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GATE201365
After several defeats in wars, Robert Bruce went in exile and wanted to commit suicide. Just before committing suicide, he came across a spider attempting tirelessly to have its net. Time and again, the spider failed but that did not deter it to refrain ... is the pillar of success. Honesty is the best policy. Life begins and ends with adventures. No adversity justifies giving up hope.
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GATE201364
The current erection cost of a structure is $Rs$. $13,200$. If the labour wages per day increase by $1/5$ of the current wages and the working hours decrease by $1/24$ of the current period, then the new cost of erection in $Rs$. is $16,500$ $15,180$ $11,000$ $10,120$
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GATE201363
Find the sum of the expression $\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+.............+\frac{1}{\sqrt{80}+\sqrt{81}}$ $7$ $8$ $9$ $10$
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GATE201362
A tourist covers half of his journey by train at $60$ $km$/$h$, half of the remainder by bus at $30$ $km$/$h$ and the rest by cycle at $10$ $km$/$h$. The average speed of the tourist in $km$/$h$ during his entire journey is $36$ $30$ $24$ $18$
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GATE201361
Out of all the $2$digit integers between $1$ and $100$, a $2$digit number has to be selected at random. What is the probability that the selected number is not divisible by $7$? $13/90$ $12/90$ $78/90$ $77/90$
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GATE201360
What will be the maximum sum of $44$, $42$, $40$, ...... ? $502$ $504$ $506$ $500$
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GATE201359
Choose the grammatically INCORRECT sentence: He is of Asian origin. They belonged to Africa. They belonged to Africa. They migrated from India to Australia.
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GATE201358
Which one of the following options is the closest in meaning to the word given below? Nadir Highest Lowest Medium Integration
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GATE201357
Were you a bird, you ___________________ in the sky. would fly shall fly should fly shall have flown
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GATE201356
Complete the sentence: Universalism is to particularism as diffuseness is to _______________. specificity neutrality generality adaptation
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GATE201355
In a simple Brayton cycle, the pressure ratio is $8$ and temperatures at the entrance of compressor and turbine are $300$ $K$ and $1400$ $K$, respectively. Both compressor and gas turbine have isentropic efficiencies equal to $0.8$. For the gas, assume a constant value ... and potential energies. The thermal efficiency of the cycle in percentage (%) is $24.8$ $38.6$ $44.8$ $53.1$
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GATE201354
In a simple Brayton cycle, the pressure ratio is $8$ and temperatures at the entrance of compressor and turbine are $300$ $K$ and $1400$ $K$, respectively. Both compressor and gas turbine have isentropic efficiencies equal to $0.8$. For the gas, assume a constant value of $c_p$ ( ... . The power required by the compressor in $kW$/$kg$ of gas flow rate is $194.7$ $243.4$ $304.3$ $378.5$
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Feb 19, 2017
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GATE201353
In orthogonal turning of a bar of $100$ $mm$ diameter with a feed of $0.25$ $mm$/$rev$, depth of cut of $4$ $mm$ and cutting velocity of $90$ $m$/$min$, it is observed that the main (tangential) cutting force is perpendicular to the friction force acting ... tangential) cutting force is $1500$ $N$. The normal force acting at the chiptool interface in $N$ is $1000$ $1500$ $2000$ $2500$
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GATE201352
In orthogonal turning of a bar of $100$ $mm$ diameter with a feed of $0.25$ $mm$/$rev$, depth of cut of $4$ $mm$ and cutting velocity of $90$ $m$/$min$, it is observed that the main (tangential) cutting force is perpendicular to the friction force acting at ... (tangential) cutting force is $1500$ $N$. The orthogonal rake angle of the cutting tool in degree is zero $3.58$ $5$ $7.16$
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GATE201351
Water (specific heat, $c_p$ = $4.18$ $kJ$/$kgK$) enters a pipe at a rate of $0.01$ $kg$/$s$ and a temperature of $20^0$ $C$.The pipe, of diameter $50$ $mm$ and length $3$ $m$, is subjected to a wall heat flux ${q_{w}}''$ in $W$/$m^2$: If $W$ ... $ $W$/$m^2$K$, the temperature in $_{}^{0}\textrm{C}$ at the inner surface of the pipe at the outlet is $71$ $76$ $79$ $81$
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GATE201350
Water (specific heat, $c_p$ = $4.18$ $kJ$/$kgK$) enters a pipe at a rate of $0.01$ $kg$/$s$ and a temperature of $20^0$ $C$.The pipe, of diameter $50$ $mm$ and length $3$ $m$, is subjected to a wall heat flux ${q_{w}}''$ in $W$/$m^2$ ... of flow (x = $0$ at the inlet), the bulk mean temperature of the water leaving the pipe in $_{}^{0}\textrm{C}$ is $42$ $62$ $74$ $104$
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Feb 19, 2017
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GATE201349
A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material details. width of the plate w = $200$ $mm$, thickness of the plate $t$ = $5$ $mm$, number of rivets $n$ = $3$, diameter of the rivet $d_r$ ... If the plates are to be designed to avoid tearing failure, the maximum permissible load $P$ in $kN$ is $83$ $125$ $167$ $501$
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Feb 19, 2017
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GATE201348
A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material details. width of the plate w = $200$ $mm$, thickness of the plate $t$ = $5$ $mm$, number of rivets $n$ = $3$, diameter of the rivet $d_r$ ... are to be designed to avoid crushing failure, the maximum permissible load $P$ in $kN$ is $7.50$ $15.00$ $22.50$ $30.00$
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Feb 19, 2017
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GATE201347
The value of the definite integral $\int_{1}^{e}\sqrt{x}ln(x)dx$ is $\frac{4}{9}\sqrt{e^3}+\frac{2}{9}$ $\frac{2}{9}\sqrt{e^3}\frac{4}{9}$ $\frac{2}{9}\sqrt{e^3}+\frac{4}{9}$ $\frac{4}{9}\sqrt{e^3}\frac{2}{9}$
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GATE201346
The solution to the differential equation $\frac{d^2u}{dx^2}k\frac{du}{dx}=0$ where $k$ is a constant, subjected to the boundary conditions $u(0)$ = $0$ and $u(L)$ = $U$, is $u=U\frac{x}{L}$ $u=U(\frac{1e^{kx}}{1e^{kL}})$ $u=U(\frac{1e^{kx}}{1e^{kL}})$ $u=U(\frac{1+e^{kx}}{1+e^{kL}})$
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GATE201345
The probability that a student knows the correct answer to a multiple choice question is $\frac{2}{3}$ . If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is $\frac{1}{4}$. Given that the student has answered ... the student knows the correct answer is $\frac{2}{3}$ $\frac{3}{4}$ $\frac{5}{6}$ $\frac{8}{9}$
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Feb 19, 2017
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GATE201344
The pressure, temperature and velocity of air flowing in a pipe are $5$ $bar$, $500$ $K$ and $50$ $m$/$s$, respectively. The specific heats of air at constant pressure and at constant volume are $1.005$ $kJ$/$kgK$ and $0.718$ $kJ$/$kgK$, respectively. Neglect potential ... $bar$ and $300$ $K$, respectively, the available energy in $kJ$/$kg$ of the air stream is $170$ $187$ $191$ $213$
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Feb 19, 2017
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GATE201343
A hinged gate of length $5$ $m$, inclined at $30^0$ with the horizontal and with water mass on its left, is shown in the figure below. Density of water is $1000$ $kg$/$m^3$. The minimum mass of the gate in $kg$ per unit width (perpendicular to the plane of paper), required to keep it closed is $5000$ $6600$ $7546$ $9623$
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Feb 19, 2017
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GATE201342
Two large diffuse gray parallel plates, separated by a small distance, have surface temperatures of $400$ $K$ and $300$ $K$. If the emissivities of the surfaces are $0.8$ and the StefanBoltzmann constant is $5.67$ × $10^{8}$ $W$/$m^2$ $K^4$, the net radiation heat exchange rate in $kW$/$m^2$ between the two plates is $0.66$ $0.79$ $0.99$ $3.96$
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Feb 19, 2017
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GATE201341
A simply supported beam of length $L$ is subjected to a varying distributed load $\sin(3\pi x/L) Nm^{1}$ , where the distance $x$ is measured from the left support. The magnitude of the vertical reaction force in $N$ at the left support is zero $L/3\pi$ $L/\pi$ $2L/\pi$
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Feb 19, 2017
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GATE201340
A bar is subjected to fluctuating tensile load from $20$ $kN$ to $100$ $kN$. The material has yield strength of $240$ $MPa$ and endurance limit in reversed bending is $160$ $MPa$. According to the Soderberg principle, the area of crosssection in $mm^2$ of the bar for a factor of safety of $2$ is $400$ $600$ $750$ $1000$
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Feb 19, 2017
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GATE201339
A single degree of freedom system having mass $1$ $kg$ and stiffness $10$ $kN/m$ initially at rest is subjected to an impulse force of magnitude $5$ $kN$ for $10^{4}$ seconds. The amplitude in $mm$ of the resulting free vibration is $0.5$ $1.0$ $5.0$ $10.0$
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GATE201338
During the electrochemical machining $(ECM)$ of iron $(atomic weight = 56, valency = 2)$ at current of $1000$ $A$ with $90$% current efficiency, the material removal rate was observed to be $0.26 gm/s$. If Titanium $(atomic weight = 48, valency = 3)$ is machined by the ... $90$% current efficiency, the expected material removal rate in $gm/s$ will be $0.11$ $0.23$ $0.30$ $0.52$
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GATE201337
Cylindrical pins of $25^{\begin{Bmatrix} +0.020\\ +0.010 \end{Bmatrix}$}$ $mm$ diameter are electroplated in a shop. Thickness of the plating is $30^{\pm 2.0}$ $micron$. Neglecting gage tolerances, the size of the $GO$ gage in $mm$ to inspect the plated components is $25.042$ $25.052$ $25.074$ $25.084$
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GATE201336
A linear programming problem is shown below. Maximize $3x + 7y$ Subject to $3x + 7y ≤ 10$ $4x + 6y ≤ 8$ $x, y ≥ 0$ It has an unbounded objective function. exactly one optimal solution. exactly two optimal solutions. infinitely many optimal solutions.
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GATE201335
In a $CAD$ package, mirror image of a $2D$ point $P(5,10)$ is to be obtained about a line which passes through the origin and makes an angle of $45^0$ counterclockwise with the $X$axis. The coordinates of the transformed point will be $(7.5, 5)$ $(10, 5)$ $(7.5, 5)$ $(10, 5)$
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GATE201334
Two cutting tools are being compared for a machining operation. The tool life equations are: Carbide tool: $VT^{1.6}$ = $3000$ HSS tool: $VT^{0.6}$ = $200$ where $V$ is the cutting speed in $m/min$ and $T$ is the tool life in $min$. The carbide tool will provide higher tool life if the cutting speed in $m/min$ exceeds $15.0$ $39.4$ $49.3$ $60.0$
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GATE201333
A pin jointed uniform rigid rod of weight $W$ and length $L$ is supported horizontally by an external force $F$ as shown in the figure below. The force $F$ is suddenly removed. At the instant of force removal, the magnitude of vertical reaction developed at the support is zero $W/4$ $W/2$ $W$
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GATE201332
A compound gear train with gears $P$, $Q$, $R$ and $S$ has number of teeth $20$, $40$, $15$ and $20$, respectively. Gears $Q$ and $R$ are mounted on the same shaft as shown in the figure below. The diameter of the gear $Q$ is twice that of the gear $R$. If the module of the gear $R$ is $2$ $mm$, the center distance in $mm$ between gears $P$ and $S$ is $40$ $80$ $120$ $160$
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GATE201331
A flywheel connected to a punching machine has to supply energy of $400 Nm$ while running at a mean angular speed of $20 rad/s$. If the total fluctuation of speed is not to exceed $±2%$, the mass moment of inertia of the flywheel in $kg$$m^2$ is $25$ $50$ $100$ $125$
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GATE201330
A steel ball of diameter $60$ $mm$ is initially in thermal equilibrium at $1030^0C$ in a furnace. It is suddenly removed from the furnace and cooled in ambient air at $30^0C$, with convective heat transfer coefficient $h = 20 W/m^2K$. The thermophysical properties of ... time required in seconds to cool the steel ball in air from $1030^0C$ to $430^0C$ is $519$ $931$ $1195$ $2144$
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GATE201329
Water is coming out from a tap and falls vertically downwards. At the tap opening, the stream diameter is $20$ $mm$ with uniform velocity of $2$ $m/s$. Acceleration due to gravity is $9.81$ $m/s^2$. Assuming steady, inviscid flow, constant atmospheric pressure everywhere ... tension effects, the diameter in mm of the stream $0.5$ $m$ below the tap is approximately $10$ $15$ $20$ $25$
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GATE201328
Specific enthalpy and velocity of steam at inlet and exit of a steam turbine, running under steady state, are as given below: Specific enthalpy $(kJ/kg)$ Velocity $(m/s)$ Inlet steam condition $3250$ $180$ Exit steam condition $2360$ $5$ The rate of heat loss from the turbine ... developed in $kW$ by the steam turbine per $kg$ of steam flow rate, is $901.2$ $911.2$ $17072.5$ $17082.5$
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GATE201327
The function $f(t)$ satisfies the differential equation $\frac{d^2f}{dt^2}+f=0$ and the auxiliary conditions, $f(0)=0$, $\frac{d(f)}{d(t)}(0)=4$. The Laplace transform of $f(t)$is given by $\frac{2}{s+1}$ $\frac{4}{s+1}$ $\frac{4}{s^2+1}$ $\frac{2}{s^4+1}$
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GATE201326
The following surface integral is to be evaluated over a sphere for the given steady velocity vector field $F$ = $xi$ + $yj$+ $zk$ defined with respect to a Cartesian coordinate system having $i$, $j$ and $k$ ... and n is the outward unit normal vector to the sphere. The value of the surface integral is $\pi$ $2\pi$ $3\pi/4$ $4\pi$
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