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GATE2017255
In the graph below, the concentration of a particular pollutant in a lake is plotted over (alternate) days of a month in winter (average temperature $10^{\circ} C$) and a month in summer (average temperature $30^{\circ} C$). Consider the following statements based ... days in the winter month. Which one of the following options is correct? Only i Only ii Both i and ii Neither i nor ii
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GATE2017254
All people in a certain island are either 'Knights' or 'Knaves' and each person knows every other person's identity. Knights never lie, and Knaves ALWAYS lie. $P$ says "Both of us are Knights". Q says "None of us are Knaves". Which one of the following can ... $P$ and $Q$ are Knaves. The identities of $P, Q$ cannot be determined.
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GATE2017253
There are $4$ women $P, Q, R, S$ and $5$ men $V, W, X, Y, Z$ in a group. We are required to form pairs each consisting of one woman and one man. $P$ is not to be paired with $Z$, and $Y$ must necessarily be paired with someone. In how many ways can $4$ such pairs be formed? $74$ $76$ $78$ $80$
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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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GATE2017251
"If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will ... impartial recording of these matters." Which of the following is closest in meaning to 'cleaving' ? deteriorating arguing departing splitting
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GATE2017250
$P$ looks at $Q$ while $Q$ looks at $R$. $P$ is married, $R$ is not. The number of pairs of people in which a married person is looking at an unmarried person is $0$ $1$ $2$ Cannot be determined.
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GATE2017249
A couple has $2$ children. The probability that both children are boys if the older one is a boy is $1/4$ $1/3$ $1/2$ $1$
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GATE2017248
If $a$ and $b$ are integers and $ab$ is even, which of the following must always be even? $ab$ $a^{2}+b^{2}+1$ $a^{2}+b+1$ $abb$
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GATE2017247
If you choose plan P, you will have to _________ plan Q, as these two are mutually ________. forgot, exclusive forget, inclusive accept, exhaustive adopt, intrusive
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GATE2017246
The ways in which this game can be played _________ potentially infinite. is is being are are being
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GATE2017239
A project starts with activity A and ends with activity F. The precedence relation and durations of the activities are as per the following table: Activity Immediate predecessor Duration (days) A  4 B A 3 C A 7 D B 14 E C 4 F D, E 9 The minimum project completion time (in days) is _________.
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GATE2017243
A cylindrical pin of $25^{+0.020}_{+0.010}$ mm diameter is electroplated. Plating thickness is $2.0^{\pm0.005}$ mm. Neglecting the gauge tolerance, the diameter (in mm, up to $3$ decimal points accuracy) of the GO ring gauge to inspect the plated pin is __________.
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GATE2017240
A rod of length $20$ mm is stretched to make a rod of length $40$ mm. Subsequently, it is compressed to make a rod of final length $10$ mm. Consider the longitudinal tensile strain as positive and compressive strain as negative. The total true longitudinal strain in the rod is $0.5$ $0.69$ $0.75$ $1.0$
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Feb 27, 2017
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GATE2017245
In an orthogonal machining with a tool of $9^{\circ}$ orthogonal rake angle, the uncut chip thickness is $0.2$ mm. The chip thickness fluctuates between $0.25$ mm and $0.4$ mm. The ratio of the maximum shear angle to the minimum shear angle during machining is ___________.
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GATE2017244
During the turning of a $20$ mm diameter steel bar at a spindle speed of $400$ rpm, a tool life of $20$ minute is obtained. When the same bar is turned at $200$ rpm, the tool life becomes $60$ minute. Assume that Taylor's tool life equation is valid. When the bar is turned at $300$ rpm, the tool life (in minute) is approximately. $25$ $32$ $40$ $50$
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GATE2017242
A strip of $120$ mm width and $8$ mm thickness is rolled between two $300$ mmdiameter rolls to get a strip of $120$ mm width and $7.2$ mm thickness. The speed of the strip at the exit is $30$ m/min. There is no front or back tension. Assuming ... of $200$ MPa in the roll bite and $100$% mechanical efficiency, the minimum total power (in kW) required to drive the two rolls is _______.
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GATE2017241
Maximise $Z=5x_{1}+3x_{2}$ subject to $x_{1}+2x_{2} \leq 10$, $x_{1}x_{2} \leq 8$, $x_{1}, x_{2} \geq 0$. In the starting Simplex tableau, $x_{1}$ and $x_{2}$ are nonbasic variables and the value of $Z$ is zero. The value of $Z$ in the next Simplex tableau is _______.
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GATE2017238
A product made in two factories, P and Q, is transported to two destinations, R and S. The per unit costs of transportation (in Rupees) from factories to destinations are as per the following matrix: Factory/Destinations R S P 10 7 Q 3 4 Factory P produces $7$ units and factory ... minimum) total transportation cost is $Y$ (in Rupees), then $(XY)$, in Rupees, is $0$ $15$ $35$ $105$
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GATE2017237
A metal ball of diameter $60$ mm is initially at $220^{\circ}$ C. The ball is suddenly cooled by an air jet of $20^{\circ}$ C. The heat transfer coefficient is $200 W/m^{2}.K$. The specific heat, thermal conductivity and density of the metal ball are $400$ ... $^{\circ} C$) after $90$ seconds will be approximately $141$ $163$ $189$ $210$
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GATE2017236
In a counterflow heat exchanger, water is heated at the rate of $1.5$ kg/s from $40^{\circ}$ C to $80^{\circ}$ C by an oil entering at $120^{\circ}$ C and leaving at $60 ^{\circ}$ C. The specific heats of water and oil are $4.2$ kJ/kg.K and $2$ kJ/kg.K, ... transfer coefficient is $400 W/m^{2}.K$. The required heat transfer surface area (in $m^{2}$) is $0.104$ $0.022$ $10.4$ $21.84$
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GATE2017235
The volume and temperature of air (assumed to be an ideal gas) in a closed vessel is $2.87 m^{3}$ and $300$ K, respectively. The gauge pressure indicated by a manometer fitted to the wall of the vessel is $0.5$ bar. If the gas constant of air is $R=287$ J/kg.K and the atmospheric pressure is $1$ bar, the mass of air (in kg) in the vessel is $1.67$ $3.33$ $5.00$ $6.66$
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GATE2017234
One kg of an ideal gas (gas constant $R= 287$ J/kg.K) undergoes an irreversible process from state1 (1 bar, 300 K) to state2 (2 bar, 300 K). The change in specific entropy $(s_{2}  s_{1})$ of the gas (in J/kg.K) in the process is _________.
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GATE2017233
A calorically perfect gas (specific heat at constant pressure $1000$ J/kg .K) enters and leaves a gas turbine with the same velocity. The temperatures of the gas at turbine entry and exit are $1100$ K and $400$ K, respectively. The power produced is $4.6$ MW and heat escapes at ... casing. The mass flow rate of the gas (in kg/s) through the turbine is $6.14$ $7.00$ $7.50$ $8.00$
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GATE2017232
In the Rankine cycle for a steam power plant, the turbine entry and exit enthalpies are $2803$ kJ/kg and $1800$ kJ/kg, respectively. The enthalpies of water at pump entry and exit are $121$ kJ/kg and $124$ kJ/kg, respectively. The specific steam consumption (in kg/kW.h) of the cycle is _________.
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GATE2017231
For the laminar flow of water over a sphere, the drag coefficient $C_{F}$ is defined as $C_{F}=F/(\rho U^{2} D^{2})$, where $F$ is the drag force, $\rho$ is the fluid density, $U$ is the fluid velocity and $D$ is the diameter of ... $200$ mm under dynamically similar conditions, the drag force (in N) on this sphere is ________.
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GATE2017230
A $60$ mmdiameter water jet strikes a plate containing a hole of $40$ mm diameter as shown in the figure. Part of the jet passes through the hole horizontally and the remaining is deflected vertically. The density of water is $1000 kg/m^{3}$. If velocities are as indicated in the figure, the magnitude of horizontal force (in N) required to hold the plate is _________.
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GATE2017229
The arrangement shown in the figure measures the velocity $V$ of a gas of density $1$ kg/$m^{3}$ flowing through a pipe. The acceleration due to gravity is $9.81 m/s^{2}$. If the manometric fluid is water (density 1000 kg/$m^{3}$) and the velocity $V$ is $20 m/s$, the differential head $h$ (in mm) between the two arms of the manometer is __________.
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gate20172
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GATE2017228
The rod $PQ$ of length $L=\sqrt{2}$ m, and uniformly distributed mass of $M=10$ kg, is released from rest at the position shown in the figure. The ends slide along the frictionless faces $OP$ and $OQ$. Assume acceleration due to gravity, $g=10 m/s^{2}$. ... figure is $(ML^{2}/12)$. At this instant, the magnitude of angular acceleration (in radian/$s^{2}$) of the rod is __________.
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gate20172
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GATE2017227
The principal stresses at a point in a critical section of a machine component are $\sigma _{1}=60$ MPa, $\sigma _{2}=5$ MPa and $\sigma _{3}=40$ MPa. For the material of the component, the tensile yield strength is $\sigma _{y}=200$ MPa. According to the maximum shear stress theory, the factor of safety is $1.67$ $2.00$ $3.60$ $4.00$
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GATE2017226
A singleplate clutch has a friction disc with inner and outer radii of $20$ mm and $40$ mm, respectively. The friction lining in the disc is made in such a way that the coefficient of friction $\mu$ varies radially as $\mu=0.01r$, where $r$ is in mm ... needs to transmit a friction torque of $18.85$ kN.mm. As per uniform pressure theory, the pressure (in MPa) on the disc is ________.
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GATE2017225
A steel plate, connected to a fixed channel using three identical bolts $A, B$ and $C$, carries a load of $6$ kN as shown in the figure. Considering the effect of direct load and moment, the magnitude of resultant shear force (in kN) on bolt $C$ is $13$ $15$ $17$ $30$
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gate20172
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GATE2017224
Three masses are connected to a rotating shaft supported on bearings $A$ and $B$ ... and for a shaft angular speed of $1000$ radian/s, the magnitude of the bearing reaction (in N) at location $B$ is ___________.
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GATE2017223
A helical compression spring made of a wire of circular crosssection is subjected to a compressive load. The maximum shear stress induced in the crosssection of the wire is $24$MPa. For the same compressive load, if both the wire diameter and the mean coil diameter are doubled, the maximum shear stress (in MPa) induced in the crosssection of the wire is __________.
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GATE2017222
A gear train shown in the figure consists of gears $P, Q, R,$ and $S$. Gear $Q$ and gear $R$ are mounted on the same shaft. All the gears are mounted on parallel shafts and the number of teeth of $P, Q, R$ and $S$ are $24, 45, 30,$ and $80$, respectively. Gear $P$ is rotating at $400$ rpm. The speed (in rpm) of the gear $S$ is __________.
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GATE2017221
The radius of gyration of a compound pendulum about the point of suspension is $100$ mm. The distance between the point of suspension and the centre of mass is $250$ mm. Considering the acceleration due to gravity as $9.81 m/s^{2}$, the natural frequency (in radian/s) of the compound pendulum is ________.
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GATE2017220
Block $2$ slides outward on link $1$ at a uniform velocity of $6$ m/s as shown in the figure. Link $1$ is rotating at a constant angular velocity of $20$ radian/s counterclockwise. The magnitude of the total acceleration (in $m/s^{2}$) of point $P$ of the block with respect to fixed point $O$ is __________.
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GATE2017219
If $f(z)=(x^{2}+ay^{2})+i bxy$ is a complex analytic function of $z=x+iy$, where $i=\sqrt{1}$, then $a=1, b=1$ $a=1, b=2$ $a=1, b= 2$ $a=2, b=2$
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GATE2017218
Consider the matrix $A=\begin{bmatrix} 50 &70 \\ 70 & 80 \end{bmatrix}$ whose eigenvectors corresponding to eigenvalues $\lambda _{1}$ and $\lambda _{2}$ are $x_{1}=\begin{bmatrix} 70 \\ \lambda_{1}50 \end{bmatrix}$ and $x_{2}=\begin{bmatrix} \lambda _{2}80\\ 70 \end{bmatrix}$, respectively. The value of $x^{T}_{1} x_{2}$ is _________.
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GATE2017217
Consider the differential equation $3y" (x)+27 y (x)=0$ with initial conditions $y(0)=0$ and $y'(0)=2000$. The value of $y$ at $x=1$ is ________.
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GATE2017216
The surface integral $\int \int _{s} F.n $ dS over the surface $S$ of the sphere $x^{2}+y^{2}+z^{2}=9$, where $F=(x+y) i+(x+z) j+(y+z)k$ and $n$ is the unit outward surface normal, yields ________.
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gate20172
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