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GATE Mechanical 2014 Set 3 | Question: 37
A four-wheel vehicle of mass $1000 \: kg$ moves uniformly in a straight line with the wheels revolving at $10 \: rad/s$. The wheels are identical, each with a radius of $0.2 \: m$. Then a constant braking torque is applied to all the ... a uniform deceleration. For the vehicle to stop in $10 \: s$, the braking torque (in $N.m$) on each wheel is______

A four-wheel vehicle of mass $1000 \: kg$ moves uniformly in a straight line with the wheels revolving at $10 \: rad/s$. The wheels are identical, each with a radius of $...

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GATE Mechanical 2014 Set 3 | Question: 36
Consider a rotating disk cam and a translating roller follower with zero offset. Which one of the following pitch curves, parameterized by $t$, lying in the interval $0$ to $2 \pi$, is associated with the maximum translation of the follower during one full rotation of the cam rotating ... $x(t)$= $\dfrac{1}{2}$+$\cos t$ , $y(t)=\sin t$

Consider a rotating disk cam and a translating roller follower with zero offset. Which one of the following pitch curves, parameterized by $t$, lying in the interval $0$ ...

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GATE Mechanical 2014 Set 3 | Question: 35
A force $P$ is applied at a distance $x$ from the end of the beam as shown in the figure. What would be the value of $x$ so that the displacement at ‘$A$’ is equal to zero? $0.5L$ $0.25L$ $0.33L$ $0.66L$

A force $P$ is applied at a distance $x$ from the end of the beam as shown in the figure. What would be the value of $x$ so that the displacement at ‘$A$’ is equal to...

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GATE Mechanical 2014 Set 3 | Question: 34
An annular disc has a mass $m$, inner radius $R$ and outer radius $2R$. The disc rolls on a flat surface without slipping. If the velocity of the center of mass is $v$, the kinetic energy of the disc is $\dfrac{9}{16}mv^2 \\$ $\dfrac{11}{16}mv^2 \\$ $\dfrac{13}{16}mv^2 \\$ $\dfrac{15}{16}mv^2$

An annular disc has a mass $m$, inner radius $R$ and outer radius $2R$. The disc rolls on a flat surface without slipping. If the velocity of the center of mass is $v$, t...

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GATE Mechanical 2014 Set 3 | Question: 33
The damping ratio of a single degree of freedom spring-mass-damper system with mass of $1 kg$, stiffness $100 N/m$ and viscous damping coefficient of $25 N.s/m$ is _______

The damping ratio of a single degree of freedom spring-mass-damper system with mass of $1 kg$, stiffness $100 N/m$ and viscous damping coefficient of $25 N.s/m$ is ______...

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GATE Mechanical 2014 Set 3 | Question: 32
Consider a simply supported beam of length, $50h$, with a rectangular cross-section of depth, $h$, and width, $2h$. The beam carries a vertical point load, P, at its mid-point. The ratio of the maximum shear stress to the maximum bending stress in the beam is $0.02$ $0.10$ $0.05$ $0.01$

Consider a simply supported beam of length, $50h$, with a rectangular cross-section of depth, $h$, and width, $2h$. The beam carries a vertical point load, P, at its mid-...

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GATE Mechanical 2014 Set 3 | Question: 31
A body of mass (M) $10$ $kg$ is initially stationary on a $45^{\circ}$ inclined plane as shown in figure. The coefficient of dynamic friction between the body and the plane is $0.5$. The body slides down the plane and attains a velocity of $20 m/s$. The distance traveled (in meter) by the body along the plane is _______

A body of mass (M) $10$ $kg$ is initially stationary on a $45^{\circ}$ inclined plane as shown in figure. The coefficient of dynamic friction between the body and the pla...

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GATE Mechanical 2014 Set 3 | Question: 30
A drum brake is shown in the figure. The drum is rotating in anticlockwise direction. The coefficient of friction between drum and shoe is $0.2$. The dimensions shown in the figure are in $mm$. The braking torque (in $N.m$) for the brake shoe is _______

A drum brake is shown in the figure. The drum is rotating in anticlockwise direction. The coefficient of friction between drum and shoe is $0.2$. The dimensions shown in ...

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GATE Mechanical 2014 Set 3 | Question: 29
The real root of the equation $5x − 2 \cos x −1 = 0$ (up to two decimal accuracy) is _______

The real root of the equation $5x − 2 \cos x −1 = 0$ (up to two decimal accuracy) is _______

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GATE Mechanical 2014 Set 3 | Question: 28
A machine produces $0$, $1$ or $2$ defective pieces in a day with associated probability of $1/6$, $2/3$ and $1/6$, respectively. The mean value and the variance of the number of defective pieces produced by the machine in a day, respectively, are $1$ and $1/3$ $1/3$ and $1$ $1$ and $4/3$ $1/3$ and $4/3$

A machine produces $0$, $1$ or $2$ defective pieces in a day with associated probability of $1/6$, $2/3$ and $1/6$, respectively. The mean value and the variance of the n...

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GATE Mechanical 2014 Set 3 | Question: 27
Consider two solutions $x(t)=x_1(t)$ and $x(t)=x_2(t)$ of the differential equation $\dfrac{d^2x(t)}{dt^2}+x(t)=0, \: t>0$ such that $x_1(0)=1, \dfrac{dx_1(t)}{dt} \bigg \vert_{t=0}=0$, $x_2(0)=0, \dfrac{dx_2(t)}{dt}\bigg \vert _{t=0}=1$. The ... $t=\pi /2$ is $1$ $-1$ $0$ $\pi /2$

Consider two solutions $x(t)=x_1(t)$ and $x(t)=x_2(t)$ of the differential equation $\dfrac{d^2x(t)}{dt^2}+x(t)=0, \: t>0$ such that $x_1(0)=1, \dfrac{dx_1(t)}{dt} \bigg ...

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GATE Mechanical 2014 Set 3 | Question: 26
An analytic function of a complex variable $z = x + i y$ is expressed as $f (z) = u(x, y) + i v(x, y)$ , where $i=\sqrt{-1}$ . If $u(x, y) = x^2 − y^2$ , then expression for $v(x, y)$ in terms of $x$, $y$ and a general constant $c$ would be $xy + c \\$ $\dfrac{x^2+y^2}{2}+c \\$ $2xy+c \\$ $\dfrac{(x-y)^2}{2}+c$

An analytic function of a complex variable $z = x + i y$ is expressed as $f (z) = u(x, y) + i v(x, y)$ , where $i=\sqrt{-1}$ . If $u(x, y) = x^2 − y^2$ , then expressi...

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GATE Mechanical 2014 Set 3 | Question: 25
The hot tearing in a metal casting is due to high fluidity high melt temperature wide range of solidification temperature low coefficient of thermal expansion

The hot tearing in a metal casting is due tohigh fluidityhigh melt temperaturewide range of solidification temperaturelow coefficient of thermal expansion

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GATE Mechanical 2014 Set 3 | Question: 24
The stress-strain curve for mild steel is shown in the figure given below. Choose the correct option referring to both figure and table. ... $P-3, Q-4, R-1, S-5,T-2, U-6$ $P-4, Q-1, R-5, S-2,T-3, U-6$

The stress-strain curve for mild steel is shown in the figure given below. Choose the correct option referring to both figure and table.$\begin{array}{|l|l|}\hline \textb...

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GATE Mechanical 2014 Set 3 | Question: 23
Cutting tool is much harder than the workpiece. Yet the tool wears out during the tool-work interaction, because extra hardness is imparted to the workpiece due to coolant used oxide layers on the workpiece surface impart extra hardness to it extra hardness is imparted to the workpiece due to severe rate of strain vibration is induced in the machine tool

Cutting tool is much harder than the workpiece. Yet the tool wears out during the tool-work interaction, becauseextra hardness is imparted to the workpiece due to coolant...

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GATE Mechanical 2014 Set 3 | Question: 22
Match the casting defects (Group A) with the probable causes (Group B): ... $P-4, Q-3, R-2, S-1$ $P-3, Q-4, R-2, S-1$ $P-1, Q-2, R-4, S-3$

Match the casting defects (Group A) with the probable causes (Group B):$\begin{array}{|l|l|}\hline \textbf{Group A} & \textbf{Group B} \\ \hline \text{P: Hot tears} & ...

Arjun

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GATE Mechanical 2014 Set 3 | Question: 21
A minimal spanning tree in network flow models involves all the nodes with cycle/loop allowed all the nodes with cycle/loop not allowed shortest path between start and end nodes all the nodes with directed arcs

A minimal spanning tree in network flow models involvesall the nodes with cycle/loop allowedall the nodes with cycle/loop not allowedshortest path between start and end n...

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GATE Mechanical 2014 Set 3 | Question: 20
A straight turning operation is carried out using a single point cutting tool on an AISI $1020$ steel rod. The feed is $0.2$ $mm/rev$ and the depth of cut is $0.5$ $mm$. The tool has a side cutting edge angle of $60^{\circ}$. The uncut chip thickness (in $mm$) is _______

A straight turning operation is carried out using a single point cutting tool on an AISI $1020$ steel rod. The feed is $0.2$ $mm/rev$ and the depth of cut is $0.5$ $mm$. ...

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GATE Mechanical 2014 Set 3 | Question: 19
The actual sales of a product in different months of a particular year are given below: ... $4$-month moving average method, for the month of February is _______

The actual sales of a product in different months of a particular year are given below:$$\begin{array}{|c|c|c|c|c|c|c|}\hline \text{September} & \text{October} & \text{...

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GATE Mechanical 2014 Set 3 | Question: 18
The process utilizing mainly thermal energy for removing material is Ultrasonic Matching Electrochemical Matching Abrasive Jet Matching Laser Beam Matching

The process utilizing mainly thermal energy for removing material isUltrasonic MatchingElectrochemical Matching Abrasive Jet MatchingLaser Beam Matching

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GATE Mechanical 2014 Set 3 | Question: 17
A sample of moist air at a total pressure of $85$ $kPa$ has a dry bulb temperature of $30^oC$ (saturation vapour pressure of water = $4.24$ $kPa$). If the air sample has a relative humidity of $65$%, the absolute humidity (in gram) of water vapour per $kg$ of dry air is _______

A sample of moist air at a total pressure of $85$ $kPa$ has a dry bulb temperature of $30^oC$ (saturation vapour pressure of water = $4.24$ $kPa$). If the air sample has ...

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GATE Mechanical 2014 Set 3 | Question: 16
A source at a temperature of $500$ $K$ provides $1000$ $kJ$ of heat. The temperature of environment is $27^oC$. The maximum useful work (in $kJ$) that can be obtained from the heat source is _______

A source at a temperature of $500$ $K$ provides $1000$ $kJ$ of heat. The temperature of environment is $27^oC$. The maximum useful work (in $kJ$) that can be obtained fro...

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GATE Mechanical 2014 Set 3 | Question: 15
For a gas turbine power plant, identify the correct pair of statements. P. Smaller in size compared to steam power plant for same power output Q. Starts quickly compared to steam power plant R. Works on the principle of Rankine cycle S. Good compatibility with solid fuel P, Q R, S Q, R P, S

For a gas turbine power plant, identify the correct pair of statements.P. Smaller in size compared to steam power plant for same power outputQ. Starts quickly compared to...

Arjun

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GATE Mechanical 2014 Set 3 | Question: 14
Consider the turbulent flow of a fluid through a circular pipe of diameter, D. Identify the correct pair of statements. The fluid is well-mixed The fluid is unmixed $Re_D$ < $2300$ $Re_D$ > $2300$ $I, III$ $II, IV$ $II, III$ $I, IV$

Consider the turbulent flow of a fluid through a circular pipe of diameter, D. Identify the correct pair of statements.The fluid is well-mixedThe fluid is unmixed$Re_D$ <...

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GATE Mechanical 2014 Set 3 | Question: 13
Which one of the following pairs of equations describes an irreversible heat engine? $\oint \delta Q> 0$ and $\oint \dfrac{\delta Q}{T} < 0 \\$ $\oint \delta Q< 0$ and $\oint \dfrac{\delta Q}{T} < 0 \\$ $\oint \delta Q> 0$ and $\oint \dfrac{\delta Q}{T} > 0 \\$ $\oint \delta Q< 0$ and $\oint \dfrac{\delta Q}{T} > 0$

Which one of the following pairs of equations describes an irreversible heat engine?$\oint \delta Q 0$ and $\oint \dfrac{\delta Q}{T} < 0 \\$$\oint \delta Q< 0$ and $\oin...

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GATE Mechanical 2014 Set 3 | Question: 12
Consider a long cylindrical tube of inner and outer radii, $r_i$ and $r_o$ , respectively, length, $L$ and thermal conductivity, $k$. Its inner and outer surfaces are maintained at $T_i$ and $T_o$ , respectively ( $T_i > T_o$ ). Assuming one-dimensional steady ... $\dfrac{1}{4\pi kL}\ln \bigg (\dfrac{r_o}{r_i} \bigg )$

Consider a long cylindrical tube of inner and outer radii, $r_i$ and $r_o$ , respectively, length, $L$ and thermal conductivity, $k$. Its inner and outer surfaces are mai...

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GATE Mechanical 2014 Set 3 | Question: 11
Gear $2$ rotates at $1200$ $rpm$ in counter clockwise direction and engages with Gear $3$. Gear $3$ and Gear $4$ are mounted on the same shaft. Gear $5$ engages with Gear $4$. The numbers of teeth on Gears $2$, $3$, $4$ ... angular speed of Gear $5$ is $300$ $rpm$ counterclockwise $300$ $rpm$ clockwise $4800$ $rpm$ counterclockwise $4800$ $rpm$ clockwise

Gear $2$ rotates at $1200$ $rpm$ in counter clockwise direction and engages with Gear $3$. Gear $3$ and Gear $4$ are mounted on the same shaft. Gear $5$ engages with Gear...

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GATE Mechanical 2014 Set 3 | Question: 10
Which one of following is NOT correct? Intermediate principal stress is ignored when applying the maximum principal stress theory The maximum shear stress theory gives the most accurate results amongst all the failure theories As per ... the maximum distortion energy theory, failure occurs when the distortion energy per unit volume exceeds a critical value

Which one of following is NOT correct?Intermediate principal stress is ignored when applying the maximum principal stress theoryThe maximum shear stress theory gives the ...

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GATE Mechanical 2014 Set 3 | Question: 9
A mass $m_1$ of $100$ $kg$ traveling with a uniform velocity of $5$ $m/s$ along a line collides with a stationary mass $m_2$ of $1000$ $kg$. After the collision, both the masses travel together with the same velocity. The coefficient of restitution is $0.6$ $0.1$ $0.01$ $0$

A mass $m_1$ of $100$ $kg$ traveling with a uniform velocity of $5$ $m/s$ along a line collides with a stationary mass $m_2$ of $1000$ $kg$. After the collision, both the...

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GATE Mechanical 2014 Set 3 | Question: 8
Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase angle (in degree) of the displacement with respect to the exciting force is $0$ $45$ $90$ $135$

Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase angle (in degree) of the displacement with respect to...

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GATE Mechanical 2014 Set 3 | Question: 7
Two solid circular shafts of radii $R_1$ and $R_2$ are subjected to same torque. The maximum shear stresses developed in the two shafts are $\tau _1$ and $\tau _2$. If $R_1$/ $R_2$=$2$, then $\tau _2/\tau _1$ is _______

Two solid circular shafts of radii $R_1$ and $R_2$ are subjected to same torque. The maximum shearstresses developed in the two shafts are $\tau _1$ and $\tau _2$. If $R_...

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GATE Mechanical 2014 Set 3 | Question: 6
A rotating steel shaft is supported at the ends. It is subjected to a point load at the center. The maximum bending stress developed is $100$ $MPa$. If the yield, ultimate and corrected endurance strength of the shaft material are $300$ $MPa$, $500$ $MPa$ and $200$ $MPa$, respectively, then the factor of safety for the shaft is _______

A rotating steel shaft is supported at the ends. It is subjected to a point load at the center. The maximum bending stress developed is $100$ $MPa$. If the yield, ultimat...

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GATE Mechanical 2014 Set 3 | Question: 5
The definite integral $\int_{1}^{3}\dfrac{1}{x}$ is evaluated using Trapezoidal rule with a step size of $1$. The correct answer is _______

The definite integral $\int_{1}^{3}\dfrac{1}{x}$ is evaluated using Trapezoidal rule with a step size of $1$. The correctanswer is _______

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GATE Mechanical 2014 Set 3 | Question: 4
A group consists of equal number of men and women. Of this group $20$% of the men and $50$% of the women are unemployed. If a person is selected at random from this group, the probability of the selected person being employed is _______

A group consists of equal number of men and women. Of this group $20$% of the men and $50$% of the women are unemployed. If a person is selected at random from this group...

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GATE Mechanical 2014 Set 3 | Question: 3
Divergence of the vector field $x_2z\hat{i}+xy\hat{j}-yz\hat{k}$ at $(1,-1,1)$ is $0$ $3$ $5$ $6$

Divergence of the vector field $x_2z\hat{i}+xy\hat{j}-yz\hat{k}$ at $(1,-1,1)$ is$0$$3$$5$$6$

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GATE Mechanical 2014 Set 3 | Question: 2
If a function is continuous at a point, the limit of the function may not exist at the point the function must be derivable at the point the limit of the function at the point tends to infinity the limit must exist at the point and the value of limit should be same as the value of the function at that point

If a function is continuous at a point,the limit of the function may not exist at the pointthe function must be derivable at the pointthe limit of the function at the poi...

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GATE Mechanical 2014 Set 3 | Question: 1
Consider a $3×3$ real symmetric matrix S such that two of its eigenvalues are $a\neq 0$, $b\neq 0$ with respective eigenvectors $\begin{bmatrix} x_1\\ x_2\\ x_3 \end{bmatrix}$, $\begin{bmatrix} y_1\\ y_2\\ y_3 \end{bmatrix}$ If $a\neq b$ then $x_1y_1+x_2y_2+x_3y_3$ equals $a$ $b$ $ab$ $0$

Consider a $3×3$ real symmetric matrix S such that two of its eigenvalues are $a\neq 0$, $b\neq 0$ with respective eigenvectors $\begin{bmatrix} x_1\\ x_2\\ x_3 \end{bma...

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GATE Mechanical 2014 Set 2 | GA Question: 10
It takes $30$ minutes to empty a half-full tank by draining it at a constant rate. It is decided to simultaneously pump water into the half-full tank while draining it. What is the rate at which water has to be pumped in so that it gets ... $4$ times the draining rate $3$ times the draining rate $2.5$ times the draining rate $2$ times the draining rate

It takes $30$ minutes to empty a half-full tank by draining it at a constant rate. It is decided to simultaneously pump water into the half-full tank while draining it. W...

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GATE Mechanical 2014 Set 2 | GA Question: 9
The total exports and revenues from the exports of a country are given in the two charts shown below. The pie chart for exports shows the quantity of each item exported as a percentage of the total quantity of exports. The pie chart for the revenues ... among the following has generated the maximum revenue per $kg$? Item $2$ Item $3$ Item $6$ Item $5$

The total exports and revenues from the exports of a country are given in the two charts shown below. The pie chart for exports shows the quantity of each item exported a...

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GATE Mechanical 2014 Set 2 | GA Question: 8
The sum of eight consecutive odd numbers is $656$. The average of four consecutive even numbers is $87$. What is the sum of the smallest odd number and second largest even number?

The sum of eight consecutive odd numbers is $656$. The average of four consecutive even numbers is $87$. What is the sum of the smallest odd number and second largest eve...

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