Questions by Arjun / GO Mechanical

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GATE2015-1-27
Consider an ant crawling along the curve $(x-2)^2+y^2=4$ , where $x$ and $y$ are in meters. The ant starts at the point $(4, 0)$ and moves counter-clockwise with a speed of $1.57$ meters per second. The time taken by the ant to reach the point $(2, 2)$ is (in seconds) ____________

Consider an ant crawling along the curve $(x-2)^2+y^2=4$ , where $x$ and $y$ are in meters. The ant starts at the point $(4, 0)$ and moves counter-clockwise with a speed ...

asked Feb 24, 2017

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GATE2015-1-28
Find the solution of $\dfrac{d^2y}{dx^2}=Y$ which passes through the origin and the point $\left(\ln 2,\dfrac{3}{4}\right)$ $y=\dfrac{1}{2}e^x-e^{-x} $ $y=\dfrac{1}{2}(e^x+e^{-x}) $ $y=\dfrac{1}{2}(e^x-e^{-x}) $ $y=\dfrac{1}{2}e^x+e^{-x} $

Find the solution of $\dfrac{d^2y}{dx^2}=Y$ which passes through the origin and the point $\left(\ln 2,\dfrac{3}{4}\right)$$y=\dfrac{1}{2}e^x-e^{-x} $$y=\dfrac{1}{2}(e^x+...

asked Feb 24, 2017

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GATE2015-1-29
The probability of obtaining at least two “SIX” in throwing a fair dice $4$ times is $425/432$ $19/144$ $13/144$ $125/432$

The probability of obtaining at least two “SIX” in throwing a fair dice $4$ times is$425/432$$19/144$$13/144$$125/432$

asked Feb 24, 2017

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GATE2015-1-30
In the assembly shown below, the part dimensions are: $L_1 = 22.0^{\pm 0.01} \: mm$, $L_2 = L_3$ = $10.0^{\pm 0.005} \: mm$. Assuming the normal distribution of part dimensions, the dimension $L_4$ in $mm$ for assembly condition would be: $2 .0^{\pm 0.008}$ $2 .0^{\pm 0.012}$ $2 .0^{\pm 0.016}$ $2 .0^{\pm 0.020}$

In the assembly shown below, the part dimensions are:$L_1 = 22.0^{\pm 0.01} \: mm$,$L_2 = L_3$ = $10.0^{\pm 0.005} \: mm$.Assuming the normal distribution of part dimens...

asked Feb 24, 2017

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GATE2015-1-31
A DC welding power source has a linear voltage-current ($V$-$I$) characteristic with open circuit voltage of $80$ $V$ and a short circuit current of $300$ $A$. For maximum arc power, the current (in Amperes) should be set as_________

A DC welding power source has a linear voltage-current ($V$-$I$) characteristic with open circuit voltage of $80$ $V$ and a short circuit current of $300$ $A$. For maximu...

asked Feb 24, 2017

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GATE2015-1-32
A triangular facet in a CAD model has vertices: $P1(0,0,0)$; $P2(1,1,0)$ and $P3(1,1,1)$. The area of the facet is $0.500$ $0.707$ $1.414$ $1.732$

A triangular facet in a CAD model has vertices: $P1(0,0,0)$; $P2(1,1,0)$ and $P3(1,1,1)$. The area of the facet is$0.500$$0.707$$1.414$$1.732$

asked Feb 24, 2017

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GATE2015-1-33
Following data refers to the activities of a project, where, node $1$ refers to the start and node $5$ ... (CP) in the network is $1$-$2$-$3$-$5$ $1$-$4$-$3$-$5$ $1$-$2$-$3$-$4$-$5$ $1$-$4$-$5$

Following data refers to the activities of a project, where, node $1$ refers to the start and node $5$ refers to the end of the project.$\begin{array}{|l|l|} \hline \text...

asked Feb 24, 2017

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GATE2015-1-34
For a canteen, the actual demand for disposable cups was $500$ units in January and $600$ units in February. The forecast for the month of January was $400$ units. The forecast for the month of March considering smoothing coefficient as $0.75$ is ________

For a canteen, the actual demand for disposable cups was $500$ units in January and $600$ units in February. The forecast for the month of January was $400$ units. The fo...

asked Feb 24, 2017

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GATE2015-1-9
For an ideal gas with constant values of specific heats, for calculation of the specific enthalpy, it is sufficient to know only the temperature both temperature and pressure are required to be known both temperature and volume are required to be known both temperature and mass are required to be known

For an ideal gas with constant values of specific heats, for calculation of the specific enthalpy,it is sufficient to know only the temperatureboth temperature and pressu...

asked Feb 24, 2017

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GATE2015-1-10
A Carnot engine ($CE_1$) works between two temperature reservoirs $A$ and $B$, where $T_A$ = $900$ $K$ and $T_B$ = $500$ $K$. A second Carnot engine ($CE_2$) works between temperature reservoirs $B$ and $C$, where $T_C$ = $300$ $K$ ... $CE_1$ from reservoir $A$ is $150$ $MJ$, the net heat rejected to reservoir $C$ by $CE_2$ (in $MJ$) is ______________

A Carnot engine ($CE_1$) works between two temperature reservoirs $A$ and $B$, where $T_A$ = $900$ $K$ and $T_B$ = $500$ $K$. A second Carnot engine ($CE_2$) works betwee...

asked Feb 24, 2017

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GATE2015-1-11
Air enters a diesel engine with a density of $1.0$ $kg$/$m^3$. The compression ratio is $21$. At steady state, the air intake is $30 × 10^{-3}$ $kg/s$ and the net work output is $15$ $kW$. The mean effective pressure (in $kPa$) is ____________

Air enters a diesel engine with a density of $1.0$ $kg$/$m^3$. The compression ratio is $21$. At steady state, the air intake is $30 × 10^{-3}$ $kg/s$ and the net work o...

asked Feb 24, 2017

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GATE2015-1-12
A stream of moist air (mass flow rate $= 10.1 \: kg/s$) with humidity ratio of $0.01 \: \dfrac{kg}{\text{kg dry air}}$ mixes with a second stream of superheated water vapour flowing at $0.1 \: \text{kg/s}$. Assuming proper and uniform mixing with no condensation, the humidity ratio of the final stream $\big($in $\dfrac{kg}{\text{kg dry air}} \big )$ is _____________

A stream of moist air (mass flow rate $= 10.1 \: kg/s$) with humidity ratio of $0.01 \: \dfrac{kg}{\text{kg dry air}}$ mixes with a second stream of superheated water va...

asked Feb 24, 2017

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GATE2015-1-13
A wheel of radius $r$ rolls without slipping on a horizontal surface shown below. If the velocity of point $P$ is $10$ $m/s$ in the horizontal direction, the magnitude of velocity of point $Q$ (in $m/s$) is ______

A wheel of radius $r$ rolls without slipping on a horizontal surface shown below. If the velocity of point $P$ is $10$ $m/s$ in the horizontal direction, the magnitude of...

asked Feb 24, 2017

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GATE2015-1-14
Consider a slider crank mechanism with nonzero masses and inertia. A constant torque $\tau$ is applied on the crank as shown in the figure. Which of the following plots best resembles variation of crank angle, $\theta$ versus time

Consider a slider crank mechanism with nonzero masses and inertia. A constant torque $\tau$ is applied on the crank as shown in the figure. Which of the following plots b...

asked Feb 24, 2017

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GATE2015-1-15
Consider a stepped shaft subjected to a twisting moment applied at $B$ as shown in the figure. Assume shear modulus, $G$ = $77$ $GPa$. The angle of twist at $C$ (in degrees) is __________

Consider a stepped shaft subjected to a twisting moment applied at $B$ as shown in the figure. Assume shear modulus, $G$ = $77$ $GPa$. The angle of twist at $C$ (in degre...

asked Feb 24, 2017

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GATE2015-1-16
Two identical trusses support a load of $100$ $N$ as shown in the figure. The length of each truss is $1.0$ $m$; cross-sectional area is $200$ $mm^2$; Young’s modulus $E$ = $200$ $GPa$. The force in the truss $AB$ (in $N$) is _________

Two identical trusses support a load of $100$ $N$ as shown in the figure. The length of each truss is $1.0$ $m$; cross-sectional area is $200$ $mm^2$; Young’s modulus $...

asked Feb 24, 2017

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GATE2015-1-17
Consider a steel (Young’s modulus $E$ = $200 \: GPa$) column hinged on both sides. Its height is $1.0 \: m$ and cross-section is $10 \: mm \times 20$ $mm$. The lowest Euler critical buckling load (in $N$) is __________

Consider a steel (Young’s modulus $E$ = $200 \: GPa$) column hinged on both sides. Its height is $1.0 \: m$ and cross-section is $10 \: mm \times 20$ $mm$. The lowest E...

asked Feb 24, 2017

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GATE2015-1-18
A swimmer can swim $10$ $km$ in $2$ hours when swimming along the flow of a river. While swimming against the flow, she takes $5$ hours for the same distance. Her speed in still water (in $km/h$) is _____

A swimmer can swim $10$ $km$ in $2$ hours when swimming along the flow of a river. While swimming against the flow, she takes $5$ hours for the same distance. Her speed i...

asked Feb 24, 2017

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GATE2015-1-19
Which one of the following is the most conservative fatigue failure criterion? Soderberg Modified Goodman ASME Elliptic Gerber

Which one of the following is the most conservative fatigue failure criterion?SoderbergModified GoodmanASME EllipticGerber

asked Feb 24, 2017

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GATE2015-1-20
Which one of the following types of stress-strain relationship best describes the behaviour of brittle materials, such as ceramics and thermosetting plastics, ($\sigma$ = stress and $\varepsilon$ = strain)?

Which one of the following types of stress-strain relationship best describes the behaviour of brittle materials, such as ceramics and thermosetting plastics, ($\sigma$ =...

asked Feb 24, 2017

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GATE2015-1-21
Match the following products with preferred manufacturing processes: ... $P-4, Q-3, R-2, S-1$ $P-2, Q-4, R-3, S-1$ $P-3, Q-4, R-2, S-1$

Match the following products with preferred manufacturing processes:$\begin{array}{|l|l|} \hline \textbf{Product} & \textbf{Process} \\ \hline \text{P. Rails} & \text{1. ...

asked Feb 24, 2017

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GATE2015-1-22
Holes of diameter $25.0^{{+0.020} \\ {+0.040}}$ $mm$ are assembled interchangeably with the pins of diameter $25.0^{{+0.008}\\{+0.005}}$ $mm$. The minimum clearance in the assembly will be $0.048$ $mm$ $0.015$ $mm$ $0.005$ $mm$ $0.008$ $mm$

Holes of diameter $25.0^{{+0.020} \\ {+0.040}}$ $mm$ are assembled interchangeably with the pins of diameter $25.0^{{+0.008}\\{+0.005}}$ $mm$. The minimum clearance in th...

asked Feb 24, 2017

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GATE2015-1-1
If any two columns of a determinant $P=\begin{bmatrix} 4 & 7 & 8\\ 3 & 1 & 5\\ 9 & 6 & 2 \end{bmatrix}$ are interchanged, which one of the following statements regarding the value of the determinant is CORRECT? ... . Both absolute value and sign will change. Absolute value will change but sign will not change. Both absolute value and sign will remain unchanged.

If any two columns of a determinant $P=\begin{bmatrix} 4 & 7 & 8\\ 3 & 1 & 5\\ 9 & 6 & 2 \end{bmatrix}$ are interchanged, which one of the following statements regarding ...

asked Feb 24, 2017

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GATE2015-1-2
Among the four normal distributions with probability density functions as shown below, which one has the lowest variance? $I$ $II$ $III$ $IV$

Among the four normal distributions with probability density functions as shown below, which one has the lowest variance?$I$$II$$III$$IV$

asked Feb 24, 2017

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GATE2015-1-3
Simpson’s $\dfrac{1}{3}$ rule is used to integrate the function $f(x)=\dfrac{3}{5}x^2+\dfrac{9}{5}$ between $x = 0$ and $x=1$ using the least number of equal sub-intervals. The value of the integral is ______________

Simpson’s $\dfrac{1}{3}$ rule is used to integrate the function $f(x)=\dfrac{3}{5}x^2+\dfrac{9}{5}$ between $x = 0$ and $x=1$ using the least number of equal sub-interv...

asked Feb 24, 2017

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GATE2015-1-4
The value of $\displaystyle{} \lim_{x\rightarrow 0}\dfrac{1- \cos(x^2)}{2x^4}$ is $0 \\$ $\dfrac{1}{2} \\$ $\dfrac{1}{4} \\$ undefined

The value of $\displaystyle{} \lim_{x\rightarrow 0}\dfrac{1- \cos(x^2)}{2x^4}$ is$0 \\$$\dfrac{1}{2} \\$$\dfrac{1}{4} \\$undefined

asked Feb 24, 2017

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GATE2015-1-5
Given two complex numbers $z_1=5+(5\sqrt{3})i$ and $z_2=\dfrac{2}{\sqrt{3}}+2i$ , the argument of $\dfrac{z_1}{z_2}$ in degrees is $0$ $30$ $60$ $90$

Given two complex numbers $z_1=5+(5\sqrt{3})i$ and $z_2=\dfrac{2}{\sqrt{3}}+2i$ , the argument of $\dfrac{z_1}{z_2}$ in degrees is$0$$30$$60$$90$

asked Feb 24, 2017

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GATE2015-1-6
Consider fully developed flow in a circular pipe with negligible entrance length effects. Assuming the mass flow rate, density and friction factor to be constant, if the length of the pipe is doubled and the diameter is halved, the head loss due to friction will increase by a factor of $4$ $16$ $32$ $64$

Consider fully developed flow in a circular pipe with negligible entrance length effects. Assuming the mass flow rate, density and friction factor to be constant, if the ...

asked Feb 24, 2017

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GATE2015-1-7
The Blasius equation related to boundary layer theory is a third-order linear partial differential equation third-order nonlinear partial differential equation second-order nonlinear ordinary differential equation third-order nonlinear ordinary differential equation

The Blasius equation related to boundary layer theory is athird-order linear partial differential equationthird-order nonlinear partial differential equationsecond-order ...

asked Feb 24, 2017

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GATE2015-1-8
For flow of viscous fluid over a flat plate, if the fluid temperature is the same as the plate temperature, the thermal boundary layer is thinner than the velocity boundary layer thicker than the velocity boundary layer of the same thickness as the velocity boundary layer not formed at all

For flow of viscous fluid over a flat plate, if the fluid temperature is the same as the plate temperature, the thermal boundary layer isthinner than the velocity boundar...

asked Feb 24, 2017

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GATE Mechanical 2014 Set 4 | GA Question: 5
In a sequence of $12$ consecutive odd numbers, the sum of the first $5$ numbers is $425$. What is the sum of the last $5$ numbers in the sequence?

In a sequence of $12$ consecutive odd numbers, the sum of the first $5$ numbers is $425$. What is the sum of the last $5$ numbers in the sequence?

asked Feb 19, 2017

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GATE Mechanical 2014 Set 4 | GA Question: 6
Find the next term in the sequence: $13M, 17Q, 19S$, ___ $21W$ $21V$ $23W$ $23V$

Find the next term in the sequence: $13M, 17Q, 19S$, ___$21W$$21V$$23W$$23V$

asked Feb 19, 2017

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GATE Mechanical 2014 Set 4 | GA Question: 7
If ‘KCLFTSB’ stands for ‘best of luck’ and ‘SHSWDG’ stands for ‘good wishes’, which of the following indicates ‘ace the exam’? MCHTX MXHTC XMHCT XMHTC

If ‘KCLFTSB’ stands for ‘best of luck’ and ‘SHSWDG’ stands for ‘good wishes’, which of the following indicates ‘ace the exam’?MCHTXMXHTCXMHCTXMHTC

asked Feb 19, 2017

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GATE Mechanical 2014 Set 4 | GA Question: 8
Industrial consumption of power doubled from $2000$-$2001$ to $2010$-$2011$. Find the annual rate of increase in percent assuming it to be uniform over the years. $5.6$ $7.2$ $10.0$ $12.2$

Industrial consumption of power doubled from $2000$-$2001$ to $2010$-$2011$. Find the annual rate of increase in percent assuming it to be uniform over the years.$5.6$$7....

asked Feb 19, 2017

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GATE Mechanical 2014 Set 4 | GA Question: 9
A firm producing air purifiers sold $200$ units in $2012$. The following pie chart presents the share of raw material, labour, energy, plant & machinery, and transportation costs in the total manufacturing cost of the firm in $2012$. ... all other expenses increased by $20\%$. What is the percentage increase in total cost for the company in $2013$?

A firm producing air purifiers sold $200$ units in $2012$. The following pie chart presents the share of raw material, labour, energy, plant & machinery, and transportati...

asked Feb 19, 2017

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GATE Mechanical 2014 Set 4 | GA Question: 10
A five digit number is formed using the digits $1,3,5,7$ and $9$ without repeating any of them. What is the sum of all such possible five digit numbers? $6666660$ $6666600$ $6666666$ $6666606$

A five digit number is formed using the digits $1,3,5,7$ and $9$ without repeating any of them. What is the sum of all such possible five digit numbers?$6666660$$6666600$...

asked Feb 19, 2017

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GATE Mechanical 2014 Set 4 | GA Question: 1
Which of the following options is the closest in meaning to the word underlined in the sentence below? In a democracy, everybody has the freedom to disagree with the government. dissent descent decent decadent

Which of the following options is the closest in meaning to the word underlined in the sentence below?In a democracy, everybody has the freedom to disagree with the gover...

asked Feb 19, 2017

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GATE Mechanical 2014 Set 4 | GA Question: 2
After the discussion, Tom said to me, 'Please revert!'. He expects me to _________. retract get back to him move in reverse retreat

After the discussion, Tom said to me, 'Please revert!'. He expects me to _________.retractget back to himmove in reverseretreat

asked Feb 19, 2017

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GATE Mechanical 2014 Set 4 | GA Question: 3
While receiving the award, the scientist said, "I feel vindicated". Which of the following is closest in meaning to the word ‘vindicated’? punished substantiated appreciated chastened

While receiving the award, the scientist said, "I feel vindicated". Which of the following is closest in meaning to the word ‘vindicated’?punishedsubstantiatedappreci...

asked Feb 19, 2017

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GATE Mechanical 2014 Set 4 | GA Question: 4
Let $f(x,y)=x^n y^m=P$ If $x$ is doubled and $y$ is halved, the new value of $f$ is $2^{n-m}P$ $2^{m-n}P$ $2(n-m)P$ $2(m-n)P$

Let $f(x,y)=x^n y^m=P$ If $x$ is doubled and $y$ is halved, the new value of $f$ is$2^{n-m}P$$2^{m-n}P$$2(n-m)P$$2(m-n)P$

asked Feb 19, 2017