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GATE2017252
X bullocks and Y tractors take $8$ days to plough a field. If we have the number of bullocks and double the number of tractors, it takes $5$ days to plough the same field. How many days will it take X bullocks alone to plough the field? $30$ $35$ $40$ $45$
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GATE2019155
A project consists of six activities. The immediate predecessor of each activity and the estimated duration is also provided in the table below: ... amount of time, the maximum duration (in weeks) of the activity $S$ without delaying the completion of the project is ________
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GATE2019154
Five jobs (J1, J2, J3, J4 and J5) need to be processes in a factory. Each job can be assigned to any of the five different machines (M1, M2, M3, M4 and M5). The time durations taken (in minutes) by the machines for each of the jobs, are given in the table. However, each ...
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GATE2019153
Taylor’s tool life equation is given by $VT^n=C$, where $V$ is in $m/min$ and $T$ is in $min$. In a turning operation, two tools X and Y are used. For tool X, $n=0.3$ and $C=60$ and for tool Y, $n=0.6$ and $C=90$. Both the tools will have the same tool life for the cutting speed (in $m/min$, round off to one decimal place) of ________
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GATE2019152
In ASA system, the side cutting and end cutting edge angles of a sharp turning tool are $45^{\circ}$ and $10^{\circ}$, respectively. The feed during cylindrical turning is $0.1 \: mm/rev$. The center line average surface roughness (in $\mu m$, round off to one decimal place) of the generated surface is ______
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GATE2019151
The value of the following definite integral is ______ (round off to three decimal places) $\int_1^e (x \: \ln \: x) dx$
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GATE2019150
A gas turbine with air as the working fluid has an isentropic efficiency of $0.70$ when operating at a pressure ratio of $3$. Now, the pressure ratio of the turbine is increased to $5$, while maintaining the same inlet conditions. Assume air as a ... both the cases, the isentropic efficiency of the turbine at the pressure ratio of $5$ is _______ (round off to two decimal places)
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GATE2019149
A steam power cycle with regeneration as shown below on the $T$s diagram employs a single open feedwater heater for efficiency improvement. The fluid mix with each other in an open feedwater heater. The turbine is isentropic and the input (bleed) to the feedwater heater ... the turbine as a percentage of the total mass flow rate at the int=let to the turbine at state $1$ is _______
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GATE2019148
If one mole of $H_2$ has occupies a rigid container with a capacity of $1000$ litres and the temperature is raised from $27^{\circ} C$ to $37^{\circ} C$, the change in pressure of the contained gas (round off to two decimal places), assuming ideal gas behaviour, is _______ Pa. $(R=8.314 \: J/mol \cdot K)$
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GATE2019147
Three slabs are joined together as shown in the figure. There is no thermal contact resistance at the interfaces. The center slab experiences a nonuniform internal heat generation with an average value equal to $10000 \: Wm^{3}$, while the left and right slabs have no ... $T_1$ is measured to be $100^{\circ} C$, the right extreme face temperature $T_2$ is ______$^{\circ} C$.
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GATE2019146
A cube of side $100 \: mm$ is placed at the bottom of an empty container on one of its faces. The density of the material of the cube is $800 \: kg/m^3$. Liquid of density $1000 \: kg/m^3$ is now poured into the container. The minimum height to which the loquid needs to be poured into the container for the cube to just lift up is ____$mm$.
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GATE2019145
Two immiscible, incompressible, viscous fluids having same densities but different viscosities are contained between two infinite horizontal parallel plates, $2 \: m$ apart as shown below. The bottom plate is fixed and the upper plate moves to the right with a constant velocity ... fluid, $\mu_1$, then the velocity at the interface (round off to two decimal places) is _______ $m/s$.
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GATE2019144
A single block brake with a short shoe and torque capacity of $250 \: N \cdot m$ is shown. THe cylindrical brake drum rotates anticlockwise at $100 \: rpm$ and the coefficient of friction is $0.25$. The value of $a$ in mm (round off to one decimal place), such that the minimum actuating force $P$ is $2000 \: N$, is ___________
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GATE2019143
A uniform thin disk of mass $1 \: kg$ and radius $0.1 \: m$ is kept on a surface as shown in the figure. A spring of stiffness $k_1=400 \: N/m$ is connected to the disk center $A$ and another spring of stiffness $k_2=100 \: N/m$ ... the disk. For small disturbance from the equilibrium, the natural frequency of vibration of the system is _____ $rad/s$ (round off to oe decimal place).
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GATE2019142
At a critial point in a component, the state of stress is given as $\sigma_{xx}=100 \: MPa, \: \sigma_{yy}=220 \: MPa, \: \sigma_{xy}= \sigma_{yx} = 80 \: MPa$ and all other stress cmponents are zero. The yield strength of the material is $468 \: MPa$ The factor of safety on the basis of maximum shear stress theory is ______ (round off to one decimal place)
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GATE2019141
In a UTM experiment, a sample of length $100 \: mm$, was loaded in tension until failure. The failure load was $40 \: kN$. The displacement, measured using the crosshead motion, at failure, was $15 \: mm$. The compliance of the UTM is constant and is given $5 \times 10^{8} \: m/N$. The strain at failure in the sample is ______$\%$
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GATE2019139
Consider an elastic straight beam of length $L= 10 \pi \: m$, with square crosssection of side $a=5 \: mm$, and Young's modulus $E=200 \: GPa$. This straight beam was bent in such a way that the two ends meets, to form a circle ... $R$. Assuming that EulerBernoulli beam theory is applicable to this bending problem, the maximum tensile bending stress in the bent beam is _____ $MPa$.
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GATE2019138
A truss is composed of members AB, BC, CD, AD and BD, as shown in the figure. A vertical load of $10 \: kN$ is applied at point D. The magnitude of force (in kN) in the member BC is ______
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GATE2019137
Match the following sand mold casting defects with their respective causes. ... $P3, Q4, R2, S1$ $P2, Q4, R1, S3$ $P3, Q4, R1, S2$
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GATE2019136
A circular shaft having diameter $65.00_{0.05}^{+0.01} \: mm$ is manufactured by turning process. A $50 \: \mu m$ thick coating of TiN is deposited on the shaft. Allowed variation in TiN film thickness is $\pm 5 \mu m$. The minimum hole diameter (in mm) to just provide clearance fit is $65.01$ $65.12$ $64.95$ $65.10$
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GATE2019135
In orthogonal turning of a cylindrical tube of wall thickness $5 \: mm$, the axial and the tangential cutting forces were measured as $1259 \: N$ and $1601 \:N$, respectively. The measured chip thickness after machining was found to be $0.3 \: mm$ ... solution, the shear strength of the material is closest to $722 \: MPa$ $920 \: MPa$ $200 \: MPa$ $875 \: MPa$
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GATE2019134
A planestrain compression (forgoing) of a block is shown in the figure. The strain in the $z$direction is zero. The yield strength $(S_y)$ in uniaxial tension/compression of the material of the block is $300 \: MPa$ and it follows the Tresca (maximum shear stress) criterion. ... $340 \: MPa$ (compressive) $340 \: MPa$ (tensile) $260 \: MPa$ (compressive) $260 \: MPa$ (tensile)
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GATE2019133
A gas is heated in a duct as it flows over a resistance heater. Consider a $101 \: kW$ electric heating system. The gas enters the heating section of the duct at $100 \: kPa$ and $27^{\circ}$ with a volume flow rate of $51 \: kW$, the exit temperature of the gas is (Assume constant pressure, ... $32^{\circ} C$ $37^{\circ} C$ $53^{\circ} C$ $76^{\circ} C$
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100
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GATE2019140
Consider a prismatic straight beam of length $L=\pi \: m$, pinned at the two ends as shown in the figure. The beam has a square crosssection of side $p=6 \: mm$. The Young’s modulus $E=200 \: GPa$, and the coefficient of thermal expansion $\alpha = 3 \times 10^{6} K^{1}$. The minimum temperature rise required to cause Euler buckling of the beam is _______$K$.
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GATE2019132
The wall of a constant diameter pipe of length $1 \: m$ is heated uniformly with flux $q''$ by wrapping a heater coil around it. The flow at the inlet to the pipe is hydrodynamically fully developed. The fluid is incompressible and the flow is assumed to be laminar and steady ... the location P, Q and R, the flow is thermally developed at P, Q and R P and Q only Q and R only R only
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GATE2019131
The rotor of a turbojet engine of an aircraft has a mass $180 \: kg$ and polar moment of inertia $10 \: kg \cdot m^2$ about the rotor axis. The rotor rotates at a constant speed of $1100 \: rad/s$ in the clockwise direction when viewed from the front of the aircraft. The ... and the nose goes down $162.9 \: N \cdot m$ and the nose goes up $162.9 \: N \cdot m$ and the nose goes down
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100
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GATE2019130
In a four bar planar mechanism shown in the figure, $AB= 5 \: cm, AD=4 \: cm $ and $DC=2 \: cm$. In the configuration shown, both AB and DC are perpendicular to AD. The bar AB rotates with an angular velocity of $10 \: rad/s$. The magnitude of angular velocity (in rad/s) of bar DC at this instant is $0$ $10$ $15$ $25$
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GATE2019129
A car having weight $W$ is moving in the direction as shown in the figure. The center of gravity (CG) of the car is located at height $h$ from the ground, midway between the front and rear wheels. The distance between real and front wheel is $l$. The acceleration of the car is $a$, and ... $R_f=R_r = \frac{W}{2}+\frac{W}{g} \big( \frac{h}{l} \big) a$
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GATE2019128
The variable $x$ takes a value between $0$ and $10$ with uniform probability distribution. The variable $y$ takes a value between $0$ and $20$ with uniform probability distribution. The probability of the sum of variables $(x+y)$ being greater then $20$ is $0$ $0.25$ $0.33$ $0.50$
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GATE2019127
A harmonic function is analytic if it satisfies the Laplace equation. If $u(x,y)=2x^22y^2+4xy$ is a harmonic function, then it is conjugate harmonic function $v(x,y)$ is $4xy2x^2+2y^2+ \text{constant}$ $4y^24xy + \text{constant}$ $2x^22y^2+ xy + \text{constant}$ $4xy+2x^22y^2+ \text{constant}$
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GATE2019126
The set of equations $x+y+z=1$ $axay+3z=5$ $5x3y+az=6$ has infinite solutions, if $a=$ $3$ $3$ $4$ $4$
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GATE2019125
Consider the stressstrain curve for an ideal elasticplastic strain hardening metal as shown in the figure. The metal was loaded in uniaxial tension starting from $O$. Upon loading, the stressstrain curve passes through initial yield point at $P$, and then ... same specimen is reloaded in tension from point $R$, the value of stress at which the material yields again is _______ MPa.
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GATE2019124
Air of mass $1$ kg, initially at $300$ K and $10$ bar, is allowed to expand isothermally till it reaches a pressure of $1$ bar. Assuming air as an ideal gas with gas constant of $0.287 \: kJ/kg.K$, the change in entropy of air (in $kJ/kg.K$, round off to two decimal places) is ______
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Apr 17
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GATE2019123
Water flows through a pipe with a velocity given by $\overrightarrow{V}= \big( \frac{4}{t}+x+y \big) \hat{j} \: m/s$, where $\hat{j}$ is teh unit vector in the $y$ direction, $t(>0)$ is in seconds, and $x$ and $y$ are in meters. The magnitude of total acceleration at the point $(x,y)=(1,1)$ at $t=2\: s$ is ______$m/s^2$
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GATE2019122
During a high cycle fatigue test, a metallic specimen is subjected to cyclic loading with a mean stress of $+140$ MPa, and a minimum stress of $70$ MPa. The $R$ration (minimum stress to maximum stress) for this cyclic loading is _____ (round off to one decimal place)
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GATE2019121
A solid cube of side $1$ m is kept at a room temperature of $32^{\circ} C$. The coefficient of linear thermal expansion of the cube material is $1 \times 10^{5} / ^{\circ}C$ and the bulk modulus is $200$ GPa. If the cube is constrained all around and heated uniformly to $42^{\circ}C$, then the magnitude of volumetric (mean) stress (in MPa) included due to heating is _______
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GATE2019120
A cylindrical rod of diameter $10$ mm and length $0.1$m fixed at one end. The other end is twisted by an angle of $10^{\circ}$ by applying a torque. If the maximum shear strain in the rod is $p \times 10^{3}$, then $p$ is equal to ____ (round off to two decimal places).
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GATE2019119
A block of mass $10$ kg rests on a horizontal floor. The acceleration due to gravity is $9.81 \: m/s^2$. The coefficient of static friction between the floor and the block is $0.2$. A horizontal force of $10$ N is applied on the block as shown in the figure. The magnitude of force of friction (in N) on the block is _____
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GATE2019118
Evaluation of $\int_2^4 x^3 dx$ using a $2$equalsegment trapezoidal rule gives a value of _______
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GATE2019117
The table presents the demand of a product. By simple threemonths moving average method, the demandforecast of the product for the month of September is ... $490$ $510$ $530$ $536.67$
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