Questions by Arjun / GO Mechanical

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GATE2018-2-51
The arc lengths of a directed graph of a project are as shown in the figure. The shortest path length from node $1$ to node $6$ is __________

The arc lengths of a directed graph of a project are as shown in the figure. The shortest path length from node $1$ to node $6$ is __________

asked Feb 17, 2018

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GATE2018-2-39
A force of $100 \: N$ applied to the centre of a circular disc, of mass $10 \: kg$ and radius $1 \: m$, resting on a floor as shown in the figure. If the disc rolls without slipping on the floor, the linear acceleration (in $m/s^2$) of the centre of the disc is _______ (correct to two decimal places).

A force of $100 \: N$ applied to the centre of a circular disc, of mass $10 \: kg$ and radius $1 \: m$, resting on a floor as shown in the figure. If the disc rolls witho...

asked Feb 17, 2018

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GATE2018-2-40
A frictionless circular piston of area $10^{-2} \: m^2$ and mass $100 \: kg$ sinks into a cylindrical container of the same area filled with water of density $1000 \: kg/m^3$ ... water to be incompressible, the magnitude of the piston velocity (in $m/s$) at the instant shown is _____ (correct to three decimal places).

A frictionless circular piston of area $10^{-2} \: m^2$ and mass $100 \: kg$ sinks into a cylindrical container of the same area filled with water of density $1000 \: kg/...

asked Feb 17, 2018

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GATE2018-2-41
A $0.2 \:m$ thick infinite black plate having a thermal conductivity of $3.96 \: W/m-K$ is exposed to two infinite black surfaces at $300 \: K$ and $400 \: K$ as shown in the figure. At steady state, the surface temperature of the plate facing the ... $1-D$ heat conduction, the magnitude of the heat flux through the place (in $W/m^2$) is ___________ (correct to two decimal places)

A $0.2 \:m$ thick infinite black plate having a thermal conductivity of $3.96 \: W/m-K$ is exposed to two infinite black surfaces at $300 \: K$ and $400 \: K$ as shown in...

asked Feb 17, 2018

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GATE2018-2-42
Air is held inside a non-insulated cylinder using a piston (mass $M=25 \: kg$ and area $A=100 \: cm^2$) and stoppers (of negligible area), as shown in the figure. The initial pressure $P_i$ and temperature $T_i$ ... of the air inside the cylinder ($^{\circ}C$) at which the piston will begin to move is ______ (correct to two decimal places).

Air is held inside a non-insulated cylinder using a piston (mass $M=25 \: kg$ and area $A=100 \: cm^2$) and stoppers (of negligible area), as shown in the figure. The ini...

asked Feb 17, 2018

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GATE2018-2-43
A standard vapor compression refrigeration cycle operating with a condensing temperature of $35^{\circ}C$ and an evaporating temperature of $-10^{\circ}C$ develops $15 \: kW$ of cooling. The $p-h$ diagram shows the enthalpies at various states. If the isentropic ... of the compressor is $0.75$, the magnitude of compressor power (in $kW$) is _________ (correct to two decimal places)

A standard vapor compression refrigeration cycle operating with a condensing temperature of $35^{\circ}C$ and an evaporating temperature of $-10^{\circ}C$ develops $15 \:...

asked Feb 17, 2018

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GATE2018-2-44
Ambient air is at a pressure of $100 \: kPa$, dry bulb temperature at $30^{\circ} C$ and $60 \%$ relative humidity. The saturation pressure of water at $30^{\circ} C$ id $4.24 \: kPa$. The specific humidity of air (in $g/kg$ of dry air) is _______ (correct to two decimal places).

Ambient air is at a pressure of $100 \: kPa$, dry bulb temperature at $30^{\circ} C$ and $60 \%$ relative humidity. The saturation pressure of water at $30^{\circ} C$ id ...

asked Feb 17, 2018

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GATE2018-2-33
A bimetallic cylindrical bar cross sectional area $1 \: m^2$ is made by bonding Steel (Young's modulus $= 210 \: GPa$) and Aluminium (Young's modulus =$70 \: GPa$) as shown in the figure. To maintain tensile axial strain of magnitude $10^{-6}$ in ... in Aluminium bar, the magnitude of the required force $P$ (in $kN$) along the indicated direction is $70$ $140$ $210$ $280$

A bimetallic cylindrical bar cross sectional area $1 \: m^2$ is made by bonding Steel (Young's modulus $= 210 \: GPa$) and Aluminium (Young's modulus =$70 \: GPa$) as sho...

asked Feb 17, 2018

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GATE2018-2-34
Air flows at the rate of $1.5 \: m^3/s$ through a horizontal pipe with a gradually reducing cross-section as shown in the figure. The two cross-sections of the pipe have diameters of the $400 \: mm$ and $200 \: mm$. Take the air density as $1.2 \: kg/m^3$ and assume inviscid ... change in pressure $(p_2-p_1)$ (in $kPa$) between sections $1$ and $2$ is $-1.28$ $2.56$ $- 2.13$ $1.28$

Air flows at the rate of $1.5 \: m^3/s$ through a horizontal pipe with a gradually reducing cross-section as shown in the figure. The two cross-sections of the pipe have ...

asked Feb 17, 2018

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GATE2018-2-35
The problem of maximizing $z=x_1-x_2$ subject to constraints $x_1+x_2 \leq 10, \: x_1 \geq 0, x_2 \geq 0$ and $x_2 \leq 5$ has no solution one solution two solutions more than two solutions

The problem of maximizing $z=x_1-x_2$ subject to constraints $x_1+x_2 \leq 10, \: x_1 \geq 0, x_2 \geq 0$ and $x_2 \leq 5$ hasno solutionone solutiontwo solutionsmore tha...

asked Feb 17, 2018

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GATE2018-2-36
Given the ordinary differential equation $\dfrac{d^2y}{dx^2}+\dfrac{dy}{dx}-6y=0$ with $y(0)=0$ and $\dfrac{dy}{dx}(0)=1$, the value of $y(1)$ is __________ (correct to two decimal places).

Given the ordinary differential equation $$\dfrac{d^2y}{dx^2}+\dfrac{dy}{dx}-6y=0$$ with $y(0)=0$ and $\dfrac{dy}{dx}(0)=1$, the value of $y(1)$ is __________ (correct to...

asked Feb 17, 2018

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GATE2018-2-37
A thin-walled cylindrical can with rigid end caps has a mean radius $R=100\:mm$ and a wall thickness of $t=5 \: mm$. The can is pressurized and an additional tensile stress of a $50 \: MPa$ is imposed along the axial direction as shown in ... circumferential components of stress in the can are equal, the pressure (in $MPa$) inside the can is ___________ (correct to two decimal places)

A thin-walled cylindrical can with rigid end caps has a mean radius $R=100\:mm$ and a wall thickness of $t=5 \: mm$. The can is pressurized and an additional tensile stre...

asked Feb 17, 2018

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GATE2018-2-38
A bar is subjected to a combination of a steady load of $60 \: kN$ and a load fluctuating between $-10 \: kN$ and $90 \: kN$. The corrected endurance limit of the bar is $150 \: MPa$, the yield strength of the material is $480 \: MPa$ and the ... safety is $2$, the value of $a$ (in $mm$), according to the modified Goodman's criterion, is _____ (correct to two decimal places).

A bar is subjected to a combination of a steady load of $60 \: kN$ and a load fluctuating between $-10 \: kN$ and $90 \: kN$. The corrected endurance limit of the bar is ...

asked Feb 17, 2018

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GATE2018-2-26
Let $z$ be a complex variable. For a counter-clockwise integration around a unit circle $C$, centered at origin, $\oint_C \frac{1}{5z-4} dz=A \pi i$, the value of $A$ is $2/5$ $1/2$ $2$ $4/5$

Let $z$ be a complex variable. For a counter-clockwise integration around a unit circle $C$, centered at origin, $$\oint_C \frac{1}{5z-4} dz=A \pi i$$, the value of $A$ i...

asked Feb 17, 2018

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GATE2018-2-27
Let $X_1$ and $X_2$ be two independent exponentially distributed random variables with means $0.5$ and $0.25$, respectively. Then $Y=\text{min}(X_1, X_2)$ is exponentially distributed with mean $1/6$ exponentially distributed with mean $2$ normally distributed with mean $3/4$ normally distributed with mean $1/6$

Let $X_1$ and $X_2$ be two independent exponentially distributed random variables with means $0.5$ and $0.25$, respectively. Then $Y=\text{min}(X_1, X_2)$ isexponentially...

asked Feb 17, 2018

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GATE2018-2-28
For a position vector $\overrightarrow{r} = x \hat{i}+y \hat{j} + z\hat{k}$ the norm of the vector can be defined as $\mid \overrightarrow{r} \mid = \sqrt{x^2+y^2+z^2}$. Given a function $\phi =\text{ln} \mid \overrightarrow{r} \mid$, its ... $\dfrac{\overrightarrow{r}}{\overrightarrow{r} \cdot \overrightarrow{r} } \\ $ $\dfrac{\overrightarrow{r}}{\mid \overrightarrow{r} \mid^3} $

For a position vector $\overrightarrow{r} = x \hat{i}+y \hat{j} + z\hat{k}$ the norm of the vector can be defined as $\mid \overrightarrow{r} \mid = \sqrt{x^2+y^2+z^2}$. ...

asked Feb 17, 2018

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GATE2018-2-29
In a rigid body in plane motion, the point R is accelerating with respect to point P at $10 \angle 180^{\circ} \: m/s^2$. If the instantaneous acceleration of point $Q$ is zero, the acceleration (in $m/s^2$) of point $R$ is $8 \angle 233^{\circ}$ $10 \angle 225^{\circ}$ $10 \angle 217^{\circ}$ $8 \angle 217^{\circ}$

In a rigid body in plane motion, the point R is accelerating with respect to point P at $10 \angle 180^{\circ} \: m/s^2$. If the instantaneous acceleration of point $Q$ i...

asked Feb 17, 2018

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GATE2018-2-30
A rigid rod of length $1 \: m$ is resting at an angle $\theta =45^{\circ}$ as shown in the figure. The end $P$ is dragged with a velocity of $U=5 \: m/s$ to the right. At the instant shown, the magnitude of the velocity $V$ (in $m/s$) of point $Q$ as it moves along the wall without losing contact is $5$ $6$ $8$ $10$

A rigid rod of length $1 \: m$ is resting at an angle $\theta =45^{\circ}$ as shown in the figure. The end $P$ is dragged with a velocity of $U=5 \: m/s$ to the right. At...

asked Feb 17, 2018

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GATE2018-2-31
A bar of circular cross section is clamped at ends P and Q as shown in the figure. A torsional moment $T=150 \: Nm$ is applied at a distance of $100 \: mm$ from end $P$. The torsional reactions $(T_P, T_Q)$ in $Nm$ at ends $P$ and $Q$ respectively are $(50, 100)$ $(75, 75)$ $(100, 75)$ $(120, 30)$

A bar of circular cross section is clamped at ends P and Q as shown in the figure. A torsional moment $T=150 \: Nm$ is applied at a distance of $100 \: mm$ from end $P$. ...

asked Feb 17, 2018

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GATE2018-2-32
In a cam-follower, the follower rises by $h$ as the cam rotates by $\delta$ (radians) at constant angular velocity $\omega$ (radians/s). The follower is uniformly accelerating during the first half of the rise period and it is uniformly decelerating in the latter half of the rise period ... is $\dfrac{4h \omega}{\delta} \\$ $h \omega \\$ $\dfrac{2h \omega}{\delta} \\$ $2h \omega$

In a cam-follower, the follower rises by $h$ as the cam rotates by $\delta$ (radians) at constant angular velocity $\omega$ (radians/s). The follower is uniformly acceler...

asked Feb 17, 2018

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GATE2018-2-20
A hollow circular shaft of inner radius $10 \: mm$ outer radius $20 \: mm$ length $1 \: m$ is to be used as a torsional spring. If the shear modulus of the material of the shaft is $150 \: GPa$, the torsional stiffness of the shaft (in $kN-m/rad$) is ________ (correct to two decimal places).

A hollow circular shaft of inner radius $10 \: mm$ outer radius $20 \: mm$ length $1 \: m$ is to be used as a torsional spring. If the shear modulus of the material of th...

asked Feb 17, 2018

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GATE2018-2-21
Fatigue life of a material for a fully reversed loading condition is estimated from $\sigma_a=1100N^{-0.15}$, where $\sigma_a$ is teh stress amplitude in $MPa$ and $N$ is the failure life in cycles. The maximum allowable stress amplitude (in $MPa$) for a life of $1 \times 10^5$ cycles under the same loading condition is ________ (correct to two decimal places).

Fatigue life of a material for a fully reversed loading condition is estimated from $$\sigma_a=1100N^{-0.15}$$, where $\sigma_a$ is teh stress amplitude in $MPa$ and $N$ ...

asked Feb 17, 2018

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GATE2018-2-22
The viscous laminar flow of air over a flat plate results in the formation of a boundary layer. The boundary layer thickness at the end of the plate of length $L$ is $\delta_L$. When the plate length is increased to twice its original length, the ... laminar boundary layer thickness at the end of the plate (with respect to $\delta_L$ is _______ (correct to two decimal palces).

The viscous laminar flow of air over a flat plate results in the formation of a boundary layer. The boundary layer thickness at the end of the plate of length $L$ is $\de...

asked Feb 17, 2018

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GATE2018-2-23
An engine operates on the reversible cycle as shown in the figure. The work output from the engine (in (kJ/cycle) is ____ (correct to two decimal places).

An engine operates on the reversible cycle as shown in the figure. The work output from the engine (in (kJ/cycle) is ____ (correct to two decimal places).

asked Feb 17, 2018

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GATE2018-2-24
The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of $30$ customers/hour. The probability that the time between successive customer arrival is between $1$ and $3$ minutes is _____ (correct to two decimal places)

The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of $30$ customers/hour. The probability that the time between s...

asked Feb 17, 2018

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GATE2018-2-25
A ball is dropped from rest from a height of $1 \: m$ in a frictionless tube as shown in the figure. If the tube profile is approximated by two straight lines (ignoring the curved portion), the total distance travelled (in $m$) by the ball is _____ (correct to two decimal places)

A ball is dropped from rest from a height of $1 \: m$ in a frictionless tube as shown in the figure. If the tube profile is approximated by two straight lines (ignoring t...

asked Feb 17, 2018

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GATE2018-2-13
During solidification of a pure molten metal, the grains in the casting near the mould wall are coarse and randomly oriented fine and randomly oriented fine and ordered coarse and ordered

During solidification of a pure molten metal, the grains in the casting near the mould wall arecoarse and randomly orientedfine and randomly orientedfine and orderedcoars...

asked Feb 17, 2018

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GATE2018-2-14
Match the following products with the suitable manufacturing process: ... $P-2, Q-1, R-3, S-4$ $P-4, Q-1, R-2, S-3$ $P-1, Q-3, R-4, S-2$

Match the following products with the suitable manufacturing process:$\begin{array}{|l|l|l|l|} \hline & \textbf{Product} && \textbf{Manufacturing Process} \\ \hline P. & ...

asked Feb 17, 2018

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GATE2018-2-15
Feed rate in slab milling operation is equal to rotation per minute (rpm) product of rpm and number of teeth in the cutter product of rpm, feed per tooth and number of teeth in the cutter product of rpm, feed per tooth and number of teeth in contact

Feed rate in slab milling operation is equal torotation per minute (rpm)product of rpm and number of teeth in the cutterproduct of rpm, feed per tooth and number of teeth...

asked Feb 17, 2018

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GATE2018-2-16
Metal removal in electric discharge machining takes place through ion displacement melting and vaporization corrosive and reaction plastic shear

Metal removal in electric discharge machining takes place throughion displacementmelting and vaporizationcorrosive and reactionplastic shear

asked Feb 17, 2018

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GATE2018-2-17
The preferred option for holding an odd-shaped workpiece in a centre lathe is live and dead centres three jaw chuck lathe dog four jaw chuck

The preferred option for holding an odd-shaped workpiece in a centre lathe islive and dead centresthree jaw chucklathe dogfour jaw chuck

asked Feb 17, 2018

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GATE2018-2-18
A local tyre distributor expects to sell approximately $9600$ steel belted radial tyres next year. Annual carrying cost is Rs. $16$ per tyre and ordering cost is Rs. $75$. The economic order quantity of the tyres is $64$ $212$ $300$ $1200$

A local tyre distributor expects to sell approximately $9600$ steel belted radial tyres next year. Annual carrying cost is Rs. $16$ per tyre and ordering cost is Rs. $75$...

asked Feb 17, 2018

1 answers

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GATE2018-2-19
If $A=\begin{bmatrix}1 & 2 & 3 \\ 0 & 4 & 5 \\ 0 & 0 & 1 \end{bmatrix}$ then $\text{det}(A^{-1})$ is _______ (correct to two decimal palces).

If $A=\begin{bmatrix}1 & 2 & 3 \\ 0 & 4 & 5 \\ 0 & 0 & 1 \end{bmatrix}$ then $\text{det}(A^{-1})$ is _______ (correct to two decimal palces).

asked Feb 17, 2018

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GATE2018-2-7
In a single degree of freedom underdamped spring-mass-damper system as shown in the figure, an additional damper is added in parallel such that the system still remains underdamped. Which one of the following statements is ALWAYS ... will increase Transmissibility will decrease Time period of free oscillations will increase Time period of free oscillations will decrease

In a single degree of freedom underdamped spring-mass-damper system as shown in the figure, an additional damper is added in parallel such that the system still remains u...

asked Feb 17, 2018

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GATE2018-2-8
Pre-tensioning of a bolted joint is used to strain harden the bolt head decrease stiffness of the bolted joint increase stiffness of the bolted joint prevent yielding of the thread root

Pre-tensioning of a bolted joint is used tostrain harden the bolt headdecrease stiffness of the bolted jointincrease stiffness of the bolted jointprevent yielding of the ...

asked Feb 17, 2018

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GATE2018-2-9
The peak wavelength of radiation emitted by a black body at a temperature of $2000 \: K$ is $1.45 \: \mu m$. If the peak wavelength of emitted radiation changes to $2.90 \: \mu m$, then the temperature (in $K$) of the black body is $500$ $1000$ $4000$ $8000$

The peak wavelength of radiation emitted by a black body at a temperature of $2000 \: K$ is $1.45 \: \mu m$. If the peak wavelength of emitted radiation changes to $2.90 ...

asked Feb 17, 2018

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GATE2018-2-10
For an ideal gas with constant properties undergoing a quasi-static process, which one of the following represents the change of entropy $(\Delta s$) from state $1$ to $2$? $\Delta s = C_p \ln \bigg( \dfrac{T_2}{T_1} \bigg) - R \ln \bigg( \dfrac{P_2}{P_1} \bigg) \\$ ... $\Delta s = C_V \ln \bigg( \dfrac{T_2}{T_1} \bigg) + R \ln \bigg( \dfrac{V_1}{V_2} \bigg)$

For an ideal gas with constant properties undergoing a quasi-static process, which one of the following represents the change of entropy $(\Delta s$) from state $1$ to $2...

asked Feb 17, 2018

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GATE2018-2-11
Select the correct statement for $50\%$ reaction stage in a steam turbine. The rotor blade is symmetric The stator blade is symmetric The absolute inlet flow angle is equal to absolute exit flow angle The absolute exit flow angle is equal to inlet angle of rotor blade

Select the correct statement for $50\%$ reaction stage in a steam turbine.The rotor blade is symmetricThe stator blade is symmetricThe absolute inlet flow angle is equal ...

asked Feb 17, 2018

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GATE2018-2-12
Denoting $L$ as liquid and $M$ as solid in a phase-diagram with the subscripts representing different phases, a $\textit{eutectoid}$ reaction is described by $M_1 \rightarrow M_2+M_3$ $L_1 \rightarrow M_1+M_2$ $L_1+M_1 \rightarrow M_2$ $M_1 +M_2 \rightarrow M_3$

Denoting $L$ as liquid and $M$ as solid in a phase-diagram with the subscripts representing different phases, a $\textit{eutectoid}$ reaction is described by$M_1 \rightar...

asked Feb 17, 2018

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GATE2018-2-2
The divergence of the vector field $\overrightarrow{u}=e^x(\cos \: y\hat{i}+\sin \: y \hat{j})$ is $0$ $e^x \cos y + e^x \sin y$ $2e^x \cos y$ $2e^x \sin y$

The divergence of the vector field $\overrightarrow{u}=e^x(\cos \: y\hat{i}+\sin \: y \hat{j})$ is$0$$e^x \cos y + e^x \sin y$$2e^x \cos y$$2e^x \sin y$

asked Feb 17, 2018