Category: Coachings

GATE 2020 Agricultural Engineering Previous Year Paper

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 cardiovascular disease, cancer, etc. 

(A) in, of 

(b)from, of 

(c) during, from 

(d) from, from 

Q. 2 He was not only accused of theft__________of conspiracy. 

(A) rather 

(B)but also 

(c) but even 

(D) rather than 

Q. 3 Select the word that fits the analogy: 

Explicit: Implicit :: Express: 

(A) Impress 

(B) Repress 

(c) Compress 

(D) Suppress 

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

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

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

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

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

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

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

(A) Ex

(B) x

(C) 1/x

(D) e^-x

Q6 – Q10 carry two marks each. 

Q. No. 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 the USA in 2007. The subprime lending crisis led to the banking crisis in 2008 with the collapse of Lehman Brothers in 2008. The subprime lending refers to the provision of loans to those borrowers who may have difficulties in repaying loans, and it arises because of excess liquidity following the East Asian crisis. 

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

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

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

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

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

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

(A) 0⁰

(B) 7.5° 

(C) 15° 

(D) 22.5° 

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

(A) a2-a2

(B) a2-2a2

(C) a2-2a2

(D) a2-3a2

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

(A) β = b/a 

(B) β² = ac 

(C) β³ = bc/(2a²) 

(D) b² ≠ 4ac 

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

(A) 8:23 

(B) 23:8 

(C) 23:31 

(D) 31:23 

Agricultural Engineering 

Q1 – Q25 carry one mark each. 

Q. 1 The function f(x) = x⁴ – 4x³ + 6x² – 4x + 1 has a 

(A) Maxima at x = 0 

(B) Minima at x = 0

(C) Maxima at x = 1 

(D) Minima atx= 

Q. 2 A linear system of equations has n unknowns. The ranks of the coefficient matrix and the augmented matrix of the linear system of equations are ri and r2, respectively. The condition for the equations to be consistent with a unique solution is

(A) r₁ ≠ r₂ < n 

(B) r₁ ≠ r₂ = n 

(C) r₁ = r₂ < n 

(D) r₁ ≠ r₂ > n 

Q. 3 General solution to the ordinary differential equation, is

Q. 4 In a tractor steering system, the angle made by the kingpin axis projected on the longitudinal plane of the tractor with the vertical axis is known as 

(A) Kingpin inclination 

(B) Caster angle 

(C) Camber angle 

(D) Steering angle 

Q. 5 A tractor operated 9-row precision planter has 16 cells on the metering plates. The speed ratio of the metering plates to the ground drive wheel is 1:2 and the rolling diameter of the ground drive wheel is 40 cm. Assuming no skid, the plant to plant spacing in rows in mm is 

(A) 39 

(B) 50 

(C) 157 

(D) 314 

Q. 6 A self-propelled wheel does not have 

(A) Wheel torque 

(B) Tractive power 

(C) Rolling resistance 

(D) Drawbar pull 

Q. 7 Match the following items between Column I and Column II with the most appropriate combinations: 

(A) P-3, 0-2, R-I, S-4 

(B)P-2, Q-3, R-1, S-4 

(C) P-2, Q-3, R-4, S-1 

(D) P-3, Q-2, R-4, S-1 

Q. 8 From the performance evaluation of drippers, the discharge exponent value and the coefficient of variation were obtained as 0.5 and 0.04, respectively. The drippers are categorized as 

(A) Pressure compensating drippers of excellent quality 

(B) Turbulent flow-tortuous path orifice type drippers of good quality 

(C) Turbulent flow-tortuous path orifice type drippers of marginal quality 

(D) Laminar flow drippers of excellent quality 

Q. 9 In a basin, rainfall is recorded by five automatic weather stations A, B, C, D and E with respective average annual rainfall of 1020, 810, 675, 940 and 780 mm. In a particular year, station A was non-operational and the remaining stations B, C, D and E recorded annual rainfall of 890, 725, 980 and 850 mm, respectively. The estimated rainfall at the station A in that particular year in mm 

(A) 758 

(B) 878 

(C) 1038 

(D) 1098 

Q. 10 A field crop is irrigated when the available soil water reduces to 60%. The moisture content at field capacity and wilting point are 32% and 12%, respectively. The bulk density of the soil is 1.5 g cm3. The field water application efficiency is 75% and the crop root zone depth is 50 cm. The gross depth of irrigation required to bring soil moisture content to field capacity in cm 

(A) 6

(B) 8

(C) 9

(D) 12

Q. 11 A cold storage takes 5 hours to bring down the temperature of 100 metric tons of potato from 35 °C to 8 °C. The specific heat capacity of potato is 3.1 kJ kg-1 °C-!. The coefficient of performance (COP) and the latent heat of vaporization of the refrigerant (R–22) at an evaporation temperature of -10 °C are 3.66 and 230 kJ kg !, respectively. Neglecting respiration heat load of potato, and assuming no power loss, the values of refrigerant flow rate and the power input to the compressor are 

(A) 121.3 kg min’ and 127.1 kW 

(B) 124.7 kg min-and 121.3 kW 

(C) 127.1 kg min and 121.3 kW 

(D) 124.7 kg min-and 127.1 kW 

Q. 12 Hydrothermal treatment of paddy makes 

(A) Shelling more difficult 

(B) Polishing of parboiled rice easier 

(C) Higher retention of vitamins and minerals 

(D) Kernel soft, resulting in faster cooking 

Q. 13 Both particle formation and drying process are carried out by 

(A) Flash dryer 

(B) Fluidized bed dryer 

(C) Pneumatic conveyor dryer 

(D) Spray dryer 

Q. 14 If one of the two Eigenvalues of a matrix [3/2 2/1] is 4.236, then the other Eigenvalue (round off to 3 decimal places)

is ____________

Q. 15 is ______________.

Q. 16 At the maximum power output of a solar panel, the voltage and current are 18 V and 5.56 A, respectively. If the open circuit voltage and short circuit current of the same solar panel are 21.6 V and 6.11 A, respectively, the fill factor of the panel (round off to 2 decimal places) is____________

Q. 17 The sound pressure level on the operator’s seat of a tractor is 80 dB. If the reference sound pressure is 2×10-5 N m2, the root mean square (RMS) sound pressure in N m2 (round off to 2 decimal places) is_______________

Q. 18 A towed pneumatic wheel with an unloaded radius of 330 mm covers a distance of 9.9 m in 5 revolutions without any skid. Assuming the rolling radius to be same as the static loaded radius of the wheel, the deflection of the wheel in mm (round off to 1 decimal place) is ____________

Q. 19 The grain to straw ratio of 500 kg feed material is 3:2. The blown grain loss, separation loss and cleaning efficiency of the thresher are 0.05%, 0.5% and 99.1%, respectively. Considering 100% threshing efficiency, grain recovery at the main grain outlet in kg (round off to 2 decimal places) is_______________

Q. 20 A tubewell has a discharge of 40 mph and operates daily for 20 h during irrigation season. The irrigation interval is 20 days and the depth of irrigation is 8 cm. The command area of tubewell in ha is_________________

Q. 21 The drainage coefficient of a watershed of 720 ha area is 1.2 cm. The design discharge of the drain in m³ s^-l is_____________. 

Q. 22 The following data were used for a watershed experiencing soil erosion problem: 

Rainfall Erosivity Index = 280 MJ mm ha’ h’ yearl, Soil Erodibility Index = 0.38 ton ha h MJ-‘ mm”!, Slope length = 200 m, Average slope of the land = 8%, Slope steepness factor = 0.85, Cropping management factor = 0.35, and Conservation practice factor = 0.60 If the slope length is reduced to half, percentage reduction in soil loss (round off to 2 decimal places) is__________________

Q. 23 Fresh tomato juice containing 6% (w/w) total solids enters in a single effect evaporator at a feed rate of 500 kg h-‘ to concentrate up to 36% (w/w) solids. In this process, the rate of water removal in kg h’ (round off to I decimal place) is___________

Q. 24 Heat gain is occurring through a composite cold storage wall, made of brick and polyurethane foam insulation (thickness and thermal conductivity values are given below). If the exposed surfaces of brick and insulation are at 45 °C and 10°C, respectively, the temperature at the interface of brick and insulation in °C (round off to 1 decimal place) is Material _____________________

Q. 25 A milk processing plant pasteurizes a batch of 12500 L whole milk to inactivate the pathogen Coxiella burnetii, (decimal reduction time of 14 seconds at 72 °C) prior to packing in 500 milliliter pouches. The initial count of the noted organism is 10 per milliliter. For this batch pasteurization process at 72 °C, resulting in no survivor in any of the packages, the process F-value in seconds is _______________

Q26 – Q55 carry two marks each. 

Q. 26 A particle moves along the curve R = (2t3 + 4t2)i + (3t2 – 5t) j + (7t2 + 6t)k, where t is the time. The velocity component of the particle in the direction 3î + 2 j + at time 1 = 2 is 

Q. No. 27 Let a function f(t) = 4 cos 2t + 6 e-84. The Laplace transform of the given function f(t), L{f(t)} = F(s) = $. f(t)e-s dt is 

Q. 28 In an irrigation channel of uniform section, water passes through a 90° triangular weir measuring 36 cm head over the crest. After traveling certain distance in the same channel, water passes through 1.0 m long rectangular weir. There is no loss of water in between two weirs. Using Francis’ formula, the head over the crest of rectangular weir in cm is 

(A) 22.1 

(B) 18.4 

(C) 15.0 

(D) 11.8 

Q. 29 Two ends of a differential mercury manometer are connected at two points on a pipe carrying oil. The manometer shows difference in mercury level of 20 cm. The specific gravity of oil and mercury are 0.8 and 13.6, respectively. The density of water is 1000 kg m-3 at 4 °C and acceleration due to gravity (g) is 9.81 m s2. At the same two points in pipe, the difference of pressure in N m2 is 

(A) 25.11 

(B) 251.14 

(C) 25113.60 

(D) 251136.00 

Q. 30 Match the following items between Column I and Column II with the most appropriate combinations: 

(A) P-4, Q-5, R-6, S-3, T-1, U-2 

(B) P-5, Q-4, R-6, S-3, T-2, U-1 

(C) P-4, Q-5, R-3, S-6, T-2, U-1 

(D) P-4, Q-5, R-6, S-3, T-2, U-1 

Q. 31 A retaining wall of 5 m height retains cohesionless dry soil having density of 1.9 Mg m-3 and angle of internal friction of 289. The surface of the backfill soil is horizontal. The active and passive earth pressures per meter length of the wall in kN are _______and _______, respectively. [Take g = 9.81ms^-2] 

(A) 84.11, 645.38 

(B) 645.38, 84.11 

(c) 142.12, 381.63 

(D) 381.63, 142.12 

Q. 32 A 40 cm diameter tube well is constructed in a 10 m thick confined aquifer having hydraulic conductivity of 25 m per day. The piezometric surface is observed to be 40 m high from the impervious stratum at the radius of influence of 500 m. The drawdown in the tubewell is 30 m. If the thickness of aquifer is doubled and diameter of tubewell is reduced to half, keeping all other parameters and conditions same, the change in discharge from the well is [Take = 3.14] 

(A) Increased by 83.72% 

(B) Decreased by 83.72% 

(C) Increased by 82.28% 

(D) Decreased by 82.28% 

Q. 33 Choose the correct combination of process (Column I ) performed by corresponding machine component(s) (Column II) 

(A) P-4, Q-1, R-3, S-2 

(B) P-4, Q-3, R-1, S-2 

(C) P-1. Q-4, R-3, S-2 

(D) P-2, Q-1, R-4, S-3 

Q. 34 Saturated steam at 121 °C is used to sterilize pineapple juice by direct steam injection. The initial temperature of the juice is 80 °C and after sterilization, the blend of diluted juice exits the sterilizer at 95 °C. The enthalpy values of steam and condensate water are given in Table below. Specific heat capacity of the juice is 3.9 kJ kg-1 °C-!. Assuming no energy loss to the surroundings in the process of sterilization, the ratio of juice sterilized to steam utilized is 

(A) 34.79 

(B) 37.94 

(C) 39.47 

(D) 43.97 

Q. 35 Hot refined oil at 120 °C enters a concentric tube-in-tube heat exchanger (HE) at the rate of 20 kg min! The oil is cooled by water entering at a temperature of 30 °C from the other end of the HE at the rate of 50 kg min!. Specific heat capacities of oil and water are 1.9 and 4.2 kJ kg-1 °C, respectively. The effectiveness of the HE may be taken as 0.7. Assuming no heat loss to the surrounding under steady-state condition, the exit temperature of water from the HE in C is 

(A) 39.9 

(B) 41.4 

(C) 57.7 

(D) 63.0 

Q. 36 Taking six intervals, each of 1/12 and using Simpson’s one-third rule, the value of the definite integral 02cos (round off to 3 decimal places) is ____________.

Q. 37 Two playing cards are drawn at random, but in succession from a pack of red cards (26 in number) without replacement. The probability of drawing a king first, followed by drawing a queen is Px10-3. The value of P (round off to 3 decimal places)

is ____________

Q. 38 A hydraulic sprayer when operating at a speed of 10 km h’ and working pressure of 420 kPa covers a width of 4.5 m. The power requirement and efficiency of the pump are 0.75 kW and 70%, respectively. Out of total pump discharge, 10% is bypassed for agitation purposes. The working pressure is increased to 500 kPa. Assuming no change in the width of coverage, the application rate of the sprayer in L ha-l (round off to 1 decimal place) is ______________

Q. 39 A tractor PTO operated rotary disc mower has 4 rotating discs and the width of the cut of each disc is 60 cm without any overlap. The specific power losses to air, stubble and gear-train friction is 2.5 kW per meter of cutting width. The specific cutting energy requirement is 2.0 kJ m2. If the machine is operated at a forward speed of 6 km h!, the PTO power requirement in kW (round off to 2 decimal places) is _________

Q. 40 A water pumping system is driven by a horizontal axis multi-bladed wind turbine at a power coefficient (Cp) of 0.4. The total pumping head and discharge are 20 m and 15 L sl, respectively. The mean wind velocity is 8 ms and the pump efficiency is 70%. The density of air and water are 1.2 and 1000 kg m-3, respectively. If the transmission efficiency from wind turbine to the pump is 90%, the required diameter of the wind turbine in m (round off to 2 decimal places) is _____________

Q. 41 A two-wheel drive tractor with a total weight of 25 kN has a wheelbase of 2.2 m and its centre of gravity lies 0.7 m ahead of the centre of rear axle. A steady horizontal pull is applied at a drawbar hitch height of 0.5 m on a concrete surface such that the weight on the front axle becomes 20% of the static weight of the tractor. The coefficient of net traction (round off to 2 decimal places) is _______________

Q. 42 The cooling system of a tractor fitted with diesel engine rejects 0.58 kW of heat per kW of brake power. It requires 0.16 L sl of water per kW of heat rejection from the engine to maintain a temperature drop of 6°C of water as it moves from the top of the radiator to its bottom. If the engine develops 45 kW brake power, the required water flow rate in the radiator in L s’ (round off to 2 decimal places) is ______________

Q. 43 A V-belt drive transmits 10 kW power at a belt velocity of 8 ms. The angle of contact on the smaller pulley is 170° and the groove angle of the pulley is 38°. The coefficient of friction between the pulley and the belt is 0.28 and the maximum permissible stress of the belt is limited to 4 MPa. Neglecting centrifugal effect of the belt, the minimum cross-sectional area of the V-belt in mm2 (round off to I decimal place) is _________

Q. 44 A chaff cutter is operated by an electric motor running at 1440 rpm. The speed reduction from motor to the main shaft of the cutting unit is 4:1. The feed rollers of 10 cm diameter each are driven by the main shaft through a suitable gear drive with a speed reduction of 15:1. If the chaff cutter has two knives, the theoretical length of cut chaff in mm (round off to 2 decimal places) is ______________

Q. 45 A tractor drawn right-hand offset disk harrow experiences longitudinal and side soil reactions in the front gang as 3.0 kN and 2.5 kN, respectively as compared to 3.5 kN and 4.0 kN in the rear gang. The longitudinal distance of centers of front and rear gangs are located at 2.5 m and 4.0 m, respectively behind the tractor hitch point. The required amount of offset of the disk harrow in m (round off to 2 decimal places) is ____________

Q. 46 A diesel engine when operates with biodiesel blend B20 (20% biodiesel and 80% diesel by volume) develops a brake power of 10 kW with a brake specific fuel consumption of 0.26 kg kW-‘ h’. If the density of biodiesel is 880 kg m-3 and that of diesel is 850 kg m-, the amount of biodiesel required to run the engine for 3 hours in L (round off to 2 decimal places) is _____________

Q. 47 Area enclosed by different contours of a pond is given in the following Table. Using trapezoidal formula, the total estimated capacity of pond in mo is_ 

Q. 48 At a speed of 1800 rpm, a centrifugal pump discharges 50 L s at its best point of efficiency for a total head of 25 m. The specific speed of the pump in rpm (round off to 2 decimal places) is _______________

Q. 49 The Curve Number (CN) of a watershed of 40 ha area under given hydrologic soil group, land use and management practices, and Antecedent Moisture Condition (AMC)-II is 80. The initial abstraction is 20% of maximum retention. For the rainfall event of 40 mm, the direct runoff in mm (round off to 2 decimal places) is ________.

Q. 50 The underside beam of a railway bridge, marked as permanent Bench Mark (BM) with Reduced Level (RL) of 85.168 m, is taken as reference for leveling operation. The Back Sight (BS) on the staff held vertically inverted to the BM is 3.645 m. For the Fore Sight (FS) of 1.523 m at a point in the construction site, the RL or elevation in mis 

Q.  51 Air-water vapour mixture at 30°C DBT and 40% RH is heated to 65 °C DBT and 30°C WBT and is used as a drying medium under the constant rate period drying of spinach leaves. Specific heat capacities of dry air and pure water vapour are 1.005 and 1.88 kJ kg-1 °C-1, respectively. Using the properties given in Table below, the value of absolute humidity in kg water vapour per kg dry air (round off to 3 decimal places) for the dryer exit air at DBT of 45 °C is _____________

Q. 52 Tray type paddy separator is employed to separate paddy from a binary mixture of paddy and brown rice at a feed rate of 1200 kg h’. Mass fractions of paddy in feed, separated paddy and brown rice streams are 0.2, 0.75 and 0.02, respectively. The amount of paddy in separated paddy stream in kg h’ (round off to 2 decimal places) is ________

Q. 53 A cylindrical silo with 3.0 m diameter and height to diameter ratio of 5:1 is filled with 60 metric ton wheat grains having bulk density of 725 kg m. The coefficient of friction between grain and silo wall is 0.42 and the ratio of lateral pressure to vertical pressure is 0.5. The vertical pressure at the bottom of silo in kPa (round off to 2 decimal places) is __________. [use 1 kgf = 9.81 N] 

Q. 54 A bucket elevator for lifting parboiled paddy (bulk density = 840 kg m) is operated at a linear speed of 2 m sł. The width of the bucket is 25.4 cm and its cross section is making a subtending angle of 75 at the centre of a circle having 12.7 cm radius. The space between two adjacent buckets on the elevator belt is 40 cm. If the buckets are filled to 80% of their volumetric capacity, the lifting capacity of elevator in kg min (round off to 2 decimal places) is _________________.

Q. 55 A contact plate freezer extracts thermal energy from a 24 mm thick slab of boneless meat containing 85% (w/w) water. Initially the slab is at the freezing point of meat, that is 272.5 K and corresponding latent heat of freezing is 335 kJ kg water. The plate temperature of the freezer is assumed steady at 247.5 K. Bulk density of the slab is 750 kg m-3. The thermal conductivity value for frozen meat is 1.5 W m-K-!. The minimum duration required for complete freezing of the slab in seconds is _________.

Answer Key – AG: Agricultural Engineering 

GATE 2020 Electronics and Communication Engineering Previous Year Paper

GENERAL APTITUDE 

Section -A

Q.1 Time at quarter past three angle between hour hand and minute hand is 

Ans. (7.5°) 

Q.2 Radius of circle is ‘a’ and PQR is the maximum possible area of rectangle. 

Find shaded area 

(a) πa² – 2a² 

(b) π 2a ² − a ² 

(c) π 3a ² − a ² 

(d) None of these 

Ans. (a) 

Q.3 Implicit : Explicit : : Express : __________? 

(a) Compress 

(b) Suppress

(c) Impress 

(d) Repress 

Ans. (b) 

Q.4 He was not only accused of theft _______ of conspiracy. 

(a) Rather than

(b) Rather 

(c) But also 

(d) But even 

Ans. (c) 

Q.5 The untimely loss of life is a course of serious global concern as thousands of people get killed ________ accidents every year while many others die _____ disease like cardiovascular disease cancer etc. 

(a) during, from 

(b) in, of 

(c) of, from 

(d) None of these 

Ans. (b) 

Q.6 The Canadian constitution requires equal importance to English and French. Last year air Canada lost a lawsuit and had to pay a six figure fine to French speaking couple after they filed a complaint about formal in-flight announcements in English lasting 15 seconds as compared to informal announcements in French lasting only for 5 seconds. The French speaking couples were upset at 

(a) The English announcements being longer than French once 

(b) The English announcements being clearer than French 

(c) Equal importance given to English and French 

(d) The in-flight announcement being made in English 

Ans. (a) 

Q.7 The global financial crisis in 2008 was considered to be the most serious worldwide FC. Which started with the subprime lending crisis (SPLC) in the USA in 2007? The SPLC led to a banking crisis in 2008 with the collapse of Lehman brothers in 2008. The SPL refers to the provision of loans to those borrowers. Who may have difficulties in repaying loans and its arises because of excess liquidity following the East Asian crisis. The correct precedence according to Paragraph is 

(a) Banking crisis — Subprime lending crisis — Global financial crisis — East Asian crisis

(b) Subprime lending crisis — Global financial crisis — Banking crisis — East Asian crisis

(c) Global financial crisis — East Asian crisis — Banking crisis — Subprime lending crisis

(d) East Asian crisis — Subprime lending crisis — Banking crisis — Global financial crisis 

Ans. (d) 

Q.8 Following quadratic equation is ax² – bx + c = 0 and it has equal root which is β and a, b, c are the real number which is true 

(a) β³ = _{2 2}bC_a 

(b) b ≠ 4ac 

(c) β = ac 

(d) β³ = ₂ab 

Ans. (a) 

Section- B

Q.1 Given a binary number 1100 and p, q, r represents its sign magnitude, 1’s complement, 2’s complement representation respectively. Then 6 digit 2’s complement form of p + q + r is 

Ans. (110101) 

Given, binary number 1100 

1’s complement of 1100 = –3 Sign magnitude of 1100 = –4 2’s complement of 1100 = –4 ∴ P + Q + R = –4 – 3 – 4 = –11 The 6 digit 2’s complement of (–11) = 110101 

Q.2 Output of 4 × 1 MUX F(P, Q, R) is 

Ans. 

Output, F = PQR + PQR + 

F = QR + PQ₀ 

Q.3 For 10 bit D/A converter, full range of voltage 0-10, then find the output value for V_input 13A (in hexadecimal) in volts is ______V. 

Ans. (3.066) 

Given, n = 10 

V_FS = 10 V Input voltage = (13A)₁₆ = (314)₁₀ Output voltage = Resolution × Decimal equivalent of input 

V_o = ₂ 10 ₁₀ × ₃₁₄ = 3.066 V

Q.4 Given: y ( t ) = ∫ _−∞ W ( t ) ⋅ φ ( t ) W(t) is the random variable having PSD 3W/Hz and .

Find the variance of y(t)? 

Ans. (6) 

Q.5 Given that m(t) = 4cos1000πt and c(t) = cos2πf_ct ; where f_c = 1 MHz. Given that s(t) = m(t) cos2πf_ct and s(t) is demodulated using a demodulator. 

Then y(t) is 

Ans. 

cos [2 π ( f _c + 40 ) t ] S(t) = m(t) cos 2πf_ct S(t) = 4 cos 1000πt cos 2π (10⁶)t Output of multiplier = [4 cos 1000πt cos 2π 10⁶t] cos 2π (f_ct + 40)t] = [2 [cos [2π (500 + 10⁶)t] + cos [2π (10⁶ 500)t] cos 2π(f_c + 40)t = 2 cos 2π (500 + 10⁶)t cos 2π ((f_ct + 40)t) + 2 cos [2π (10⁶ – 500)t) cos 2π (f_c + 40)t = cos [2π (2f_c +540t) + cos(60t) + cos [2f_c – 460)t + cos(540t)] Output of Low pass filter 

= cos [2π (460)]t = cos 920 πt 

Q.6 Given phase modulated and frequency modulated signals 

where, k_p is the phase deviation constant (rad/volt), k_f is the frequency deviation constant (rad/sec/volt). If the highest instantaneous frequencies of S_Pm(t) and S_Fm(t) are same, then the value of the ratio K_p/K_f is ________ sec. 

Find Kp/K_f. 

Ans. (2)

Q.7 A digital communication system is used to transmit a block of N-bits, if the probability of receiving 1-bit in error is α and all bits are transmitted independently. The received block is said to be erroneous if at least one bit in error. The probability of the block to be erroneous is ______. 

(a) α^N 

(b) 1 – (1 – α)^N 

(c) N(1 – α) 

(d) 1 – α^N 

Ans. (b) 

Probability of error in decoding single bit = α Then probability of no error will be 1 – α. Total N-bits transmitted, so that probability of no error in received block 

= (1 – α) (1 – α) … N times = (1 – α)^N The probability of received block is erroneous = 1 – (1 – α)^N 

Q.8 A binary random variable takes two values as +2 and –2 with probability P(X = 2) = α; then the value of α for which entropy will be maximum is ______. 

Ans. (1/2) 

Given that P(X = 2) = α Entropy will be maximum; provided probabilities are equal. 

i.e. P(X = 2) = P ( X = − 2) = α = 

₂ ¹ α = ¹2 

Q.9 Given that X(ω) is Fourier transform of x(t) then find

Ans. 

Q.10 Given that

Then which one of the following is the correct pole zero plot of above given system? 

Ans. (b) 

Q.11 Discrete time signals output is y(n) = max[X(k)], –∞ ≤ K ≤ n 

(a) unit impulse 

(b) unit step function 

(c) a constant function

 (d) zero 

Ans. (b) 

Q.12 A finite duration discrete time signals x(n) is obtained by sampling x(t) = cos[200πt] of sample instant = n/400, n = 0, 1, 2, … 7. The 8-point DFT of x(n) is defined as 

(a) X(3) and X(5) are non-zero 

(b) X(4) is non-zero 

(c) X(2) and X(6) are non-zero 

(d) All X(k) are non-zero 

Ans. (c) 

Q.13 The transfer function of a stable discrete time LTI system is H( Z) ₌ K(z − α) /( z + 0.5) when α and K are constants and |α| > 1. If the magnitude response is constant for all frequencies then the value of α is ____. 

Ans. (–2)

Q.14 For the impedance Z = jX, having X values from –∞ to ∞, which of the following is correct in the Smith chart? 

(a) A circle of radius 1, with centre at (0, 0) 

(b) A point at the centre of the Smith chart 

(c) A circle of radius 0.5 with centre at (0.5, 0) 

(d) A line passing through the centre of the Smith chart 

Ans. (a) 

For given impedance Normalized impedance is Z⁼ jX_Z 0 Z = jX ⇒ Z=0 + jX Normalized resistance = 0 ⇒ r = 0 X = –∞ to ∞ r = 0 and X from –∞ to ∞ is a unit circle (radius 1) and centre (0, 0) on a complex reflection coefficient plane: 

Q.15 Which one of the following is correct? 

(a) ∇ ² 0A = then ‘A’ is irrotational 

(b) ∇ ( ∇ ·A ) = ∇× ( ( ∇× A ) −∇ ² A ) 

(c) ∇ · 0A = then vector is A is solenoidal 

(d) ∇× A is also a vector quantity 

Ans. (a) 

Q.16 Given the magnetic field intensity of a uniform plane wave in vacuum is H ( x , y , z , t ) = ( aˆ_x + 2 aˆ_y + baˆ_z )cos( ω t + 3 x − y − z ) then find value of b _____. 

Ans. (1) 

Q.17 For a given two port ideal lossless transformer, the parameter S₂₁ for a reference impedance of 1 Ω is 

Ans. (0.8) 

Q.18 For an infinitely small dipole in free space, the electric field ‘E’ in the far field is proportional to (e^{− jkr}/r sinθ). Where K = 2π/λ  . A vertical infinite small dipole (δI << λ) is placed at a distance h(h > 0) above an infinite ideal condcutive plane as shown in figure. The minimum value of ‘h’, for which one of maximum in the far-field radiation pattern occurs at θ = 60° is _____. 

(a) 0.5 λ 

(b) λ 

(c) 0.7 λ 

(d) 0.25 λ 

Ans. (b) 

Q.19 For a given transistor T₁, base region has uniform doping of 10¹⁷/cm³ and transistor T₂ has base region with doping varying linearly with x. If all other parameters of the transistor are the same, then find the ratio of common emitter current gain of transistor T₁ to transistor T₂? 

(a) 0.3 times that of T₂ 

(b) 0.7 times that of T₂ 

(c) 2 times that of T₂ 

(d) 2.5 times that of T₂ 

Ans. (c) 

Q.20 For a solar cell, P_in = 100 mW/cm², surface area = 1 cm², V_oc = 0.7V, fill factor = 0.8, efficiency = 15%. If thickness of the cell is 200 μm, then the light generation rate will be 

Ans. 

η = ( FF) V_OCI _SC / P_in 

0.15 = 0.8 × 0.7 × I_SC /100 mW

⇒ I_SC = 15/ 0.56 mA 

G_L =  I_SC / q ×Area× thickness 

= 15 × 10⁻³ / 0.56 × 1.6 × 10⁻¹⁹ × 1 × 200 × 10⁻⁴ 

= 0.837 × 10 ¹⁹ /cm ³ /second 

Q.21 Given that a semiconductor has density of state function in conduction band N_C is half of density of state function in valence band N_V, then the shift in the intrinsic fermi level from the centre of forbidden gap is ____ meV. 

Ans. (9.01)

Q.22 In a MOS capacitor, threshold voltage is –0.16V, metal work function is 3.7V, bandgap of semiconductor is 1eV whose band diagram is shown below. C′_x = 100 pF/cm². Oxide is free from non-idealities. When the voltage across the capacitor is equal to threshold voltage, what will be the depletion charge present in the semiconductor? 

Ans. 

MOS capacitance 

φ_m = 3.7, φ_s = 4.8, φ_ms = –1.1

V_T = φ_ms – Q_ox/C_ox – Q_d/C_ox + 2 φ _Fp 

φ_Fp = E_i – E_F = 0.5 – 0.2 = 0.3 

–0.16 = -1.1-0 ₋ Q′^d/C_ox + 2 × 0.3 

Q′_d /C_ox = 0.6 + 0.16 – 1.1 = –0.34 

Q_b = –0.34 × C_ox 

      = –0.34 × 100 × 10^–9 

      = -34 nC/cm² 

Q.23 Consider the following MOSFET, find the equivalent Norton’s resistance 

Ans. 

v_π = –V_x 

V_x = (I_x – g_m V_x) r_ds + I_xR 

V_x(1 + g_m r_ds) = (r_ds + R)I_x 

R_N = V_x/I_x = R +r_ds / 1+g_mr_ds

Q.24 A sinusoidal voltage is applied to the given circuit, then the steady state output voltage V_o is _______ V. 

Ans. (650.4) 

Voltage doubles, V_o =2 V_m = 2 × 230√2 ≅ 650.4V 

Q.25 Consider the op-amp shown below: 

The current “I₀” is ________ mA. 

Ans. (6) 

V_o = (1 + 1) × 2 = 4 V

 2−4 /1 + I _o + 0− 4/1= 0

-2+I _o-4 =0

⇒ I_o = 6 mA 

Q.26 

The output V₀ is 

(a) square wave with an amplitude of 5V 

(b) sinusoidal of amplitude 10V 

(c) inverted sinusoidal of input 

(d) constant signal with either +5V and –5V 

Ans. (a) 

The given circuit is a Schmitt trigger, which produces a square wave at the output. 

Q.27 Find the state matrix (consider v and i as state variables). 

Ans. 

From source transformation, 

KVL in loop 1, 

2I₁ = 2 i + 0.5di/dt + v

di/dt= –2V + 4i + 4I₁                     (i) 

KCL at node, 

i = 0.25 dv/dt +V − I₂/ 1 

dv/dt = –4V + 4i + 4I₂                                     (ii) 

Q.28 When base current of given BJT is negligible. Given that V_t = 26 mV and V_BE = 0.7V. 

Voltage gain at low frequencies is 

Ans. (–89.423) 

Q.29 In the given Nyquist contour the pole zero locations are indicated as shown. If the given contour is transformed from s-plane to G(s) H(s) plane then which one of the following is true 

(a) encircles the origin in clockwise 

(b) encircles the –1 + j0 in clockwise 

(c) encircles the –1 + j0 in anticlockwise 

(d) encircles the origin in anticlockwise 

Ans. (b) 

Q.30 Given op-amp circuit 

R = 10 kΩ, C = 0.1 μF, then the 3dB cut-off frequency of op-amp circuit is ____ Hz. 

Ans. (159.2) 

Op-amp active filter (LPF) inverting type 3 dB cut-off frequency, 

f_c = 1/2πRC

= 1 /2 π × 10⁴ × 10⁻⁷ 

= 1000 / 2π 

= 159.2 Hz 

Q.31 In the following circuit, assume that I_B = 0, V_BE = 0.7V for both the transistors. If V_in = 15V (unregulated) and V₀ = 9V (regulated), then the resistance R is equal to _______ Ω. 

Ans. (800) 

Q.32 Consider the below figure. 

G(s) = 1/( s + 1) ( s + α )  Find the value of α. 

Ans. (4)

Q.33 Given: C(s) = K (s+1) / (s+3), G(s) = 1/ s(s +1) . If steady state error for ramp input is 0.1, then find the value of k or negative feedback unity gain system 

Ans. (30) 

Q.34 If the value of current i = 10 cos [5t− π /4 ] , the value of inductance L is 

Ans. (2.828) 

Q.35 For given open loop transfer function G(s)H(s)=k(s+11) / s(s+2) (s +8) . Find value of k for which system is marginally stable. 

Ans. (160) 

Q.36 A two port network has an impedance [Z] = find [Z_L] for maximum power transfer. Find Z_L = ? 

Ans. (48) 

Q.37 Find value of V_th

Ans. (3.6) 

By applying source transformation 

V_th = 3.6 V 

Q.38 Find the value of I_o 

Ans. (143.7)

Q.39 In a transmission line given Z₀ = 50, Z_L = 400, l = 3λ/ 4, find Z_in 

Ans. (6.25)

Z_in for (l = λ/4) = Z²₀ / ZL =  50²/400  = 25/4 = 6.25 Ω 

Q.40 For the given characteristic equation 

Q(s) = s³ + 3s² + (K + 2)s + 3K = 0 

The root locus plot will have breakaway or break-in point in the region. 

(a) (0, –1) 

(b) (–1, –3) 

(c) (–∞, –3) 

(d) None of these 

Ans. (a) 

Q(s) = 1 + G(s) H(s) = 0 s³ + 3s² + 2s + ks + 3k = 0 

–k = s³ + 3s² + 2s / s+3 

− dk/ds = ( s + 3)(3s²+6s+2)− (s³+3s²+2s) / (s+ 3)² = 0 

3s³ + 6s² + 2s + 9s² + 18s + 6 – s³ – 3s² – 2s = 0 

2s³ + 12s² + 18s + 6 = 0 

s = –0.46, –3.87, –1.65 

Q.41 d²y /dx² − 6dy/dx + 9 = 0.Find the solution of differential equation.

(a) (C₁ + C₂ x)e^3x 

(b) (C₁ + C₂ x)e^–3x

 (c) C₁ e^3x 

(d) None of these 

Ans. (a) 

Q.42 In sequential circuit, the maximum clock frequency at which given circuit can operate reliably? 

Ans. (76.92) 

Total propagation delay = (t_pd + t_set-up)_max = 8ns = 5 ns = 13 ns 

∴ Frequency of operations = 1000/13 MHz = 76.92 MHz 

Q.43 f(x, y, z) = e^{(1 – x cosy)} + x ze^{− 1/1+y2} partial differentiation of f(x, y, z) with respect to x 

at point (1, 0, e) will be 

Ans. (0)

Q.44 f(x₂ + x₂) ≥ f(x₁) + f(x₂) 

(a) ¹x 

(b) square root of x 

(c) e ^x 

(d) e ^–x 

Ans. (c) 

Q.45 ∫∫∫ xdxdydz

Ans. (9/4) 

Q.46 If x is having uniform distribution between [– 2, 10] and y = 2x – 6 then P (y <7 / x >5 ) 

Ans. (0.3) 

Q.47 dy / dx = ( y−1) x solution of equation satisfies. 

(a) ln y − 1 = 0.5x² + c and y = – 1 

(b) ln y − 1 = 2x² + c and y = 1 

(c) ln y − 1 = 0.5x² + c and y = 1 

(d) ln y − 1 = 2x² + c and y = –1 

Ans. (a) 

Q.48 Two sides of a fair coin are labelled as 0 and 1. The coin is tossed two times independently. Let M and N denote labels corresponding to the outcomes of those processes for random variable X, where X = min(M, N), E(X) = _______. 

Ans. (0.25)

Q.49 In a digital communication system, 4 symbols are transmitted (s₁ = –3, s₂ = –1, s₃ = 1, s₄ = 2) through an AWGN channel. The variable at the input of decision device is s_i + W, where W is a Gaussian random variable with mean zero and unit variance. ML decoding is used. The conditional error probability when symbol s_i is transmitted is P_i. The value of “i” that result in maximum P_i is _____. 

Ans. (3)

Since the noise variable is Gaussian with zero mean and ML decoding is used, the decision boundary between two adjacent signal points will be their arithmetic mean. In the following graphs, the shaded area indicates the conditional probability of decoding a symbol correctly when it is transmitted. 

By comparing the above graphs, we can conclude that P₃ is larger among the four. 

Q.50 V₁, V₂, V₃, V₄, V₅, V₆ six vector in R⁴ which of the following statements is false? 

(a) Any 4 base for R⁴ 

(b) If V₁, V₃, V₅, V₇ span R⁴ then it forms a basis of R⁴ 

(c) These vectors are not linearly independent 

(d) It is not necessary that vector span R⁴ 

Ans. (a) 

Q.51 In 8085 microprocessor to access a memory of 16 kB number of address lines required is ____. 

Ans. (14) 

2ⁿ = N 

n → Number of address lines 

N → Number of Memory locations 

∴ 2ⁿ = 16 kB 

        = 2⁴ (2¹⁰)        [∵ 1 kB = 2¹⁰] 

         = 2¹⁴ 

    n = 14 

GATE 2020 Computer Science and Information Technology Previous Year Paper

GENERAL APTITUDE 

Q.1 Raman is confident of speaking English _____ six months. He has been practicing regularly ________ the last three weeks

(a) during, for

(b) for, since

(c) within, for

(d) for, in 

Ans. (c) 

• ‘Within’ is a preposition that is used to express something that occurs inside a particular period of time. 
• ‘for’ is used here because 

(i) Sentence is in ‘present perfect continuous tense’. 

(ii) For is used when we talk about a period of time. 

Q.2 Select the word that fits the analogy 

Cook : Cook :: Fly : 

(a) Flighter 

(b) Flew 

(c) Flyer 

(d) Flying 

Ans. (c) 

Flyer: Relation is Verb : Noun 

One who cooks is a cook and one who flies any aircraft is a flyer. 

Q.3 This knowledge of the subject was excellent but his class room performance was ____. 

(a) Extremely poor 

(b) Praise worthy 

(c) Desirable 

(d) Good 

Ans. (a) 

‘But’ is used for introducing an idea which contrasts with the statement that has been already said. 

Q.4 Mode a and e are toll booths which costs 200 and all other toll both b, c, d, f costs only 100. Minimum cost for each from 1 to 2. (Path was given) 

Ans. (*) 

Q.5 Goods services tax (GST) is an indirect tax introduced in India in 2014 that is imposed on the supply of goods and services used and it subsumes all indirect taxes except few. It is a district based tax imposed on goods and services used; it is not imposed at the point of origin from where goods come. GST also has a few components specific to state government, central government and UTs? Which one of the following can be inferred from the given passage? 

(a) GST includes all indirect taxes 

(b) GST is imposed on the product of goods and services 

(c) GST imposed at point of usage of goods and services 

(d) GST does not has a component specific for UT 

Ans. (c) 

Q.6 If P = 3, R = 27, T = 243, then Q + S = 

(a) 80 

(b) 110 

(c) 90 

(d) 40 

Ans. (c) 

Q.7 The total revenue of a company during 2014-2018 is shown in a bar graph. The total expenditure of the company in each year is 500 million rupees. The aggregate profit/ loss percentage on the total expenditure of the company during 2014-2018 is ______. 

Ans. (20% profit) 

Total expenditure = 2500 million 

Total revenue = 3000 million 

So, profit % = 500/2500 × 100 = 20% 

Q.8 The figure below shows an angular ring with outer inner radii b and a. The angular space has been pointed in the form of a blue colour circle touching the outer and inner peripheral gular space. If a maximum n number of circles can be pointed then the unpainted area available in angular space is ________. 

(a) π[(b² – a²) -n (b – a)²]

(b) π[(b² – a²) -n (a/2)²]

(c) π[(a² – b²) -n (b/2)²]

(d) π[(b² – a²) -n (b-a/2)²]

Ans. (d) 

The area of unpainted region will be 

π[(b² – a²) -n (b – a/2)²]

Q.9 The straight lines are drawn perpendicular to each other in the XY plane. The angle α and β are acute angles made by line as with x-axis then α + β = ? 

(a) 180° 

(b) 90° 

(c) 60° 

(d) 120° 

Ans. (b) 

Q.10 In a decoder with in input lines and n output lines, then 1 KB RAM is given and now find (m + n). 

Ans. (1034) 

We need 2¹⁰ outputs to map 1 kB RAM. 

For this we need 10 × 2¹⁰ decoder. 

Here m = 10 and n = 2¹⁰ 

m + n = 1034 

Q.11 Given main memory with single level paging main memory access time 100 ns TLB access time 20 ns. TLB hit ratio 95% page fault rate 10% and when there is page fault in 20% cases it uses write back and retrieve page from secondary memory with 5000 ns access time calculate average access time? With upto 1 decimal place. 

Ans. (*) 

Q.12 Consider the following statements: 

I. Daisy chain uses priorities for selecting devices. 

II. When there is vectored interrupt and polling is used for getting an address. 

III. Polling processor uses periodically checks status bit to check if interrupt needs to process. 

IV. DMA access processor and DMA controller can simultaneously access at the same  time. 

(a) I and II only 

(b) I and III only 

(c) I, II and IV only 

(d) I, and IV only 

Ans. (b) 

Q.13 A non-pipeline processor having 2.5 GHz clock frequency. Where each instruction takes 5 cycles and when this processor utilizes a same 5 stage pipeline having 2 GHz clock frequency and 30% are memory instruction 60% are ALU instruction and remaining are branch instruction. Given that 5% memory instruction takes 50 stall cycles and 50% branch instruction takes 2 cycles then what will be the speed up when the pipeline processor is used over the non-pipeline processor ________. 

Ans. (2.16) 

Q.14 A 16-bit instruction having two type of instruction i.e. R-type and I-type where 16-bit instruction supports 64 registers set. Now I-type of instruction has 1 register field and 4-bit immediate field. R-type instruction supports 2 register address fields and given that there are 8 different I-type instructions then how many different R-types of instruction are possible _______. 

Ans. (14) 

Given, 16 bit instruction and 64 registers 

I type: 

R type: 

1. Primitive instruction 

R-type: 

2. Number of operations possible = 2⁴ = 16 3. Number of tree opcodes = (16 – x) 

Assume x is the number of R-type instructions existed. 4. Number of I-type instruction possible = (16 – x) × 2² 8=64 – 4x 4x = 64 – 8 = 56 

x = 56/4

^{⇒ 14} 

Q.15 The number of permutations of the characters LILAC if no characters appears in its the original position if two Ls are indistinguishable is _______. 

Ans. (12) 

Number of derangements. 

Since both L’s are indistinguishable. 

First L’s can be arranged remaining 3 positions in ³C₂ ways. 

[i.e., _ L _ L _ or _ L _ L _ or _ L _ _ L _] 

For each of these cases remaining 3 letters can be deranged in 2 × 2! ways = 4 ways 

[i.e., L L C can lake only 1 or 3 positions → 2 ways. For each of these IA can be arranged in remaining 2 positions in 2 ways]. 

Number of derangements = ³C₂ × 2 × 2! = 12 

Q.16 A = {1, 2, 3}. What is the probability of getting reflexive relation on A. By choosing any relation randomly. 

Ans. (0.125) 

Q.17 A graph G K_{3, 4} is given. Suppose, a vertex ‘S’ is added which is adjacent to every vertex in K_{3, 4} then the minimum number of edge-color required ________. 

Ans. (7)

Minimum number of edge-colors required = 3 + 4 = 7. 

Q.18 Rank(M) is rank of matrix M and det(M) is determinant of matrix M then 

1.Rank(AB) = Rank(A) ⋅ Rank(B)

2.det(AB) = det(A) ⋅ det(B)

3.Rank(A + B) ≤ Rank(A) + Rank(B)

4.det(A + B) ≤ det(A) + det(B)

Which of the above statements is correct?

(a) 2 and 3

(b) 3 and 4

(c) 1 and 2

(d) 1 and 4 

Ans. (a) 

Statement 2 and 3 are correct statements directly based on properties of matrices. 

Q.19 A group with 35 elements has subgroups. The maximum size of the proper subgroup is ________. 

Ans. (7) 

Size of group = Ο(G) = 35 

Let H be subgroup of G 

∴ Ο(H)⏐Ο(G) 

Possible orders of H are 1, 5, 7, 35 

Size of largest possible proper subgroup = 7. 

Q.20 Which of the following is not valid? 

(a) ∃x (p(x) → w) ≡ ∀x p(x) → w 

(b) ∀x (p(x) → w) ≡ ∀x p(x) → w 

(c) ∃x (p(x) ∧ w) ≡ ∃x p(x) ∧ w 

(d) ∀x (p(x) ∨ w) ≡ ∀x p(x) ∨ w 

Ans. (b) 

∀x (p(x) → w) ≡ ∀x p(x) → w is wrong 

Since ∀x [p(x) → w] 

≡ ∀x [¬p(x) ∨ w] 

≡ ∀x (¬p(x) ∨ w

≡ ¬(∃x p(x)) ∨ w

≡ ∃x p(x) → w 

Q.21 Given vertex set (v₁, v₂, v₃, ….. v₁₀₀), the edge weight is ⏐v_i – v_j ⏐ where i ≤ i ≤ j ≤ 100 then the weight of the minimum spanning tree is ________. 

Ans. (99) 

Q.22 T(n) = T(n^1/a) + 1, T(b) = 1 find T(n) 

(a) θ(log_b log_an)

(b) θ(log_a log_bn) 

(c) θ(log_abn) 

(d) θ(log₂n) 

Ans. (a) 

Q.23 What is the worst case time complexity of inserting n elements in empty linked list in the sorted order? 

(a) n 

(b) n logn 

(c) n² 

(d) n² logn 

Ans. (b) 

Insert element at the beginning of linked list, take Ο(1) 

Q.24 In the AVL tree n element are there what is the time complexity of inserting other n² elements? 

(a) n² 

(b) Ο(n² logn) 

(c) Ο(n) 

(d) Ο(n logn) 

Ans. (b) 

AVL with n element: [height balanced [–1, 0, +1] BST] 

logn level due to balanced BST. 

(i) Every insertion of element: 

logn: Find place to insert. 

logn: If property is not satisfied do rotation. 

∴ n² element insertion: 

For 1 element ≡ 2 logn 

So, for n² element ≡ Ο(n² logn) 

Q.25 There are n elements in the balanced binary search tree. What is the time complexity to report the k elements in the range [a, b]? 

(a) Ο(logn + k) 

(b) Ο(k logn) 

(c) Ο(k) 

(d) Ο(kn) 

Ans. (a) 

Let a = 16, b = 42 

16: Find the ‘16’ element in the BST = Ο(logn) 

42: Find the ‘42’ element in the BST = Ο(logn) 

[16, 42]: Inorder sorted element between 

16 to 42 {16, 18, 19, 20, 25, 30, 35, 40, 42} ⇒ requires Ο(k) time for k element 

So total time: Ο(2 logn + k) ≡ Ο(logn + k) 

Q.26 Binary min-heap has 1023 elements. Find the number of comparisons required to find the maximum element? 

Ans. (511) 

Number of element = [1023/2] = 512

No bubble sort requires 511 comparisons. 

Q.27 Let A, B, C be the inputs which give output Z as shown in below figure. The minterms required to represent the output function Z(A, B, C) is ________. 

(a) ∑m(1, 3, 5, 6, 7) 

(b) ∑m(1, 4, 5, 6, 7) 

(c) ∑m(1, 2, 3, 6, 7) 

(d) ∑m(4, 5, 6, 7) 

Ans. (b)

∴ Z(A, B, C) = A + BC 

K-map of the output Z is 

∴ Z(A, B, C) = ∑m(1, 4, 5, 6, 7) 

Q.28 You are given accumulator and memory of 32 registers in between then there is a multiplexer the number of select lines in multiplexer. 

Ans. (5)

Number of registers = n = 32 Required multiplexer size is n : 1 i.e. 32 : 1 No of select lines required to the multiplexer = m ∴ m = log₂ n 

m = log₂ 32 m=5 

Q.29 

SELECT S.sno, S.sname

FROM Supplier S, catalog C

WHERE S.sno = C.sno AND

cost > (SELECT AVG (cost)

FROM Catalog

WHERE pno = ‘P₄’ GroupBy pno);

Number of rows returned by above query ________.

Ans. (4) 

SELECT S.sno, S.sname

FROM Supplier S, catalog C

WHERE S.sno = C.sno AND

cost > (SELECT AVG (cost)

FROM Catalog

WHERE pno = ‘P₄’ GroupBy pno);

Q.30 Given relation is in 3NF but not in BCNF 

(a) because for non-trivial FD x → A, with x is not super key and A is prime attribute. 

(b) because for non-trivial FD x → A, with x is not super key and A is not prime attribute, x is not a proper subset of key. 

(c) because for non-trivial FD x → A with x is not super key and A is not prime attribute, x is a proper subset of the key. 

(d) None of these 

Ans. (a) 

Q.31 For a database we are using B⁺ tree indexing with 1 million records in the database, each record fits in one block. Block size is 8 KB and search key size is 12 bytes, block pointer size is 8 bytes. Minimum number of block access required for database record is ________. 

Ans. (4) 

Total = 3 + 1 = 4 block access 

Q.32 Which of the following many-to-one rules of weak-entity set in an ER diagram? 

(a) Oval shape with double/bold borders 

(b) Diamond shape with double/bold borders 

(c) Rectangular shape with double bold/borders 

(d) Oval shape with identifier underlined 

Ans. (b) 

Diamond shape with double/bold borders 

Q.33 TCP connection maximum segment size = 2 KB is starting at t = 0 and threshold is 32 KB and calculates sender window size at (t + 60 ms) where (RTT = 6 ms) given 50 KB as maximum segment. 

Ans. (44) 

Q.34 A web page has some text and 4 small size images, used non-persistent HTTP connection, then the number of HTTP connections required ________. 

Ans. (5) 

In non persistent HTTP for every object there is a TCP connection required. Hence 1 TCP connection for text and 4 TCP connections for images required. 

Q.35

L₁ = {wxyx⏐w, x, y ∈ (0 + 1)⁺} 

L₂ = {xy⏐x, y, ∈ (a + b)*, ⏐x⏐=⏐y⏐, x ≠ y}

(a) L₁ is not regular but L₂ is CFL

(b) L₁ is CFL and L₂ is not CFL

(c) L₁ and L₂ are not CFL

(d) L₁ is regular and L₂ is CFL 

Ans. (d) 

L₁ is regular and L₂ is CFL. 

In L₁ putting x as 0 and 1 we get a subset 

w0y0 + w1y1 = (0 + 1)⁺ 0 (0 + 1)⁺ 0 + (0 + 1)⁺ 1(0 + 1)⁺ 1 

Now by putting x as 00, 01, 10, 11 we can show that above minimal regular expression covers all such things and hence above expression is not a subset but is equal to given language. Since we wrote regular expressions for L₁, it is regular. 

Q.36 S → aSB⏐d B → b “aaadbbb” using bottom up parser, how many steps required? 

Ans. (7) 

S → aSB

→ aaSBB [S → aSB]

→ aaaSBBB [S → aSB]

→ aaadBBB [S → d]

→ aaadbBB [B → b]

→ aaadbbB [B → b]

→ aaadbbb [B → b]

Total 7 steps required

Q.37 Which of the following regular expressions will contain a set of all binary strings containing an odd number of 1’s?

(a) 1 0* (0* 1 0* 1 0*)* 

(b) 0* (0* 1 0* 1 0*)* 1 0* 

(c) (0* 1 0* 1 0*)* 0* 1 

(d) ((0 + 1)* 1 + (0 + 1)*) 1 0* 

Ans. (b) 

Try to find a counterexample to show the expression incomplete. 

(a) is incorrect because it forces the string to start with “1” and hence cannot generate 

a string like “01”, which has an odd number of ones. 

(c) is incorrect because it forces it to end with “1” and hence cannot generate “10”. 

(d) is same as (0 + 1)*10* which will generate some wrong strings like “110” which 

has an even number of 1’s. It is a superset and hence not correct. 

(b) is same as (0* 1 0* 1 0*)* 1 0* which is correct. 

Q.38 Given L = {aⁿ⏐n ≥ 0} ∪ {aⁿbⁿ⏐n ≥ 0}. Tell us where L is 

(a) DCFL 

(b) Non-DCFL 

(c) Context-free language 

(d) CFL but not DCFL 

Ans. (a) 

{aⁿbⁿ⏐n ≥ 0} is a well known DCFL. 

{aⁿ⏐n ≥ 0} is a well known regular language.

So, L = DCFL ∪ Regular = DCFL by closure properly 

DCFL is the strongest correct answer. 

Q.39 Given four languages, which of the following are undecidable?

Where <M> denotes encoding of a Turing Machine M 

L₁ = {<M>⏐L(M) = φ} 

L₂ = {<M>⏐L(M) is non recursive} 

L₃ = {< M, w, q >⏐M will visit the state q when M execute on w and take exactly 100 steps]

L₄ = {<M>⏐L(M) accept strings where strings length is at least 20}

Which one of the following are/in undecidable? 

(a) L₁ and L₂ 

(b) L₂ and L₃ 

(c) L₁ and L₄ 

(d) L₁, L₂ and L₃ 

Ans. (d) 

(i) L(M) = φ is emptiness problem of TM, which is undecidable, by Rice’s theorem since 

it is a non-trivial problem. 

(ii) L(M) = non-recursive is also a non-trivial question, since some TM can accept non- recursive language and some may not, so by Rice’s theorem it is undecidable. 

(iii) Rice’s theorem applied and hence L₃ is undecidable. 

(iv) With UTM we can check if M accepts a string by 100 steps. So L₄ decidable L₁, L₂ and L₃ are undecidable. 

Q.40 Which of the following is true? 

I. If L₁ ∪ L₂ is regular, then both L₁ and L₂ must be regular. 

II. The class of regular language is closed under infinite union. 

(a) I only 

(b) Both I and II 

(c) II only 

(d) Neither I nor II 

Ans. (d) 

I is false, since {a_nb_n} ∪ {a_nb_n} = ∑* which is regular, but {anbn} not regular. 

II is false, since many infinite languages can be broken into individual strings which will be an infinite union of finite languages. So if regular is closed under infinite union, then all infinite language will become regular, which is untrue. So II is also false. 

Q.41 The number of states in a minimal DFA accepting all strings on {a, b}* with number of a’s multiple of 2 but not multiple of 3 is ________. 

Ans. (6) 

L = {w ∈ {a, b}*⏐n_a(w) = multiple of 2 but not 3} 

Let, L₁ = {w ∈ {a, b}*⏐n_a(w) = multiple of 2} 

L₂ = {w ∈ {a, b}*⏐n_a(w) = multiple of 3} 

Given language is L₁ – L₂ = L₁ ∩ L₂c 

We can make a DFA for L₁ with 2 states. 

We can make a DFA for L₂c with 3 states. 

Then use product automata construction to get a DFA for L₁ – L₂ = L₁ ∩ L₂c with 6 states. Since neither of the L₁ or L₂c has a trap state, the resulting product automata also has no trap state. 

So, min DFA has 6 states. 

Alternate solution: 

We can directly design DFA for multiple of 2 but not 3 with 6 states as shown below with 6 states by accepting 2a’s, 4a’s but not 6a’s in trap. 

Q.42 Preorder of a binary search tree is 15, 10, 12, 11, 20, 18, 16, 19. Then what would be its post order. 

(a) 11, 12, 10, 16, 19, 18, 20, 15 

(b) 12, 10, 16, 19, 18, 20, 15, 11 

(c) 15, 16, 12, 19, 11, 18, 20, 15

(d) 15, 20, 10, 16, 19, 18, 11, 12 

Ans. (a) 

Post order: 11, 12, 10, 16, 19, 18, 20, 15 

Q.43 Consider the codes given below: 

fun 1 (int n)

{

static int i = 0;

if(n > 0)

{

i++;

fun1(n – 1);

}

return (i);

}

fun2 (int n)

{

static int i = 0;

if(n > 0)

{

i = i + fun1(n);

fun2(n – 1);

}

return i;

}

What the program will return when fun2(5) is called ________

Ans. (55) 

Q.44 Consider the C program: 

Arr [4] [5] = {{1, 2, 3, 4, 5} 

                    {6, 7, 8, 9, 10} 

                    {11, 12, 13, 14, 15} 

                     {16, 17, 18, 19, 20}} 

printf(“%d”, *(*(a + **a) + 3)) 

The output of the above C program is ________. 

Ans. (19) 

Q.45 Consider to semaphore a and b whose initial values are 1 and 0 respectively. Count is the shared variable which is not used in code section P: 

Code section P 

wait (a); 

if (count == n); signal(b); 

signal(a); wait(b); signal(b); 

Code section Q 

What does this code achieve? 

(a) At any time there will be 2 processes in Q. 

(b) All processes will run P and then enter into Q. 

(c) (n – 1) process will run P and then Q. 

(d) All processes run P in a mutually exclusive manner. 

Ans. (a) 

Q.46 Assume all the processes arrive at time 0. Find the absolute difference between average Turnaround Time (TAT) in SJF and Round Robin if time quantum 4 ns 

Ans. (5.25) 

Turn Around Time (TAT) = (21 – 0) + (13 – 0) + (2 – 0) + (6 – 0) 

Average TAT = ⁴²/₄ = 10.5 

Turn Around Time (TAT) = (18 – 0) + (21 – 0) + (10 – 0) + (14 – 0) 

= 18 + 21 + 10 + 14 

Average TAT = ⁶³/₄ = 15.75 

Hence, ⏐SJF (TAT) – RR(TAT)⏐ 

= ⏐10.5 – 15.75⏐ = 5.25 

Q.47 Consider the following state changes for a preemptive scheduling OS: 

I. Ready to running 

II. Running to ready 

III. Blocked to running 

IV. Blocked to ready Which of the above statement 

(a) I and II only 

(b) I only 

(c) I and III only 

(d) I, II and IV only 

Ans. (d) 

Q.48 A new process needs to be allocated memory. The size of the process cannot be exactly fit in available holes. If memory is allocated to any of the available holes, then a new smaller hole will be created. Which of the following options is correct in this context? 

(a) The size of hole created using best fit is never greater than size created by first fit 

(b) The size of hole created using best fit is never greater than size created by next fit 

(c) The size of hole created using next fit is never greater than size created by first fit 

(d) The size of hole created using worst fit is never greater than size created by first fit 

Ans. (a) 

Q.49 Which of the following statements are TRUE? 

1. Symbol table is accessed only during lexical analysis and syntax analysis. 
2. Compilers for programming L that support recursion necessarily need heap storage for memory allocation in the runtime environment. 
3. Errors violating the condition any variable must be declared before its use are detected during syntax analysis. 

(a) None of 1, 2, 3 

(b) 1 and 3 

(c) 2 only 

(d) 1 only 

Ans. (a) 

Q.50 Consider A → PQ, A → XY are production of a grammar P, Q, X, Y, A are non-terminals, s is synthesized attribute, i is inherited attribute 

Rule 1: P . i = A. i + 2, Q . i = P . i + A . i, A . s = P . s + Q . s 

Rule 2: X . i = A. i + Y . s and Y . i = X . s + A . i 

Which of the following is TRUE? 

(a) Only Rule 1 is L attributed 

(b) Rule 1 and Rule 2 are L attributed 

(c) Neither Rule 1 Nor Rule 2 

(d) Only Rule 2 is L attributed 

Ans. (a) 

GATE 2020 Civil Engineering Previous Year Paper

Civil Engineering 

General Aptitude 

Q.1 Sum of two positive numbers is 100. After subtracting 5 from each number product of  the resulting number is 0. One of the original number is 

(a) 95 

(b) 92 

(c) 85 

(d) 90 

Ans. (a) 

Let the two positive numbers be x and y. 

∴ x + y = 100 …(i) 

(x – 5) (y – 5) = 0 …(ii) 

⇒ x = 5 or y = 5 

If x = 5 then y = 95 

If y = 5 then x = 95 

∴ One of the numbers is 95 since 5 is not in any of the options. 

Q.2 If 0, 1, 2, …… 8, 9 are coded as O, P, Q, ….. W, X then 45 is coded as 

(a) TS 

(b) SS 

(c) ST 

(d) SU 

Ans. (c) 

∴ 45 is coded as ‘ST’.

Q.3 Unit place in 26591749¹¹⁰⁰¹⁶ is 

(a) 6 

(b) 1 

(c) 3 

(d) 9 

Ans. (b) 

≃ 26591749^(110016) 

≃ Unit place of 9° = 1 

∴ Cycle of equation is (9, 1) (9, 1), (9, 1) 

So the answer will be 1.

Q.4 Insert seven numbers between 2 and 34 such is an AP. The sum of those seven inserted seven number is 

(a) 124 

(b) 130 

(c) 120 

(d) 126 

Ans. (d) 

2, a, (a + d), (a + 2d), …… (a + 6d), 34 

∴ Total number of terms of AP(n) = 9 

Let sum of seven inserted numbers = S 

∴ S = 7/2[a + (a + 6d )] = 7[a + 3d ]

T_n = 34

Also, a – 2 = (a + d – a)

⇒ a – d = 2

Similarly a – 2 = 34 – (a + 6d)

⇒ a – 2 = 34 – a – 6d

⇒ 2a = 36 – 6d = 36 – 6(a – 2)

⇒ 2a = 36 – 6a + 12

⇒ 8a = 48

⇒ a = 6

∴ d = a – 2 = 6 – 2 = 4

∴ S = 7(a + 3d) = 7(6 + 3 × 4) = 126

General English 

Q.5 It is a common criticism that most of the academicians live in their ________, so they are not aware of the real life challenge. 

(a) Ivory tower 

(b) homes 

(c) Glass palaces 

(d) Big flats 

Ans. (a) 

Q.6 His hunger for reading is insatiable. He reads indiscriminately. He is most certainly a/an _________ reader. 

(a) all round 

(b) voracious 

(c) wise 

(d) precarious 

Ans. (b) 

Q.7 If Fuse : Fusion :: Use : ___________. 

(a) Usage 

(b) Usion 

(c) Uses 

(d) User 

Ans. (a) 

Solid Mechanics 

Q.1 In a 2-D stress analysis, the state of stress at point P is .The necessary and sufficient condition for existence of the state of pure shear at point P 

(a) (σ_xx – σ_yy)² + 4τ²xy ^{= 0} 

(b) τ_xy 

(c) σ_xx + σ_yy = 0 

(d) σ_xxσ_yy – τ²xy ^{= 0} 

Ans. (c) 

In pure shear condition 

σ_x = 0, σ_y = 0, τ_xy = τ 

For this condition (c) is correct 

σ_xx + σ_yy = 0 

Q.2 A cantilever beam PQ of uniform flexural rigidity is subjected to concentrated moment M at R 

Deflection at free end Q. 

(a) 3ML²/8EI 

(b) ML²/6EI 

(c) 3ML²/4EI 

(d) ML²/6EI

Ans. (b) 

(d) M 

δc = δ1 = CC₁ + C1C₂

= BB₁ + C1C₂

= ML222EI+ML2EIL2

δc = 3ML28EI

Q.3 The initial condition is shown in figure. Axial stiffness of each of the bars is 10 kN/mm. A load W is applied such that the system remains horizontal and total deflection is 5 mm. The load W will be ________. 

Ans. (130 kN) 

Structural Analysis 

Q.4 How many zero force members are there in the above truss 

(a) 6 

(b) 7 

(c) 8 

(d) 9 

Ans. (c) 

As Δ_AB = 0, hence F_AB = 0 

Total number of zero force member = 8 

Q.5 A planer elastic structure is subjected to UDL as shown in figure. Where maximum BM any in the structure will be ________. 

Ans. (0) 

M_x = 0 of all points 

Q.6 Distributed load (continuous or in patches) of 50 kN/m may occupy any position on the grid the maximum –ve BM at R will be 

(a) 56.25 kN-m 

(b) 150 kN-m 

(c) 93.75 kN-m 

(d) 22.5 kN-m 

Ans. (a) 

ILD for MS 

∴ M_max at support = − [½ × 1.5 × 1.5 × 50]

= –56.25 kNm or 56.25 kNm (hogging) 

ILD for BM at the centre of span ‘QS’ 

M_C = − [½ × 1.5 × 0.75 × 50] × 2

= –56.25 kNm or 56.25 kNm (hogging) 

So, it can be concluded that for maximum hogging moment, overhang span (PQ & ST) can be loaded. And because of symmetry, the magnitude of maximum hogging moment remains the same throughout span QS. 

Irrigation Engineering 

Q.7 For a certain region:

Pan evaporation = 100 mm

Effective rainfall = 20 mm

Crop coefficient = 0.4

Irrigation efficiency = 0.5

What will be the amount of water required for irrigation?

Ans. (40 mm) 

Water required by crop = 100 × 0.4 mm = 40 mm

Effective rainfall = 20 mm

Additional water required = 20 mm

Amount of water required after accounting irrigation efficiency = 20/0.5 = 40mm

Geotechnical Engineering 

Q.8 Water flows in upward direction in a tank through 2.5 m thick sand layer. The e and G of sand are 0.58 and 2.7. Sand is fully saturated. γ_w is 10 kN/m³. Effective stress at point A, located 1 m above the base of the tank is _____ kN/m². 

Ans. (8.94 kN/m ²) 

Q.9 SPT was conducted at a survey 1.5 m internal upto 30 m depth. At 3 m depth, the observed no. of hammer blows for 3 successive 150 mm penetration were 8, 6 and 9. SPT, N value at 3 m depth is 

(a) 15 

(b) 23 

(c) 17 

(d) 14 

Ans. (a) 

No. of blows for each 150 mm penetration 8, 6 and 9.

We will not consider the first 150 mm number of blows.

Hence, for the last 300 mm, the number of blows is 15.

Hence, observed SPT number = 15.

Q.10 Velocity of flow is proportional to the first power of hydraulic gradient in Darcy’s law, the law is applicable to 

(a) turbulent flow in porous media

(b) transitional flow in porous media

(c) laminar flow in porous media

(d) laminar as well as turbulent flow in porous media

Ans. (c) 

Darcy’s law is valid for laminar flow conditions. 

Q.11 A drained triaxial test is conducted on a sand sample. If σ_d = 150 kPa and consolidation stress is 50 kPa the calculated the value of angle of internal friction (φ)? 

Ans. (36.87°) 

Q.12 A fully submerged infinite sandy slope has an inclination of 30° with the horizontal. γ_sat and effective angle of internal friction of sand are 18 kN/m³ and 38°. Assume γ_w = 10 kN/m³. Seepage is parallel to the slope. Factor of safety against shear failure is ______. 

Ans. (0.601) 

Q.13 A vertical retaining wall of 5 m height has to support soil of γ = 18 kN/m³, effective cohesion 12 kN/m² and effective friction angle 30°. As per Rankine, assuming that tension crack has occurred the lateral active thrust on wall per meter length is _____. 

Ans. (21.714 kN/m) 

After tension crack

Pa =½ × 16.144(5 – 2.309)

= 21.714 kN/m

Q.14 The water table is at a depth of 3 m below ground level, γ_w = 9.81 kN/m³. Surcharge is applied instantaneously Immediately after pre-loading, the effective stress (kN/m²) at point P and Q will be 

(a) 54 and 95 

(b) 36 and 90 

(c) 36 and 126 

(d) 124 and 204 

Ans. (a) 

( σ )_P =q + 3γ = 3 × 18 = 54 Surcharge is applied suddenly. 

∴ Excess pore water pressure developed. 

( σ )_Q = ( q + 3 γ _b + 4 γ _sat ) − (4 γ _w + 70) 

= 70 + 3 × 18 + 4 × 20 – (4 × 9.81 + 70) 

= 94.76 kN/m² 

Q.15 A fill of 2 m thick sand with unit weight of 20 kN/m³ is placed above the clay layer to accelerate the rate of consolidation of clay, c_v = 9 × 10^–2 m²/year. m_v = 2.2 × 10^–4 m²/kN. The settlement of clay layer 10 year after the construction is ____________. 

Ans. (18.832) 

Fluid Mechanics 

Q.16 Uniform flow with velocity u makes angle Q with axis. The velocity potential φ is 

(a) ±u(x sinθ – y cosθ) 

(b) ±u(y sinθ + x cosθ) 

(c) ±u(x sinθ + y cosθ) 

(d) ±u(y sinθ – x cosθ) 

Ans. (c) 

Velocity in x-depth, u_x = usinθ 

Velocity in y-depth, u_y = ucosθ 

₋ ∂φ/∂x = u_x 

Integrating it φ = –u_xx + f(x) + c 

= –(usinθ)x + f(y) + c …(i) 

− ∂φ/∂y= u _y

Integrating it φ = –u_y y + f(x) + c 

= –(ucosθ)y + f(x) + c …(ii) 

By equation (i) and (ii), 

φ = − u ( x sin θ + y cos θ ) 

If we take ∂φ/∂x = u_x and ∂φ/∂y = u_y

Then φ = u( x sin θ + y cos θ ) 

So, φ = ± u (xsinθ + ycosθ) 

Q.17 A floating body in a liquid is in a stable condition if 

(a) metacentre lies above centre of gravity

(b) metacentre lies below centre of gravity

(c) centre of buoyancy lies below the centre of gravity

(d) centre of buoyancy lies above the centre of gravity

Ans. (a) 

For stability of floating body M lies above G 

GM > 0 

Q.18 A circular water tank of 2 m dia has circular orifice of dia 1 m at bottom. Water is entering the tank at 20 l/s and escaping through orifice. Take C_D for orifice = 0.8. Neglect any friction losses. g = 9.81 m/s². Height of the water level in the tank at a steady rate is _____. 

Ans. (0.5164 m) 

Open Channel Flow 

Q.19 For an open channel flow discharge is 12 m³/s and width is 6 m. Hydraulic jump is formed. Depth at upstream was 30 cm. Take g = 9.81 m/s² and ρ_w = 100 kg/m³. Calculate the energy loss in jump? 

(a) 114.2 MW 

(b) 114.2 kW 

(c) 141.2 J/s 

(d) 141.2 HP 

Ans. (a) 

Q.20 For a rectangular open channel flow, the width of section is 4 m. The discharge is 6 m³/s. The Manning’s roughness coefficient is 0.02. The critical velocity for the channel will be ____________. 

Ans. (2.45 m/s) 

Critical depth (Y_C) = q2g1/3

=1.529.811/3=0.612 cm

Critical velocity (V_C) = gYc = 9.81 × 0.612 = 2.45 m/s 

Engineering Hydrology 

Q.21 The probability that a 50 year flood may not occur at all during the 25 year life of a project is _________. 

Ans. (0.603) 

P = 1/T = 1/50 = 0.02

q = 1 – P = 0.98 

∴ Probability of non-occurrence of an event is given by, 

Assurance = qⁿ 

= (0.98)²⁵ 

= 0.603 

Environmental Engineering 

Q.22 In a homogenous unconfined aquifer of area 3 km², water table elevation is 102 m. After natural recharge of volume 0.9 million cubic meter (Mm³) the water table rose to 103.2 m. After this recharge, pumping took place and W_T dropped down to 101.20 m. The volume of groundwater pumped after the natural recharge is __________ Mm³. 

Ans. (1.5 Mm³) 

V_R = 0.9 Mm³ 

V = 3 × (103.2 – 102) 

= 3 × 1.2 = 3.6 Mm³ 

y_s or y_R = VR_V = ^0.9/_3.6 

Now, 1/S ⁼ V_D/V 

V_D = ^0.9/_3.6  [ 3 × ( 103.2 − 101.2 ) ]

V_D = 1.5 Mm³ 

Q.23 35.67 mg HCl is added to distilled water and the total solution is made 1 l. The atomic weight of H and Cl is 1 and 35.5. Neglecting the dissociation of H₂O, the pH of solution is 

(a) 3.5 

(b) 2.5 

(c) 2.01 

(d) 3.01 

Ans. (d) 

HCl →H⁺ + Cl^– 

1 mole of HCL gives 1 mole H⁺ ions 

36.5 gm of HCl gives 1 gm of H⁺ ions 

35.67 mg = 1/36.5 × 35.67 = 0.977 mg of H ⁺

 = 0.977 × 10^{− 3}/1 = 9.77 × 10 ^{− 4} moles of H⁺ 

pH = –log₁₀[H⁺] = –log₁₀[9.77 × 10^–4] 

= –log₁₀9.77 + 4log₁₀10 

= 4 – 0.989 = 3.01 

Q.24 As chlorine reacts rapidly with water to form Cl^–, HOCl and H⁺. The most active disinfectant in the chlorination process is 

Cl_2(g) + H₂O ⇌ HOC l + Cl⁻ + H⁺ 

(a) HOCl 

(b) H⁺ 

(c) H₂O 

(d) Cl^– 

Ans. (a) 

Q.25 A gaseous chemical has a concentration of 41.6 μmole/m³ in air at 1 atm pressure and temp 293 k gas constant R is 82.05 × 10^–6 m³/atm/molK. Assume ideal gas law is valid, the concentration of gaseous chemical will be __________ ppm. 

Ans. (1) 

Q.26 For a river the discharge is 1000 MLD. BODs for the river are 5 mg/l and dissolved oxygen is 8 mg/l before receiving wastewater discharge at a location. For existing environment conditions dissolved oxygen is 10 mg/l. Waste water discharge of 100 MLD drains into the river. BOD ultimate of waste water is 200 mg/l and dissolved oxygen is 2 mg/l falls at a location. Assume complete mixing. Immediate do deficit is ______ mg/l. 

Ans. (2.545) 

Q.27 Surface overloading rate of primary settling tank (discrete) is 200 l/m² per day. ν = 1.01 × 10^–2 cm²/s. G = 2.64, the minimum dia of particle that will be removed with 80% of efficiency will be _______ μm. 

Ans. (14.53) 

Q.28 Stream with a flow rate of 5 m³/sec, BOD_U = 30 mg/L. Waste water discharge 0.2 m³/s, BOD₅ = 500 mg/l joins the stream at a location and mix up instantaneously. Area of stream 40 m² which remains constant. BOD exertion rate constant is 0.3/day (log_e). BOD remaining 3 km downstream from the mixing location is _________. 

Ans. (49.57) 

Q.29 A water supply scheme transport 10 MLD water through a 450 mm diameter pipe for a distance 2.5 km. A chlorine dose of 3.5 mg/L is applied at the starting point. It is decided to increase the flow from 10 MLD to 13 MLD in the pipeline. Assume exponent for concentration n = 0.36 with this increased flow in order to attain the same level of disinfection. The chlorine is applied at the starting point. 

(a) 3.95 

(b) 4.4 

(c) 5.55 

(d) 4.75 

Ans. (d) 

Construction Materials 

Q.30 The los angeles test for stone aggregate is used to examine 

(a) crushing strength 

(b) abrasion 

(c) toughness 

(d) none of these 

Ans. (b) 

Los Angeles test of stone is used for Abrasion resistance. 

Q.31 During the process of hydration of cement, due to increase in C₂S content in cement ,clinker, the heat of hydration 

(a) does not change 

(b) initially decrease the increase 

(c) decrease 

(d) increase 

Ans. (c) 

Geomatics Engineering 

Q.32 An open traverse PQRST is surveyed using theodolite 

If the independent coordinated (Northing and Easting) of station P are (400, 200 m) the independent coordinates of station T are 

(a) 194.7, 370.1 

(b) 405.3, 229.9 

(c) 205.3, 429.9 

(d) 394.7, 170.1 

Ans. (d) 

ΔL = –5.3

ΔD = –29.9

T, Northing{400 + (–5.3) = 394.7

T, Easting{200 + (–29.9) = 170.1

T [394.7 m, 170.1 m]

Q.33 The length of line segment SP is __________. 

Ans. (44.784 m) 

ΔL = 40cos80° + 50cos10° + 30cos210° 

= 30.20 

ΔD = 40sin80° + 50sin10° + 30sin210° 

= 33.07 

Length, SP = √ΔL² + ΔD² 

= 44.784 m 

Highway Engineering 

Q.34 Gradient of a road is 4.5%, radius is 100 m the compensated as per IRC will be _____. 

Ans. (4%) 

Gradient = 4.5%, R = 100 m 

Grade compensation = (30 + R/R) ⊁ (75/R)% = 30 + 100/100 ⊁ 75/100 = 1.3% ⊁ 0.75} G.C = 0.75 

 Compensated Gradient = Gradient G.C = 4.5% – 0.75 = 3.75 ⊀ 4% 

Hence C.G = 4% 

Q.35 As per IRC, the minimum width of median in urban areas is ____________. 

Ans. (1.2 m) 

Desirable width of median in urban roads = 5m 

And As per IRC : 86-1983 min. width = 1.2m 

Q.36 For the contraction joint, which is correct position of dowel bar 

Ans. (b) 

RCC Structures and Prestressed Concrete 

Q.37 Calculate the design bending moment of a singly reinforced section 

If width = 300 mm

Effective depth = 450 mm

Area of steel in tension = 942 mm²

Grade of concrete is M25 and Fe500 Steel

Ans. (158.28 kN-m) 

Q.38 A simply supported prismatic concrete beam of rectangular cross-section of span 8 m is prestressed with effective prestress force of 600 kN. Eccentricity is zero at support and varies linearly to value ‘e’ at mid span. Required value of e ________. 

Ans. (40 mm) 

P = 600 kN

Simply supported span = L = 8 m

To support a point load applied at mid span (W)

= 12 kN

Balancing load = Point load

2P sin θ = W

2P (E/L/2) = 2

2Pe × 2/L = W

4Pe/L = W

e = WL/4P = 12000N × 8000mm/ 4 × 600 × 1000N

= 40mm

Q.39 The variation of bond stress varies as 

Ans. (c) 

Design of Steel Structures 

Q.40 For a given beam shown below the permissible stress in the weld is 20 N/mm², 

I_xx = 7.73 × 10⁶ mm⁴. The allowable shear force in kN will be __________. 

Ans. (323.527 kN) 

Engineering Mathematics 

Q.41 The area of an ellipse represented by an equation is 

(a) πab/4

(b) 4πab/3

(c) πab 

(d) πab/2

Ans. (c) 

Q.42 The value of

(a)  1/2

(b) 1/4

(c) 0 

(d) 1 

Ans. (b) 

Q.43 for the ordinary differential equation d²x/dt² -5dx/dt+6x=0,intial condition x(0) =0 and dx/dt (0) =10 ,the solution of the given equation

(a) -10e^2t+10e^3t

(b)10e^2t+10e^3t

(c) 5e^2t+6e^3t

(d) -5e^2t+6e^3t

Ans.(a)

Q.44 value of X₃ will be

Ans.(3)

Q.45 If C represents, a line segment between (0, 0, 0) and (1, 1, 1) in Cartesian coordinate system, the value of line integral ∫_C[ ( y + z ) dx + ( x + z )dy + ( x + y )dz] is 

Ans. (3)

Q.46 If the true value of ln2 is 0.69. If value of ln2 is also calculated by linear regression between ln1 and ln6 then calculate the percentage error in the value of ln2. 

Ans. (48.11%) 

Q.47 θ = f(t, z) and D = f(θ), k = f(θ) then _{D ( θ ) ∂} ∂ _z2 θ 2 ₊ ∂ k _∂ ( _z θ ) ₋ ∂θ _{∂ t = 0} is _______. 

(a) Second order linear equation 

(b) Second order nonlinear equation 

(c) Second degree linear equation 

(d) Second degree non-linear equation 

Ans. (d) 

∵ 1^st term of given D. Equation contains a product of dependent variable with its derivative, so it is non-linear and also we have 2nd order derivative so it’s order is two i.e., 2^nd order is non linear. 

GATE 2019 Computer Science and Information Technology Previous Year Paper

General Aptitude

Section -A

Q. 1 – Q. 5 carry one mark each. 

Q.1 The expenditure on the project _____ as follows: equipment Rs.20 lakhs, salaries Rs.12 

lakhs, and contingency Rs.3 lakhs. 

(A) break down 

(B) break 

(C) breaks down 

(D) breaks 

Q.2 The search engine’s business model ___________ around the fulcrum of trust. 

(A) revolves 

(B) plays 

(C) sinks 

(D) bursts 

Q.3 Two cars start at the same time from the same location and go in the same direction. The speed of the first car is 50 km/h and the speed of the second car is 60 km/h. The number of hours it takes for the distance between the two cars to be 20 km is ___. 

(A) 1 

(B) 2 

(C) 3 

(D) 6 

Q.4 Ten friends planned to share equally the cost of buying a gift for their teacher. When two of them decided not to contribute, each of the other friends had to pay Rs 150 more. The cost of the gift was Rs. ____. 

(A) 666 

(B) 3000

(C) 6000 

(D) 12000 

Q.5 A court is to a judge as _____________ is to a teacher. 

(A) a student 

(B) a punishment 

(C) a syllabus 

(D) a school 

Q. 6 – Q. 10 carry two marks each. 

Q.6 The police arrested four criminals – P, Q, R and S. The criminals knew each other. They 

made the following statements: P says “Q committed the crime.” Q says “S committed the crime.” R says “I did not do it.” S says “What Q said about me is false.” Assume only one of the arrested four committed the crime and only one of the statements made above is true. Who committed the crime? 

(A) P 

(B) R 

(C) S 

(D) Q 

GA 1/3 

Q.7 In the given diagram, teachers are represented in the triangle, researchers in the circle and administrators in the rectangle. Out of the total number of the people, the percentage of administrators shall be in the range of ___________. 

(A) 0 to 15 

(B) 16 to 30 

(C) 31 to 45 

(D) 46 to 60 

Q.8 “A recent High Court judgement has sought to dispel the idea of begging as a disease — which leads to its stigmatization and criminalization — and to regard it as a symptom. The underlying disease is the failure of the state to protect citizens who fall through the social security net.” 

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

(A) Beggars are lazy people who beg because they are unwilling to work 

(B) Beggars are created because of the lack of social welfare schemes 

(C) Begging is an offence that has to be dealt with firmly 

(D) Begging has to be banned because it adversely affects the welfare of the state 

Q.9 In a college, there are three student clubs. Sixty students are only in the Drama club, 80 students are only in the Dance club, 30 students are only in the Maths club, 40 students are in both Drama and Dance clubs, 12 students are in both Dance and Maths clubs, 7 students are in both Drama and Maths clubs, and 2 students are in all the clubs. If 75% of the students in the college are not in any of these clubs, then the total number of students in the college is _____. 

(A) 1000 

(B) 975 

(C) 900 

(D) 225 

GA 2/3 

Q.10 Three of the five students allocated to a hostel put in special requests to the warden. Given the floor plan of the vacant rooms, select the allocation plan that will accommodate all their requests. 

Request by X: Due to pollen allergy, I want to avoid a wing next to the garden. 

Request by Y: I want to live as far from the washrooms as possible, since I am very sensitive to smell. 

Request by Z: I believe in Vaastu and so want to stay in the South-west wing. The shaded rooms are already occupied. WR is washroom. 

Section – B

Q.1 A certain processor uses a fully associative cache of size 16 kB. The cache block size is 16 bytes. Assume that the main memory is byte addressable and uses a 32-bit address. How many bits are required for the Tag and the Index fields respectively in the addresses generated by the processor? 

(A) 24 bits and 0 bits 

(B) 28 bits and 4 bits 

(C) 24 bits and 4 bits 

(D) 28 bits and 0 bits 

Q.2 The chip select logic for a certain DRAM chip in a memory system design is shown below. Assume that the memory system has 16 address lines denoted by A15 to A0. What is the range of addresses (in hexadecimal) of the memory system that can get enabled by the chip select (CS) signal? 

(A) C800 to CFFF 

(B) CA00 to CAFF 

(C) C800 to C8FF 

(D) DA00 to DFFF 

Q.3 Which one of the following kinds of derivation is used by LR parsers? 

(A) Leftmost

(B) Leftmost in reverse 

(C) Rightmost 

(D) Rightmost in reverse 

Q.4 In 16-bit 2’s complement representation, the decimal number −28 is: 

(A) 1111 1111 0001 1100 

(B) 0000 0000 1110 0100 

(C) 1111 1111 1110 0100 

(D) 1000 0000 1110 0100 

Q.5 Let U = {1,2,…,n}. Let A = {(x,X)|x ∈ X,X ⊆ U}. Consider the following two statements 

on |A|. 

I. |A| = n2ⁿ⁻¹ 

II. Which of the |A| above =k=1nk(ⁿ_k) 

statements k(ⁿk⁾ is/are TRUE? 

(A) Only I 

(B) Only II 

(C) Both I and II 

(D) Neither I nor II 

Q.6 Which one of the following is NOT a valid identity? 

(A) (x ⊕ y) ⊕ z = x ⊕ (y ⊕ z) 

(B) (x + y) ⊕ z = x ⊕ (y + z) 

(C) x ⊕ y = x + y, if xy = 0 

(D) x ⊕ y = (xy + x′y′)′ 

Q.7 If L is a regular language over Σ = {a,b}, which one of the following languages is NOT 

regular ? 

(A) L ⋅ L^R = {xy | x ∈ L,y^R ∈ L} 

(B) {ww^R | w ∈ L} 

(C) Prefix (L) = {x ∈ Σ^∗|∃y ∈ Σ^∗ such that xy ∈ L} 

(D) Suffix (L) = {y ∈ Σ^∗|∃x ∈ Σ^∗ such that xy ∈ L} 

Q.8 Consider Z = X – Y, where X, Y and Z are all in sign-magnitude form. X and Y are each represented in n bits. To avoid overflow, the representation of Z would require a minimum of:

(A) n bits

(B) n − 1 bits 

(C) n + 1 bits 

(D) n + 2 bits 

Q.9 Let X be a square matrix. Consider the following two statements on X. 

I. X is invertible. II. Determinant of X is non-zero. 

Which one of the following is TRUE? 

(A) I implies II; II does not imply I. 

(B) II implies I; I does not imply II. 

(C) I does not imply II; II does not imply I. 

(D) I and II are equivalent statements. 

Q.10 Let G be an arbitrary group. Consider the following relations on G: 

𝑅₁: ∀𝑎,𝑏∈𝐺,𝑎 𝑅₁𝑏 if and only if ∃𝑔∈𝐺 such that 𝑎=𝑔⁻¹𝑏𝑔

𝑅₂:∀𝑎,𝑏∈𝐺,𝑎 𝑅₂𝑏 if and only if 𝑎=𝑏⁻¹

Which of the above is/are equivalence relation/relations? 

(A) R₁ and R₂ 

(B) R₁ only 

(C) R₂ only 

(D) Neither R₁ nor R₂ 

Q.11 Consider the following two statements about database transaction schedules: 

I. Strict two-phase locking protocol generates conflict serializable schedules that 

are also recoverable. 

II. Timestamp-ordering concurrency control protocol with Thomas’ Write Rule can generate view serializable schedules that are not conflict serializable. 

Which of the above statements is/are TRUE? 

(A) I only 

(B) II only 

(C) Both I and II 

(D) Neither I nor II 

Q.12 Let G be an undirected complete graph on n vertices, where n > 2. Then, the number of 

different Hamiltonian cycles in G is equal to 

(A) n!

(B) (n − 1)! 

(C) 1 

(D) (n−1)! 

Q.13 Compute x3x4-812×2-5x-3

(A) 1 

(B) 53/12 

(C) 108/7 

(D) Limit does not exist 

Q.14 Which one of the following statements is NOT correct about the B+ tree data structure used 

for creating an index of a relational database table? 

(A) B+ Tree is a height-balanced tree 

(B) Non-leaf nodes have pointers to data records 

(C) Key values in each node are kept in sorted order 

(D) Each leaf node has a pointer to the next leaf node 

Q.15 For Σ = {a,b}, let us consider the regular language L = { x |x = a^2+3k or x = b^10+12k, k ≥ 0}. Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for L ? 

(A) 3 

(B) 5 

(C) 9 

(D) 24 

Q.16 Which of the following protocol pairs can be used to send and retrieve e-mails (in that order)? 

(A) IMAP, POP3
(B) SMTP, POP3 

(C) SMTP, MIME 

(D) IMAP, SMTP 

Q.17 The following C program is executed on a Unix/Linux system: 

#include <unistd.h>

int main()

{

int i;

for (i=0; i<10; i++)

if (i%2 == 0) fork();

return 0;

}

The total number of child processes created is ________.

Q.18 Consider the following C program:

#include <stdio.h>

int jumble(int x, int y){

x=2*x+y;

return x;

}

int main(){

int x=2, y=5;

y=jumble(y,x);

x=jumble(y,x);

printf(“%d \n”, x);

return 0;

}

The value printed by the program is ________.

Q.19 Consider the grammar given below: 

S → Aa 

A → BD 

B → b | ε 

D → d | ε 

Let a, b, d, and $ be indexed as follows: 

Compute the FOLLOW set of the non-terminal B and write the index values for the symbols in the FOLLOW set in the descending order. (For example, if the FOLLOW set is {a, b, d, $}, then the answer should be 3210) 

Q.20 An array of 25 distinct elements is to be sorted using quicksort. Assume that the pivot element is chosen uniformly at random. The probability that the pivot element gets placed in the worst possible location in the first round of partitioning (rounded off to 2 decimal places) is ________. 

Q.21 The value of 3⁵¹ mod 5 is ________. 

Q.22 Two numbers are chosen independently and uniformly at random from the set {1,2 ,…,13}. The probability (rounded off to 3 decimal places) that their 4-bit (unsigned) binary representations have the same most significant bit is ___________. 

Q.23 Consider three concurrent processes P1, P2 and P3 as shown below, which access a shared variable D that has been initialized to 100. 

The processes are executed on a uniprocessor system running a time-shared operating system. If the minimum and maximum possible values of D after the three processes have completed execution are X and Y respectively, then the value of Y – X is _____________. 

Q.24 Consider the following C program: 

#include <stdio.h>

int main(){

int arr[]={1,2,3,4,5,6,7,8,9,0,1,2,5}, *ip=arr+4;

printf(“%d\n”, ip[1]);

return 0;

}

The number that will be displayed on execution of the program is ___________

Q.25 Consider a sequence of 14 elements: A = [−5, −10, 6, 3, −1, −2, 13, 4, −9, −1, 4, 12, −3, 0]. 

The subsequence where 0 ≤ i ≤ j < sum 14. S(i,j) (Divide = and ∑ conquer ^jk=i A[k] approach ^{. Determine the maximum of} may be used.) 

^S(i,j), 

Q.26 Consider I the following C function. 

void convert(int n){

if(n<0)

printf(“%d”,n);

else {

convert(n/2);

printf(“%d”,n%2);

}

}

Which one of the following will happen when the function convert is called with any positive integer n as argument? 

(A) It will print the binary representation of n and terminate (B) It will print the binary representation of n in the reverse order and terminate (C) It will print the binary representation of n but will not terminate (D) It will not print anything and will not terminate 

Q.27 Consider the following C program: 

#include <stdio.h>

int r(){

static int num=7;

return num–;

}

int main(){

for (r();r();r())

printf(“%d”,r());

return 0;

}

Which one of the following values will be displayed on execution of the programs? 

(A) 41 

(B) 52 

(C) 63 

(D) 630 

Q.28 Consider three machines M, N, and P with IP addresses 100.10.5.2, 100.10.5.5, and 100.10.5.6 respectively. The subnet mask is set to 255.255.255.252 for all the three machines. Which one of the following is true? 

(A) M, N, and P all belong to the same subnet 

(B) Only M and N belong to the same subnet 

(C) Only N and P belong to the same subnet 

(D) M, N, and P belong to three different subnets 

Q.29 Suppose that in an IP-over-Ethernet network, a machine X wishes to find the MAC address of another machine Y in its subnet. Which one of the following techniques can be used for this? 

(A) X sends an ARP request packet to the local gateway’s IP address which then finds the 

MAC address of Y and sends to X 

(B) X sends an ARP request packet to the local gateway’s MAC address which then finds 

the MAC address of Y and sends to X 

(C) X sends an ARP request packet with broadcast MAC address in its local subnet 

(D) X sends an ARP request packet with broadcast IP address in its local subnet 

Q.30 Consider three 4-variable functions f1, f2, and f3, which are expressed in sum-of-minterms as 

f₁ = ∑ (0, 2, 5, 8, 14), f₂ = ∑ (2, 3, 6, 8, 14, 15), f₃ = ∑ (2, 7, 11, 14) 

For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as: 

(A) ∑ (7, 8, 11) 

(B) ∑ (2, 7, 8, 11, 14) 

(C) ∑ (2, 14) 

(D) ∑ (0, 2, 3, 5, 6, 7, 8, 11, 14, 15) 

Q.31 Which one of the following languages over Σ = {a,b} is NOT context-free? 

(A) {ww^R |w ∈ {a,b}^∗}

(B) {waⁿbⁿw^R |w ∈ {a,b}^∗,n ≥ 0} 

(C) {waⁿw^Rbⁿ |w ∈ {a,b}^∗,n ≥ 0} 

(D) {aⁿbⁱ | i ∈ {n,3n,5n},n ≥ 0} 

Q.32 Let the set of functional dependencies F = {QR → S, R → P, S → Q} hold on a relation schema X = (PQRS). X is not in BCNF. Suppose X is decomposed into two schemas Y and Z, where Y = (PR) and Z = (QRS). 

Consider the two statements given below. 

I. Both Y and Z are in BCNF

II. Decomposition of X into Y and Z is dependency preserving and lossless 

Which of the above statements is/are correct? 

(A) Both I and II 

(B) I only 

(C) II only 

(D) Neither I nor II 

Q.33 Assume that in a certain computer, the virtual addresses are 64 bits long and the physical addresses are 48 bits long. The memory is word addressible. The page size is 8 kB and the word size is 4 bytes. The Translation Look-aside Buffer (TLB) in the address translation path has 128 valid entries. At most how many distinct virtual addresses can be translated without any TLB miss? 

(A) 16×2¹⁰ 

(B) 256×2¹⁰ 

(C) 4×2²⁰ 

(D) 8×2²⁰ 

Q.34 Consider the following sets: 

S1. Set of all recursively enumerable languages over the alphabet {0,1} 

S2. Set of all syntactically valid C programs 

S3. Set of all languages over the alphabet {0,1} 

S4. Set of all non-regular languages over the alphabet {0,1} 

Which of the above sets are uncountable? 

(A) S1 and S2 

(B) S3 and S4 

(C) S2 and S3 

(D) S1 and S4 

Q.35 Consider the first order predicate formula φ: 

∀x [(∀z z|x ⇒ ((z = x) ∨ (z = 1))) ⇒ ∃w (w > x) ∧ (∀z z|w ⇒ ((w = z) ∨ (z = 1)))] 

Here ‘a|b’ denotes that ‘a divides b’, where a and b are integers. Consider the following sets: 

S1. {1,2,3,…,100} S2. Set of all positive integers S3. Set of all integers 

Which of the above sets satisfy φ? 

(A) S1 and S2 

(B) S1 and S3 

(C) S2 and S3 

(D) S1, S2 and S3 

Q.36 Consider the following grammar and the semantic actions to support the inherited type declaration attributes. Let 𝑋₁, 𝑋₂, 𝑋₃, 𝑋₄, 𝑋₅, and 𝑋₆ be the placeholders for the non-terminals D, T, L or L1 in the following table: 

Which one of the following are the appropriate choices for X₁, X₂, X₃ and X₄? 

(A) 𝑋₁=𝐿 , 𝑋₂=𝑇, 𝑋₃=𝐿1, 𝑋₄=𝐿

(B) 𝑋₁=𝑇 , 𝑋₂=𝐿, 𝑋₃=𝐿1, 𝑋₄=𝑇

(C) 𝑋₁=𝐿 , 𝑋₂=𝐿, 𝑋₃=𝐿1, 𝑋₄=𝑇 

(D) 𝑋₁=𝑇 , 𝑋₂=𝐿, 𝑋₃=𝑇, 𝑋₄=𝐿1

Q.37 There are n unsorted arrays: A1, A2, …, An. Assume that n is odd. Each of A1, A2, …, An contains n distinct elements. There are no common elements between any two arrays. The worst-case time complexity of computing the median of the medians of A1, A2, …, An is 

(A) O(n) 

(B) O(n log n) 

(C) O(n²) 

(D) Ω(n² log n) 

Q.38 Let G be any connected, weighted, undirected graph. 

I. G has a unique minimum spanning tree, if no two edges of G have the same weight. II. G has a unique minimum spanning tree, if, for every cut of G, there is a unique 

minimum-weight edge crossing the cut. 

Which of the above two statements is/are TRUE? 

(A) I only 

(B) II only 

(C) Both I and II 

(D) Neither I nor II 

Q.39 Consider the following snapshot of a system running n concurrent processes. Process i is holding currently Xin _i instances of exactly two instances of a resource R, 1 ≤ i ≤ n. Assume that all instances of R are use. Further, for all i, process i can place R while holding processes p the and q Xsuch _i instances that it already Y_p = Y_q a request for at most has. Of the n processes, Y_i additional there are = 0. Which one of the following conditions guarantees that no other process apart from p and q can complete execution? 

(A) X_p + X_q < Min {Y_k | 1 ≤ k ≤ n ,k ≠ p,k ≠ q} 

(B) X_p + X_q < Max {Y_k | 1 ≤ k ≤ n ,k ≠ p,k ≠ q} 

(C) Min (X_p ,X_q) ≥ Min {Y_k | 1 ≤ k ≤ n ,k ≠ p,k ≠ q} 

(D) Min (X_p,X_q) ≤ Max {Y_k | 1 ≤ k ≤ n ,k ≠ p,k ≠ q} 

Q.40 Consider the following statements: 

I. The smallest element in a max-heap is always at a leaf node 

II. The second largest element in a max-heap is always a child of the root node 

III. A max-heap can be constructed from a binary search tree in Θ(n) time 

IV. A binary search tree can be constructed from a max-heap in Θ(n) time 

Which of the above statements are TRUE? 

(A) I, II and III 

(B) I, II and IV 

(C) I, III and IV 

(D) II, III and IV 

Q.41 Consider the following four processes with arrival times (in milliseconds) and their length of CPU bursts (in milliseconds) as shown below: 

These processes are run on a single processor using preemptive Shortest Remaining Time First scheduling algorithm. If the average waiting time of the processes is 1 millisecond, then the value of Z is________. 

Q.42 The index node (inode) of a Unix-like file system has 12 direct, one single-indirect and one double-indirect pointers. The disk block size is 4 kB, and the disk block address is 32-bits long. The maximum possible file size is (rounded off to 1 decimal place) _________ GB. 

Q.43 Consider the augmented grammar given below: 

S’ → S 

S → 〈L〉 | id

L → L,S | S 

Let I₀ = CLOSURE ({[S’ → •S]}). The number of items in the set GOTO (I₀, 〈 ) is: ________. 

Q.44 Consider the following matrix: 

The absolute value of the product of Eigenvalues of R is . 

Q.45 A certain processor deploys a single-level cache. The cache block size is 8 words and the word size is 4 bytes. The memory system uses a 60-MHz clock. To service a cache miss, the memory controller first takes 1 cycle to accept the starting address of the block, it then takes 3 cycles to fetch all the eight words of the block, and finally transmits the words of the requested block at the rate of 1 word per cycle. The maximum bandwidth for the memory system when the program running on the processor issues a series of read operations is __________× 10⁶ bytes/sec. 

Q.46 Let T be a full binary tree with 8 leaves. (A full binary tree has every level full.) Suppose two leaves a and b of T are chosen uniformly and independently at random. The expected value of the distance between a and b in T (i.e., the number of edges in the unique path between a and b) is (rounded off to 2 decimal places) . 

Q.47 Suppose Y is distributed uniformly in the open interval (1,6). The probability that the polynomial 3x² + 6xY + 3Y + 6 has only real roots is (rounded off to 1 decimal place) ________. 

Q.48 Let Σ be the set of all bijections from {1,…,5} to {1,…,5}, where id denotes the identity function, i.e. id(j) = j,∀j. Let ∘ denote composition on functions. For a string x = xConsider ₁ x₂ ⋯x_n the ∈ language Σⁿ, n ≥ 0 , L let π(x) = = {x ∈ Σ^∗| xπ(x) ₁ ∘ x₂ = ∘ id ⋯∘ }. x_nThe . minimum number of states in any DFA accepting L is . 

Q.49 Consider that 15 machines need to be connected in a LAN using 8-port Ethernet switches. Assume that these switches do not have any separate uplink ports. The minimum number of switches needed is__________. 

Q.50 What is the minimum number of 2-input NOR gates required to implement a 4-variable function expressed in sum-of-minterms form as f = ∑ (0, 2, 5, 7, 8, 10, 13, 15)? Assume that all the inputs and their complements are available. 

Q.51 A relational database contains two tables Student and Performance as shown below: 

Student Roll_no. Student_name 1 Amit 2 Priya 3 Vinit 4 Rohan 5 Smita 

The primary key of the Student table is Roll_no. For the Performance table, the columns Roll_no. and Subject_code together form the primary key. Consider the SQL query given below: 

SELECT S.Student_name, sum(P.Marks)

FROM Student S, Performance P

WHERE P.Marks > 84

GROUP BY S.Student_name;

The number of rows returned by the above SQL query is ________. 

Q.52 Consider the following C program: 

#include <stdio.h>

int main(){

float sum = 0.0, j = 1.0, i = 2.0;

while (i/j > 0.0625){

j = j + j;

sum = sum + i/j;

printf(“%f\n”, sum);

}

return 0;

}

The number of times the variable sum will be printed, when the above program is executed, is _________________.

Q.53 Consider the following C program: 

#include <stdio.h>

int main()

{

int a[] = {2, 4, 6, 8, 10};

int i, sum = 0, *b = a + 4;

for (i = 0; i < 5; i++)

sum = sum + (*b – i) – *(b – i);

printf (“%d\n”, sum);

return 0;

}

The output of the above C program is __________.

Q.54 In an RSA cryptosystem, the value of the public modulus parameter n is 3007. If it is also known that φ(n) = 2880, where φ() denotes Euler’s Totient Function, then the prime factor of n which is greater than 50 is ____________________. 

Q.55 Consider the following relations P(X,Y,Z), Q(X,Y,T) and R(Y,V). 

How many tuples will be returned by the following relational algebra query? 

Π_𝑋(𝜎(𝑃.𝑌=𝑅.𝑌 ∧ 𝑅.𝑉=V2)(𝑃×𝑅)) − Π_𝑋(𝜎(𝑄.𝑌=𝑅.𝑌 ∧ 𝑄.𝑇>2)(𝑄×𝑅))

Answer: