 MCQ IN C 2 36 NAT IN 0 to 0 2 37 MCQ IN D 2 38 NAT IN 8.9 to 9.1 2 39 MCQ IN D 2 40 NAT IN Marks to All 2 41 NAT IN 17.5 to 17.9 2 42 NAT IN 0.98 to 1.00 2 43 MCQ IN B 2 44 MCQ IN C 2 45 NAT IN 279 to 282 2 46 MCQ IN A 2 47 NAT IN 2.49 to 2.53 2 48 NAT IN 0.9 to 1.1 2 49 NAT IN 221 to 223 2 50 NAT IN 3.5 to 5.7 2 51 NAT IN 0.48 to 0.51 2 52 NAT IN 10.6 to 11.0 2 53 NAT IN 352000 to 352000 2 54 NAT IN 249 to 251 2 55 NAT IN 29 to 31 2
Official key not published for this paper.
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Source: GATE. Question paper published by GATE.