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GATE 2020 Metallurgical Engineering Previous Year Paper

GATE 2020 Metallurgical Engineering Previous Year Paper

GA – General Aptitude

Q1 – Q5 carry one mark each.

Q. 1He is known for his unscrupulous ways. He always sheds __________tears to deceive people.

(A)fox’s
(B)crocodile’s
(C)crocodile
(D)fox

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

(A) more fast
(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%

MT: Metallurgical Engineering

Q1 – Q 25 carry one mark each.

Q. 1 The general solution to the following homogeneous ODE,

The values of λ₁ and λ, are:

(A) -1 and -3
(B) -3 and -3
(C) 1 and -3

(D) 1 and 3

Q. 2 The number of independent elastic constants of an isotropic material is:

(A) 1
(B) 2
(C) 3

(D) 4

Q. 3 A slip system consists of a slip plane and a slip direction. Which one of the following is NOT a valid slip system in a FCC copper crystal?

(A) (111)[110]
(B) (111)[011]
(C) (111)[101]

(D) (111)[101]

Q. 4 A dielectric material is:

(A) Electrical conductor

(B) Metallic magnet

(D) Electrical insulator

Q. 5 Which one of the following processes is an example of an electrolytic cell?

(A) Corrosion of a metal rod in ambient atmosphere

(B) Charging of a rechargeable battery

(D) Sacrificial cathodic protection system

Q. 6 Which one of the following statements regarding selective leaching of a binary alloy is TRUE?

(A) The lower atomic weight element is leached.

(B) The element having higher diffusivity is leached.

(D) The element with lower density is leached.

Q. 7 In green sand casting, which one of the following is NOT a part of the gating system?

(A) Runner

(B) Sprue

(D) Pouring basin

Q. 8 For a material to exhibit superplasticity, one of the requirements is:

(A) Coarse-grained microstructure

(B) High strain-rate sensitivity

(D) High modulus of elasticity

Q. 9 The dye penetrant test for detecting flaws is based on:

(A) Magnetism

(B) Sound propagation

(D) Capillary action

Q. 10 When 1 mole of C3H8 at 300 K is burnt with a stoichiometric amount of oxygen at 300 K to form CO2 and H20, the adiabatic flame temperature is 5975 K. If C3Hg is burnt under the same conditions but with excess oxygen, the adiabatic flame temperature will be

(A) equal to 5975 K irrespective of the amount of excess oxygen.

(B) higher than 5975 K irrespective of the amount of excess oxygen.

(D) higher or lower than 5975 K depending on the amount of excess oxygen.

Q. No. 11 Two solid spheres X and Y of identical diameter are made of different materials having thermal diffusivities 100 x 10-6 m?s-1 and 25 x 10-6 ms-1 respectively. Both spheres are heated in a furnace maintained at 1000 K. If the center of the sphere X reaches 800 K in 1 hour, time required for the center of sphere Y to reach 800 K is

(A) 1 hour

(B) 2 hours.

(D) 16 hours.

Q. 12 Select the correct spectra (shown on a log-log scale in the figures) for emission from a gray surface and a black body, both maintained at 1000 K.

Q. 13 Given the three vectors X =-i-j+k, Y=-i+2j + k and Z= i + k, which one of the following statements is TRUE?

(A) X, Y and Z are mutually perpendicular.

(B) X, Y and Z are coplanar.

(D) Z makes an angle of 60° with the normal to the plane containing X and Y.

Q. 14 Angle between two neighboring tetrahedral bonds in Si having a diamond cubic structure is:

(A) 102.5°

(B) 109.50

(D) 135.5⁰

Q. 15 The sequence of precipitation during aging of Al – 4 wt% Cu alloy is:

Q. 16 The indenter used in Rockwell hardness measurements on C scale is

(A) diamond cone.

(B) 10 mm steel ball.

(D) 1/16-in. steel ball

Q. 17 For the function y=a*, the derivative, at x = 1 is:

(A) 1
(B) a
(C) a²

(D) alna

Q. 18 Cupola is a furnace used to produce

(A) cast irons.
(B) plain carbon steels.
(C) copper alloys

(D) aluminium alloys.

Q. 19 The functions y = e* and y = e-* intersect at the point:

(A) (1,3)
(B) (-2, 2)
(C) (0, 1)

(D) (-1,-1)

Q. 20 A heavily cold-worked metal will

(A) yield a coarser recrystallized grain size.
(B) possess a lower driving force for recrystallization.
(C) have a higher energy barrier for nucleation of recrystallized grains.

(D) recrystallize at lower temperatures.

Q. 21 For the function f(x) given in the figure, the value of S(1 – f(x)) dx is_______(round off to one decimal place).

Q. 22 A component subjected to tensile stress in a mechanical device is monitored periodically for cracks by NDT. The NDT technique can only detect cracks (both surface and internal) which are larger than 1 mm. Keeping a 10% margin of safety, the maximum allowed tensile stress on the component will be______—–MPa (round off to the nearest integer).

Given, fracture toughness Kic=30 MPa m12 and assume crack geometry factor of unity.

Q. 23 An iron plate with a total exposed surface area of 50 cm2 undergoes atmospheric corrosion. If 200 g of weight is lost over a period of 10 years, then the corrosion rate is ________kg.m2 year” (round off to the nearest integer).

Q. 24 In cold-rolling, for the sheet to be drawn into rolls, the angle of contact (or angle of bite) should be less than or equal to _______degree (round off to one decimal place).

Given, the coefficient of friction between sheet and roll is 0.1

Q. 25 The number of atoms per unit area in (100) plane of Pb is _______(round off to the nearest integer).

Given, crystal structure and atomic radius of Pb are FCC and 0.175 nm respectively.

Q26 – Q55 carry two marks each.

Q. 26 In the edge dislocation configuration given in the figure, dislocations X and Y are fixed and separated by a distance 2h on the same slip plane. Dislocation Z is free to glide on a parallel slip plane. The two slip planes are separated by a distance h. Which one of the following statements is TRUE regarding the stability of dislocation Z at positions 1, 2 and 3?

Assume all dislocations have identical Burgers vector.

(A) Position 1: unstable equilibrium; Position 2: unstable; Position 3: unstable
(B) Position 1: stable equilibrium; Position 2: unstable; Position 3: unstable
(C) Position 1: unstable equilibrium; Position 2: stable; Position 3: unstable

(D) Position 1: stable equilibrium; Position 2: unstable; Position 3: stable

Q. 27 Which one of the following dislocation reactions is NOT feasible in a FCC crystal?

Q. 28 A galvanic cell is formed by connecting Zn (E2n2+/Zn = -0.76 V) and Fe (Efez+/Fe = -0.44 V) wires immersed in their respective ion solutions. The cell discharges spontaneously with a voltage of 0.5 V. The ratio of the concentration of [Fe2+] to [Zn2+] ions in the cell is of the order of:

Given, R = 8.314 J.mol-‘.K!, F = 96500 C.mol-‘, T = 298 K

(A) 10^-6
(B) 10^-5
(C) 10⁶

(D) 10⁷

Q. 29 The divergence of the vector field (x3 + y3)i + 3xy?j + 3zyak is:

Q. 30 Match the products in Column I with the manufacturing processes in Column II.

(A) P-1, Q-2, R-3, S-4
(B) P-2, Q-3, R-1, S-4
(C) P-4, Q-1, R-2, S-3

(D) P-4, Q-2, R-1, S-3

Q. 31 f(x) = x ln(x) + (1 – x) In(1 – x) + 3 x (1 – x) has______at x = 0.5

(A) a local minimum
(B) a local maximum
(C) a point of inflection

(D) a non-zero slope

Q. 32 Match the processes in Column I with the most appropriate mechanisms in Column II.

(A) P-1, Q-4, R-2, S-3
(B) P-3, Q-1, R-2, S-4
(C) P-3, 0-4, R-2, S-1

(D) P-1, Q-2, R-3, S-4

Q. 33 Match the reactors in Column I with the corresponding products in Column II.

(A) P-1, Q-3, R-2, S-4
(B) P-3, Q-4, R-2, S-1
(C) P-3, Q-1, R-2, S-4

(D) P-3, Q-1, R-4, S-2

Q. 34 X-ray diffraction pattern from an elemental metal with a FCC crystal structure shows the first peak at a Bragg angle 0 = 24.650. The lattice parameter of this metal is ___________nm.

Given, the wavelength of the X-ray used is 0.1543 nm.

(A) 0.185
(B) 0.262
(C) 0.320

(D) 0.370

Q. 35 Match the materials in Column I with their common applications in Column II.

(A) P-1, Q-3, R-2, S-4
(B) P-4, Q-2, R-1, S-3
(C) P-2, Q-1, R-4, S-3

(D) P-2, Q-3, R-1, S-4

Q. 36 The Mg-Sn phase diagram exhibits two eutectics on either side of the high melting intermetallic line compound, Mg2Sn, as given below.

After the eutectic reaction has gone to completion and equilibrium has been attained at a temperature just below 561°C, the amount of eutectic constituent present in the alloy, Mg-50 wt.% Sn, is approximately ______________(in wt.%).

Given, atomic weight of Sn is 118.7 and Mg is 24.3

(A) 25
(B) 38
(C) 68

(D) 75

Q. 37 Determine the correctness or otherwise of the following Assertion [a] and the Reason [r]

Assertion [a]: Low-alloy steels used for medium-temperature creep resistance often have additions of strong carbide-forming elements.

Reason [r]: During creep deformation, the particles with higher misfit with the matrix, lose coherency.

(A) Both [a] and [r] are true and [r] is the correct reason for [a].
(B) Both [a] and [r] are true but [r] is not the correct reason for [a].
(C) Both [a] and [r] are false.

(D) [a] is true but [r] is false.

Q. 38 Determine the correctness or otherwise of the following Assertion [a] and the

Reason [r]

Assertion [a]: The rate of homogenization in a dilute substitutional solid solution of B in A is controlled by the diffusivity of B.

Reason [r]: Atomic migration cannot occur along dislocations and grain boundaries.

(A) Both [a] and [r) are true and [r] is the correct reason for [a]
(B) Both [a] and [r] are true but [r] is not the correct reason for [a]
(C) Both [a] and [r] are false

(D) [a] is true but [r] is false

Q. 39 Match the elements in Column I with their electronic behaviour given in

(A) P-1, Q-2, R-3, S-4
(B) P-3, Q-4, R-1, S-2
(C) P-4, Q-1, R-2, S-3

(D) P-4, Q-3, R-1, S-2

Q. 40 Radius of the largest interstitial atom that can be accommodated in an octahedral void in BCC iron without distorting the lattice is_________nm (round off to three decimal places).

Assume hard sphere model and radius of Fe atom as 0.124 nm.

Q. 41 The production process of cylindrical pipes results in a statistical scatter in their diameter which is modelled by a normal distribution with a mean value of 10 mm. If the area under the normal curve between 9 mm and 10 mm is 0.35, then the probability of producing pipes of diameter greater than 11 mm is________(round off to two decimal places).

Q. 42 The solution (using trapezoidal rule) of the integral

by dividing the range 0 to 1 into two equal intervals is_______(round off to two decimal places).

Q. 43 Iron is corroding in fresh water which has dissolved oxygen concentration of 15 mM. The anodic current density at an overpotential of 120 mV is________A.cm2 (round off to three decimal places).

Given:

1. Anodic Tafel slope is 0.06 V.

2. Diffusion coefficient of oxygen is 2.42 x 10^-5 cm².s^-1

3. Diffusion layer thickness is 0.06 cm.

Q. 44 A metal oxidizes at 1200 K with a parabolic rate constant of 3×10-6 g².cm^-4.s^-1 Time taken for the oxide film to grow to a thickness of 2 um is_______s (round off to two decimal places).

Given, the density of oxide is 6.5 g.cm^-3.

Q.No.45 Two plates of composition, Fe^-10 wt.% Ni and Fe^-20 wt.% Cr^-5 wt% Ni are fusion-welded using a filler rod of composition 20 wt.% Ni-80 wt.% Cr. Contribution to dilution of the weld pool is 20% from each plate. The Ni content in the weld pool is________w t.% (round off to the nearest integer).

Q. 46 Figure shows schematic of a venturimeter. The cross sectional area is 100 mm at A and is 50 mm at B. If air is flowing through the venturimeter at a flow rate of 10-3 mos’, the height H in the air-over-water manometer is mm_____________ (round off to the nearest integer).

Assume:

1. Incompressible flow with no friction losses.

2. Density of air is 1 kg m^-3.

3. Density of water is 1000 kg m^-3.

4. Acceleration due to gravity is 9.8 m s^-2.

Q. 47 For effective communication in a ball mill, it is desired that the balls travelling along the mill wall leave the wall at point C and travel freely in air along the path CDA, as shown in the figure. If ZBOC is 120°, the rotational speed of the mill is _____ rpm (rounded off to one decimal place) by performing suitable force balance at point C.

Assume:

1. There is no slip between the ball and mill wall.

2. O is the rotational axis of the mill and OB is parallel to the vector g.

3. Inner diameter of ball mill is 3.26 m.

4. Acceleration due to gravity g is 9.8 m s2.

Q. 48 If liquid copper is cooled to 1353 K, the magnitude of the driving force for liquid to transform to solid is_______J.mol^-1 (round off to one decimal place).

Given, melting temperature and enthalpy of melting of copper are 1356 K and 13 kJ.mol^-1 respectively.

Q. 49 1000 kg of liquid steel containing 0.03 wt.% S needs to be desulphurized using a slag to bring the sulphur content down to 0.015 wt.%. The quantity of slag needed is_________kg (round off to the nearest integer).

Assume:

1. Thermodynamic equilibrium

2. No sulphur in the slag prior to desulphurization treatment

Given the equilibrium sulphur partition ratio between slag and steel, is 50.

Q. 50 Zone refining of Si results in residual P content of 0.1 parts per billion by weight. The electrical conductivity of this zone refined Si is _________22.m-1 (round off to two decimal places).

Given:

1. Avogadro number is 6.02×1023.

2. Density of Si is 2.33 g.cm .

3. Atomic weight of P is 30.97.

4. Charge of electron is 1.6×10-19 A.S

5. Mobility of electron is 0.2 m2.Vol.s!

Q. 51 The steady state creep rate of a material increases by a factor of 20 when the temperature is increased from 890 K to 980 K. The creep rate at a temperature of______K (round off to the nearest integer) will be 5 times the creep rate at 890 K.

Q. 52 Crack growth is being continuously measured in a test specimen subjected to constant amplitude cyclic stress with a mean stress of zero. The crack growth rate is related to the stress intensity range, AK as

where, a is the crack length and N is the number of cycles. When the crack length increases by a factor of two, the crack growth rate will increase by a factor of_______(round off to one decimal place).

Q. 53 In a top gated mold, liquid metal enters the mold cavity as a freely falling stream under gravity from a height of 0.5 m. Ignore the fluid friction due to viscosity and the drag due to changes in the direction of flow. If the volume of the mold cavity is 10 m, then the time required to fill the mold is__________ (round off to nearest integer).

Given:

1. Acceleration due to gravity is 9.8 m.s². 2. Cross-sectional area of the gate is 0.2 m2.

Q. 54 A Basic Oxygen Furnace operator, at the end of oxygen blow, measures the dissolved oxygen content in the steel as 0.03 wt.% and the steel temperature as 1800 K. The carbon content [C] in the steel is ___________wt.% (round off to two decimal places).

Assume:

1) Equilibrium between dissolved carbon (C), dissolved oxygen [O], and

CO (gas) at 1 atmosphere.

2) Henry’s law is valid for both [C] and [O]

Given:

[C]1 wt.% Henrian Std. State + [O]1 wt.% Henrian Std. State → (CO)1 atm. Std. State

△G° = -19840 – 40.65 T J

R= 8.314 J.mol^-1.K^-1

Q. 55 M and N are 3 x 3 matrices. If the det(M) is -9 and the det(N) is -14, then the det(NM) is ______________(round off to the nearest integer).

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	D	B	C	MTA	B	D	C
Q.No.	11	12	13	14	15	16	17	18	19	20
ANS	C	D	A	B	A	A	D	A	C	D
Q.No.	21	22	23	24	25	26	27	28	29	30
ANS	0.5 TO 0.5	480 TO 494	4 TO 4	5.6 TO 5.8	7 TO 9	A	B	C	D	D
Q.No.	31	32	33	34	35	36	37	38	39	40
ANS	B	C	C	C	D	C	B	D	C	0.018 TO 0.020
Q.No.	41	42	43	44	45	46	47	48	49	50
ANS	14 TO 16	0.71 TO 0.75	0.190 TO 0.238	0.54 TO 0.58	15 TO 15	14 TO 16	15.6 TO 17.6	28.6 TO 29.0	19 TO 21	0.14 TO 0.16
Q.No.	51	52	53	54	55
ANS	933 TO 939	2.6 TO 3.0	14 TO 18	0.06 TO 0.08	126 TO 126

GATE 2020 Mining Engineering Previous Year Paper

GATE 2020 Mining Engineering Previous Year Paper

GA – General Aptitude

Q1 – Q5 carry one mark each.

Q. 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. 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. 3 Select the word that fits the analogy:

Cover : Uncover :: Associate :

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

Q. 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. 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. 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. 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. 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 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. 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

MN: Mining Engineering

Q1-Q25 carry one mark each.

Q. 1 The eigenvalues of the matrix are

(A)6,4
(B)4,5
(C)-2,5
(D)-4, 5

Q. 2 For the electric delay detonator shown in the figure, the components P, Q and R,

(A) fuse head, delay element, priming charge
(B) fuse head, priming charge, delay element
(C) priming charge, delay element, fuse head
(D) delay element, fuse head, priming charge

Q. 3 Match the following safety arrangements for a surface-to-underground shaft hoist with their corresponding safety functions.

(A) P-1, Q-2, R – 3
(B) P-3, Q – 1, R – 2
(C) P-2,Q – 3, R – 1
(D) P – 1,Q-3, R – 2

Q.No.4 The fore bearings and back bearings of the lines of an open compass traverse are given below.

The stations that are free from local attraction are

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

Q.No.5 The plane stress condition is given by

Q. 6 Match the following metals with their corresponding minerals.

(A) P-4,Q-2, R-1, S – 3
(B) P-4,Q – 1, R-3, S-2
(C) P-3, Q-4, R – 1, S-2
(D) P-2, Q-3, R-4, S – 1

Q. 7 Match the wire rope types with their corresponding cross-sectional diagrams.

(A) P-3, Q-2, R-4, S-1
(B) P-3, -1, R-2, S-4
(C) P-1, -3, R-4, S-2
(D) P-4, Q-2, R-3, S-1

Q. 8 The “ratchet and pawl’ mechanism in a jack hammer drill

(A)forces down the piston
(B)provides a twisting force to the drill steel
(C)engages rifle bar with rifle nut
(D)prevents reverse rotation of rifle bar

Q. 9 Post-pillar method of stoping is a variant of

(A) cut and fill stoping
(B) sublevel stoping
(C) vertical crater retreat method
(D) sublevel caving

Q. 10 “Cross-measure borehole method is used for

(A) rock slope monitoring
(B) methane drainage
(C) connecting two drifts
(D) subsidence monitoring

Q. 11 The dry and wet bulb temperatures at the inlet of the airstream are 30 °C and 25 °C, respectively. The corresponding values at the outlet of the airstream are 26 °C and 25 °C, respectively. The psychrometric process that occurs in the airstream is described as

(A) latent cooling

(B) sensible cooling

(D) evaporative cooling

Q. 12 For a mixture of inflammable gases, the lower and upper explosibility limits can be computed using

(A) Dalton’s law

(B) Graham’s law

(D) Boyle’s law

Q. 13 The code for the lowest category of mineral resources under United Nations Framework Classification (UNFC) system is

(A) 444
(B) 123
(C) 334
(D) 111

Q. 14 Match the following sampling patterns with the corresponding sampling types.

(A) P-1,Q – 3, R-2, S-4
(B) P-1,Q – 3, R-4, S-2
(C) P-1,Q – 2, R-3, S-4

(D) P-4,Q-2, R – 1, S-3

Q. 15 In the context of gas testing using flame safety lamp, the correct statement is

(A) Each accumulation test has to be necessarily followed by percentage test
(B) Accumulation test is always done after percentage test
(C) Either percentage test or accumulation test can be done first
(D) Percentage test is done only in the event of accumulation test giving negative result

Q. 16 For x in the range of [-3, 3], the maximum value for the function

Q. 17 A rock sample has a coefficient of thermal diffusivity 1.282×10-6 m/s, specific heat 900 J/(kg °C) and density 2600 kg/m3. The coefficient of thermal conductivity of the rock sample in W/(m °C) is__________(round off to I decimal place).

Q. 18 A random variable X has the following probability mass function.

The expected value of the variable X is___________(round off to 1 decimal place).

Q. 19 A random sample has five observations as shown below.

The coefficient of variation of the sample is________(round off to 3 decimal places).

Q. 20 Rock strata has unit weight of 25 kN/m2 and Poisson’s ratio 1/3. At a depth of 200 m, the horizontal stress in MPa is_________(round off to 1 decimal place).

Q. 21 A shovel of bucket capacity 4.2 m³ makes 900 passes per day with a fill factor of 0.8. If the swell factor of the rock is 1.4, then in-situ volume handled by the shovel in a month of 24 working days in m³ is__________(round off to 1 decimal place).

Q. 22 A cylindrical sample of granular material has the following measurements:

Length: 10 cm

Diameter: 5 cm

Weight: 350 g

Assume the sample is completely dry with specific gravity of solid grains 2.8. The void ratio of the sample is__________(round off to 3 decimal places).

Q. 23 The following consecutive readings were taken at uniform intervals with a level and a levelling staff on continuously sloping ground.

The number of change points is___________.

Q. 24 The cost of a slurry pump is Rs. 50,000 and it has an estimated life of 7 years. If the salvage value is Rs. 8,000, the annual depreciation following straight-line depreciation method, in Rupees, is___________(round off to I decimal place).

Q. 25 In a mine bench, the shovel loading time follows exponential distribution with a mean loading time of 5 min per dumper. The arrival rate of dumpers that are identical in capacity, follows Poisson distribution with a mean arrival rate of 8 per hour. The probability that the shovel remains idle is___________(round off to 2 decimal places).

Q26 – Q55 carry two marks each.

Q. 26 For , the value of dw/dt is

Q. 27 For the differential equation y1-x2dy+x1-y2dx=0, assuming the constant of integration to be C, the general solution is

Q. 28 A belt-drive used for power transmission between two parallel shafts has a belt of mass 1.2 kg/m, and the maximum allowable belt tension is 2250 N. If the centrifugal tension is one third of the maximum allowable belt tension, the speed at which maximum power is transmitted by the belt, in m/s, is

(A) 46.48
(B) 38.73
(C) 25.00
(D) 35.36

Q.No.29 An air receiver of a compressor, having volume 0.5 m?, supplies air for charging ANFO in drill holes. During the charging process the absolute pressure of the air receiver falls from 900 kPa to 700 kPa. Assuming the entire process is isothermal, the volume of air supplied by the receiver at 100 kPa ambient pressure, in m is

(A) 1.00
(B) 0.39
(C) 0.64
(D) 4.48

Q. 30 A conveyor belt consumes 60 kW power while running at a speed of 3.0 m/s. The angle of lap is 180o and the coefficient of friction between belt and pulley is 0.2. The maximum tension (kN) in the belt is

(A) 21.7
(B) 61.7
(C) 82.9
(D) 42.9

Q. 31 A linear programming problem is stated below.

Maximize Z = 3x₁ + 5x₂

subject to, 2x₁ + x₂ 8

6x₁ + 8x₂ 30

x₁, x₂ 0

The objective function has

(A) infinite number of solutions
(B) unbounded solution
(C) unique solution
(D) infeasible solution

Q. 32 An explosive mixture has 80 g of ammonium nitrate (NH4NO3) and 14 g of fuel oil (C10H20). The oxygen balance in the mixture is

(A)surplus by 32 g
(B)deficient by 24 g
(C)surplus by 16 g
(D)deficient by 32 g

Q. 33 A cylindrical sample of cross-sectional area A, length L, and Young’s Modulus E, is subjected to a constant uniaxial load P. Within the elastic limit of loading, the total strain energy stored is

Q. 34 A surface mine production system along with the reliability of the individual components is shown below. The system reliability is_______(round off to 3 decimal places).

Q. 35 The selling price of one rock bolt (in Rs.) is given as, S = (200 – 10n-0.5), where n is the number of bolts produced. The manufacturing cost of rock bolts has a fixed component of Rs. 15000, and a variable component of Rs. 100 per bolt. The minimum break-even production, in number of rock bolts, is______(round off to 1 decimal place).

Q. 36 Two underground mines are separated by a horizontal coal barrier of 60 m thickness. One mine is inundated, whereas the other mine has a blind heading of dimensions 4.0 m wide and 2.5 m height terminating at the barrier. The overall in-situ shear strength of the coal mass is 500 kPa. Assume that the failure mode is in shear. At a factor of safety of 10, the maximum water head that can be withstood by the coal barrier, in m, is____________(round off to 1 decimal place).

Q. 37 Air enters from ambient atmosphere into a level duct of uniform cross-section area 0.2 m- at a flow rate of 2.0 m³/s and density of 1.2 kg/m³. The entry shock loss factor is 1.0 and the resistance of the duct per meter length is 1.0 Ns²/m⁸. The static pressure measured at a distance of 20 m from the duct entrance in Pa, is___________(round off to 1 decimal place).

Q. 38 A sealed-off area air sample consists of 16.0% O₂, 3.0% CO₂, and the rest is N₂. Assume that the standard composition of atmospheric air is 21.0% O₂ and 79,0% N₂. The percentage of blackdamp in the air sample is_______(round off to 2 decimal places).

Q. 39 A diesel loader produces 60 l/s of exhaust fumes containing 5000 ppm of CO. The incoming air has 10 ppm of CO. The minimum amount of air flow in m3/s that is needed at the loader to dilute Co to a permissible level of 50 ppm is___________(round off to 1 decimal place).

Q. 40 The equation for peak particle velocity (PPV) from blast induced ground vibration is given by , where k and B are site constants.

In a field study, the following readings are recorded.

The value of B is______________(round off to 3 decimal places).

Q. 41 An underground copper mine sends 2500 tonnes of ore per day to the concentrator plant having an average grade of 1.2% Cu. The plant produces concentrate of 25.0% Cu with a recovery of 93.0%. The solids portion of tailings generated from the plant per day in tonnes is_____________(round off to 1 decimal place).

Q. 42 A mine gallery is supported by regularly placed roof bolts of 100 kN allowable pull force per bolt, as shown below. Assuming unit weight of the immediate roof is 25 kN/m2, the factor of safety of the support system is______(round off to 2 decimal places).

Q. 43 The slip circle of radius 30.0 m in an overburden slope is shown with the centre of slip circle at point O. The tension crack is completely filled with water. For one meter width of the slope, the moment exerted by the force of water about O in kN-m is____________(round off to 1 decimal place).

Q. 44 The function values at four points of x are shown in the table. The area under the function, using trapezoidal method, is ______________(round off to 1 decimal place).

Q. 45 A particle starting from rest moves in a straight line such that after time, 1 (seconds), the acceleration becomes (6 – t/4) cm/s2. When the acceleration becomes zero, the velocity of the particle in cm/s is____________(round off to I decimal place).

Q. 46 A parallelepiped has edge vectors as shown below.

The volume of the parallelepiped is

(round off to 1 decimal place).

Q. 47 For a development heading, the blasting parameters are

Cross-section: 6.0 m × 5.0 m

Total number of holes: 72

Number of trimmer holes: 30

Depth of each hole: 3.5 m

Charge per hole (except trimmers): 3.5 kg

Charge per trimmer hole: 1.8 kg

Pull per round: 90% of hole depth

The powder factor for the development round in my/kg is_________(round off to 2 decimal places).

Q. 48 The following figure represents the observations from the level survey of an underground gallery.

If the reduced level of station A is 100.0 m, the reduced level of station D in m is___________(round off to 1 decimal place).

Q. 49 A tacheometer was setup at station P and the following readings were taken at two stations A and B with the staff held vertical and the line of sight horizontal.

The additive and multiplying constants of the tacheometer are 0 and 100, respectively. The length of AB in m is _____________ (round off to 1 decimal place).

Q. 50 The geometry of a simple planar curve (ADB) is shown below. The value of the mid-ordinate of the curve in m is_____________(round off to I decimal place).

Q. 51 A steel cube of side 50 mm is subjected to a uniform pressure of 200 MPa acting on each face. The Young’s modulus and Poisson’s ratio of the material are 200 GPa and 0.25, respectively. The decrease in the side of the cube in mm is (round off to 3 decimal places).

Q. 52 In the figure shown below, the friction coefficient between the block and the inclined plane is 0.2, and all the pulleys are weightless. The weight of the block is 10 N. The minimum force P in Newtons that is needed to slide the block up the inclined plane is____________(round off to 2 decimal places).

Q. 53 An assignment problem is given below with the cost of assignment as shown.

If only one task can be assigned to one group, the minimum cost of assignment is ______.

Q. 54 A vertical stoping block of length 60.0 m, height 40.0 m, and average width 1.5 m has sharp boundary walls. However, the mining width of the stopping block is 2.0 m. The tonnage factors are 3.0 tonne/m2 for ore and 2.5 tonne/for wall rocks. The average grade of ore is 10.0%. The overall grade of ore mined on account of dilution in percentage is ____________ (round off to 2 decimal places).

Q. 55 A bauxite ore body has four boreholes as shown below. For each borehole, the grade of alumina, the thickness of the ore body, and the triangular area of influence are as shown.

The average grade of ore body in the region ABCD in percentage is_______(round off to 1 decimal place).

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	A	D	B	B	C	A	D	A	B
Q.No.	11	12	13	14	15	16	17	18	19	20
ANS.	D	C	C	B	D	18.0 TO 20.0	2.9 TO 3.1	5.4 TO 5.6	0.120 TO 0.125	2.4 TO 2.6
Q.No.	21	22	23	24	25	26	27	28	29	30
ANS.	51830.0 TO 51850.0	0.560 TO 0.580	2 TO 2	5990.0 TO 6010.0	0.32 TO 0.34	B	D	C	A	D
Q.No.	31	32	33	34	35	36	37	38	39	40
ANS.	C	D	D	0.530 TO 0.550	148.0 TO 154.0	358.0 TO 410.0	-205.0 TO -195.0	22.00 TO 25.00	7.2 TO 7.7	-1.255 TO -1.165
Q.No.	41	42	43	44	45	46	47	48	49	50
ANS.	2380.0 TO 2396.0	2.10 TO 2.45	3360.0 TO 3480.0	71.0 TO 72.0	71.0 TO 73.0	87.0 TO 89.0	0.44 TO 0.50	100.4 TO 100.6	157.0 TO161.0	248.0 TO 252.0
Q.No.	51	52	53	54	55
ANS.	0.020 TO 0.030	67.00 TO 69.00	18 TO18	7.70 TO 7.95	30.8 TO 31.6

GATE 2020 Biomedical Engineering Previous Year Paper

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

(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

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,

(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

(D) uncertain

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

Cover : Uncover :: Associate :

(A) Unassociate

(B) Inassociate

(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.

(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

(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.

(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.

(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

(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

(D) 16

(A) 15:17

(B) 16:17

(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

(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

(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

(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

(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

(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)

(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

(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

(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

(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

(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

(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

(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 >

(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

(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}

(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) = ½e³^it, 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

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

(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

(D) rather then

Q. 3 Select the word that fits the analogy:

Explicit: Implicit :: Express: _________

(A) Impress

(B) Repress

(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.

(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.

(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°

(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

(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.

(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.

(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

(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

(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

(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

(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

(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

(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.

(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

(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

(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

(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

(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

(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.

(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

(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

(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

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

(d) 270

Ans. (a)

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

(a) 279

(b) 280

(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

(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

(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

(d) parking

Ans. (c)

Q.7 Select the word do :

undo : : trust :

(a) distrust

(b) entrust

(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

(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

(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_ththe values of R₁and R₂will be (Diode in figure is silicon diode)

(a) R₁high, R₂high

(b) R₁low, R₂low

(d) R₁high, R₂low

Ans. (b)

Q.13 For the given circuit the value of V_this ______.

Ans. (14)

Q.14 In the given circuit rms value of I₁is _____.

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

(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

(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^thorder and stable

(b) 4^thorder and unstable

(d) 3^rdorder 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 – k₁z) + a_y(3z + k₂x) + a_z(k₃y – 4x)

represent a conservative field, where a_x, a_y, a_zare unit vector along x, y, z directions, respectively the value of constant k₁, k₂and k₃________.

(a) 4, 5, 3

(b) 8, 3, 7

(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

(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_Ais terminal voltage and E_fis 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

(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

(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

(d) None of above

Ans. (c)

Q.38 For a common source amplifier g_m= 520 μA/V²and 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

(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)

(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

(d) Z < ½

Ans. (a)

Q.42 If x_Aand x_Rare average and rms values of signal x(t) = x(t – T) respectively. y_Aand y_Rare 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

(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|²power x(t)

⇒ Rms y²(t) = |K|²Rms x ²( t )

⇒ Rms y(t) = |K|²Rms 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_iand 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

(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, Q₁₂is the sending reactive power from 1 to 2. On changing the bus 1 voltage, Q₁₂increases 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 T₁is fired at α and T₂is 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°

(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^rdharmonic is completely eliminated. Find the percentage magnitude of 5^thharmonic 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

(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