Author: Vidhyarthi Darpan

GATE 2020 Biomedical Engineering Previous Year Paper

GA – General Aptitude 

Q1 – Q5 carry one mark each. 

Q.No. 1 Rajiv Gandhi Khel Ratna Award was conferred Mary Kom, a six-time world champion in boxing, recently in a ceremony at the Rashtrapati Bhawan (the President’s official residence) in New Delhi. 

(A) with, at 

(B) on, in 

(C)on, at 

(D) to, at 

 

Q.No. 2 Despite a string of poor performances, the chances of K. L. Rahul’s selection in the team are 

(A) slim
(B) bright
(C) obvious
(D) uncertain

 

Q.No. 3 Select the word that fits the analogy: 

Cover : Uncover :: Associate : 

(A) Unassociate
(B) Inassociate
(C) Misassociate
(D) Dissociate

 

Q.No.4 Hit by floods, the kharif (summer sown) crops in various parts of the country have been affected. Officials believe that the loss in production of the kharif crops can be recovered in the output of the rabi (winter sown) crops so that the country can achieve its food-grain production target of 291 million tons in the crop year 2019-20 (July-June). They are hopeful that good rains in July-August will help the soil retain moisture for a longer period, helping winter sown crops such as wheat and pulses during the November-February period.  

Which of the following statements can be inferred from the given passage? 

(A) Officials declared that the food-grain production target will be met due to good rains.
(B) Officials want the food-grain production target to be met by the November-February period.
(C)Officials feel that the food-grain production target cannot be met due to floods.
(D)Officials hope that the food-grain production target will be met due to a good rabi produce.

 

Q.No.5 The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is 

(A) n² – n
(B) n² + n
(C) 2n² – n
(D) 2n² + n

Q6 – Q10 carry two marks each. 

Q.No. 6 Repo rate is the rate at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks. 

Which of the following statements can be inferred from the above passage? 

(A) Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks.
(B) Increase in repo rate will decrease cost of borrowing and increase lending by commercial banks.
(C) Increase in repo rate will decrease cost of borrowing and decrease lending by commercial banks.
(D) Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks. 

 

Q.No. 7 P, Q, R, S, T, U, V, and W are seated around a circular table. 

I. S is seated opposite to W. 

II. U is seated at the second place to the right of R. 

III. T is seated at the third place to the left of R. 

IV. V is a neighbour of S. 

Which of the following must be true? 

(A) P is a neighbour of R.
(B) Q is a neighbour of R.
(C) P is not seated opposite to Q.
(D) R is the left neighbor of S. 

 

Q.No. 8 The distance between Delhi and Agra is 233 km. A car P started traveling from Delhi to Agra and another car Q started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car Q started. Both cars were traveling at a constant speed. The speed of car P was 10 km/hr more than the speed of the car. How many kilometers the car Q had travelled when the cars crossed each other? 

(A) 66.6
(B) 75.2
(C) 88.2
(D) 116.5

 

Q.No.9 For a matrix M = [mj]; i, j = 1,2,3,4, the diagonal elements are all zero and mij = -mji. The minimum number of elements required to fully specify the matrix is 

(A) 0
(B) 6
(C) 12
(D) 16

 

Q.No. 10 The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013 – 2018 is Company P Company 

(A) 15:17
(B) 16:17
(C) 17:15
(D) 17:16 

BM: Biomedical Engineering 

Q1 – Q25 carry one mark each. 

Q. 1 m1 and m2 are the roots of the characteristic equation of a linear second-order physical system. Match the nature of the roots with the natural response of the system. 

(A) P-L, Q-M, R-K

(B) P-M, Q-L, R-K

(C) P-L, Q-K, R-M

(D) P-M, Q-K, R-L

 

Q.No. 2 A person is sitting in a chair with feet on the ground. While rising up on his feet, the kinematic motion NOT occurring is 

(A) Hip extension
(B) Plantar flexion
(C) Hip flexion
(D) Knee extension

 

Q.No. 3 The equipment that measures elasticity of blood vessel in vivo is 

(A) Rheometer
(B) Dimension analyser
(C) Thermomechanical analyser
(D) Dynamic mechanical analyser

 

Q.No. 4 Biomaterials with shape memory effects are NOT used in 

(A) Intracranial aneurysm clips 

(B) Arterial blood vessel closure devices
(C) Orthopedic total joint replacements
(D) Orthodontic dental arch wires

 

Q.No. 5 The MRI scanner parameter of long Trep or short Techo will generate a __________contrast image 

(A) Proton Density -weighted
(B) T2-weighted
(C) T1-weighted
(D) T2 – weighted

 

Q.No. 6 In diagnostic X-ray imaging, the following is NOT a part of primary EM radiation interaction in soft tissue. 

(A) Photoelectric effect
(B) Characteristic radiation production
(C) Compton scattering
(D) Pair-production

 

Q.No.7 A 5 MHz ultrasound pulse is used to image a tumor at a depth of 2 cm in a soft tissue. It takes time t for the reflected echo from the tumor to come back to the receiver. Instead, if a 2.5 MHz wave is used, how long will it take for the echo from the same tumor to arrive at the receiver? 

(A) t/2
(B) T
(C) 2t
(D) 4t

 

Q.No. 8 X(s) is the Laplace transform of a signal x(t). 

The Laplace transform dx(t)/dt of love, assuming x(0) = 0, is 

 

Q.No. 9 Which of the following are odd functions? 

P: Sin(t) 

Q: Cos(t) 

R: Sin((t) + Cos(t) 

S: Sin(t)Cos(t) 

(A) Q and S
(B) P and Q
(C) P and S
(D) R and Q

 

Q.No. 10 State-space model of a system is given as: 

The conditions for the system to be controllable are 

(A) a = 0, b ≠ 0
(B) a ≠ 0,b=0
(C) a ≠ 0,b ≠ 0
(D) a = 0, b = 0

 

Q.No. 11 In microprocessor systems with memory mapped I/O, which of the following is true? 

(A) Only I/O devices with internal memory can be interfaced.
(B) I/O devices can be accessed using IN and OUT instructions
(C) Each I/O device can be addressed as a memory location

(D) Arithmetic and logic operations cannot be directly performed with the I/O data 

 

Q.No. 12 The number of electrodes used in recording standard 12-lead Electrocardiogram (ECG) is 

(A) 13
(B) 12
(C) 11
(D) 10
 

 

Q.No. 13 Which of the following is NOT a part of the knee joint? 

(A) Patella
(B) Tibia
(C) Femur
(D) Fibula

 

Q.No. 14 During a routine stethoscopic examination at the left midclavicular-5th intercostal space, murmurs were noted between first and second heart sound. The possible abnormality among the following could be 

(A) Aortic stenosis
(B) Mitral regurgitation
(C) Mitral stenosis
(D) Aortic regurgitation

 

Q.No. 15 The thin filament of a muscle fiber is comprised of 

(A) Troponin, Tropomyosin, Actin
(B) Troponin, Tropomyosin, Titin
(C) Tropomyosin, Titin, Actin
(D) Actin, Myosin, Troponin

 

Q.No. 16 The value of the integral evaluated over the contour C:\z = 3/2 is 

 

Q.No. 17 The eigenvalues of a 3 x 3 non-singular matrix P are 1, 2 and 3. The trace of matrix P. (rounded off to two decimal places) is ______________

 

Q.No. 18 The following recursion relation, when started from a finite positive non-zero value, converges to ___________________

 

Q.No. 19 In a nuclear imaging system, Sodium Iodide (Nal) crystals are used to detect gamma rays of 120 keV. The percentage (%) of gamma-rays that will pass through 1 cm of Nal crystal, assuming the Half-Value-Layer (HVL) of Nal as 0.2 cm, is________(rounded off to one decimal place). 

 

Q.No. 20 The distal end of an endoscope is placed at a distance of 1 mm from the gastrointestinal wall. The refractive indices of the fiber core and cladding are 1.5 and 1.45, respectively. 

The maximum field of view for the endoscope is_______degrees (rounded off to one decimal place). 

 

Q.No. 21 Two inductors with the details given below are wound separately on two identical ring type ferromagnetic cores.The ratio L2/L, is  

 

Q.No. 22 Two dyes X and Y having concentrations in the ratio 0.25 in identical cuvettes were subjected to absorption measurements in a spectrophotometer. The estimated ratio of their absorbance is 0.5. The ratio of their molar extinction coefficients is_________ 

 

Q.No. 23  Hydrolysis of one ATP molecule provides an energy of____kilo calories(correct up to one decimal place). 

 

Q.No. 24 An 830 nm laser Doppler flow meter probe is oriented at an angle of 60° to the flow axis. If the average flow velocity is 3 cm/s, the magnitude of Doppler shift frequency (kHz) is ________(rounded off to one decimal place). 

 

Q.No. 25 A 100 mA single current pulse from a pulse generator is used for artificial pacing of heart at the right ventricle. If the delivered energy does not exceed the fibrillation threshold of 300 uJ, the safe duration of the pulse that could be applied to the tissue mass having an impedance of 500ᘯ is________________us. 

Q26 – Q55 carry two marks each. 

Q.No.26 The resting potential of a mammalian nerve cell is – 80 mV. A certain drug administered to the body changes the intracellular K* concentration from 150 mmol/L to 55 mmol/L. The nearest value of cell membrane potential after the drug administration, assuming that the external equilibrium of K does not get changed during the event, is (Gas constant = 8.315 J/mol/K, core temperature = 37° C and Faraday constant = 96500 C/mol) 

(A) -117 mV
(B) -18.71 m V
(C) -53.32 mV
(D) -141.30 mV

 

Q.No. 27 The arrangement of four resistors of equal value in the diaphragm of a physiological pressure measurement catheter is shown below. The applied pressure is observed to cause an increase in length of resistors R2, R4 and an increase in cross sectional area in R1 and R3. The operation results in an equal change in the values of all four resistors. Which among the configurations given below should be used to connect the resistors to form a Wheatstone bridge so that bridge output voltage is proportional to the change in resistance of individual resistors’? 

(A) I only
(B) II only
(C) Neither I nor II
(D) Both I and II

 

Q.No. 28 For the given input voltage, Vin = 10 sin(2nt) to the functional circuit shown below, the output signal will be 

Q.No. 29 During a non-invasive measurement of blood pressure, mean arterial pressure was observed to be 100 mm Hg. If systolic pressure is 150 mm Hg, the diastolic pressure would be 

(A) 110 mm Hg
(B) 75 mm Hg
(C) 70 mm Hg
(D) 50 mm Hg

 

Q.No.30 Two loads are connected to AC supply mains as depicted in the figure. One load draws 10 kW whereas the other load of 10 kVA is operated at 0.6 pf lagging. To achieve an overall power factor of 0.9544 lagging, the nearest kVAr rating of the capacitor bank needed to be connected across the supply mains is equal to 

(A) 3
(B) 5
(C) 7
(D) 9

 

Q.No. 31 The nearest value of power dissipated in the 3 12 resistance in the circuit is 

(A) 3W
(B) 25/3 W
(C) 12 W
(D) 25/12 W

 

Q.No. 32 A second order low pass filter is being constructed by cascading two first order low pass filters with the following transfer functions 

where w, and W2 are the respective 3dB cut off frequencies. 

The undamped natural frequency wc of the resulting second order low pass filter is 

 

Q.No. 33 Match the bridge type with the application given below: 

(A) P-L, Q-K, R-N, S-M 

(B) P-N, Q-K, R-L, S-M 

(C)P-N, Q-L, R-M, S-K 

(D) P-L, Q-M, R-N, S-K 

 

Q.No. 34 For a non-unity feedback system with G(s) = 12/S+2, and H(s) = 2/S+3, the magnitude of steady-state error to a unit step-input is 

(A) 0.50
(B) 0.45
(C) 0.25
(D) 0.20

 

Q.No. 35 Match the Boolean expression with its minimal realization 

(A) P-K, Q-L, R-N, S-M
(B) P-L, Q-K, R-N, S-M
(C) P-L, Q-N, R-M, S-K
(D) P-M, Q-K, R-L, S-N

 

Q.No. 36 The glomerular filtration process of the kidney is modeled as a flat membrane with pores of radius 1 nm and length of pore 60 nm. The viscosity of the fluid is 0.002 Pa s. The aggregate area of the pores makeup 5% of the total surface area of the membrane. The average pressure on the blood side of the membrane is 8000 Pa and on the ultrafiltrate side is 6200 Pa. The total available area of the membrane is 1.5 m2. The nearest value of resulting filtration rate in cm/min is
(A) 0.14
(B) 1.40
(C) 8.43
(D) 84.37

 

Q.No. 37 During resting state, the voltage outside the cell membrane compared to that inside the membrane is . Under such conditions, the intracellular and extracellular regions have and _concentrations, respectively. 

(A) More positive, more Potassium [K⁺], more Sodium [Na⁺]
(B) More negative, more Potassium [K⁺], more Sodium [Na⁺]
(C) More negative, more Sodium [Na⁺], more Potassium [K⁺]
(D) More positive, more Sodium [Na⁺], more Potassium [K⁺] 

 

Q.No. 38 The tensile strength of a degradable suture used for a surgical procedure in the human body is observed to decrease exponentially from its original strength by 40% and 50% after 10 days and 20 days, respectively. The closest approximation of the time taken for the tensile strength to decay to 20% of its original value would be

(A) 35 days
(B) 45 days
(C) 60 days
(D) 70 days
 

Q.No. 39 A 60 kg person is standing on one foot on a force plate. The ground reaction force is found to act 40 mm anterior to the ankle joint. The mass center of a foot is 60 mm from the Trochanter Knee Ankle (TKA) line. If the weight of the foot is 0.8 kg, the closest value of magnitude of moment acting on the ankle joint is

(A) 23 Nm
(B) 48 Nm
(C) 235 Nm
(D) 466 Nm

 

Q.No. 40 The temperature of bone cement is increased from 37°C to 87°C during the femoral hip arthroplasty. The cement thickness is noted to be 20 mm. The stress developed due to exothermic reaction of bone cement during the polymerization process and shrinkage of the bone cement, respectively, are 

Assume that 

(i) bone, cement, and implant are modeled as a set of concentric cylinders 

(ii) no direct adhesion takes place between bone and cement 

(iii) temperature is uniform 

Coefficient of thermal expansion of bone cement = 90 x 10^-6/°C 

Young’s modulus of bone cement = 3.5 GPa 

(A) 15.75 MPa, 90 μm
(B) 15.75 MPa, 110 μm
(C) 6.85 MPa, 110 μm
(D) 6.85 MPa, 90 μm

 

Q.No. 41 A patient is initially imaged in a 1 Tesla MRI scanner and induced voltage is found to be equal to V). The expression for the magnitude of the received voltage in the RF coil is given below. 

Vs: MR slice volume, Mo: Magnitude of resultant magnetic vector at equilibrium,

Yo: Larmor frequency, a: tip angle, BT: Magnetic field sensitivity of receive coil. 

When the patient is shifted to a 3 Tesla MRI scanner that uses the same RF coil and the slice thickness is halved, the magnitude of the induced voltage was found to be equal to V2. The ratio V2/V1 is 

(A) 1.5
(B) 3.0
(C) 4.5
(D) 6.0

Q.No. 42 A 3 MHz ultrasound transducer transmits a 3-cycle long pulse into a soft tissue at normal incidence to fat and liver interface. The axial resolution (mm) and the amplitude reflection coefficient at fat-liver interface, respectively, are 

Use C_tissue = 1500 m/s, C_fat = 1450 m/s, C_liver = 1570 m/s, 

P_fat = 920 kg/m³, P_liver = 1060 kg/m3 

(A) 0.5, 0.22
(B) 0.75, 0.22
(C) 0.5, 0.11
(D) 0.75, 0.11

 

Q.No. 43 The forward biased current of a silicon (Si) diode is being calculated from the exponential model of the V-I characteristics. If the diode current Ip = 1 mA at a voltage drop Vo -0.7 V, the nearest value of Id when Vp -0.8 V is 

Assume thermal voltage V1 = 25.3 m V for Si diode
(A) 0.133 mA
(B) 2 mA
(C) 52 mA
(D) 90 mA

Q.No.44 A continuous random variable x has a probability density function given by 

where a is a real constant. The variance of x is __________(correct up to one decimal place). 

 

Q.No. 45 The magnitude of the gradient of the function f(x,y) = x2 + y2 at the point (1,1) is_ (rounded off to two decimal places). 

 

Q.No. 46 The value of following double integral is_________(correct up to three decimal places). 

where R is the first quadrant of the circle with center at the origin and radius of one unit. 

 

Q.No. 47 A gynaecologist recorded the blood pressure (BP) of patients as shown in the Table below. Using the Regression process, the diastolic BP of a 38 year old patient (mm Hg) is___________(rounded off to two decimal places). 

 

Q.No. 48 A person in standing position first flexes the hip by 50° from the initial Trochanter knee ankle (TKA) line and then flexes knee by 20°. The distance of the ankle joint from the initial TKA line is (rounded off to the nearest integer). 

(i) the distance between hip joint and knee joint is 400 mm

(ii) the distance between knee joint and ankle joint is 300 mm. 

 

Q.No. 49 A chest radiograph of 36 cm x 48 cm is digitized. If we want to preserve details in the image to a spatial resolution of 6 cycles/mm, the approximate image data size in MB for an 8 bit quantization is__________(rounded off to two decimal places). 

 

Q.No.50 An X-ray radiography scenario is shown in the figure. If the number of incident photons (Ni) is equal to 2 x 100 at 50 keV, the number of photons (Nd) that exit the tissue is ____________ X 10⁶ (rounded off to two decimal places). 

(use linear attenuation coefficient for soft tissue and blood at 50 keV as 0.4 cm! and 0.2 cm*’, respectively). 

Q.No.51 The wavelength of an electron accelerated to a potential of 1V is (rounded off to two decimal places). 

Mass of electron = 9.11×10-31 kg 

Planck’s constant, h=6.63×10-34 Js 

Charge of electron = 1.6 X10-19 C 

 

Q.No. 52 In a permanent magnet moving coil (PMMC) instrument having following specifications, the angular deflection of the pointer for a coil current of 100 uA will be __________degrees (rounded off to one decimal place). 

Magnetic flux density = 1.5 Tesla 

Torsional spring constant = 2×10^-6 Nm/deg 

Cross sectional area of the coil = 2.5 cm? 

Number of turns of the coil = 500 

 

Q.No.53 Arterial blood extracted from a healthy adult showed an oxygen partial pressure value of 40 mm Hg. The total oxygen content in the arterial blood measured in %V/V is _______(rounded off to one decimal place). 

Given: Solubility of oxygen in blood = 0.003 ml/mm Hg/dL 

Hemoglobin oxygen saturation = 95% 

Oxygen carrying capacity of Hb = 1.34 ml/g 

Arterial blood hemoglobin concentration = 15g/dL 

 

Q.No. 54 In the process of measuring blood flow from an artery using C-clamp magnetic flow probe, the voltage recorded across diametrically opposite sites of the artery is 3.75 nV. The blood flow rate through the artery is cm3/s (rounded off to two decimal places). 

The inner diameter of the C-clamp = 0.5 cm, 

The magnetic flux density = 1.5 x 10^-5 Wb/mo. 

 

Q.No. 55 A cell is injected with a current i(t) = u(t) to produce a change in the intracellular membrane voltage v (t). The cell-membrane is modeled as a linear system with impulse response h (t) = A e^-t/t u(t). The cell membrane voltage output at 5 ms is________mV. Use A = -34 V/s; t = 3 ms. 

Answer Key

Q.No.	1	2	3	4	5	6	7	8	9	10
ANS	C	B	D	D	B	D	C	B	B	B
Q.No.	1	2	3	4	5	6	7	8	9	10
ANS	C	C	B	C	MTA	B OR D	B	A	C	C
Q.No.	11	12	13	14	15	16	17	18	19	20
ANS	C	D	D	B	A	-1.1 TO -0.9	1.82 TO 1.84	1 TO	3.0 TO 3.2	44 TO 46
Q.No.	21	22	23	24	25	26	27	28	29	30
ANS	4 TO4	2 TO 2	7.25 TO 7.35	35.8 TO 36.4	60 TO 60	C	A	D	B	A
Q.No.	31	32	33	34	35	36	37	38	39	40
ANS	A	A	A	D	B	C	A	D	A	A
Q.No.	41	42	43	44	45	46	47	48	49	50
ANS	C	D	C	0.5 TO 0.5	2.8 TO 2.9	0.125 TO 0.125	86.5 TO 87.7	456 TO 457	23.70 TO 23.75	0.5 TO 0.6
Q.No.	51		52		53		54		55
ANS	1.20 TO 1.25		9.0 TO 9.6		19.2 TO 19.4		0.95 TO 0.99		-84 TO -81

 

GATE 2020 Mathematics Previous Year Paper

GA – General Aptitude 

Q1 – Q5 carry one mark each. 

Q.No. 1 Rajiv Gandhi Khel Ratna Award was conferred Mary Kom, a six-time world champion in boxing, recently in a ceremony the Rashtrapati Bhawan (the President’s official residence) in New Delhi. 

(A) with,

(B) at on,

(C) on, at

(D) to, at

 

Q.No. 2 Despite a string of poor performances, the chances of K. L. Rahul’s selection in the team are

(A) slim 

(B) bright 

(C) obvious

(D) uncertain

 

Q.No. 3 Select the word that fits the analogy: 

Cover : Uncover :: Associate : 

(A) Unassociate 

(B) Inassociate

(C) Misassociate

(D) Dissociate

 

Q.No. 4 Hit by floods, the kharif (summer sown) crops in various parts of the country have been affected. Officials believe that the loss in production of the kharif crops can be recovered in the output of the rabi (winter sown) crops so that the country can achieve its food-grain production target of 291 million tons in the crop year 2019-20 (July-June). They are hopeful that good rains in July-August will help the soil retain moisture for a longer period, helping winter sown crops such as wheat and pulses during the November-February period. 

Which of the following statements can be inferred from the given passage?

(A) Officials declared that the food-grain production target will be met due to good rains.

(B) Officials want the food-grain production target to be met by the November-February period. 

(C) Officials feel that the food-grain production target cannot be met due to floods. 

(D) Officials hope that the food-grain production target will be met due to a good rabi produce. 

 

Q.No. 5 The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is _____________

(A) n²

(B) n² + n

(C) 2n² – n 

(D) 2n² +n

Q6 – Q10 carry two marks each. 

Q.No. 6 Repo rate is the rate at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks. 

Which of the following statements can be inferred from the above passage? 

(A) Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks. 

(B) Increase in repo rate will decrease the cost of borrowing and increase lending byC commercial banks. 

(C) Increase in repo rate will decrease cost of borrowing and decrease lending by commercial banks. 

(D) Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks. 

 

Q.No. 7 P, Q, R, S, T, U, V, and W are seated around a circular table. 

I. S is seated opposite to W. 

II. U is seated at the second place to the right of R. 

III. T is seated at the third place to the left of R. 

IV. V is a neighbour of S. 

Which of the following must be true? 

(A) P is a neighbour of R.

(B) Q is a neighbour of R.

(C) P is not seated opposite to Q. 

(D) R is the left neighbour of S.

 

Q.No. 8 The distance between Delhi and Agra is 233 km. A car P started travelling from Delhi to Agra and another car started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car started. Both cars were travelling at constant speed. The speed of car P was 10 km/hr more than the speed of car Q. How many kilometers the car Q had travelled when the cars crossed each other? 

(A) 66.6

(B) 75.2

(C) 88.2

(D) 116.5 

 

Q. No. 9 For a matrix M = [m_ij]; i, j = 1,2,3,4, the diagonal elements are all zero and m_ij = -m_ij: The minimum number of elements required to fully specify the matrix is______ 

(A) 0

(B) 6

(C) 12

(D) 16

 

Q.No. 10 The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013 – 2018 is Company P Company Q 

(A) 15:17

(B) 16:17

(C) 17:15

(D) 17:16

MA: Mathematics 

Q1 – Q25 carry one mark each. 

Q.No. 1 Suppose that I, and I2 are topologies on X induced by metrics dį and dz, respectively, such that I, S I2. Then which of the following statements is TRUE? 

(A)If a sequence converges in (X, d2) then it converges in (X, d1)

(B)If a sequence converges in (X,d1) then it converges in (X, d2) 

(C)Every open ball in (X, d1) is an open ball in (X, d2) 

(D)The map x + x from (X, d) to (X, dz) is continuous 

 

Q.No.2 Let D = [-1, 1] × [-1,1]. If the function f:D → R is defined by 

then 

(A)f is continuous at (0,0) 

(B)both the first order partial derivatives of f exist at (0,0)

(C)∫∫₀, |f(x,y)½  dx dy is finite

(D)∫∫_D, |f(x,y)| dx dy is finite

 

Q.No. 3 The initial value problem 

has 

(A) a unique solution if b = 0

(B) no solution if b = 1

(C) infinitely many solutions if b = 2

(D) a unique solution if b = 1

 

Q.No.4 Consider the following statements: 

I: log(|z|) is harmonic on C\{0} 

II: log(|z|) has a harmonic conjugate on C\{0} 

Then 

(A)  I and II are true

(B) I is true but II is false

(C) I is false but II is true

(D) both I and II are false

 

Q.No. 5 Let G and H be defined by 

Suppose f:G → C and g: H → Care analytic functions. Consider the following statements: 

I. ∫_Y f dz is independent of paths y in G joining – i and i 

II. ∫_Y g dz is independent of paths y in H joining – i and i 

Then 

(A)both I and II are true 

(B)I is true but II is false

(C)I is false but II is true

(D)both I and II are false

 

Q.No. 6 Let f (z) = e^1/z, Z ∈ C\{0} and let, for n ∈ N, 

If for a subset S of C, S denotes the closure of Sin C, then 

 

Q.No. 7 Suppose that 

Then, with respect to the Euclidean metric on R2, 

(A) both U and V are disconnected

(B) U is disconnected but V is connected

(C) U is connected but V is disconnected

(D) both U and V are connected

 

Q.No. 8 If (D1) and (D2) denote the dual problems of the linear programming problems (P1) and (P2), respectively, where 

(Pl): minimize x₁ – 2x₂ subject to – x₁ + x₂ = 10, x₁, x₂ > 0, 

(P2): minimize x₁ – 2x₂ subject to – x₁ + x₂ = 10, x₁ – x₂ = 10, x1, x2 > 0, 

then 

(A)both (D1) and (D2) are infeasible

(B)(P2) is infeasible and (D2) is feasible

(C)(D1) is infeasible and (D2) is feasible but unbounded

(D)(P1) is feasible but unbounded and (D1) is feasible 

 

Q.No. 9 If (4,0) and (0, -½) are critical points of the function 

where a, β E R, then 

(A) (4, – ½)point of local maxima of f

(B) (4, – ½) is a saddle point of f

(C) α = 4, β = 2

(D) (4, – ½) point of local minima of f 

 

Q.No. 10 Consider the iterative scheme 

with initial point x > 0. Then the sequence {X_n} 

(A)converges only if X, > 1 

(B)converges only if Xo <3

(C)converges for any Xo 

(D)does not converge for any Xo

 

Q.No. 11 Let C[0, 1] denote the space of all real-valued continuous functions on [0, 1] equipped with the supremum norm ||-||_∞ Let T: C[0,1] → C[0, 1] be the linear operator defined by 

Then 

(A) |||T|| = 1

(B) I-T is not invertible 

(C) T is surjective

(D) || I + T||= 1 + ||T|||

 

Q.No. 12 Suppose that M is a 5 x 5 matrix with real entries and p(x) = det(xl – M). Then 

(A) p(0) = det(M)

(B) every eigenvalue of M is real if p(1) + p(2) = 0 = p(2) + p(3)

(C) M-1 is necessarily a polynomial in M of degree 4 if M is invertible

(D) M is not invertible if M2 – 2M = 0

 

Q.No. 13 Let C[0, 1] denote the space of all real-valued continuous functions on [0, 1] equipped with the supremum norm ||-||_∞ … Let f ∈ C[0, 1] be such that 

For n ∈ N, let f_n(x) = f (x^1+1/N). If S = {f_n : n ∈ N}, then 

(A) the closure of S is compact

(B) S is closed and bounded

(C) S is bounded but not totally bounded

(D) S is compact

 

Q.No.14 Let K: R × (0, ∞) → R be a function such that the solution of the initial value  problem   is, given by

for all bounded continuous functions f. Then the value of ∫_R K(x, t) is _________.

 

Q.No. 15 The number of cyclic subgroups of the quaternion group is____________

Q.No. 16 The number of elements of order 3 in the symmetric group So is ________

 

Q.No. 17 Let F be the field with 4096 elements. The number of proper subfields of F is________ 

 

Q.No. 18 If (x1, x2*) is an optimal solution of the linear programming problem, and (λ1,λ2,λ3) is an optimal solution of its dual problem, then 22-1x* + =12; is equal to____________(correct up to one decimal place) 

 

Q.No. 19 Let a,b,c E R be such that the quadrature ruleis exact for all polynomials of degree less than or equal to 2. Then b is equal to _________(rounded off to two decimal places) 

 

Q.No.20 Let f(x) = x⁴ and let p(x) be the interpolating polynomial of f at nodes 1, 2 and 3. Then p(0) is equal to ____________

 

Q.No. 21 For n ≥ 2, define the sequence {xn} by Then the sequence {X_n} converges to___________(correct up to two decimal places).

 

Q.No. 22 Let L₂ [0,10] = {f:[0, 10] — R : f is Lebesgue measurable and 010f2dx>} equipped with the norm ||f|| = 010f2dx12 and let T be the linear functional on L² [0, 10) given by 

Then ||T || is equal to _______________

 

Q.No. 23 If {X13, X22, X23 = 10, X31, X32, X34} is the set of basic variables of a balanced transportation problem seeking to minimize cost of transportation from origins to destinations, where the cost matrix is, 

and λ, μ ∈ R, then X32 is equal to ______________

 

Q.No. 24 Let Z₂₂₅ be the ring of integers modulo 225. If x is the number of prime ideals and y is the number of nontrivial units in Z₂₂₅, then x + y is equal to ____________

 

Q.No. 25 Let u(x,t) be the solution of 

where f is a twice continuously differentiable function. If f(-2) = 4,f(0) = 0, and u(2, 2) = 8, then the value of u(1,3) is ________________

Q26 – Q55 carry two marks each. 

Q.No. 26 Let be an orthonormal basis for a separable Hilbert space H with the 

inner product (:, ). Define 

Then 

 

Q.No. 27 Suppose V is a finite dimensional non-zero vector space over C and T:V → V is a linear transformation such that Range(T) = Nullspace(T). Then which of the following statements is FALSE? 

(A) The dimension of V is even

(B) 0 is the only eigenvalue of T

(C) Both 0 and 1 are eigenvalues of T 

(D) T² = 0

 

Q.No. 28 Let PE M_{m × n}(R). Consider the following statements: 

I: If XPY = 0 for all X € Mixm(R) and Ye Mnx1(R), then P = 0. 

II : If m = n, P is symmetric and p2 = 0, then P = 0. 

Then 

(A) both I and II are true 

(B) I is true but II is false

(C) I is false but II is true

(D) both I and II are false

 

Q.No. 29 For n EN, let Tn: (11, II.1) → (1o, 11•||..) and T: (11, 11:||) (1o, |I||..) be the bounded linear operators defined by 

Then 

(A) || Tn || does not converge to ||T|| as n → 

(B) || Tn – T|| converges to zero as n 700

(C)for all x € 11, || Tn(x) – T(x) || converges to zero as n →

(D) for each non-zero x € 11, there exists a continuous linear functional g on lo such that g (Tn (x)) does not converge to g(T(x)) as n 

 

Q.No. 30 Let P(R) denote the power set of R, equipped with the metric 

where Xu and Xy denote the characteristic functions of the subsets U and V, respectively, of R. The set { {m}: m e Z} in the metric space (P(R), d) is bounded but not totally bounded totally bounded but not compact compact not bounded 

 

Q.No. 31 Let f:R → R be defined by 

where X(n,n+1) is the characteristic function of the interval (n,n + 1]. For a ER, let Sa = {x E R : f(x) > a}. Then 

 

Q.No. 32 For n E N, let frIn: (0,1) → R be functions defined by 

Then 

(A) {f_n} converges uniformly but {g_n} does not converge uniformly

(B) {g_n} converges uniformly but {f_n} does not converge uniformly 

(C) both {f_n} and {g_n} converge uniformly

(D) neither {f_n} nor {g_n} converge uniformly

 

Q.No. 33 Let u be a solution of the differential equation y’ + xy = 0 and let = uy be a solution of the differential equation y” + 2xy’ + (x2 + 2)y = 0 satisfying (0) = 1 and ‘(0) = 0. Then (x) is 

 

Q.No. 34 For n E NU{0}, let yn be a solution of the differential equation 

satisfying yn (0) = 1. For which of the following functions w(x), the integral 

Is equal to zero ?

 

Q.No. 35 Suppose that 

are metric spaces with metrics induced by the Euclidean metric of R². Let B_x and B_y be the open unit balls around (0,0) in X and Y, respectively. Consider the following statements: 

I: The closure of Bx in X is compact. 

II : The closure of By in Y is compact. 

Then 

(A) both I and II are true

(B) I is true but II is false

(C) I is false but II is true

(D) both I and II are false

 

Q.No. 36 If f:C\{0} → C is a function such that f(2) = f (z/|z|)and its restriction to the unit circle is continuous, then 

(A)f is continuous but not necessarily analytic

(B)f is analytic but not necessarily a constant function

(C)f is a constant function

(D)Z0f(z) exists

 

Q.No. 37 For a subset S of a topological space, let Int(s) and S denote the interior and closure of S, respectively. Then which of the following statements is TRUE? 

(A) If S is open, then S = Int(5) 

(B) If the boundary of S is empty, then S is open 

(C) If the boundary of S is empty, then S is not closed

(D) If S S is a proper subset of the boundary of S, then S is open

 

Q.No.38 Suppose I1, I2 and I3 are the smallest topologies on R containing S1, S2 and S3, respectively, where 

Then

 

Q.No. 39 Let Consider the following statements: 

I: There exists a lower triangular matrix L such that M = LL”, where Lt denotes transpose of L. 

II: Gauss-Seidel method for Mx = b (be R3) converges for any initial choice X, E R3 

Then 

(A) I is not true when a >}, B = 3

(B) II is not true when a >

(C) II is not true when a =

(D) I is true when a = 5, B = 3 

 

Q.No. 40 Let I and J be the ideals generated by {5, √10} and {4, 10} in the ring Z[110] = {a + b/10 | a, b € Z}, respectively. Then 

(A) both / and J are maximal ideals 

(B) I is a maximal ideal but is not a prime ideal 

(C) I is not a maximal ideal but ) is a prime ideal

(D) (neither / nor ) is a maximal ideal

 

Q.No. 41 Suppose V is a finite dimensional vector space over R. If W,W2 and W3 are subspaces of V, then which of the following statements is TRUE? 

(A) If W. + W2+W3 = V then span(W. U W2) U span(W2 U W3) U span(W3 U W) = V

(B)  If W W2 = {0} and W, W3 = {0}, then W, n (W2 + W3) = {0}

(C) If W+W2 = W2 + W3, then W2 = W3

(D) If W#V, then span(V \W) = V

 

Q.No.42 Let a, ER, a 0. The system 

has NO basic feasible solution if 

 

Q.No. 43 Let 0 <p < 1 and let 

For f eX, define 

Then 

(A)|·|_p defines a norm on X

(B) If + glp < If lp + Iglp for all f.g EX

(C)If+gl% = |f1 + gl% for all f, g ex

(D) if fn converges to f pointwise on R, then limfnly = Iflg.

 

Q.No. 44 Suppose that 01 and $2 are linearly independent solutions of the differential equation 

and Ø₁(0) = 0. Then the smallest positive integer n such that 

is______________.

 

Q.No. 45 Suppose that . If 

then the value of a is equal to _______________.

 

Q.No. 46 If y(t) = ½e^3it, t e [0, 2] and 

then ß is equal to______________(correct up to one decimal place) 

 

Q.No. 47 Let where is a primitive cube root of unity. Then the degree of extension of K over Q is_________________. 

 

Q.No. 48 Let a E R. If (3,0,0,B) is an optimal solution of the linear programming problem 

then the maximum value of ß-a is __________.

 

Q.No. 49 Suppose that T: R4 → R[x] is a linear transformation over R satisfying 

Then the coefficient of x4 in T(-3,5,6,6) is ______________.

 

Q.No. 50 Let F(x, y, z) = (2x – 2y cos x) î + (2y – y2 sin x) s + 4z k and let S be the surface of the tetrahedron bounded by the planes 

x = 0, y = 0, z = 0 and x + y + z = 1. If ñ is the unit outward normal to the tetrahedron, then the value of 

is__________________(rounded off to two decimal places) 

 

Q.No. 51 Let F = (x + 2y)ez î + (yez + x2) ĵ + y2z ħ and let S be the surface x2 + y2 + z = 1, 2 > 0. If ñ is a unit normal to S and 

Then a is equal to ______________.

 

Q.No. 52 Let G be a non-cyclic group of order 57. Then the number of elements of order 3 in G is ________________.

 

Q.No.53 The coefficient of (x – 1)5 in the Taylor expansion about x = 1 of the function 

is _________________ (correct up to two decimal places) 

 

Q.No. 54 Let u(x,y) be the solution of the initial value problem 

Then the value of u(0,1) is ______________ (rounded off to three decimal places) 

 

Q.No. 55 The value of 

is ________________ (rounded off to three decimal places) 

Answer Key

Q.No.	1	2	3	4	5	6	7	8	9	10
Ans.	C	B	D	D	B	D	C	B	B	B
Q.No.	1	2	3	4	5	6	7	8	9	10
Ans.	A	C	D	B	B	A OR D	C	A	B	C
Q.No.	11	12	13	14	15	16	17	18	19	20
Ans.	D	C	A	1 TO 1	5 TO 5	80 TO 80	5 TO 5	5.5 TO 5.5	1.70 TO 1.80	36 TO 36
Q.No.	21	22	23	24	25	26	27	28	29	30
Ans.	0.25 TO 0.25	3 TO 3	5 TO 5	121 TO 121	10 TO 10	A	C	A	C	A
Q.No.	31	32	33	34	35	36	37	38	39	40
Ans.	D	B	B	B	C	A	B	C	D	B
Q.No.	41	42	43	44	45	46	47	48	49	50
Ans.	D	D	C	3 TO 3	56 TO 56	0.5 TO 0.5	4 TO 4	7 TO 7	5 TO 5	1.30 TO 1.40
Q.No.	51	52	53	54	55
Ans.	2 TO 2	38 TO 38	0.04 TO 0.04	1.61 TO 1.625	2.710 TO 2.725

GATE 2020 Aerospace Engineering Previous Year Paper

GA – General Aptitude 

Q1 – Q5 carry one mark each. 

Q. 1 The untimely loss of life is a cause of serious global concern as thousands of people get killed accidents every year while many other die diseases like cardio vascular disease, cancer, etc. 

(A) in, of

(B) from, of

(C) during, form

(D) from, from

 

Q. 2 He was not only accused of theft rather but also but even rather than ________of conspiracy. 

(A) rather

(B) but also

(C) but even

(D) rather then

 

Q. 3 Select the word that fits the analogy: 

Explicit: Implicit :: Express: _________

(A) Impress 

(B) Repress 

(C) Compress 

(D) Suppress 

 

Q. 4 The Canadian constitution requires that equal importance be given to English and French. Last year, Air Canada lost a lawsuit, and had to pay a six-figure fine to a French-speaking couple after they filed complaints about formal in-flight announcements in English lasting 15 seconds, as opposed to informal 5 second messages in French. 

The French-speaking couple were upset at _________.

(A) the in-flight announcements being made in English. 

(B) the English announcements being clearer than the French ones. 

(C) the English announcements being longer than the French ones. 

(D) equal importance being given to English and French. 

 

Q. 5 A superadditive function f (.) satisfies the following property 

Which of the following functions is a superadditive function for x > 1? 

Q6 – Q10 carry two marks each. 

Q. 6 The global financial crisis in 2008 is considered to be the most serious world-wide financial crisis, which started with the subprime lending crisis in USA in 2007. The sub prime lending crisis led to the banking crisis in 2008 with the collapse of Lehman Brothers in 2008. The subprime lending refers to the provision of loans to those borrowers who may have difficulties in repaying loans, and it arises because of excess liquidity following the East Asian crisis. 

Which one of the following sequences shows the correct precedence as per the given passage? 

(A) East Asian crisis → subprime lending crisis → banking crisis → global financial crisis. 

(B) Subprime lending crisis → global financial crisis → banking crisis → East Asian crisis. 

(C) Banking crisis → subprime lending crisis → global financial crisis → East Asian crisis. 

(D) Global financial crisis → East Asian crisis → banking crisis → subprime lending crisis. 

 

Q. 7 It is quarter past three in your watch. The angle between the hour hand and the minute hand is _____

(A) 0° 

(B) 7.5°

(C) 15° 

(D) 22.5° 

 

Q. 8 A circle with centre O is shown in the figure. A rectangle PQRS of maximum possible area is inscribed in the circle. If the radius of the circle is a, then the area of the shaded portion is______

Q. 9 a,b,c are real numbers. The quadratic equation ax² – 6x + c = 0 has equal roots, which is ß, then 

 

Q. 10 The following figure shows the data of students enrolled in 5 years (2014 to 2018) for two schools P and Q. During this period, the ratio of the average number of the students enrolled in school P to the average of the difference of the number of students enrolled in schools P and Q is __________

(A) 8:23 

(B) 23 : 8 

(C) 23:31 

(D) 31:23 

AE: Aerospace Engineering 

Q1-Q25 carry one mark each. 

Q.1 For f(x)=|x|, with df/dx denoting the derivative, the mean value theorem is not applicable because 

 

Q. 2 For the function and and are constants, the maximum occurs at x=o x=0/27 

 

Q. 3 y= Ae^mx + Be^{-m x}, where A, B and m are constants, is a solution of 

 

Q. 4 Which of the following statements is true about the effect of increase in temperature on dynamic viscosity of water and air, at room temperature? 

(A) It increases for both water and air. 

(B) It increases for water and decreases for air. 

(C) It decreases for water and increases for air. 

(D) It decreases for both water and air. 

 

Q. 5 Given access to the complete geometry, surface pressure and shear stress distribution over a body placed in a uniform flow, one can estimate 

(A) the moment coefficient, and the force on the body. 

(B) the force coefficient, and the force on the body. 

(C) the moment coefficient, and the moment on the body. 

(D) the force and the moment on the body. 

 

Q. 6 A pair of infinitely long, counter-rotating line vortices of the same circulation strength I are situated a distance h apart in a fluid, as shown in the figure. The vortices will 

Q. 7 The streamlines of a steady two dimensional flow through a channel of height 0.2 m are plotted in the figure, where Y is the stream function in m²/s. The volumetric flow rate per unit depth is 

(A) 1.0 m²/s 

(B) 2.0 m²/s 

(C) 0.5 m²/s 

(D) 0.1 m²/s 

 

Q. 8 Which of the following options can result in an increase in the Mach number of a supersonic flow in a duct? 

(A) Increasing the length of the duct 

(B) Adding heat to the flow 

(C) Removing heat from the flow 

(D) Inserting a convergent-divergent section with the same cross-sectional area at its inlet and exit planes 

 

Q. 9 Which one of the following conditions needs to be satisfied for = A x⁴ +By⁴ +C xy³ to be considered as an Airy’s stress function? 

(A) A-B=0 

(B) A+B=0 

(C) A-C=0 

(D) A + C = 0 

 

Q. 10 Consider the plane strain field given by The relation between A and B needed for this strain field to satisfy the compatibility condition is 

(A) B=A 

(B) B= 2A 

(C) B = 3A 

(D) B=4A 

 

Q. 11 For hyperbolic trajectory of a satellite of mass m having velocity V at a distancer from the center of earth (G: gravitational constant, M: mass of earth), which one of the following relations is true? 

 

Q. 12 For conventional airplanes, which one of the following is true regarding roll 

control derivative and yaw control derivative where ris rudder deflection? 

 

Q. 13 The ratio of exit stagnation pressure to inlet stagnation pressure across the rotating impeller of a centrifugal compressor, operating with a closed exit, is

(A) 0 

(B) 1 

(C) >1

(D) 0.5 

 

Q. 14 Which one of the following is a hypergolic propellant combination used in rocket engines? 

(A) Liquid hydrogen – liquid oxygen 

(B) Unsymmetrical dimethyl hydrazine – nitrogen tetroxide 

(C) Rocket fuel RP-1 – liquid oxygen 

(D) Liquid hydrogen – liquid fluorine 

 

Q. 15 In aircraft engine thermodynamic cycle analysis, perfectly expanded flow in the nozzle means that the static pressure in the flow at the nozzle exit is equal to 

(A) the stagnation pressure at the engine inlet. 

(B) the stagnation pressure at the nozzle exit. 

(C) the ambient pressure at the nozzle exit. 

(D) the static pressure at the nozzle inlet. 

 

Q. 16 Three long and slender aluminum bars of identical length are subjected to an axial tensile force. These bars have circular, triangular and rectangular cross sections, with same cross sectional area. If they yield at F_circle, F_iriangle and F_rectangle, respectively, which one of the following is true? 

(A) F_circle > F_triangle > F_rectangle 

(B) F_circle < F_riangle < F_rectangle 

(C) F_triangle > F _circle > F_rectangle 

(D) F_circle = F_triangle = F_rectangle 

 

Q. 17 The positive high angle-of-attack condition is obtained in a steady pull-out maneuver at the largest permissible angle-of-attack of the wing. Under this condition, at which of the following regions of the wing does the maximum tension occur? 

(A) I 

(B) II 

(C) III 

(D)  IV 

 

Q. 18 The natural frequency of the first mode of a rectangular cross section cantilever aluminum beam is rad/s. If the material and cross-section remain the same, but the length of the beam is doubled, the first mode frequency will become 

 

Q. 19 Given the sum of squares of eigenvalues of A is 

(A) tan²θ

(B) 1

(C) sin²θ

(D) cos²θ

 

Q. 20 Burnout velocity of a space vehicle in a circular orbit at an angle 5 degrees above the local horizon around earth is 13.5 km/s. Tangential velocity of the space vehicle in the orbit is ___________ km/s (round off to two decimal places). 

 

Q. 21 Velocity of an airplane in the body fixed axes is given as [100 -10 20] m/s. The sideslip angle is _________ degrees (round off to two decimal places). 

 

Q. 22 The similarity solution for the diffusion equation,

where similarity variable,(round off to one decimal place)________.

 

Q. 23 Air enters the rotor of an axial compressor stage with no pre-whirl (C_θ=0) and exits the rotor with whirl velocity, C_θ=150 m/s. The velocity of rotor vanes, U is 200 m/s. Assuming C_p = 1005 J/(kg K), the stagnation temperature rise across the rotor is ______K (round off to one decimal place). 

 

Q. 24 A thin walled beam of constant thickness shown in the figure is subjected to a torque of 3.2 kNm. If the shear modulus is 25 GPa, the angle of twist per unit length is____________rad/m (round off to three decimal places). 

 

Q. 25 An airplane of mass 5000 kg is flying at a constant speed of 360 km/h at the bottom of a vertical circle with a radius of 400 m, as shown in the figure. Assuming that the acceleration due to gravity is 9.8 m/s², the load factor experienced at the center of gravity of the airplane is __________ (round off to two decimal places). 

Q26 – Q55 carry two marks each. 

Q. 26 The equation x dx/dy + y = C, where c is a constant, represents a family of exponential curves parabolas circles hyperbolas 

(A) exponential curves

(B) parabolas

(C) circles

(D) hyperbolas

 

Q. 27 A wedge shaped airfoil is placed in a supersonic flow as shown in the figure (not to scale). The corners of the wedge are at x = X_A, X = X_B, X = X_C, respectively. 

Which one of the following represents the correct static pressure profiles along y = Y_I and y = Y_II? 

Q. 28 The value of Poisson’s ratio at which the shear modulus of an isotropic material is equal to the bulk modulus is 

(A) ½ 

(B) ¼ 

(C) ⅙ 

(D) ⅛ 

 

Q. 29 A load P is applied to the free end of a stepped cantilever beam as shown in the figure. The Young’s modulus of the material is E, and the moments of inertia of the two sections of length 2 m and 1 m are I and 3I, respectively. Ignoring transverse shear and stress concentration effects, the deflection at the point where the load is applied at the free end of the cantilever is 

Q. 30 The three dimensional strain-stress relation for an isotropic material, written in a general matrix form, is 

A, B and C are compliances which depend on the elastic properties of the material, Which one of the following is correct? 

 

Q. 31 For three different airplanes A, B and C, the yawing moment coefficient (C_n) was measured in a wind-tunnel for three settings of sideslip angle β and tabulated as 

Which one of the following statements is true regarding directional static stability of the airplanes A, B and C? 

(A) All three airplanes A, B, and C are stable. 

(B) Only airplane C is stable, while both A and B are unstable. 

(C) Airplane C is unstable, A and B are stable with A being more stable than B. 

(D) Airplane C is unstable, A and B are both stable with A less stable than B. 

 

Q. 32 A closed curve is expressed in parametric form as x = a cos θ and y= b sin θ, where a=7 m and b= 5 m. Approximating π = 22/7, which of the following is the area enclosed by the curve? 

(A) 110 m² 

(B) 74 m² 

(C) 35 m² 

(D) 144 m² 

 

Q. 33 An axial compressor is designed to operate at a rotor speed of 15000 rpm and an inlet stagnation temperature of 300 K. During compressor testing, the inlet stagnation temperature of the compressor measured was 280 K. What should be the rotor speed for the compressor to develop the same performance characteristics during this test as in the design condition? 

(A) 14000 rpm 

(B) 14491 rpm 

(C) 15526 rpm 

(D) 16071 rpm 

 

Q. 34 For the state of stress shown in the figure, which one of the following represents the correct free body diagram showing the maximum shear stress and the associated normal stresses? 

 

Q. 35 In the equation where A is an orthogonal matrix, the sum of the unknowns, x + y + z =________ (round off to one decimal place). 

 

Q. 36 If 01(x3-2x+1)dx is evaluated numerically using trapezoidal rule with four intervals, the difference between the numerically evaluated value and the analytical value of the integral is equal to___________(round off to three decimal places). 

 

Q. 37 The table shows the lift characteristics of an airfoil at low speeds. The maximum lift coefficient occurs at 16 degrees. 

Using Prandtl-Glauert rule, the lift coefficient for the airfoil at the angle of attack of 6 degrees and free stream Mach number of 0.6 is (round off to two decimal places). 

 

Q. 38 A low speed uniform flow U₀, is incident on an airfoil of chord c. In the figure, the velocity profile some distance downstream of the airfoil is idealized as shown for section B. The static pressure at sections A and B is the same. The drag coefficient of the airfoil is ____________ (round off to three decimal places). 

 

Q. 39 An oblique shock is inclined at an angle of 35 degrees to the upstream flow of velocity 517.56 m/s. The deflection of the flow due to this shock is 5.75 degrees and the temperature downstream is 182.46 K. Assume the gas constant R=287 J/(kg K), specific heat ratio y = 1.4, and specific heat at constant pressure C_p = 1005 J/(kg K). Using conservation relations, the Mach number of the upstream flow can be obtained as _________ (round off to one decimal place). 

 

Q. 40 The thickness of a laminar boundary layer (δ) over a flat plate is, , where x is measured from the leading edge along the length of the plate. The velocity profile within the boundary layer is idealized as varying linearly with y. For freestream velocity of 3 m/s and kinematic viscosity of 1.5 × 10^-5 m²/s, the displacement thickness at 0.5 m from the leading edge is ____mm (round off to two decimal places). 

 

Q. 41 A wing of 15 m span with elliptic lift distribution is generating a lift of 80 kN at a spccd of 90 m/s. The density of surrounding air is 1.2 kg/m³. The induced angle of attack at this condition is ________ degrees (round off to two decimal places). 

 

Q. 42 A solid circular shaft, made of ductile material with yield stress σy = 280 MPa, is subjected to a torque of 10 kNm. Using the Tresca failure theory, the smallest radius of the shaft to avoid failure is ________ cm (round off to two decimal places). 

 

Q. 43 The ratio of tangential velocities of a planet at the perihelion and the aphelion from the sun is 1.0339. Assuming that the planet’s orbit around the sun is planar and elliptic, the value of eccentricity of the orbit is _________(round off to three decimal places). 

 

Q. 44 The eigenvalues for phugoid mode of a general aviation airplane at a stable cruise flight condition at low angle of attack are . If the acceleration due to gravity is 9.8 m/s², the equilibrium speed of the airplane is m/s (round off to two decimal places). 

 

Q. 45 

 

Q. 46 A single engine, propeller driven, general aviation airplane is flying in cruise at sea level condition (density of air at sea-level is 1.225 kg/m³) with speed to cover maximum range. For drag coefficient C_D = 0.025 + 0.049 C_I² and wing loading W/S = 9844 N/m2, the speed of the airplane is_________ m/s (round off to one decimal place). 

 

Q. 47 The design flight Mach number of an ideal ramjet engine is 2.8. The stagnation temperature of air at the exit of the combustor is 2400 K. Assuming the specific heat ratio of 1.4 and gas constant of 287 J/(kg K), the velocity of air at the exit of the engine is __________ m/s (round off to one decimal place). 

 

Q. 48 The operating conditions of an aircraft engine combustor are as follows. 

The rate of total enthalpy of air entering the combustor = 28.94 MJ/s. 

The rate of total enthalpy of air leaving the combustor = 115.42 MJ/s. 

Mass flow rate of air = 32 kg/s. 

Air to fuel mass ratio = 15.6. 

heating value of the fuel = 46 MJ/kg. 

The efficiency of the combustor is__________% (round off to two decimal places). 

 

Q. 49 The figure shows the T-S diagram for an axial turbine stage. 

Assuming specific heat ratio of 1.33 for the hot gas, the isentropic efficiency of the turbine stage is___________%(round off to two decimal places). 

 

Q. 50 A rocket engine has a sea level specific impulse of 210 s and a nozzle throat area of 0.005 m². While testing at sea level conditions, the characteristic velocity and pressure for the thrust chamber are 1900 m/s and 50 bar, respectively. Assume the acceleration due to gravity to be 9.8 m/s². The thrust produced by the rocket engine is ______kN (round off to one decimal place). 

 

Q. 51 A critically damped single degree of freedom spring-mass-damper system used in a door closing mechanism becomes overdamped due to softening of the spring with extended use. If the new damping ratio (ξnew) for overdamped condition is 1.2, the ratio of the original spring stiffness to the new spring stiffness (k_org/k_new), assuming that the other parameters remain unchanged, is _______ (round off to two decimal places). 

 

Q. 52 The two masses of the two degree of freedom system shown in the figure are given initial displacements of 2 cm (x₁) and 1.24 cm (x₂). The system starts to vibrate in the first mode. The first mode shape of this system is φ₁ = [1 a]^T, where a = ______ (round off to two decimal places). 

 

Q. 53 As shown in the figure, a beam of length 1 m is rigidly supported at one end and simply supported at the other. Under the action of a uniformly distributed load of 10 N/m, the magnitude of the normal reaction force at the simply supported end is ________ N (round off to two decimal places). 

Q .54 An airplane of mass 4000 kg and wing reference area 25 m² flying at sea level has a maximum lift coefficient of 1.65. Assume density of air as 1.225 kg/m³ and acceleration due to gravity as 9.8 m/s². Using a factor of safety of 1.25 to account for additional unsteady lift during a sudden pull-up, the speed at which the airplane reaches a load factor of 3.2 is _____________ m /s (round off to two decimal places). 

 

Q. 55 A Pitot tube mounted on the wing tip of an airplane flying at an altitude of 3 km measures a pressure of 0.72 bar, and the outside air temperature is 268.66 K. Take the sea level conditions as, pressure = 1.01 bar, temperature = 288.16 K, and density = 1.225 kg/m². The acceleration due to gravity is 9.8 m/s² and the gas constant is 287 J/(kg K). Assuming standard atmosphere, the equivalent airspeed for this airplane is ________ m /s (round off to two decimal place). 

Answer Key 

Q.No.	1	2	3	4	5	6	7	8	9	10
Ans.	A	B	B	C	A	A	B	C	C	B

Q.No.	1	2	3	4	5	6	7	8	9	10
Ans.	C	D	A	C	D	C	B	C	B	D
Q.No.	11	12	13	14	15	16	17	18	19	20
Ans.	A	A	C	D	C	D	C	A	B	13.42 TO 13.47
Q.No.	21	22	23	24	25	26	27	28	29	30
Ans.	-5.62 TO -5.57	1.9 TO 2.1	29.8 TO 30.0	0.009 TO 0.011	3.50 TO 3.60	C	D	D	C	D
Q.No.	31	32	33	34	35	36	37	38	39	40
Ans.	C	A	B	B	0.9 TO 1.1	0.010 TO 0.012	0.92 TO 0.94	0.009 TO 0.011	1.9 TO 1.38	4.00 TO 4.20
Q.No.	41	42	43	44	45	46	47	48	49	50
Ans.	1.29 TO 1.38	3.55 TO 3.58	0.016 TO 0.018	55.20 TO 55.33	25.60 TO 25.70	149.0 TO 151.0	1712.0 TO 1719.0	91 TO 93	87 TO 89	270. TO 27.2
Q.No.	51	52	53	54	55
Ans.	1.43 TO 1.45	0.61 TO 0.63	3.74 TO 3.76	62.95 TO 63.08	57.10 TO 60.00

GATE 2020 Electrical Engineering Previous Year Paper

Q.1 NPA is the asset that a customer borrows and holds it for a period of time without paying any interest. RBI has reduced the holding period for NPA thrice during the period 1993- 2004. In 1993 it was four quarters (360 days) how many days is the holding period in 2004? 

(a) 90 

(b) 180 

(c) 45 

(d) 270 

Ans. (a) 

 

Q.2 Number between 1001 to 9999 how many times 37 occurs in the same sequence? 

(a) 279 

(b) 280 

(c) 270

(d) 299 

Ans. (a) 

 

Q.3 The revenue and expenditure of four companies P, Q, R, S as shown in the figure below company Q earns a profit of 10% on expenditure of 2014, the revenue of Q in 2015 is ________. 

Ans. Data insufficient 

 

Q.4 Stock markets _______ at the news of the coup. 

(a) plugged 

(b) plunged 

(c) probed 

(d) poised 

Ans. (b) 

 

Q.5 This book, including all its chapters, ________ interesting. The students as well as instructor ________ in agreement with it. 

(a) is, was 

(b) is, are 

(c) were, was 

(d) are, are 

Ans. (b) 

 

Q.6 People were prohibited ________ there vehicles near the entrance of the main administrative building. 

(a) to park 

(b) to have parked 

(c) from parking 

(d) parking 

Ans. (c) 

 

Q.7 Select the word do :

undo : : trust : 

(a) distrust 

(b) entrust 

(c) intrust 

(d) untrust 

Ans. (a) 

 

Q.8 Find the ratio of AC+BC / AB 

AB where O is center of the circle shown below. 

AB , AC and BC are chords. 

Ans. (1.414) 

 

Q.9 Z : WV : RQP : ? 

(a) KIJH 

(b) JIHG 

(c) HIJK 

(d) KJIH 

Ans. (d) 

 

Q.10 If P, Q, R, S are four individuals, how many teams of size exceeding one can be formed with Q as a member? 

(a) 5 

(b) 7 

(c) 8 

(d) 6 

Ans. (b) 

 

Q.11 A resistor and a capacitor are connected in series to a 10 V dc supply through a switch is closed at t = 0, and the capacitor voltage is found to cross ‘0’ voltage at t = 0.4τ (τ = time constant). The absolute value of % change required in the initial capacitor voltage if the zero crossing has to happen at t = 0.2τ is _____. 

Ans. (54.989) 

 

Q.12 To ensure the maximum power transfer across V_th the values of R₁ and R₂ will be (Diode in figure is silicon diode) 

(a) R₁ high, R₂ high 

(b) R₁ low, R₂ low 

(c) R₁ low, R₂ high 

(d) R₁ high, R₂ low 

Ans. (b) 

 

Q.13 For the given circuit the value of V_th is ______. 

Ans. (14) 

 

Q.14 In the given circuit rms value of I₁ is _____.

Ans. (1.732) 

 

Q.15 If 

2001 → 98H 

2002 → B1H 

LXI H, 2001H 

MVI A, 21H 

INX H 

ADD M 

INX H 

MOV M, A 

HLT 

The content of 2003H is (_____)₁₀. 

Ans. (210)

 

Q.16 A differential equation with y(t) → output and x(t) → input is 

The poles of the input 

(a) –2j, +2j 

(b) +4, –4 

(c) –2, +2 

(d) +4j, –4j 

Ans. (a) 

 

Q.17 A PMDC motor is connected to 5 V at t = 0. Its speed increases from 0 to 6.32 rad/ sec monotonically from t = 0 to t = 0.5s and finally settles down to 10 rad/sec. Assume negligible armature inductance. Find the transfer function? 

Ans. (c) 

 

Q.18 For the given open loop transfer function . If 1 + G(s)H(s) plane  encircles the origin once in counter clockwise direction then number of closed loop poles in right side of s-plane will be 

Ans. (0) 

 

Q.19 For the given open loop transfer function with unity negative feedback gain, 

K The value of gain K. For which closed loop system is marginally stable will be _________ . 

Ans. (8)

 

Q.20 A stable LTI system with single pole P, has a transfer function G(s)H(s) = s2 + 100s – P with DC gain of 5; the smallest possible frequency in radian/sec at only gain is 

(a) 11.08 

(b) 70.13 

(c) 122.07 

(d) 8.84 

Ans. (d) 

 

Q.21 For the given block diagram of the system 

Which of the following is true regarding order and stability of the system 

(a) 4^th order and stable 

(b) 4^th order and unstable 

(c) 3^rd order and unstable 

(d) 3^rd order and stable 

Ans. (b) 

 

Q.22 Which of the given below signal flow is analogous to given below system? 

Ans. () 

 

Q.23 Given , find electric flux crossing the cylinder ρ = 3 m; 3 varying from 0 to 5. 

Ans. (180π) 

 

Q.24 The vector function expressed by 

F = a_x(5y – k₁ z) + a_y(3z + k₂ x) + a_z(k₃ y – 4x) 

represent a conservative field, where a_x, a_y, a_z are unit vector along x, y, z directions, respectively the value of constant k₁, k₂ and k₃ ________. 

(a) 4, 5, 3 

(b) 8, 3, 7 

(c) 0, 0, 0 

(d) 3, 8, 5 

Ans. (a) 

 

Q.25 The value of mutual inductance figure shows long wire carrying current 2 A placed in away from square coil as shown in figure. The value mutual inductance will be ____. nH. 

Ans. (138.6) 

 

Q.26 In a dielectric medium in cylindrical, then find volume charge density 

(a) 2∈_o 

(b) 3∈_o 

(c) 4∈_o 

(d) 9∈_o 

Ans. (d) 

 

Q.27 In the given figure, the three windings having polarity as shown above, are connected to 3-φ, balanced supply. The number of turns in the supply winding is 20, the voltage seen in winding X having N = 2 turns will be 

Ans. (46)

 

Q.28 A cylindrical rotor synchronous generator delivering constant active power at a constant terminal voltage, a current of 100 A at a 0.9 p.f. lagging. A shunt reactor is connected so that the reactive power demand doubles then the new value of armature current is ______ A. 

Ans. (125.29) 

 

Q.29 A cylindrical rotor generator having internal emf 1 + j0.7 V and terminal voltages (1 + j 00 V). The synchronous reactance is 0.7 pu whereas subtransient reactance is 0.2 pu for 3-φ bolted short circuit at generator the value of subtransient generated internal emf is ______. 

Ans. (1.019) 

 

Q.30 4 kVA, 200/100 V, 50 Hz single phase transformer has no load core loss of 450 W. If high voltage side is energized by 160 V, 40 Hz, the core loss will be 320 W. Find the core loss if the high voltage side is energized by 100 V, 25 Hz. 

Ans. (162.5) 

 

Q.31 A 3-φ, 50 Hz, 4 pole induction motor runs at no load with a slip of 1%, at full load the motor runs at a slip of 5%. The percentage speed regulation of the motor is _____. 

Ans. (4.02) 

 

Q.32 A sequence detector is designed to detect precisely 3 digital inputs, with overlapping sequence detectable. For the sequence (1, 0, 1) and input data (1,1,0,1,0,0,1,1,0,1,0,1,1,0) the output is 

Ans. () 

 

Q.33 A synchronous generator has lossless reactance X_s. Then V_A is terminal voltage and E_f is internal emf voltage. 

P : If power factor is leading then always V_A > E_f 

Q : If power factor is lagging then always V_A < E_f 

Which of the statement is true? 

(a) P is false, Q is true 

(b) P is false, Q is false 

(c) P is true, Q is true 

(d) P is true, Q is false 

Ans. (a) 

 

Q.34 A 250 DC shunt motor having armature resistance of 0.2 Ω and field resistance of 100 Ω. It draws a no load current of 5 A at 1200 rpm. The brush drop is 1 V per brush at all operating conditions. If the motor draws 50 A at full load and flux per pole is decreased by 5% because of armature reaction. The speed of the motor at full load is ____ rpm. 

(a) 900 

(b) 1000 

(c) 1200 

(d) 1220 

Ans. (d) 

Q.35 Find Z(unsaturated)Z(Saturated)=?

Ans. (2.05) 

 

Q.36 DC bias voltage of 13 V is applied between gate and body time. The charge measured in the silicon dioxide layer is +Q, 

The total charge in the box region is ________ multiple of +Q. (Give answer to nearest integer) 

Ans. (#)A 

 

Q.37 A diode is biased of –0.03 V having an ideality factor of 15/13; and V_T = 26 mV; if the current has to be rased to 1.5 times of the than required voltage will be 

(a) –4.5 V 

(b) –0.09 V 

(c) –0.02 V 

(d) None of above 

Ans. (c)

 

Q.38 For a common source amplifier g_m = 520 μA/V² and r_d = 4.7 kΩ calculate gain of amplifier. 

(a) –2.447 

(b) 

(c) 

(d) 

Ans. (a) 

 

Q.39 A causal control system having poles at (–2, 1), (2, –1) and zeros at (2, 1) and (–2, –1). Identify the nature of transfer function. 

(a) Unstable, complex, all pass 

(b) Stable, real, all pass 

(c) Unstable, complex, HP 

(d) Stable, real, HPF 

Ans. (a)

All pass filters because poles and zeros are mirror-image of each other (i..e for each pole there is a mirror-image zero). Unstable because one pole in the RHS of s-plane. 

Transfer function is complex. 

h(t) or impulse response will be also complex because poles are not occuring in conjugate pairs as well as zeros are also not occuring in conjugate pair.

 

Q.40 x(t) ∗ h(t) = y(t), where h(t) is an impulse response. 

|x(t)| ∗ |h(t)| = z(t) then which of the following is correct. 

(a) For every –∞ < t < ∞, z(t) ≤ y(t) 

(b) For every –∞ < t ≤ ∞, z(t) ≥ y(t) 

(c) For some –∞ < t < ∞, z(t) ≤ y(t) 

(d) For some –∞ < t ≤ ∞, z(t) ≥ y(t) 

Ans. (b) 

Since, y(t) = x(t) + h(t) 

and z(t) = x () t × ht () 

Case-1: x( )t 

then, y(t) and z(t) 

Case-2: x( )t 

then, y(t) = z(t) 

Thus, z(t) ≥ y(t), for all ‘t’ 

 

Q.41 A signal x(n) is given by (½)ⁿ 1(n) where, 

Z-transform x(n – K) is ^, then what will be ROC of x(n – K) 

(a) Z > ½ 

(b) Z < 2 

(c) Z > 2 

(d) Z < ½ 

Ans. (a) 

 

Q.42 If x_A and x_R are average and rms values of signal x(t) = x(t – T) respectively. y_A and y_R are average and rms value of signal y(t) = Kx(t) respectively. K and T are independent of t. 

(a) y_A = Kx_A, y_R = Kx_R 

(b) y_A ≠ Kx_A, y_R = Kx_R 

(c) y_A = Kx_A, y_R ≠ Kx_R 

(d) y_A ≠ Kx_A, y_R ≠ Kx_R 

Ans. (a) 

Given that, 

⇒ Average x(t) = X_a , Rms x(t) = X_R

⇒ Average y(t) = Y_a , Rms y(t) = Y_R 

⇒ x(t) = x(t – T) 

⇒ y(t) = Kx(t) …(i) 

⇒ Y_a = KX_a 

Since, Power y(t) = |K|² power x(t) 

⇒ Rms y²(t) = |K|² Rms x ² ( t ) 

⇒ Rms y(t) = |K|² Rms x ( t ) 

⇒ Y_R = |K|X _R 

Assuming K as real and positive, 

Y_R = KX_R 

 

Q.43 Which of the following statement is true about the two sided Laplace transform? 

(a) It always exists for a signal that may or may not have Fourier transform. 

(b) It has no poles for any bounded signal that is non-zero only inside a finite time interval.

(c) If a signal can be expressed as a weighted sum of shifted one sided exponentials, then its Laplace transform will have no poles. 

(d) The number of finite poles finite zeros must be equal. 

Ans. (b) 

 

Q.44 A 50 Hz, power system network is operated under load of 100 MW. When the load is increased, the power input by the synchronous generator is increased by 10 MW and frequency of the rpm falls to 49.75 Hz. What will be the load at power system for the frequency falls to 49.25 Hz? 

Ans. (130) 

Assumed full load frequency is 50 Hz

 

Q.45 Find admittance matrix 2 bus is connected by 2 transformers having ratios 1 : T_i and T_j : 1 respectively and line having Y admittance. 

 

Q.46 A transmission line is being protected by distance protection. 80% of the line is being protected. The transfer reactance is 0.2 p.u. A solid 3-φ, fault occurred at the end of the transmission line. The minimum level of fault current to activate the relay 

(a) 6.25 

(b) 5 

(c) 1.25 

(d) 3 

Ans. (a) 

 

Q.47 Voltage at bus 1 = 1.1 p.u. Voltage at bus 2 = 1 p.u. 

Voltage at bus 2 is kept constant, Q₁₂ is the sending reactive power from 1 to 2. On changing the bus 1 voltage, Q₁₂ increases by 20%. Active power is zero in both the condition find the new value of bus 1 voltage. 

Ans. (#)A 

 

Q.48 In AC voltage controller shown below. Thyristor T₁ is fired at α and T₂ is fired at 180° + α. To control the output power over range 0 to 2 kW. The minimum range of variation in α is 

(a) 0° to 60° 

(b) 0° to 120° 

(c) 60° to 120° 

(d) 60° to 180°# 

Ans. (d) 

 

Q.49 A 1-φ, fully controlled rectifier is connected to highly inductive RL load with R = 10 Ω at 230 V, 50 Hz. The source inductance is 2.28 mH. If the firing angle α = 45°, then the overlapping angle will be 

Ans. (4.25) 

 

Q.50 Value of σ adjusted so that 3^rd harmonic is completely eliminated. Find the percentage magnitude of 5^th harmonic w.r.t. fundamental component at this condition. 

Ans. (20) 

 

Q.51 A single-phase, 50 Hz full bridge rectifier with highly inductive RL load. The two most dominant frequency components will be 

(a) 50 Hz, 150 Hz 

(b) 50 Hz, 100 Hz 

(c) 150 Hz, 250 Hz 

(d) 50 Hz, 0 Hz 

Ans. (a) 

1-φ full bridge rectifier, 

n = 1, 3, 5, … 

f = 50, 150, 250 dominant 

 

Q.52 A DC-DC converter shown below having switching frequency of 10 kHz with duty ratio 0.6. All the components are ideal and the initial inductor current is zero. Energy stored in the inductor (in mJ) at the end of 10 switching cycles is 

Ans. (5)

Buck boost converter

 

Q.53 R_T → Thermistor R_T = 2(1 + αT) Temperature rise = 150% Find errors in the output voltage? 

R₁ = 1 kHz, R₂ = 1.3 kΩ, R₃ = 2.6 kΩ 

Ans. () 

 

Q.54 A vector function is given by . The line integral of the above function along the curve C given by y = x² as shown below ________. 

Ans. (–2.33) 

 

Q.55 dy/dx = 2x – y, y(0) = 1. Find y at x = ln2 

Ans. (0.886) 

 

Q.56 Value of integral z2 + 1z2 – 2z along the contour |z| = 1 is 

(a) πi 

(b) –πi 

(c) 8πi 

(d) –8πi 

Ans. (b) 

 

Q.57 The number of purely real elements in lower triangular representation of given 3 × 3 matrix obtained through given decomposition is 

Ans. (#) 

 

 

Q.58 If y = 3x² + 3x + 1, for x∈[–2, 0], find maximum and minimum value in the given range. 

(a) 4 and 1 

(b) 7 and ¼ 

(c) ¼ and 1 

(d) –2 and 1/-2 

Ans. (b) 

 

Q.59 Which of the following is true? 

Ans. (d) 

GATE 2020 Instrumentation Engineering Previous Year Paper

General Aptitude 

Q1 – Q5 carry one mark each. 

Q. 1  He is known for his unscrupulous ways.tears to deceive people.

(a) He always sheds fox’s 

(b) crocodile’s 

(C)crocodile 

(d) fox 

 

Q. 2  Jofra Archer, the England fast bowler, is than accurate.

(A) more fast (a)

(B) faster 

(C) less fast 

(D) more faster 

 

Q.No.3 Select the word that fits the analogy: 

Build : Building :: Grow: 

(A) Grown 

(B)  Grew

(C) Growth

(D) Growed 

 

Q. 4 I do not think you know the case well enough to have opinions. Having said that, I agree with your other point. What does the phrase “having said that” mean in the given text?  

(A) as opposed to what I have said 

(B)  despite what I have said 

(C) in addition to what I have said 

(D) contrary to what I have said 

 

Q. 5 Define [x] as the greatest integer less than or equal to x, for each x € (-00,00). If y = [x], then area under y for x € [1,4] is 

(A) 1

(B) 3 

(C) 4

(D) 6

Q6 – Q10 carry two marks each. 

Q. 6 Crowd funding deals with mobilisation of funds for a project from a large number of people, who would be willing to invest smaller amounts through web-based platforms in the project. 

Based on the above paragraph, which of the following is correct about crowd funding? 

(A) Funds raised through unwilling contributions on web-based platforms. 

(B) Funds raised through large contributions on web-based platforms. 

(C) Funds raised through coerced contributions on web-based platforms. 

(D) Funds raised through voluntary contributions on web-based platforms.

 

Q. 7 P, Q, R and S are to be uniquely coded using a and B. If P is coded as aa and Q as aß, then R and S, respectively, can be coded as 

(A) Ba and aß 

(B) BB and ac

(C) aß and BB 

(D) Ba and BB

 

Q. 8 The sum of the first n terms in the sequence 8, 88,888, 8888, … is 

Q. 9 Select the graph that schematically represents BOTH y = x” and y = x1/m properly in the interval OS X < 1, for integer values of m, where m > 1. 

 

Q. 10 The bar graph shows the data of the students who appeared and passed in an examination for four schools P, Q, R and S. The average of success rates in percentage) of these four schools is 

(A) 58.5 %

(B) 58.8%

(C) 59.0 % 

(D) 59.3%

IN: Instrumentation Engineering 

Q1 – Q25 carry one mark each. 

Q. 1 The unit vectors along the mutually perpendicular x, y and z axes are în s and k  respectively. Consider the plane z = 0 and two vectors à and b on that plane  such that a = a b for any scalar a. A vector perpendicular to both ả and b is ___________.

(A) k

(B) i – j

(C) -j 

(D) i

 

Q. 2 Consider the recursive equation Xn+1 = Xn – h(F(X») – Xn), with initial condition X, = 1 and h> 0 being a very small valued scalar. This recursion numerically solves the ordinary differential equation 

 

Q. 3 A set of linear equations is given in the form Ax = b, where A is a 2 x 4 matrix with real number entries and b +0. Will it be possible to solve for x and obtain a unique solution by multiplying both left and right sides of the equation by A” (the super script T denotes the transpose) and inverting the matrix ATA ? Answer is___________.

(A) Yes, it is always possible to get a unique solution for any 2 × 4 matrix A.

(B) No, it is not possible to get a unique solution for any 2 × 4 matrix A.

(C) Yes, can obtain a unique solution provided the matrix AT A is well conditioned

(D) Yes, can obtain a unique solution provided the matrix A is well conditioned

 

Q. 4 In the circuit shown below, the safe maximum value for the current I is 

(A) 1.0 A

(B) 0.5 A

(C) 0.1 A

(D) 0.05 A

 

Q. 5 A differentiator has a transfer function whose 

(A) phase increases linearly with frequency

(B) magnitude remains constant

(C) magnitude increases linearly with frequency

(D) magnitude decreases linearly with frequency

 

Q. 6 A phase lead network has the transfer function G15 = 1+0.2s/1+0.05s. The angular frequency at which the maximum phase shift for the network occurs is_______.

(A) 10 rad/s

(B) 20 rad/s

(C) 100 rad/s

(D) 200 rad/s

 

Q. 7 If the diodes in the circuit shown are ideal and the breakdown voltage V2 of the Zener diode is 5 V, the power dissipated in the 100 S2 resistor (in watts) is 

(A) 0

(B) 1

(C) 25/100

(D) 225/100 

 

Q. 8 Given f(A,B,C,D) = ∑m(0,1,2,6,8,9,10,11) + ∑d(3,7,14, 15) is a Boolean function, where m represents min-terms and d represents don’t cares. The minimal sum of products expression for f is ______________.

(A) f = AB + CB

(B) f=B+C

(C) f = D +A

(D) f = ĀB + CD

 

Q. 9 AQ meter is best suited for the measurement of the 

(A) Quality factor of a capacitance.

(B) Distributed capacitance of a coil. 

(C) Quality factor of piezoelectric sensor.

(D) Turns-ratio of a transformer

 

Q. 10 If I is the current flowing through a Hall effect sensor and B is the magnetic flux density perpendicular to the direction of the current (in the plane of the Hall effect sensor), the Hall voltage generated is ____________

(A) Directly proportional to I and inversely proportional to B

(B) Directly proportional to both I and B

(C) Inversely proportional to both I and B

(D) Inversely proportional to I and directly proportional to B

 

Q. 11 The Boolean expression for the shaded regions as shown in the figure is ______.

 

Q. 12 The Boolean operation performed by the following circuit at the output O is ___

Q. 13 Consider the signal x[n] = sin (2—-) u[n]=

The period of this signal x[n] is _____

(A) 4

(B) 3

(C) 2

(D) 1

Q. 14 The closed loop transfer function of a control system is given by , For the input r(t) = sin t, the steady state response c(t) is __________

 

Q. 15 Let f(z) = 1/z+a, a > 0. The value of the integral $ f(z)dz over a circle C with center (-a, 0) and radius R > 0 evaluated in the anti-clockwise direction is__________.

 

Q. 16 A player throws a ball at a basket kept at a distance. The probability that the ball falls into the basket in a single attempt is 0.1. The player attempts to throw the ball twice. Considering each attempt to be independent, the probability that this player puts the ball into the basket only in the second attempt (rounded off to two decimal places) is 

 

Q. 17 Assuming ideal opamps, the output voltage at V, in the figure shown (in volts) 

 

Q. 18 Three 400 Ω resistors are connected in delta and powered by a 400 V (rms), 50 Hz, balanced, symmetrical R-Y-B sequence, three-phase three-wire mains. The rms value of the line current (in amperes, rounded off to one decimal place) is_________. 

 

Q. 19 x(t) e-jwt dt Consider the signal be the Fourier transform of x(t). The value of X(0) is ______________.

 

Q. 20 A second order system has closed loop poles located at s = -3 + j4. The time t at which the maximum value of the step response occurs in seconds, rounded off to two decimal places) is _________________

 

Q. 21 Assume that the opamp in the circuit shown is ideal. The value of (in ką) is _ 

 

Q. 22 A sinusoid of 10 kHz is sampled at 15 k samples/s. The resulting signal is passed through an ideal low pass filter (LPF) with cut-off frequency of 25 kHz. The maximum frequency component at the output of the LPF (in kHz) is ___________

 

Q. 23 A 200 mV full-scale dual-slope analog to digital converter (DS-ADC) has a reference voltage of 100 mV. The first integration time is set as 100 ms. The DS ADC is operated in the continuous conversion mode. The conversion time of the DS-ADC for an input voltage of 123.4 mV (in ms, rounded off to one decimal place) is________

 

Q. 24 The capacitance Cx of a capacitive type sensor is (1000 x) pF, where x is the input to the sensor. As shown in the figure, the sensor is excited by a voltage 10 sin (1001 t) V. The other terminal of the sensor is tied to the input of a high input impedance amplifier through a shielded cable, with shield connected to ground. The cable capacitance is 100 pF. The peak of the voltage VA at the input of the amplifier when x = 0.1 (in volts) is 

 

Q. 25 Two 100 ᘯ resistors having tolerance 3 % and 4 % are connected in series. The effective tolerance of the series combination (in %, rounded off to one decimal place) is 

 

Q26 – Q55 carry two marks each. 

 

Q. 26 11 -1 01 Consider the matrix . One of the eigenvectors of M is 

 

Q. 27 Consider the differential equation * = sin(x), with the initial condition x(0) = 0. The solution to this ordinary differential equation is __________

(A) x(t) = 0

(B) x(t) = sin(t)

(C) x(t) = cos(t)

(D) x(t) = sin(t) – cos(t)

 

Q. 28 A straight line drawn on an x-y plane intercepts the x-axis at -0.5 and the y-axis at 1. The equation that describes this line

is ____________

(A) y=-0.5 x + 1 

(B) y=x-0.5

(C) y=0.5x – 1

(D) y= 2x +1

Q. 29 The loop transfer function of a negative feedback system is . The Nyquist plot for the above system_____________

(A) encircles (-1 + jo point once in the clockwise direction

(B) encircles (-1 + jo) point once in the counterclockwise direction

(C) does not encircle (-1 +jo) point

(D) encircles (-1 + jo) point twice in the counterclockwise direction

 

Q. 30 I₁, I₂ and I₃ in the figure below are mesh currents. The correct set of mesh equations for these currents, in matrix form, is__ 

 

Q. 31 Consider the function f(x, y) = x2 + y2. The minimum value the function attains on the line x + y = 1 (rounded off to one decimal place) is _________

 

Q. 32 Consider two identical bags B1 and B2 each containing 10 balls of identical shapes and sizes. Bag B1 contains 7 Red and 3 Green balls, while bag B2 contains 3 Red and 7 Green balls. A bag is picked at random and a ball is drawn from it, which was found to be Red. The probability that the Red ball came from bag Bl (rounded off to one decimal place) is ___________

 

Q. 33 The rms value of the phasor current I in the circuit shown in amperes) is 

Q. 34 In the circuit shown, the rms value of the voltage across the 100 Ω resistor (in volts) is______________

 

Q. 35 Let olnl

Consider y[n] = h[n] g[n], where denotes the convolution operator. The value of y[2] is 

 

Q. 36 The loop transfer function of a negative feedback system is given by where K > 0. The value of K at the breakaway point of the root locus for the above system (rounded off to one decimal place) is ___________

 

Q. 37 The system shown in Fig. (a) has a time response y(t) to an input r(t) = 10 u(t) as shown in Fig. (b), u(t) being the unit step input. Both K, t are positive. The gain K of the system is _____________

 

Q. 38 Assuming that the opamp used in the circuit shown is ideal, the reading of the 1 Hz bandwidth, permanent magnet moving coil (PMMC) type voltmeter (in volts) is 

 

Q. 39 If the opamps in the circuit shown are ideal and Vx = 0.5 mV, the steady state value of V. (in volts, rounded off to two decimal places) is ____________

 

Q. 40 Two T-flip flops are interconnected as shown in the figure. The present state of the flip flops are: A = 1, B = 1. The input x is given as 1, 0, 1 in the next three clock cycles. The decimal equivalent of (ABy)2 with A being the MSB and y being the LSB, after the 3rd clock cycle is ____________

 

Q. 41 The address lines A9 … A2 of a 10 bit, 1.023 V full-scale digital to analog converter (DAC) is connected to the data lines D7 to Do of an 8-bit microprocessor, with A, and Ao of the DAC grounded. Now, D7 … Do is changed from 1010 1010 to 1010 1011. The corresponding change in the output of the DAC (in mV, rounded off to one decimal place) is ____________

 

Q. 42 The real power drawn by a balanced load connected to a 400 V, 50 Hz, balanced, symmetrical 3-phase, 3-wire, RYB sequence mains is measured using the two wattmeter method. Wattmeter W is connected in the R line and wattmeter W2 is connected in the B line. The line current is measured If the wattmeter W reads zero, the reading on W2 (in watts) is 6/2__________

 

Q. 43 The 6½ digit timer-counter is set in the time period’ mode of operation and the range is set as ‘ns”. For an input signal, the timer-counter displays 1000000. With the same input signal, the timer-counter is changed to ‘frequency’ mode of operation and the range is set as ‘Hz’. The display will show the number 

 

Q. 44 The circuit shown uses ideal opamp powered from a supply Vcc = 5 V. If the charge qp generated by the piezoelectric sensor is of the form qp = 0.1 sin(10000) uC, the peak detector output after 10 cycles of qp (in volts, rounded off to one decimal place) is 

 

Q. 45 A metallic strain gauge of resistance Rx with a gauge factor of 2 is bonded to a structure made of a metal with modulus of elasticity of 200 GN/m2. The value of Rx is 1 kO2 when no stress is applied. Rx is a part of a quarter bridge with three identical fixed resistors of 1 k 2 each. The bridge is excited from a DC voltage of 4 V. The structure is subjected to a stress of 100 MN/m2. Magnitude of the output of the bridge (in mV, rounded off to two decimal places) is __________

 

Q. 46 A laser beam of 10 mm beam diameter is focused onto an optical fibre using a thin biconvex lens as shown in the figure. The refractive index of the lens is 1.5. The refractive indices of the core and cladding of the fibre are 1.55 and 1.54 respectively, The minimum value of the focal length of the lens to attain the maximum coupling to the fibre (in mm, rounded off to one decimal place) is ____________

 

Q. 47 As shown in the figure, a slab of finite thickness t with refractive index nz = 1.5, has air (n1 = 1) above and below it. Light of free space wavelength 600 nm is incident normally from air as shown. For a destructive interference to be observed at R, the minimum value of thickness of the slab t (in nm) is 

 

Q. 48 Consider the finite sequence X = (1,1,1). The Inverse Discrete Fourier Transform (IDFT) of X is given as (x(0), x(1), x(2)). The value of x(2) is ________

 

Q. 49 A circuit consisting of capacitors, DC voltage source and an amplifier having a voltage gain G= -5 is shown in the figure. The effective capacitance across the nodes A and B (in uF, rounded off to one decimal place) is_____________

 

Q. 50 Consider the following state variable equations: .

The initial conditions are x1(0) = () and x2(0) = 1. At t = 1 second, the value of X. (1) (rounded off to two decimal places) is 

 

Q. 51 Assume the diodes in the circuit shown are ideal. The current Ix flowing through the 3 k2 resistor (in mA, rounded off to one decimal place) is 

 

Q. 52 A 1000/1 A, 5 VA, UPF bar-primary measuring current transformer has 1000 secondary turns. The current transformer exhibits a ratio error of – 0.1 % and a phase error of 3.438 minutes when the primary current is 1000 A. At this operating condition, the rms value of the magnetization current of the current transformer (in amperes, rounded off to two decimal places) is ___________

 

Q. 53 The mutual inductances between the primary coil and the secondary coils of a linear variable differential transformer (LVDT) shown in the figure are M, and M2. Assume that the self-inductances Lsi and Ls2 remain constant and are independent of x. When x=0, M1 = M2 = Mo. When x is in the range +10 mm, M1 and M2 change linearly with x. At x = +10 mm or -10 mm, the change in the magnitudes of M, and M2 is 0.25 Mo. For a particular displacement x = D, the voltage across the detector becomes zero when V21 = 1.25 Vil. The value of D (in mm, rounded off to one decimal place) is _______________

 

Q. 54 In the Maxwell-Wien bridge shown, the detector D reads zero when C1= 100 nF and R1 = 100 k 2. The Q factor of the coil

is _______________

 

Q. 55 The loop transfer function of a negative feedback system is G(s)H(s) = 24$32). The phase margin of the system (in degrees, rounded off to one decimal place) is_________

 

Answer Key 

Q.No.	1	2	3	4	5	6	7	8	9	10
Ans.	C	A	C	B	D	D	D	D	A	C
Q.No	1	2	3	4	5	6	7	8	9	10
Ans.	A	B	B	C	C	A	A	B	B	B
Q.No	11	12	13	14	15	16	17	18	19	20
Ans.	A	A	D	D	B	0.09 TO 0.09	7 TO 7	1.7 TO 1.8	2 TO 2	0.78 TO 0.79
Q.No	21	22	23	24	25	26	27	28	29	30
Ans.	-4 TO -4	25 TO  25	223.3 TO 223.5	5 TO 5	2.5 TO 2.5	D	A	D	A	A
Q.No	31	32	33	34	35	36	37	38	39	40
Ans.	0.5 TO 0.5	0.7 TO 0.7	1 TO 1	115 TO 116	0 TO 0	5.0 TO 5.1	4 TO 4	1 TO 1	0.45 TO 0.55	7 TO 7
Q.No	41	42	43	44	45	46	47	48	49	50
Ans.	3.5  TO 405	199 TO 201	999 TO 1001	3.4 TO 3.6	0.95 TO 1.05	27.5 TO 28.5	200 TO 200	0 TO 0	14.5 TO 15.0	-0.13 TO -0.11
Q.No	51	52	53	54	55
Ans.	1.8 TO 1.8	0.95 TO 1.05	4.6 TO 4.6	10 TO 10	65.4 TO 65.6