Questions by Arjun / GO Mechanical

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GATE2019 ME-1: 36
A circular shaft having diameter $65.00_{-0.05}^{+0.01} \: mm$ is manufactured by turning process. A $50 \: \mu m$ thick coating of TiN is deposited on the shaft. Allowed variation in TiN film thickness is $\pm 5 \mu m$. The minimum hole diameter (in mm) to just provide clearance fit is $65.01$ $65.12$ $64.95$ $65.10$

A circular shaft having diameter $65.00_{-0.05}^{+0.01} \: mm$ is manufactured by turning process. A $50 \: \mu m$ thick coating of TiN is deposited on the shaft. Allowed...

asked Feb 9, 2019

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GATE2019 ME-1: 37
Match the following sand mold casting defects with their respective causes. ... $P-3, Q-4, R-2, S-1$ $P-2, Q-4, R-1, S-3$ $P-3, Q-4, R-1, S-2$

Match the following sand mold casting defects with their respective causes.$\begin{array}{|l|l|l|l|} \hline \\ {} & \text{Defect} & {} & \text{Cause} \\ \hline P & \text{...

asked Feb 9, 2019

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GATE2019 ME-1: 38
A truss is composed of members AB, BC, CD, AD and BD, as shown in the figure. A vertical load of $10 \: kN$ is applied at point D. The magnitude of force (in kN) in the member BC is __________

A truss is composed of members AB, BC, CD, AD and BD, as shown in the figure. A vertical load of $10 \: kN$ is applied at point D. The magnitude of force (in kN) in the m...

asked Feb 9, 2019

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GATE2019 ME-1: 39
Consider an elastic straight beam of length $L= 10 \pi \: m$, with square cross-section of side $a=5 \: mm$, and Young's modulus $E=200 \: GPa$. This straight beam was bent in such a way that the two ends meets, to form a ... $MPa$.

Consider an elastic straight beam of length $L= 10 \pi \: m$, with square cross-section of side $a=5 \: mm$, and Young’s modulus $E=200 \: GPa$. This straight beam was ...

asked Feb 9, 2019

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GATE2019 ME-1: 40
Consider a prismatic straight beam of length $L=\pi \: m$, pinned at the two ends as shown in the figure. The beam has a square cross-section of side $p=6 \: mm$. The Young’s modulus $E=200 \: GPa$, and the coefficient of thermal expansion $\alpha = 3 \times 10^{-6} K^{-1}$. The minimum temperature rise required to cause Euler buckling of the beam is _______$K$.

Consider a prismatic straight beam of length $L=\pi \: m$, pinned at the two ends as shown in the figure. The beam has a square cross-section of side $p=6 \: mm$. The You...

asked Feb 9, 2019

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GATE2019 ME-1: 41
In a UTM experiment, a sample of length $100 \: mm$, was loaded in tension until failure. The failure load was $40 \: kN$. The displacement, measured using the cross-head motion, at failure, was $15 \: mm$. The compliance of the UTM is constant and is given $5 \times 10^{-8} \: m/N$. The strain at failure in the sample is ______$\%$

In a UTM experiment, a sample of length $100 \: mm$, was loaded in tension until failure. The failure load was $40 \: kN$. The displacement, measured using the cross-head...

asked Feb 9, 2019

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GATE2019 ME-1: 42
At a critical point in a component, the state of stress is given as $\sigma_{xx}=100 \: MPa, \: \sigma_{yy}=220 \: MPa, \: \sigma_{xy}= \sigma_{yx} = 80 \: MPa$ and all other stress components are zero. The yield strength of the material is $468 \: MPa$ The factor of safety on the basis of maximum shear stress theory is ___________ (round off to one decimal place)

At a critical point in a component, the state of stress is given as $\sigma_{xx}=100 \: MPa, \: \sigma_{yy}=220 \: MPa, \: \sigma_{xy}= \sigma_{yx} = 80 \: MPa$ and all o...

asked Feb 9, 2019

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GATE2019 ME-1: 43
A uniform thin disk of mass $1 \: kg$ and radius $0.1 \: m$ is kept on a surface as shown in the figure. A spring of stiffness $k_1=400 \: N/m$ is connected to the disk center $A$ ... disk. For small disturbance from the equilibrium, the natural frequency of vibration of the system is _________ $rad/s$ (round off to oe decimal place).

A uniform thin disk of mass $1 \: kg$ and radius $0.1 \: m$ is kept on a surface as shown in the figure. A spring of stiffness $k_1=400 \: N/m$ is connected to the disk c...

asked Feb 9, 2019

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GATE2019 ME-1: 44
A single block brake with a short shoe and torque capacity of $250 \: N \cdot m$ is shown. The cylindrical brake drum rotates anticlockwise at $100 \: rpm$ and the coefficient of friction is $0.25$. The value of $a$ in mm (round off to one decimal place), such that the minimum actuating force $P$ is $2000 \: N$, is ___________

A single block brake with a short shoe and torque capacity of $250 \: N \cdot m$ is shown. The cylindrical brake drum rotates anticlockwise at $100 \: rpm$ and the coeffi...

asked Feb 9, 2019

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GATE2019 ME-1: 45
Two immiscible, incompressible, viscous fluids having same densities but different viscosities are contained between two infinite horizontal parallel plates, $2 \: m$ apart as shown below. The bottom plate is fixed and the upper plate moves to the right with a constant ... fluid, $\mu_1$, then the velocity at the interface (round off to two decimal places) is _______ $m/s$.

Two immiscible, incompressible, viscous fluids having same densities but different viscosities are contained between two infinite horizontal parallel plates, $2 \: m$ apa...

asked Feb 9, 2019

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GATE2019 ME-1: 46
A cube of side $100 \: mm$ is placed at the bottom of an empty container on one of its faces. The density of the material of the cube is $800 \: kg/m^3$. Liquid of density $1000 \: kg/m^3$ is now poured into the container. The minimum height to which the liquid needs to be poured into the container for the cube to just lift up is __________$mm$.

A cube of side $100 \: mm$ is placed at the bottom of an empty container on one of its faces. The density of the material of the cube is $800 \: kg/m^3$. Liquid of densit...

asked Feb 9, 2019

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GATE2019 ME-1: 47
Three slabs are joined together as shown in the figure. There is no thermal contact resistance at the interfaces. The center slab experiences a non-uniform internal heat generation with an average value equal to $10000 \: Wm^{-3}$, while the left and right slabs have no ... $T_1$ is measured to be $100^{\circ} C$, the right extreme face temperature $T_2$ is ______$^{\circ} C$.

Three slabs are joined together as shown in the figure. There is no thermal contact resistance at the interfaces. The center slab experiences a non-uniform internal heat ...

asked Feb 9, 2019

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GATE2019 ME-1: 48
If one mole of $H_2$ has occupies a rigid container with a capacity of $1000$ litres and the temperature is raised from $27^{\circ} C$ to $37^{\circ} C$, the change in pressure of the contained gas (round off to two decimal places), assuming ideal gas behaviour, is _______ Pa. $(R=8.314 \: J/mol \cdot K)$

If one mole of $H_2$ has occupies a rigid container with a capacity of $1000$ litres and the temperature is raised from $27^{\circ} C$ to $37^{\circ} C$, the change in pr...

asked Feb 9, 2019

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GATE2019 ME-1: 49
A steam power cycle with regeneration as shown below on the $T-s$ diagram employs a single open feedwater heater for efficiency improvement. The fluid mix with each other in an open feedwater heater. The turbine is isentropic and the input (bleed) to the feedwater ... from the turbine as a percentage of the total mass flow rate at the inlet to the turbine at state $1$ is _______

A steam power cycle with regeneration as shown below on the $T-s$ diagram employs a single open feedwater heater for efficiency improvement. The fluid mix with each other...

asked Feb 9, 2019

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GATE2019 ME-1: 50
A gas turbine with air as the working fluid has an isentropic efficiency of $0.70$ when operating at a pressure ratio of $3$. Now, the pressure ratio of the turbine is increased to $5$, while maintaining the same inlet conditions. Assume air as a ... the cases, the isentropic efficiency of the turbine at the pressure ratio of $5$ is ___________ (round off to two decimal places)

A gas turbine with air as the working fluid has an isentropic efficiency of $0.70$ when operating at a pressure ratio of $3$. Now, the pressure ratio of the turbine is in...

asked Feb 9, 2019

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GATE2019 ME-1: 51
The value of the following definite integral is __________ (round off to three decimal places) $\int_1^e (x \: \ln \: x) dx$

The value of the following definite integral is __________ (round off to three decimal places)$$\int_1^e (x \: \ln \: x) dx$$

asked Feb 9, 2019

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GATE2019 ME-1: 52
In ASA system, the side cutting and end cutting edge angles of a sharp turning tool are $45^{\circ}$ and $10^{\circ}$, respectively. The feed during cylindrical turning is $0.1 \: mm/rev$. The center line average surface roughness (in $\mu m$, round off to one decimal place) of the generated surface is __________

In ASA system, the side cutting and end cutting edge angles of a sharp turning tool are $45^{\circ}$ and $10^{\circ}$, respectively. The feed during cylindrical turning i...

asked Feb 9, 2019

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GATE2019 ME-1: 53
Taylor’s tool life equation is given by $VT^n=C$, where $V$ is in $m/min$ and $T$ is in $min$. In a turning operation, two tools $X$ and $Y$ are used. For tool $X$, $n=0.3$ and $C=60$ and for tool $Y$, $n=0.6$ and $C=90$. Both the tools will have the same tool life for the cutting speed (in $m/min$, round off to one decimal place) of ____________

Taylor’s tool life equation is given by $VT^n=C$, where $V$ is in $m/min$ and $T$ is in $min$. In a turning operation, two tools $X$ and $Y$ are used. For tool $X$, $n=...

asked Feb 9, 2019

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GATE2019 ME-1: 54
Five jobs $(J1, J2, J3, J4$ and $J5)$ need to be processes in a factory. Each job can be assigned to any of the five different machines $(M1, M2, M3, M4$ and $M5)$. The time durations taken (in minutes) by the machines for each of the jobs, are given in the table. ...

Five jobs $(J1, J2, J3, J4$ and $J5)$ need to be processes in a factory. Each job can be assigned to any of the five different machines $(M1, M2, M3, M4$ and $M5)$. The t...

asked Feb 9, 2019

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GATE2019 ME-1: 55
A project consists of six activities. The immediate predecessor of each activity and the estimated duration is also provided in the table below: ... amount of time, the maximum duration (in weeks) of the activity $S$ without delaying the completion of the project is ________

A project consists of six activities. The immediate predecessor of each activity and the estimated duration is also provided in the table below:$\begin{array}{|c|c|c|} \h...

asked Feb 9, 2019

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GATE Mechanical 2018 Set 2 | GA Question: 10
An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head ans T stands for tail, the following are the observations from the four trials. HTHTHT TTHHHT HTTHHT ... Two T will occur. One H and one T will occur. Two H will occur. One H wll be followed by one T.

An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head ans T stands fo...

asked Feb 17, 2018

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GATE Mechanical 2018 Set 2 | GA Question: 9
A house has a number which need to be identified. The following three statements are given that can help in identifying the house number? If the house number is a multiple of $3$, then it is a number from $50$ to $59$. If the house number is NOT a multiple of ... of $6$, then it is a number from $70$ to $79$. What is the house number? $54$ $65$ $66$ $76$

A house has a number which need to be identified. The following three statements are given that can help in identifying the house number?If the house number is a multiple...

asked Feb 17, 2018

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GATE Mechanical 2018 Set 2 | GA Question: 8
A contract is to be completed in $52$ days and $125$ identical robots were employed, each operational for $7$ hours a day. After $39$ days, five-seventh of the work was completed. How many additional robots would be required to complete the work on time, if each robot is now operational for $8$ hours a day? $50$ $89$ $146$ $175$

A contract is to be completed in $52$ days and $125$ identical robots were employed, each operational for $7$ hours a day. After $39$ days, five-seventh of the work was c...

asked Feb 17, 2018

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GATE Mechanical 2018 Set 2 | GA Question: 7
A wire would enclose an area of $1936 \: m^2$, if it is bent to a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The long and the short pieces are bent into a square and a ... following choices is closest to the sum of the areas enclosed by the two pieces in square meters? $1096$ $1111$ $1243$ $2486$

A wire would enclose an area of $1936 \: m^2$, if it is bent to a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The lo...

asked Feb 17, 2018

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GATE Mechanical 2018 Set 2 | GA Question: 6
Forty students watched films A, B and C over a week. Each student watched either only one film or all three. Thirteen students watched film A, sixteen students watched film B and nineteen students watched film C. How many students watched all three films? $0$ $2$ $4$ $8$

Forty students watched films A, B and C over a week. Each student watched either only one film or all three. Thirteen students watched film A, sixteen students watched fi...

asked Feb 17, 2018

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GATE Mechanical 2018 Set 2 | GA Question: 5
The value of the expression $\dfrac{1}{1+ \log_u \: vw} + \dfrac{1}{1+ \log_v \: wu} + \dfrac{1}{1+\log_w uv}$ is _______ $-1$ $0$ $1$ $3$

The value of the expression $\dfrac{1}{1+ \log_u \: vw} + \dfrac{1}{1+ \log_v \: wu} + \dfrac{1}{1+\log_w uv}$ is _______$-1$$0$$1$$3$

asked Feb 17, 2018

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GATE Mechanical 2018 Set 2 | GA Question: 4
The perimeters of a circle, a square, and an equilateral triangle are equal. Which one of the following statements is true? The circle has the largest area The square has the largest area The equilateral triangle has the largest area All the three shapes have the same area

The perimeters of a circle, a square, and an equilateral triangle are equal. Which one of the following statements is true?The circle has the largest areaThe square has t...

asked Feb 17, 2018

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GATE Mechanical 2018 Set 2 | GA Question: 3
Find the missing group of letters in the following series: BC, FCH, LMNO, ______ UVWXY TUVWX STUVW RSTUV

Find the missing group of letters in the following series:BC, FCH, LMNO, ______UVWXYTUVWXSTUVWRSTUV

asked Feb 17, 2018

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GATE Mechanical 2018 Set 2 | GA Question: 2
" The judge's standing in the legal; community, though shaken by false allegations of wrongdoing. remained ______ ." The word that best fills the blank in the above sentence is undiminished damaged illegal uncertain

" The judge's standing in the legal; community, though shaken by false allegations of wrongdoing. remained ______ ."The word that best fills the blank in the above senten...

asked Feb 17, 2018

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GATE Mechanical 2018 Set 2 | GA Question: 1
"The dress ______ her so well that they all immediately _______ her on her appearance." The words that best fill the blanks in the above sentence are complemented, complemented complimented, complemented complimented, complimented complemented, complimented

"The dress ______ her so well that they all immediately _______ her on her appearance."The words that best fill the blanks in the above sentence arecomplemented, compleme...

asked Feb 17, 2018

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GATE2018-2-55
A vehicle powered by a spark ignition engine follows air standard Otto cycle ($\gamma =1.4$). The engine generates $70$ kW while consuming $10.3$ kg/hr of fuel. The calorific value of the fuel is $44,000 \: kJ/kg$. The compression ratio is _________ (correct to two decimal places.

A vehicle powered by a spark ignition engine follows air standard Otto cycle ($\gamma =1.4$). The engine generates $70$ kW while consuming $10.3$ kg/hr of fuel. The calor...

asked Feb 17, 2018

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GATE2018-2-54
Steam in the condenser of a thermal power plant is to be condensed at a temperature of $30^{\circ}C$ with cooling water which enters the tubes of the condenser at $14^{\circ}C$ and exists at $22^{\circ}C$ ... coefficient is $2000 \: W/m^2 \: K$. The heat transfer (in $MW$) to the condenser is _________ (correct to two decimal places).

Steam in the condenser of a thermal power plant is to be condensed at a temperature of $30^{\circ}C$ with cooling water which enters the tubes of the condenser at $14^{\c...

asked Feb 17, 2018

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GATE2018-2-53
A welding operation is being performed with voltage $= 30 \: V$ and current =$100 \: A$. The cross-sectional area of the weld bead is $20 \: mm^2$. The work-piece and filler are titanium for which the specific energy of melting is $14 \: J/mm^3$. Assuming a thermal efficiency of the welding process $70 \%$, the welding speed (in $mm/s$) is __________ (correct to two decimal places).

A welding operation is being performed with voltage $= 30 \: V$ and current =$100 \: A$. The cross-sectional area of the weld bead is $20 \: mm^2$. The work-piece and fil...

asked Feb 17, 2018

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GATE2018-2-52
A circular hole of $25 \: mm$ diameter and depth of $20 \: mm$ is machined by EDM process. The material removal rate (in $mm^3/min$) is expressed as $ 4 \times 10^4 \: IT^{-1.23}$ where $I=300 \: A $ and the melting point of the material, $T=1600^{\circ}C$. The time ( in minutes) for machining this hole is _________ (correct to two decimal places)

A circular hole of $25 \: mm$ diameter and depth of $20 \: mm$ is machined by EDM process. The material removal rate (in $mm^3/min$) is expressed as $$ 4 \times 10^4 \: I...

asked Feb 17, 2018

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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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GATE2018-2-50
For sand-casting a steel rectangular plate with dimensions $80 \: mm \times 120 \: mm \times 20 \: mm$, a cylindrical riser has to be designed. The height of the riser is equal to its diameter. The total solidification time for the casting in $2$ ... a solidification time for $3$ minutes in the riser, the diameter (in mm) of the riser is ________ (correct to two decimal places)

For sand-casting a steel rectangular plate with dimensions $80 \: mm \times 120 \: mm \times 20 \: mm$, a cylindrical riser has to be designed. The height of the riser is...

asked Feb 17, 2018

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GATE2018-2-49
Taylor's tool life equation is used to estimate the life of a batch of identical HSS twist drills by drilling through holes at constant feed in $20 \: mm$ thick mild steel plates. In test $1$, a drill lasted $300$ holes at $150$ rpm while in ... maximum number of holes that can be made by another drill from the above batch at $200$ rpm is_________ (correct to two decimal places).

Taylor's tool life equation is used to estimate the life of a batch of identical HSS twist drills by drilling through holes at constant feed in $20 \: mm$ thick mild stee...

asked Feb 17, 2018

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GATE2018-2-48
Following data correspond to an orthogonal turning of a $100 \: mm $ diameter rod on a lathe. Rake angle:$+15^{\circ}$; Uncut chip thickness: $0.5 mm$; nominal chip thickness after the cut: $1.25 \: mm$ The shear angle (in degrees) for this process is _________ (correct to two decimal places)

Following data correspond to an orthogonal turning of a $100 \: mm $ diameter rod on a lathe. Rake angle:$+15^{\circ}$; Uncut chip thickness: $0.5 mm$; nominal chip thick...

asked Feb 17, 2018

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GATE2018-2-47
A steel wire is drawn from an initial diameter $(d_i$) of $10 \: mm$ to a final diameter ($d_f$) of the $7.5 \: mm$. The half cone angle ($\alpha$) of the die is $5^{\circ}$ and the coefficient of friction ($\mu$) between the die and the wire ... The drawing stress (in MPa) required to carry out this operation is _____ (correct to two decimal places)

A steel wire is drawn from an initial diameter $(d_i$) of $10 \: mm$ to a final diameter ($d_f$) of the $7.5 \: mm$. The half cone angle ($\alpha$) of the die is $5^{\cir...

asked Feb 17, 2018

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GATE2018-2-46
The true stress (in MPa) versus true strain relationship for a metal is given by $\sigma=1020 \varepsilon^{0.4}$. The cross sectional-area at the start of the test (when the stress and strain values are equal to zero) is $100 \: mm^2$. The cross-sectional area at the time of necking ( in $mm^2$) is ______________ correct to two decimal palces.

The true stress (in MPa) versus true strain relationship for a metal is given by $$\sigma=1020 \varepsilon^{0.4}$$. The cross sectional-area at the start of the test (whe...

asked Feb 17, 2018