Graduate Aptitude Test in Engineering 2017
Question Paper Name: Instrumentation Engineering 12th Feb 2017
Subject Name: Instrumentation Engineering
Duration : 180
Total Marks: 100
1. A system is described by the following differential equation:
Where x(t) and y(t) are the input and output variables respectively. The transfer function of the inverse system is
(A) 
(B) 
(C) 
(D) 
Ans: (B)
2. If v is a non-zero vector of dimension 3×1, then the matrix A=vvT has a rank = _______
Ans: (1)
3. A periodic signal x(t) is shown in the figure. The fundamental frequency of the signal x (t) in Hz is________
Ans: (1)
4. The silicon diode, shown in the figure, has a barrier potential of 0.7 V. There will be no forward current flow through the diode, if Vdc, in volt, is greater than
(A) 0.7
(B) 1.3
(C) 1.8
(D) 2.6
Ans: (D)
5. For a first order low pass filter with unity d.c. gain and -3 dB corner frequency of 2000π rad/s, the transfer function H( jω ) is
(A) 
(B) 
(C) 
(D) 
Ans: (C)
6. A and B are the logical inputs and X is the logical output shown in the figure. The output X is related to A and B by
(A) 
(B) 
(C) 
(D) 
Ans: (C)
7. The most suitable pressure gauge to measure pressure in the range of 10−4 to 10−3 torr is
(A) Bellows
(B) Barometer
(C) Strain gauge
(D) Pirani gauge
Ans: (D)
8. The standard for long distance analog signal transmission in process control industry is
(A) 4-20 mV
(B) 0-20 mA
(C) 4-20 mA
(D) 0-5V
Ans: (C)
9. If a continuous-time signal x(t) = cos(2πt) is sampled at 4 Hz, the value of the discrete-time sequence x(n) at n = 5 is
(A) −0.707
(B) −1
(C) 0
(D) 1
Ans: (C)
10. The term hysteresis is associated with
(A) ON-OFF control
(B) P-I control
(C) Feed-forward control
(D) Ratio control
Ans: (A)
11. A current waveform, i(t), shown in the figure, is passed through a Permanent Magnet Moving coil (PMMC) type ammeter. The reading of the ammeter up to two decimal places is
(A) −0.25 A
(B) −0.12A
(C) 0.37 A
(D) 0.5 A
Ans: (A)
12. The connection of two 2-port networks is shown in the figure. The ABCD parameters of N1 and N2 networks are given as
The ABCD parameters of the combined 2-port network are
(A) 
(B) 
(C) 
(D) 
Ans: (A)
13. The figure shows a shape ABC and its mirror image A1B1C1 across the horizontal axis (X – axis). The coordinate transformation matrix that maps ABC to A1B1C1 is
(A) 
(B) 
(C) 
(D) 
Ans: (D)
14. The differential amplifier, shown in the figure, has a differential gain of Ad = 100 and common mode gain of Ac = 0.1. If V1 = 5.01 V and V2 = 5.00 V, then V0, in volt (up to one decimal place) is ______.
Ans: (1.4 to 1.6)
15. A circuit consisting of dependent and independent sources is shown in the figure. If the voltage at Node-1 is – 1 V, then the voltage at Node-2 is _________V.
Ans: (2)
16. The eigen values of the matrix 
are
(A) −1, 5, 6
(B) 1, −5 ± j6
(C) 1, 5 ± j6
(D) 1, 5, 5
Ans: (C)
17. The figure shows a phase locked loop. The output frequency is locked at f0 = 5kHz. The value of fi in kHz is __________.
Ans: (1)
18. Identify the instrument that does not exist:
(A) Dynamometer-type ammeter
(B) Dynamometer-type wattmeter
(C) Moving-iron voltmeter
(D) Moving-iron wattmeter
Ans: (D)
19. The output Vo shown in the figure, in volt, is close to
(A) −20
(B) −15
(C) −5
(D) 0
Ans: (B)
20. An 8-bit microcontroller with 16 address lines has 3 fixed interrupts i.e., Int1, Int2 and Int3 with corresponding interrupt vector addresses as 0008H. 0010H and 0018H. To execute a 32-byte long Interrupt Service Subroutine for Int1 starting at the address ISSI, The location 0008H onwards should ideally contain
(A) a CALL to ISSI
(B) an unconditional JUMP to ISSI
(C) a conditional JUMP to ISSI
(D) only ISSI
Ans: (A or B)
21. A series R-L-C circuit is excited with a 50V, 50 Hz sinusoidal source. The voltage across the resistance and the capacitance are shown in the figure. The voltage across the inductor (VL) is __________V
Ans: (50)
22. The condition for oscillation in a feedback oscillator circuit is that at the frequency of oscillation, initially the loop gain is greater than unity while the total phase shift around the loop in degree is
(A) 0
(B) 90
(C) 180
(D) 270
Ans: (A)
23. Let z = x + jy where 
(A) cos z
(B) 
(C) sin z
(D) 
Ans: (B)
24. The region of Convergence (ROC) of the Z-transform of a causal unit step discrete-time sequence is
(A) |z| < 1
(B) |z| ≤ 1
(C) |z| > 1
(D) |z| ≥ 1
Ans: (C)
25. The pressure drop across an orifice plate for a particular flow rate is 5 kg/m2. If the flow rate is doubled (within the operating range of the orifice), the corresponding pressure drop in kg/m3 is
(A) 2.5
(B) 5.0
(C) 20.0
(D) 25.0
Ans: (C)
26. The two-input voltage multiplier, shown in the figure, has a scaling factor of 1 and produces voltage output. If V1 = +15V and V2 = +3V, the value of V0 in volt is _______.
Ans: (−5 to 5)
27. For the circuit, shown in the figure, the total real power delivered by the source to the loads is _________kW
Ans: (1.75 to 1.96)
28. The magnetic flux density of an electromagnetic flow meter is 100 mWb/m2. The electrodes are wall-mounted inside the pipe having a diameter of 0.25m. A voltage of 1V is generated when a conducting fluid is passed through the flow meter. The volumetric flow rate of the fluid in m3/s is ____________.
Ans: (1.9 to 2)
29. In the circuit, shown in the figure, the MOSFET is operating in the saturation zone. The characteristics of the MOSFET is given by 
where VGS is in V. If Vs = +5V, then the value of RS in kΩ is ______.
Ans: (9.9 to 10.1)
30. The hot junction of a bare thermocouple, initially at room temperature (30℃), is suddenly dipped in molten metal at t = 0s. The cold junction is kept at room temperature. The thermocouple can be modeled as a first-order instrument with a time constant of 1.0s and a static sensitivity of 10μV/℃. If the voltage, measured across the thermocouple indicates 10.0 mV at t = 1.0s, then the temperature of the molten metal in ℃ is __________.
Ans: (1605 to 1618)
31. A series R-L-C circuit is excited with an a.c. voltage source. The quality factor (Q) of the circuit is given as Q = 30. The amplitude of current in ampere at upper half-power frequency will be __________.
Ans: (6 to 7)
32. An angle modulated signal with carrier frequency ωc = 2π × 106 rad/s is given by φm(t) = cos(ωct + 5sin(1000πt)) + 10sin(2000πt). The maximum deviation of the frequency in the angle modulated signal from that of the carrier is _________ kHz.
Ans: (12 to 13)
33. Three DFT coefficients, out of five DFT coefficients of a five-point real sequence are given as : X(0) = 4, X(1) = 1 – j1 and X(3) = 2 + j2. Then zero-th value of the sequence x(n), x(0), is
(A) 1
(B) 2
(C) 3
(D) 4
Ans: (B)
34. A closed-loop system is shown in the figure. The system parameter α is not known. The condition for asymptotic stability of the closed loop system is
(A) α < −0.5
(B) −0.5 < α < 0.5
(C) 0 < α < 0.5
(D) α > 0.5
Ans: (D)
35. The power delivered to a single phase inductive load is measured with a dynamometer type wattmeter using a potential transformer (PT) of turns ratio 200:1 and the current transformer (CT) of turns ratio 1:5. Assume both the transformers to be ideal. The power factor of the load is 0.8. If the wattmeter reading is 200W, then the apparent power of the load in kVA is _________.
Ans: (250)
36. The overall closed loop transfer function 
represented in the figure, will be
(A) 
(B) 
(C) 
(D) 
Ans: (A)
37. When the voltage across a battery is measured using a d.c. potentiometer, the reading shows 1.08V. But when the same voltage is measured using a Permanent Magnet Moving Coil (PMMC) voltmeter, the voltmeter reading shows 0.99V. If the resistance of the voltmeter is 1100Ω, the internal resistance of the battery, in Ω, is _________.
Ans: (100)
38. The probability that a communication system will have high fidelity is 0.81. The probability that the system will have both high fidelity and high selectivity is 0.18. The probability that a given system with high fidelity will have high selectivity is
(A) 0.181
(B) 0.191
(C) 0.222
(D) 0.826
Ans: (C)
39. The current response of a series R-L circuit to a unit step voltage is given in the table. The value of L is ___________H.
Ans: (1)
40. A resistance temperature detector (RTD) is connected to a circuit, as shown in the figure, Assume the op-amp to be ideal. If Vo =+ 2.0V, then the value of x is __________.
Ans: (0.19 to 0.21)
41. The circuit of a Schmitt trigger is shown in the figure. The zener-diode combination maintains the output between ±7V. The width of the hysteresis band is _________V.
Ans: (0.6 to 0.7)
42. The loop transfer function of a closed-loop system is given by 
The breakaway point of the root-loci will be ____________.
Ans: (−1.2 to 1.0)
43. The unbalanced voltage of the Wheatstone bridge, shown in the figure, is measured using digital voltmeter having infinite input impedance and a resolution of 0.1mV. If R = 1000Ω, then the minimum value of ∆R in Ω to create detectable unbalanced voltage is _________.
Ans: (0.17 to 0.23)
44. In the circuit diagram, shown in the figure, S1 was closed and S2 was open for a very long time. At t = 0, S1 is opened and S2 is closed. The voltage across the capacitor, in volt, at t = 5 μs is _______
Ans: (1.43 to 1.63)
45. The block diagram of a closed-loop control system is shown in the figure. The values of k and kp are such that the system has a damping ratio of 0.8 and an undamped natural frequency ωn of 4 rad/s respectively. The value of kp will be ___________.
Ans: (0.32 to 0.4)
46. Assuming the op-amp shown in the figure to be ideal, the frequency at which the magnitude of Vo will be 95% of the magnitude of Vin is ____________kHz.
Ans: (2.9 to 3)
47. The following table lists an nth order polynomial f(x) = anxn + an – 1 xn – 1 +…+a1x + a0 and the forward differences evaluated at equally spaced values of x. The order of the polynomial is
(A) 1
(B) 2
(C) 3
(D) 4
Ans: (D)
48. Consider two discrete-time signals:
x1(n) = {1, 1} and x2(n) = {1, 2}, for n = 0.1.
The Z-transform of the convoluted sequence x(n) = x1(n) * x2(n) is
(A) 1 + 2z−1 + 3z−2
(B) z2 + 3z + 2
(C) 1 + 3z−1 + 2z−2
(D) z−2 + 3z−3 + 2z−4
Ans: (C)
49. In the a.c. bridge, shown in the figure, R = 103Ω and C = 10−7 F. If the bridge is balanced at a frequency ω0, the value of ω0 in rad/s is ________.
Ans: (10000)
50. The junction semiconductor temperature sensor shown in the figure is used to measure the temperature of hot air. The output voltage Vo is 2.1V. The current output of the sensor is given by I = TμA where T is the temperature in K. Assuming the opamp to be ideal, the temperature of the hot air in ℃ is approximately ___________.
Ans: (76 to 78)
51. In a sinusoidal amplitude modulation scheme (with carrier) the modulated signal is given by Am(t) = 100 cos (ωct) + 50 cos(ωmt) cos (ωct), where ωc is the carrier frequency and ωm is the modulation frequency. The power carried by the sidebands in % of total power is ________%
Ans: (11 to 11.2)
52. The angle between two vectors 
and 
in radian is _____.
Ans: (0.65 to 0.8)
53. Quantum efficiency of a photodiode (ratio between the number of liberated electrons and the number of incident photons) is 0.75 at 830 nm. Given Plank’s constant h = 6.624 × 10−34 J, the charge of an electron e = 1.6 × 10−19 C and the velocity of light in the photodiode Cm = 2 × 108 m/s. For an incident optical power of 100 μW at 830 n, the photocurrent in μA is _______.
Ans: (74.5 to 75.5)
54. The two inputs A and B are connected to an R-S latch via two AND gates as shown in the figure. If A = 1 and B = 0, the output 
is
(A) 00
(B) 10
(C) 01
(D) 11
Ans: (B)
55. The Laplace transform of a causal signal y(t) is 
The value of the signal y(t) at t = 0.1 s is _______ unit.
Ans: (−2.4 to −2.0)
56. The event would have been successful if you ______ able to come.
(A) are
(B) had been
(C) have been
(D) would have been
Ans: (B)
57. Four cards lie on a table. Each card has a number printed on one side and a colour on the other. The faces visible on the cards are 2, 3, red, and blue.
Proposition: If a card has an even value on one side, then its opposite face is red.
The cards which MUST be turned over to verify the above proposition are
(A) 2, Red
(B) 2, 3, Red
(C) 2, blue
(D) 2, red, blue
Ans: (C)
58. What is the value of x when 
(A) 1
(B) −1
(C) −2
(D) Cannot be determined
Ans: (B)
59. There was no doubt that their work was thorough.
Which of the words below is closest in meaning to the underlined word above?
(A) Pretty
(B) Complete
(C) Sloppy
(D) Haphazard
Ans: (B)
60. Two dice are thrown simultaneously. The probability that the product of the numbers appearing on the top faces of the dice is a perfect square is
(A) 1/9
(B) 2/9
(C) 1/3
(D) 4/9
Ans: (B)
61. Bhaichung was observing the pattern of people entering and leaving a car service centre. There was a single window where customers were being served. He saw that people inevitably came out of the centre in the order that they went in. However, the time they spent inside seemed to vary a lot: some people came out in a matter of minutes while for others it took much longer.
From this, what can one conclude?
(A) The centre operates on a first-come-first-served basis but with variable service times, depending on specific customer needs.
(B) Customers were served in an arbitrary order since they took varying amounts of time for service completion in the centre.
(C) Since some people came out within a few minutes of entering the centre. The system is likely to operate on a last-come-first-served basis.
(D) Entering the centre early ensured that one would have shorter service times and most people attempted to do this.
Ans: (A)
62. The points in the graph below represent the halts of a lift for duration of 1 minute, over a period of 1 hour.
Which of the following statements are correct?
i. The elevator never moves directly from any non-ground floor to another non-ground floor over the one hour period
ii. The elevator stays on the fourth floor for the longest duration over the one hour period
(A) Only i
(B) Only ii
(C) Both i and ii
(D) Neither i nor ii
Ans: (D)
63. A map shows the elevations of Darjeeling, Gangtok, Kalimpong, pelling, and Siliguri, Kalimpong is at a lower elevation than Gangtok. Pelling is at a lower elevation than Gangtok. Pelling is at a higher elevation that siliguri. Darjeeling is at a higher elevation than Gangtok.
Which of the following statements can be inferred from the paragraph above?
i. Pelling is at a higher elevation than Kalimpong
ii. Kalimpong is at a lower elevation than Darjeeling
iii. Kalimpong is at a higher elevation than siliguri
iv. Siliguri is at a lower elevation than Gangtok
(A) Only ii
(B) Only ii and iii
(C) Only ii and iv
(D) Only iii and iv
Ans: (C)
64. P,Q,R,S,T and U are seated around a circular table. R is seated two places to the right of Q.P is seated three places to the left of R. S is seated opposite U. If P and U now switch seats.
Which of the following must necessarily be true?
(A) P is immediately to the right of R
(B) T is immediately to the left of P
(C) T is immediately to the left of P or P is immediately to the right of Q
(D) U is immediately to the right of R or P is immediately to the left of T
Ans: (C)
65. Budhan covers a distance of f19 km in 2 hours by cycling one fourth of the time and walking the rest. The next day he cycles (at the same speed as before) for half the time and walks the rest (at the same speed as before) and covers 26 km in 2 hours. The speed in km/h at which Budhan walks is
(A) 1
(B) 4
(C) 5
(D) 6
Ans: (D)
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