# Recent questions tagged gateme-2018-set1

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Which of the following functions describe the graph shown in the below figure? $y=\mid \mid x \mid + 1 \mid -2$ $y=\mid \mid x \mid - 1 \mid -1$ $y=\mid \mid x \mid + 1 \mid -1$ $y=\mid \mid x - 1 \mid -1\mid$
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Consider the following three statements: Some roses are red. All red flowers fade quickly. some roses fade quickly. Which of the following statements can be logically inferred from the above statements? If (i) is true and (ii) is false, then (iii) is false. If (i) is true and (ii) is false, ... is true. If (i) and (ii) are true, then (iii) is true. If (i) and (ii) are false, then (iii) is false.
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From the time the front of a train enters a platform, it takes $25$ seconds for the back of the train to leave the platform, while traveling at a constant speed of $54$ km/h. At the same speed, it takes $14$ seconds to pass a man running at $9$ km/h in the same direction as ... and that of the platform in meters, respectively? $210$ and $140$ $162.5$ and $187.5$ $245$ and $130$ $175$ and $200$
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Given that $a$ and $b$ are integers and $a+a^2 b^3$ is odd, which of the following statements is correct? $a$ and $b$ are both odd $a$ and $b$ are both even $a$ is even and $b$ is odd $a$ is odd and $b$ is even
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For integers, $a$, $b$ and $c$, what would be the minimum and maximum values respectively of $a+b+c$ if $\log \mid a \mid + \log \mid b \mid + \log \mid c \mid =0$? $\text{-3 and 3}$ $\text{-1 and 1}$ $\text{-1 and 3}$ $\text{1 and 3}$
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A number consists of two digits. The sum of the digits is $9$. If $45$ is subtracted from the number, its digits are interchanged. What is the number? $63$ $72$ $81$ $90$
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A rectangle becomes a square when its length and breadth are reduced by $10$ m and $5$ m, respectively. During this process, the rectangle loses $650 m^2$ of area. What is the area of the original rectangle in square meters? $1125$ $2250$ $2924$ $4500$
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Seven machines take $7$ minutes to make $7$ identical toys. At the same rate, how many minutes would it take for $100$ machine to make $100$ toys? $1$ $7$ $100$ $700$
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"Her _____ should not be confused with miserliness; she is ever willing to assist those in need." The word that best fills the blank in the above sentence is cleanliness punctuality frugality greatness
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"Going by the _____ that many hands make light work, the school ____ involved all the students in the task." The words that best fill the blanks in the above sentence are principle, principal principal, principle principle, principle principal, principal
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An electrochemical machining (ECM) is to be used to cut a through hole into a $12$ mm thick aluminum plate. The hole has a rectangular cross-section. $10 \: mm \times 30 \:mm$. The ECM operation will be accomplished in $2$ minutes, with efficiency of $90 \%$. Assuming specific ... , the current (in A) required is __________ (correct to two decimal places).
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Block $P$ of mass $2$ kg slides down the surface and has a speed $20 \: m/s$ at the lowest point, $Q$, where the local radius of curvature is $2$ m as shown in the figure. Assuming $g=10 \: m/s^2$, the normal force (in $N$) at $Q$ is ____ correct to two decimal places.
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The schematic of an external drum rotating clockwise engaging with a short shoe is shown in the figure. The shoe is mounted at point Y on a rigid lever XYZ hinged at point X. A force $F=100$ N is applied at the free end of the lever as shown. Given that the ... between the shoe and the drum is $0.3$, the braking torque in (Nm) applied on the drum is _____ (correct to two decimal places)
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Processing times (including setup times) and due dates for six jobs waiting to be processed at a work centre are given in the table. The average tardiness (in days) using shortest processing time rule is __________ (correct to two decimal places). ...
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The minimum value of $3x+5y$ such that $3x+5y \leq 15$ $4x+9y \leq 18$ $13x+2y \leq 2$ $x \geq 0, \: y \geq 0$ is ______
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A bar is compressed to half to its original length. The magnitude of true strain produced in the deformed bar is __________ (correct to two decimal places)
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An orthogonal cutting operation is being carried out in which uncut thickness is $0.010$ mm, cutting speed is $130$ m/min, rake angle is $15^{\circ}$ and width of cut is $6$ mm. It is observed that the chip thickness is $0.015$ mm, the cutting force is $60$ N and the thrust force is $25$ N. The ratio of friction energy to total energy is _______ (correct to two decimal places).
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The true stress $(\sigma)$ - true strain $(\varepsilon)$ diagram of a strain hardening material is shown in figure. First, there is loading up to point A, i.e., up to stress of $500$ MPa and strain of $0.5$. Then from point A, there is unloading up to ... $E=200$ GPa, te natural strain at point B$(\varepsilon_B)$ is _____ (correct to three decimal places)
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A plane slab of thickness $L$ and thermal conductivity $k$ is heated heated with a fluid on one side $(P)$, and the other side $(Q)$ is maintained at a constant temperature, $T_Q$ of $25^{\circ}C$, as shown in the figure, the fluid is at $45^{\circ}C$ and ... $T_P$ (in $^{\circ}$C) of the side which is exposed to the fluid is _____ (correct to two decimal places)
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An engine working on air standard Otto cycle is supplied with air at $0.1 MPa$ and $35^{\circ} \: C$. The compression ratio is $8$. The heat supplied is $500 \: kJ/kg \: K$. The maximum temperature (in $K$) of the cycle is _______ (correct to one decimal place)
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Steam flows through a nozzle at a mess flow rate of $m=0.1 \: kg/s$ with a heat loss of $5 \: kW$. The enthalpies at inlet and exit are $2500 \: kJ/kg$ and $2350 \: kJ/kg$, respectively. Assuming negligible velocity in inlet ($C_1 \approx 0$), the velocity ($C_2$) of steam (in $m/s$) at the nozzle exit is _____ (correct to two decimal places).
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A tank of volume $0.05 \: m^3$ contains a mixture of saturated water and saturated steam at $200 ^{\circ}C$. The mass of the liquid present is $8 \: kg$. The entropy (in $kJ/kg \: K$ ... $s_{fg}=4.1014 \: kJ/kg \: K, \: s_f=2.3309 \: kJ/kg \: K$
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A solid block of $2.0 \: kg$ mass slides steadily at a velocity $V$ along a vertical wall as shown in the figure below. A thin oil film of thickness $h=0.15 \: mm$ provides lubrication between the block and the wall. The surface area of the face of the block in contact ... $V$ (in $m/s$) of the block is ______ (correct to one decimal place)
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A sprinkler shown in the figure rotates about its hinge point in a horizontal plane due to water flow discharged through its two exit nozzles. The total flow rate Q through the sprinkler is $1$ litre/sec and the cross-sectional area of each exit nozzle is $1$ ... a frictionless hinge, the steady state angular speed of rotation (in rad/s) of the sprinkler is ______ (correct to two decimal places)
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A slider crank mechanism is shown in the figure. At some instant, the crank angle is 45$^{\circ}$ and force of $40$ N is acting towards the left on the slider. The length of the crank is $30$ mm and the connecting rod is $70$ mm. Ignoring ... and inertial forces, the magnitude of the crankshaft torque (in Nm) needed to keep the mechanism in equilibrium is ______ (correct to two decimal places)
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A machine of mass $m=200 \: kg$ is supported on two mounts, each of stiffness $k=10 \: kN/m$. The machine is subjected to an external force (in $N$) $F(t) = 50 \cos 5t$. Assuming only vertical translatory motion, the magnitude of the dynamic force (in $N$) transmitted from each mount to the ground is _________ (correct to two decimal places).
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A simply supported beam of width $100$ mm, height $200$ mm and length 4 m is carrying a uniformly distributed load of intensity $10 \: kN/m$. The maximum bending stress (in MPa) in the beam is _________ (correct to one decimal place)
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$F(s)$ is the Laplace transform of the function $f(t) =2t^2 e^{-t}$. $F(1)$ is _______ (correct to two decimal places).
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An explicit forward Euler method is used to numerically integrate the differential equation $\dfrac{dy}{dt} = y$ using a time step of $0.1$. With the initial condition $y(0)=1$, the value of $y(1)$ computed by this method is ________ (correct to two decimal places)
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The percentage scrap in a sheet metal blanking operation of a continuous strip of sheet metal as shown in the figure is _______ (correct to two decimal places)
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The maximum reduction in cross-sectional area per pass $(R)$ of a cold wire drawing process is $R=1-e^{-(n+1)}$, where $n$ represents the strain hardening coefficient. For the case of a perfectly plastic material, $R$ is $0.865$ $0.826$ $0.777$ $0.632$
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In a Lagrangian system, the position of a fluid particle in a flow is described as $x=x_0e^{-kt}$ and $y=y_oe^{kt}$ where $t$ is the time while $x_o, \: y_o$, and $k$ are constants. The flow is unsteady and one-dimensional steady and two-dimensional steady and one-dimensional unsteady and two-dimensional
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A tank open at the top with a water level of $1$ m, as shown in the figure, has a hole at a height of 0.5 m. A free jet leaves horizontally from the smooth hole. The distance X (in m) where the jet strikes the floor is $0.5$ $1.0$ $2.0$ $4.0$
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A self-aligning ball bearing has a basic dynamic load rating $(C_{10}$, for $10^6$ revolutions) of $35$ kN. If the equivalent radial load on the bearing is $45$ kN, the expected life (in $10^6$ revolutions) is below $0.5$ $0.5$ to $0.8$ $0.8$ to $1.0$ above $1.0$
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The value of the integral over the closed surface $S$ bounding a volume $V$, where $\overrightarrow{r} = x \hat{i} + y \hat{j}+z \hat{k}$ is the position vector and $\overrightarrow{n}$ is the normal to the surface $S$, is $V$ $2V$ $3V$ $4V$
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Let $X_1, \: X_2$ be two independent normal random variables with means $\mu_1, \: \ \mu_2$ and standard deviations $\sigma_1, \: \sigma_2$, respectively. Consider $Y=X_1-X_2; \: \mu_1 = \mu_2 =1, \: \sigma_1=1, \: \sigma_2=2$. Then, $Y$ is normally distributed ... $Y$ has mean $0$ and variance $5$, but is NOT normally distributed $Y$ has mean $0$ and variance $1$, but is NOT normally distributed
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A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of $\theta = 30^{\circ}$ as shown in the figure. The glue used at the interface fails is Criterion 1: the maximum normal stress exceeds $2.5$ MPa Criterion 2: the maximum ... fails only because of criterion $1$ fails only because of criterion $2$ fails because of both criterion $1$ and $2$ does not fail
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An epicyclic gear train is shown in the figure below. The number of teeth on the gears A, B and D are $20$, $30$ and $20$, respectively. Gear C has $80$ teeth on the inner surface and $100$ teeth on the outer surface. If the carrier arm AB is fixed and the sun gear A rotates at $300$ rpm in the clockwise direction, then the rpm of D in the clockwise direction is $240$ $-240$ $375$ $-375$
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The state of stress at a point, for a body in plane stress, is shown in the figure below. If the minimum principal stress is $10$ kPa, then the normal stress $\sigma_y$ (in kPa) is $9.45$ $18.88$ $37.78$ $75.50$
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A point mass is shot vertically up from ground level with a velocity of $4$ m/s at time, $t=0$. It loses $20 \%$ of its impact velocity after each collision with the ground. Assuming that the acceleration due to gravity is $10 \: m/s^2$ and that air resistance is negligible, the mass stops bouncing and comes to complete rest on the ground after a total time (in seconds) of $1$ $2$ $4$ $\infty$