# Recent questions tagged gateme-2017-set2

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 be logically inferred from ... $P$ is a knight; $Q$ is a Knave. Both $P$ and $Q$ are Knaves. The identities of $P, Q$ cannot be determined.
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? $74$ $76$ $78$ $80$
$X$ 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? $30$ $35$ $40$ $45$
"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 have in the ... for the impartial recording of these matters." Which of the following is closest in meaning to 'cleaving' ? deteriorating arguing departing splitting
$P$ 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.
A couple has $2$ children. The probability that both children are boys if the older one is a boy is $1/4$ $1/3$ $1/2$ $1$
If $a$ and $b$ are integers and $a-b$ is even, which of the following must always be even? $ab$ $a^{2}+b^{2}+1$ $a^{2}+b+1$ $ab-b$
If you choose plan $P$, you will have to _________ plan $Q$, as these two are mutually ________. forgot, exclusive forget, inclusive accept, exhaustive adopt, intrusive
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 on ... 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
The ways in which this game can be played _________ potentially infinite. is is being are are being
Maximise $Z=5x_{1}+3x_{2}$ subject to $\begin{array}{} x_{1}+2x_{2} \leq 10, \\ x_{1}-x_{2} \leq 8, \\ x_{1}, x_{2} \geq 0 \end{array}$ In the starting Simplex tableau, $x_{1}$ and $x_{2}$ are non-basic variables and the value of $Z$ is zero. The value of $Z$ in the next Simplex tableau is _______.
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 ___________.
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. $25$ $32$ $40$ $50$
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 __________.
A strip of $120$ mm width and $8$ mm thickness is rolled between two $300$ mm-diameter 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 uniform ... $200$ 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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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 $-0.5$ $-0.69$ $-0.75$ $-1.0$
A project starts with activity $A$ and ends with activity $F$ ... The minimum project completion time (in days) is _________.
A product made in two factories, $P$ and $Q$, is transported to two destinations, $R$ and $S$ ... optimized (the minimum) total transportation cost is $Y$ (in Rupees), then $(X-Y)$, in Rupees, is $0$ $15$ $35$ $105$
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 $400$ J/kg.K, ... $^{\circ} C$) after $90$ seconds will be approximately $141$ $163$ $189$ $210$
In a counter-flow 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 $4.2 \: kJ/kg.K$ ... heat transfer coefficient is $400 W/m^{2}.K$. The required heat transfer surface area (in $m^{2}$) is $0.104$ $0.022$ $10.4$ $21.84$
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 $1.67$ $3.33$ $5.00$ $6.66$
One kg of an ideal gas (gas constant $R= 287\: J/kg.K$) undergoes an irreversible process from state-$1$ ($1$ bar, $300 \: K$) to state-$2$ ($2$ bar, $300\: K$). The change in specific entropy $(s_{2} - s_{1})$ of the gas (in $J/kg.K$) in the process is _________.
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 ... the turbine casing. The mass flow rate of the gas (in $kg/s$) through the turbine is $6.14$ $7.00$ $7.50$ $8.00$
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 _________.
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 the sphere. ... $0.5$. If water now flows over another sphere of diameter $200$ mm under dynamically similar conditions, the drag force (in N) on this sphere is ________.
A $60$ mm-diameter 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 _________.
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 __________.
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, $g=10 m/s^{2}$. The mass ... the figure is $(ML^{2}/12)$. At this instant, the magnitude of angular acceleration (in radian/$s^{2}$) of the rod is __________.
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 $1.67$ $2.00$ $3.60$ $4.00$
A single-plate 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. The clutch needs to transmit a friction torque of $18.85$ kN.mm. As per uniform pressure theory, the pressure (in MPa) on the disc is ________.
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 $13$ $15$ $17$ $30$
Three masses are connected to a rotating shaft supported on bearings $A$ and $B$ as shown in the figure. The system is in a space where the gravitational effect is absent. Neglect the mass of shaft and rods connecting the masses. For $m_{1}= 10 kg, m_{2}=5 kg$ and ... $1000$ radian/s, the magnitude of the bearing reaction (in N) at location $B$ is ___________.
A helical compression spring made of a wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section 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 cross-section of the wire is __________.
If $f(z)=(x^{2}+ay^{2})+i bxy$ is a complex analytic function of $z=x+iy$, where $i=\sqrt{-1}$, then $a=-1, b=-1$ $a=-1, b=2$ $a=1, b= 2$ $a=2, b=2$
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 _________.
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 ________.
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 ________.
The standard deviation of linear dimensions $P$ and $Q$ are $3 \mu$ m and $4 \mu$ m, respectively. When assembled, the standard deviation (in $\mu$ m) of the resulting linear dimension $(P+Q)$ is _________.
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 __________.
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 ________.