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#GATE QUESTION BANK
The minimum number of equal length subintervals needed to approximate $\int_{1}^{2}xe^xdx$ to an accuracy of atleast (10^(-6))/3 using trapezoidal rule is __________.

edited Jul 15 in Numerical Methods by Gokulan K (120 points)

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GATE2020-ME-2-GA-5
If $P,Q,R,S$ are four individuals, how many teams of size exceeding one can be formed, with $Q$ as a member? $5$ $6$ $7$ $8$

answered Jul 15 in General Aptitude by prnv28 (140 points)

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GATE2020-ME-2-GA-3
Select the word that fits the analogy: Do:Undo :: Trust: _____ Entrust Intrust Distrust Untrust

answered Jul 15 in General Aptitude by TheAnteamatter (260 points)

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GATE2020-ME-2-GA-1
This book, including all its chapters,______interesting. The students as well as the instructor_____ in agreement about it. is, was are, are is, are were, was

answered Jul 15 in General Aptitude by TheAnteamatter (260 points)

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GATE2020-ME-2-GA-4
Stock markets _____at the news of the coup. poised plunged plugged probed

answered Jul 15 in General Aptitude by TheAnteamatter (260 points)

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GATE2020-ME-2-GA-7
Select the next element of the series: Z, WV, RQP,___ LKJI JIHG KJIH NMLK

answered Jul 15 in General Aptitude by TheAnteamatter (260 points)

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GATE2020-ME-2-GA-2
People were prohibited_____ their vehicles near the entrance of the main administrative building. to park from parking parking to have parked

answered Jul 3 in General Aptitude by Jay KHINCHI (220 points)

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GATE2020-ME-1: 52
One kg of air, initially at a temperature of $127^{\circ}C$ , expands reversibly at a constant pressure until the volume is doubled. If the gas constant of air is $287\: J/kg.K$, the magnitude of work transfer is ________ $kJ$ (round off to $2$ decimal places).

answered Jul 3 in Others by nadim96 (190 points)

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Self doubt
With increase in pressure the bulk modulus of elasticity__?

answered Jul 3 in Fluid Mechanics by nadim96 (190 points)

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GATE2020-ME-2-5
The value of the following complex integral, with $C$ representing the unit circle centered at origin in the counterclockwise sense, is: $\displaystyle{}\int_{C}\frac{z^{2}+1}{z^{2}-2z}dz$ $8\pi i$ $-8\pi i$ $-\pi i$ $\pi i$

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 55
The indicated power developed by an engine with compression ratio of $8$, is calculated using an air-standard Otto cycle (constant properties). The rate of heat addition is $10\: kW$ ... of the engine is $80$ percent. The brake power output of the engine is _________$kW$ (round off to one decimal place).

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 54
For a Kaplan (axial flow) turbine, the outlet blade velocity diagram at a section is shown in the figure. The diameter at this section is $3\:m$.The hub and tip diameters of the blade are $2\:m$ and $4\:m$, respectively. The water volume flow ... rotational speed of the turbine is $300\:rpm$. The blade outlet angle $\beta$ is ________ degrees (round off to one decimal place).

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 53
For an ideal Rankine cycle operating between pressures of $30$ bar and $0.04$ bar,the work output from the turbine is $903\: kJ/kg$ and the work input to the feed pump is $3\: kJ/kg$. The specific steam consumption is _________ $kg/kW.h$ round off to $2$ decimal places).

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 51
Air (ideal gas) enters a perfectly insulated compressor at a temperature of $310\: K$. The pressure ratio of the compressor is $6$. Specific heat at constant pressure for air is $1005\: J/kg . K$ and ratio of specific heats at constant pressure ... difference in enthalpies of air between the exit and the inlet of the compressor is _________ $kJ/kg$ (round off to nearest integer).

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 50
Air discharges steadily through a horizontal nozzle and impinges on a stationary vertical plate as shown in figure. The inlet and outlet areas of the nozzle are $0.1\:m^{2}\:\text{and}\:0.02\:m^{2}$ ... is $0.36\:kPa$, the gauge pressure at point $O$ on the plate is __________ $kPa$ (round off to two decimal places).

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 49
Consider steady, viscous, fully developed flow of a fluid through a circular pipe of internal diameter $\text{D}$. We know that the velocity profile forms a paraboloid about the pipe centre line, given by: $V=-C\left(r^{2}-\dfrac{D^{2}}{4}\right) m/s$ ... the control surface $\text{A-B}$, as shown in the figure, is proportional to $D^{n}$. The value of $n$ is ________.

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 48
$\textbf{Consider two cases as below.}$ $\textbf{Case 1:}$ A company buys $1000$ pieces per year of a certain part from vendor $'X'.$ The changeover time is $2$ hours and the price is $Rs.\: 10$ per piece. The holding cost rate per part is $10\%$ ... reduction in the annual cost of $\text{Case 2}$, as compared to $\text{Case 1}$ is __________ (round off to $2$ decimal places).

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 47
Two business owners Shveta and Ashok run their business in two different states. Each of them, independent of the other, produces two products $A$ and $B$, sells them at $Rs.\:2,000$ per kg and $Rs.\:3,000$ per kg, respectively, and uses ... value of the difference in daily (optimal) revenue of Shveta and Ashok is _________ thousand Rupees (round off to $2$ decimal places).

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 46
The thickness of a steel plate with material strength coefficient of $210\: MPa$, has to be reduced from $20\: mm$ to $15\: mm$ in a single pass in a two-high rolling mill with a roll radius of $450\: mm$ and rolling velocity of $28\: m/min$. If the ... ). Note: $\text{Average Flow Stress = Material Strength Coefficient}\times \dfrac{\left (\text{True Strain} \right )^{n}}{(1+n)}$

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 45
In a turning process using orthogonal tool geometry, a chip length of $100\: mm$ is obtained for an uncut chip length of $250\: mm$. The cutting conditions are: cutting speed $= 30\: m/min$, rake angle $ = 20^{\circ}$. The shear plane angle is _______ degrees (round off to one decimal place).

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 43
The following data applies to basic shaft system: tolerance for hole$ = 0.002\: mm$, tolerance for shaft$ = 0.001\: mm$, allowance $= 0.003\: mm$, basic size $= 50\: mm$. The maximum hole size is _______ $mm$ (round off to $3$ decimal places).

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 42
A slot of $25\:mm\times 25\:mm$ is to be milled in a workpiece of $300\: mm$ length using a side and face milling cutter of diameter $100\: mm$, width $25\: mm$ and having $20$ teeth.For a depth of cut $5\: mm$ ... and approach and over travel distance of $5\: mm$ each, the time required for milling the slot is ________ minutes (round off to one decimal place).

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 41
The magnitude of reaction force at joint $C$ of the hinge-beam shown in the figure is __________$kN$ (round off to $2$ decimal places).

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 40
The barrier shown between two water tanks of unit width $(1\: m)$ into the plane of the screen in modeled as a cantilever. Taking the density of water as $1000\:kg/m^{3}$ , and the acceleration due to gravity as $10\:m/s^{2}$ , the maximum absolute bending moment developed in the cantilever is _________$kN\cdot m$ (round off to the nearest integer).

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 39
A rectangular steel bar of length $500\: mm$, width $100\: mm$, and thickness $15\: mm$ is cantilevered to a $200\: mm$ steel channel using $4$ bolts, as shown For an external load of $10\: kN$ applied at the tip of the steel bar, the resultant shear load on the bolt at $B$, is _______$kN$ (round off to one decimal place).

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 36
An analytic function of a complex variable $z=x + iy \left ( i=\sqrt{-1} \right )$ is defined as $f\left ( z \right )=x^{2}-y^{2}+i\psi \left ( x,y \right ),$ where $\psi \left ( x,y \right )$ is a real function. The value of the imaginary part of $f(z)$ at $z=\left ( 1+i \right )$ is __________ (round off to $2$ decimal places).

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 35
Consider two exponentially distributed random variables $\text{X and Y}$, both having a mean of $0.50$. Let $Z=X+Y$ and $r$ be the correlation between $\text{X and Y}$.If the variance of $Z$ equals $0$, then the value of $r$ is __________ (roundoff to $2$ decimal places).

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 34
A small metal bead $(\text{radius}\: 0.5\: mm)$, initially at $100^{\circ}C$ , when placed in a stream of fluid at $20^{\circ}C$ , attains a temperature of $28^{\circ}C$ in $4.35$ ... heat transfer coefficient $(in\:W/m^{2}.K)$ between the metal bead and the fluid stream is $283.3$ $299.8$ $149.9$ $449.7$

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 33
For an assembly line, the production rate was $4$ pieces per hour and the average processing time was $60$ minutes. The $\text{WIP}$ inventory was calculated. Now, the production rate is kept the same, and the average processing time is brought down by $30$ percent. As ... , the $\text{WIP}$ inventory decreases by $25\%$ increases by $25\%$ decreases by $30\%$ increases by $30\%$

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 32
A strip of thickness $40\:mm$ is to be rolled to a thickness of $20\:mm$ using a two-high mill having rolls of diameter $200\:mm$. Coefficient of friction and arc length in $mm$, respectively are $0.45\:\text{and}\:38.84$ $0.39\:\text{and}\:38.84$ $0.39\:\text{and}\:44.72$ $0.45\:\text{and}\:44.72$

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 31
A rigid mass-less rod of length $L$ is connected to a disc (pulley) of mass $m$ and radius $r = L/4$ through a friction-less revolute joint. The other end of that rod is attached to a wall through a friction-less hinge. A spring of stiffness $2k$ is attached to the rod at its mid-span. ... ${\frac{3}{\sqrt{2}}}\sqrt{\frac{k}{m}}$ $\sqrt{3}\sqrt{\frac{k}{m}}$ $\sqrt{\frac{k}{m}}$

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 30
The truss shown in the figure has four members of length $\text{l}$ and flexural rigidity $\text{EI}$, and one member of length $l\sqrt{2}$ and flexural rigidity $\text{4EI}$. The truss is loaded by a pair of forces of magnitude $\text{P}$ ... $\frac{\pi ^{2}EI}{l^{2}}$ $\frac{2\pi ^{2}EI}{l^{2}}$ $\frac{\pi ^{2}EI}{2l^{2}}$

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 29
The $2$ kg block shown in the figure (top view) rests on a smooth horizontal surface and is attached to a massless elastic cord that has a stiffness $5\: N/m$. The cord hinged at $\text{O}$ is initially unstretched and always remains elastic. The block is given a velocity $v$ ... $0.4\: m$ is $0.83$ $1.07$ $1.36$ $1.50$

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 26
The evaluation of the definite integral $\int ^{1.4}_{ – 1}x \mid x \mid dx$ by using Simpson’s $1/3^{rd}$ (one - third) rule with step size $h=0.6$ yields $0.914$ $1.248$ $0.581$ $0.592$

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 25
In a concentric tube counter-flow heat exchanger, hot oil enters at $102^{\circ}C$ and leaves at $65^{\circ}C$. Cold water enters at $25^{\circ}C$ and leaves at $42^{\circ}C$. The log mean temperature difference $(LMTD)$ is ________ $^{\circ}C$ (round off to one decimal place).

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 24
The compressor of a gas turbine plant, operating on an ideal intercooled Brayton cycle, accomplishes an overall compression ratio of $6$ in a two-stage compression process. Intercooling is used to cool the air coming out from the first stage to the ... gas are constant, the intercooling pressure for minimum compressor work is __________ $kPa$ (rounded off to $2$ decimal places).

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 23
A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one woman will be selected is _______(round off to $2$ decimal places).

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 22
A sheet metal with a stock hardness of $250\: HRC$ has to be sheared using a punch and a die having a clearance of $\text{1 mm}$ between them. If the stock hardness of the sheet metal increases to $400\: HRC$, the clearance between the punch and the die should be _________ $mm.$

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 20
A flywheel is attached to an engine to keep its rotational speed between $100\: rad/s$ and $110\: rad/s $. If the energy fluctuation in the flywheel between these two speeds is $1.05\: kJ$ then the moment of inertia of the flywheel is____________$kg \cdot m^{2}$ (rounded off to $2$ decimal places).

retagged May 5 in Others by soujanyareddy13 (100 points)

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GATE2020-ME-1: 19
For three vectors $\overrightarrow{A}=2\widehat{j}-3\widehat{k},\:\overrightarrow{B}=-2\widehat{i}+\widehat{k}\:\:\text{and}\:\overrightarrow{C}=3\widehat{i}-\widehat{j},\:\text{where}\:\widehat{i},\:\widehat{j}\:\text{and}\:\widehat{k}$ are ... system, the value of $\left ( \overrightarrow{A}.\left ( \overrightarrow{B}\times \overrightarrow{C} \right )+6 \right )$ is __________.

retagged May 5 in Others by soujanyareddy13 (100 points)

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