Recent questions tagged gateme-2016-set3 / GO Mechanical

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GATE Mechanical 2016 Set 3 | GA Question: 8
Two and a quarter hours back,when seen in the mirror,the reflection of the wall clock without number marking seemed to show $1:30$.what is the actual current time shown by the clock? $8:15$ $11:15$ $12:15$ $12:45$

Two and a quarter hours back,when seen in the mirror,the reflection of the wall clock without number marking seemed to show $1:30$.what is the actual current time shown b...

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GATE Mechanical 2016 Set 3 | GA Question: 9
$\textbf{M}$ and $\textbf{N}$ starts from same location.$\textbf{M}$ travels $10$ $km$ East then $10$ $km$ North-East. $\textbf{N}$ travels $5$ $km$ South then $4$ $km$ South-East.What is the shortest distance (in $km$) between $\textbf{M}$ and $\textbf{N}$ at the end of their travel? $18.60$ $22.50$ $20.61$ $25.00$

$\textbf{M}$ and $\textbf{N}$ starts from same location.$\textbf{M}$ travels $10$ $km$ East then $10$ $km$ North-East. $\textbf{N}$ travels $5$ $km$ South then $4$ $km$ S...

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GATE Mechanical 2016 Set 3 | GA Question: 10
A wire of length $340$ $mm$ is to be cut into two parts. One of the parts is to be made into a square and the other into a rectangle where sides are in the ratio of $1:2$. What is the length of the side of the square (in $mm$) such that the combined area of the square and the rectangle is a $\textbf{MINIMUM}$? $30$ $40$ $120$ $180$

A wire of length $340$ $mm$ is to be cut into two parts. One of the parts is to be made into a square and the other into a rectangle where sides are in the ratio of $1:2$...

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GATE Mechanical 2016 Set 3 | GA Question: 7
Social science disciplines were in existence in an amorphous form until the colonial period when they were institutionalized. In varying degrees, they were intended to further the colonial interest. In the time of globalization and the economic rise of postcolonial countries ... (ii) only (i) and (iii) only (ii) and (iv) only (iii) and (iv) only

Social science disciplines were in existence in an amorphous form until the colonial period when they were institutionalized. In varying degrees, they were intended to fu...

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GATE Mechanical 2016 Set 3 | GA Question: 6
The Venn diagram shows the preference of the student population for leisure activities. From the data given,the number of students who like to read books or play sports is_______ $44$ $51$ $79$ $108$

The Venn diagram shows the preference of the student population for leisure activities.From the data given,the number of students who like to read books or play sports is...

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GATE Mechanical 2016 Set 3 | GA Question: 5
S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency of others but for half as many days as E worked. S and M have $6$ hour shifts in a day, whereas E and F have $12$ hours shifts. What is the ratio of contribution of M to contribution of E in the project? $1:1$ $1:2$ $1:4$ $2:1$

S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency of others but for half as many days as E worked. S and M have $6$ hou...

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GATE Mechanical 2016 Set 3 | GA Question: 4
Given $(9 \text{ inches})^{1/2}=(0.25 \text{ yards})^{1/2}$, which one of the following statements is TRUE? $3$ inches $= 0.5$ yards $9$ inches $= 1.5$ yards $9$ inches $= 0.25$ yards $81$ inches $= 0.0625$ yards

Given $(9 \text{ inches})^{1/2}=(0.25 \text{ yards})^{1/2}$, which one of the following statements is TRUE?$3$ inches $= 0.5$ yards$9$ inches $= 1.5$ yards$9$ inches $= 0...

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GATE Mechanical 2016 Set 3 | GA Question: 3
After India’s cricket world cup victory in $1985$, Shrotria who was playing both tennis and cricket till then, decided to concentrate only on cricket. And the $\textbf{rest is history}$ What does the phrase in $\textbf{bold}$ letters mean in this context? history will rest in peace rest is recorded in history books rest is well known rest is archaic

After India’s cricket world cup victory in $1985$, Shrotria who was playing both tennis and cricket till then, decided to concentrate only on cricket. And the $\textbf{...

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GATE Mechanical 2016 Set 3 | GA Question: 2
The students ___________ the teacher on teachers’ day for twenty years of dedicated teaching. facilitated felicitated fantasized facillitated

The students ___________ the teacher on teachers’ day for twenty years of dedicated teaching.facilitatedfelicitatedfantasizedfacillitated

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GATE Mechanical 2016 Set 3 | GA Question: 1
Based on the given statements, select the appropriate option with respect to grammar and usage. Statements The height of Mr. X is $6$ feet. The height of Mr. Y is $5$ feet. Mr. X is longer than Mr. Y. Mr. X is more elongated than Mr. Y. Mr. X is taller than Mr. Y. Mr. X is lengthier than Mr. Y.

Based on the given statements, select the appropriate option with respect to grammar and usage.StatementsThe height of Mr. X is $6$ feet.The height of Mr. Y is $5$ feet.M...

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GATE2016-3-55
A firm uses a turning center, a milling center and a grinding machine to produce two parts. The table below provides the machining time required for each part and the maximum machining time available on each machine. The profit per unit on parts $I$ and $II$ are $Rs. 40$ ... minutes) I II Turning machine $12$ $6$ $6000$ Milling center $4$ $10$ $4000$ Grinding Machine $2$ $3$ $1800$

A firm uses a turning center, a milling center and a grinding machine to produce two parts. The table below provides the machining time required for each part and the max...

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GATE2016-3-53
A point P $(1, 3,−5)$ is translated by $2\hat{i}+3\hat{j}-4\hat{k}$ and then rotated counter clockwise by $90^\circ $ about the $z$-axis. The new position of the point is $(−6, 3,−9)$ $(−6,−3,−9)$ $(6, 3,−9)$ $(6, 3, 9)$

A point P $(1, 3,−5)$ is translated by $2\hat{i}+3\hat{j}-4\hat{k}$ and then rotated counter clockwise by $90^\circ $ about the $z$-axis. The new position of the point...

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GATE2016-3-54
The demand for a two-wheeler was $900$ units and $1030$ units in April $2015$ and May $2015$, respectively. The forecast for the month of April $2015$ was $850$ units. Considering a smoothing constant of $0.6$, the forecast for the month of June $2015$ is $850$ units $927$ units $965$ units $970$ units

The demand for a two-wheeler was $900$ units and $1030$ units in April $2015$ and May $2015$, respectively. The forecast for the month of April $2015$ was $850$ units. Co...

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GATE2016-3-52
Two optically flat plates of glass are kept at a small angle $\theta$ as shown in the figure. Monochromatic light is incident vertically. If the wavelength of light used to get a fringe spacing of $1$ $mm$ is $450$ $nm$, the wavelength of light (in $nm$) to get a fringe spacing of $1.5$ $mm$ is _________

Two optically flat plates of glass are kept at a small angle $\theta$ as shown in the figure. Monochromatic light is incident vertically.If the wavelength of light used t...

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GATE2016-3-51
In a single point turning operation with cemented carbide tool and steel work piece, it is found that the Taylor’s exponent is $0.25$. If the cutting speed is reduced by $50 \%$ then the tool life changes by ______ times.

In a single point turning operation with cemented carbide tool and steel work piece, it is found that the Taylor’s exponent is $0.25$. If the cutting speed is reduced b...

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GATE2016-3-50
In a sheet metal of $2$ $mm$ thickness a hole of $10$ $mm$ diameter needs to be punched. The yield strength in tension of the sheet material is $100$ $MPa$ and its ultimate shear strength is $80$ $MPa$. The force required to punch the hole (in $kN$) is __________

In a sheet metal of $2$ $mm$ thickness a hole of $10$ $mm$ diameter needs to be punched. The yield strength in tension of the sheet material is $100$ $MPa$ and its ultima...

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GATE2016-3-49
For an orthogonal cutting operation, tool material is HSS, rake angle is $22^\circ $, chip thickness is $0.8 \: mm$, speed is $48 \: m/min$ and feed is $0.4 \: mm/rev$. The shear plane angle (in degrees) is $19.24$ $29.70$ $56.00$ $68.75$

For an orthogonal cutting operation, tool material is HSS, rake angle is $22^\circ $, chip thickness is $0.8 \: mm$, speed is $48 \: m/min$ and feed is $0.4 \: mm/rev$. T...

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GATE2016-3-48
Spot welding of two steel sheets each $2 \: mm$ thick is carried out successfully by passing $4 \: kA$ of current for $0.2$ seconds through the electrodes. The resulting weld nugget formed between the sheets is $5 \: mm$ in diameter. Assuming cylindrical shape for the nugget, the ...

Spot welding of two steel sheets each $2 \: mm$ thick is carried out successfully by passing $4 \: kA$ of current for $0.2$ seconds through the electrodes. The resulting ...

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GATE2016-3-47
In the vapour compression cycle shown in the figure, the evaporating and condensing temperatures are $260 \: K$ and $310 \: K$, respectively. The compressor takes in liquid-vapour mixture (state $1$) and isentropically compresses it to a dry saturated vapour condition (state ... $1$ and $0$ (in $kJ/kg$) is ____________

In the vapour compression cycle shown in the figure, the evaporating and condensing temperatures are $260 \: K$ and $310 \: K$, respectively. The compressor takes in liqu...

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GATE2016-3-46
In a $3$-stage air compressor, the inlet pressure is $p_1$, discharge pressure is $p_4$.and the intermediate pressures are $p_2$ and $p_3 ( p_2 < p_3)$. The total pressure ratio of the compressor is $10$ and the pressure ratios of the stages are equal. If $p_1 = 100$ $kPa$, the value of the pressure $p_3$ (in $kPa$) is __________

In a $3$-stage air compressor, the inlet pressure is $p_1$, discharge pressure is $p_4$.and the intermediate pressures are $p_2$ and $p_3 ( p_2 < p_3)$. The total pressur...

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GATE2016-3-45
In a mixture of dry air and water vapor at a total pressure of $750$ $mm$ of $Hg$, the partial pressure of water vapor is $20$ $mm$ of $Hg$. The humidity ratio of the air in grams of water vapor per $kg$ of dry air ($g_w/kg_{da}$) is __________

In a mixture of dry air and water vapor at a total pressure of $750$ $mm$ of $Hg$, the partial pressure of water vapor is $20$ $mm$ of $Hg$. The humidity ratio of the air...

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GATE2016-3-44
Steam at an initial enthalpy of $100$ $kJ/kg$ and inlet velocity of $100$ $m/s$, enters an insulated horizontal nozzle. It leaves the nozzle at $200$ $m/s$. The exit enthalpy (in $kJ/kg$) is __________

Steam at an initial enthalpy of $100$ $kJ/kg$ and inlet velocity of $100$ $m/s$, enters an insulated horizontal nozzle. It leaves the nozzle at $200$ $m/s$. The exit enth...

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GATE2016-3-41
For a two-dimensional flow, the velocity field is $\overrightarrow{u}=\dfrac{x}{x^2+y^2}\hat{i}+\dfrac{y}{x^2+y^2}\hat{j}$ where$\hat{i}$ and $\hat{j}$ are the basis vectors in the $x-y$ Cartesian coordinate system. Identify the CORRECT statements from below. The flow is incompressible. The flow is ... $(2)$ and $(3)$ $(1)$ and $(3)$ $(1)$ and $(2)$ $(3)$ and $(4)$

For a two-dimensional flow, the velocity field is $\overrightarrow{u}=\dfrac{x}{x^2+y^2}\hat{i}+\dfrac{y}{x^2+y^2}\hat{j}$ where$\hat{i}$ and $\hat{j}$ are the basis vec...

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GATE2016-3-43
A cylindrical steel rod, $0.01 \: m$ in diameter and $0.2 \: m$ in length is first heated to $750^ \circ C$ and then immersed in a water bath at $100^ \circ C$. The heat transfer coefficient is $250 \: W/m^2-K$. The density, specific heat and thermal ... $k=43 \: W/m-K$, respectively. The time required for the rod to reach $300^ \circ C$ is ________ seconds.

A cylindrical steel rod, $0.01 \: m$ in diameter and $0.2 \: m$ in length is first heated to $750^ \circ C$ and then immersed in a water bath at $100^ \circ C$. The heat ...

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GATE2016-3-42
Two large parallel plates having a gap of $10 \: mm$ in between them are maintained at temperatures $T_1 = 1000 \: K$ and $T_2 = 400 \: K$. Given emissivity values, $\epsilon _1 = 0.5$, $\epsilon _2=0.25$ and Stefan-Boltzmann constant $\sigma =5.67 \times 10^{−8} \: W/m^2-K^4$, the heat transfer between the plates (in $kW/m^2$) is __________

Two large parallel plates having a gap of $10 \: mm$ in between them are maintained at temperatures $T_1 = 1000 \: K$ and $T_2 = 400 \: K$. Given emissivity values, $\ep...

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GATE2016-3-40
The water jet exiting from a stationary tank through a circular opening of diameter $300 \: mm$ impinges on a rigid wall as shown in the figure. Neglect all minor losses and assume the water level in the tank to remain constant. The net horizontal force experienced by the wall is ___________ $kN$. Density of water is $1000 \: kg/m^3$. Acceleration due to gravity $g=10 \: m/s^2$.

The water jet exiting from a stationary tank through a circular opening of diameter $300 \: mm$ impinges on a rigid wall as shown in the figure. Neglect all minor losses ...

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GATE2016-3-39
Consider a fully developed steady laminar flow of an incompressible fluid with viscosity $μ$ through a circular pipe of radius $R$. Given that the velocity at a radial location of $R/2$ from the centerline of the pipe is $U_1$, the shear stress at the wall is $KμU_1$/$R$, where $K$ is __________

Consider a fully developed steady laminar flow of an incompressible fluid with viscosity $μ$ through a circular pipe of radius $R$. Given that the velocity at a radial l...

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GATE2016-3-38
A bolted joint has four bolts arranged as shown in figure. The cross sectional area of each bolt is $25$ $mm^2$. A torque $T$ = $200N-m$ is acting on the joint. Neglecting friction due to clamping force, maximum shear stress in a bolt is ______ $MPa$.

A bolted joint has four bolts arranged as shown in figure. The cross sectional area of each bolt is $25$ $mm^2$. A torque $T$ = $200N-m$ is acting on the joint. Neglectin...

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GATE2016-3-37
A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of $\sqrt{\dfrac{3k}{m}}$, the ratio of the amplitude of steady state response to the static deflection of the spring is __________

A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of $\sqrt{\dfrac{3k}{m}}$, the ratio of ...

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GATE2016-3-36
Two masses m are attached to opposite sides of a rigid rotating shaft in the vertical plane. Another pair of equal masses $m_1$ is attached to the opposite sides of the shaft in the vertical plane as shown in figure. Consider $m=1 \: kg$, $e=50 \: mm$, $e_1=20 \: mm$ ... $a=2 \: m$ and $a_1 = 2.5 \: m$. For the system to be dynamically balanced, $m_1$ should be ________ $kg$.

Two masses m are attached to opposite sides of a rigid rotating shaft in the vertical plane. Another pair of equal masses $m_1$ is attached to the opposite sides of the s...

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GATE2016-3-29
Three cards were drawn from a pack of $52$ cards. The probability that they are a king, a queen, and a jack is $\dfrac{16}{5525} \\$ $\dfrac{64}{2197} \\$ $\dfrac{3}{13} \\$ $\dfrac{8}{16575}$

Three cards were drawn from a pack of $52$ cards. The probability that they are a king, a queen, and a jack is$\dfrac{16}{5525} \\$$\dfrac{64}{2197} \\$$\dfrac{3}{13} \\$...

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GATE2016-3-28
$\displaystyle{}\lim_{x\rightarrow \infty }\sqrt{x^2+x-1}-x$ is $0$ $\infty$ $1/2$ $-\infty$

$\displaystyle{}\lim_{x\rightarrow \infty }\sqrt{x^2+x-1}-x$ is$0$$\infty$$1/2$$-\infty$

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GATE2016-3-35
A beam of length $L$ is carrying a uniformly distributed load w per unit length. The flexural rigidity of the beam is $EI$. The reaction at the simple support at the right end is $\dfrac{wL}{2} \\$ $\dfrac{3wL}{8} \\$ $\dfrac{wL}{4} \\$ $\dfrac{wL}{8}$

A beam of length $L$ is carrying a uniformly distributed load w per unit length. The flexural rigidity of the beam is $EI$. The reaction at the simple support at the righ...

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GATE2016-3-34
Two circular shafts made of same material, one solid (S) and one hollow (H), have the same length and polar moment of inertia. Both are subjected to same torque. Here, $\theta _S$ is the twist and $\tau _S$ ... $\theta _S<\theta _H$ and $\tau _S<\tau _H$ $\theta _S=\theta _H$ and $\tau _S<\tau _H$

Two circular shafts made of same material, one solid (S) and one hollow (H), have the same length and polar moment of inertia. Both are subjected to same torque. Here, $\...

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GATE2016-3-33
A square plate of dimension $L \times L$ is subjected to a uniform pressure load $p=250 \: MPa$ on its edges as shown in the figure. Assume plane stress conditions. The Young’s modulus $E=200 \: GPa$ .The deformed shape is a square of dimension $L− 2\delta$. If $L = 2 \: m$ and $\delta=0.001 \: m$, the Poisson’s ratio of the plate material is __________

A square plate of dimension $L \times L$ is subjected to a uniform pressure load $p=250 \: MPa$ on its edges as shown in the figure. Assume plane stress conditions. The Y...

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GATE2016-3-32
A rigid rod $(AB)$ of length $L=\sqrt{2} \: m$ is undergoing translational as well as rotational motion in the $x-y$ plane (see the figure). The point $A$ has the velocity $V_1=\hat{i}+2\hat{j} \: m/s$. The end B is constrained to move only along the $x$ direction. The magnitude of the velocity $V_2$ (in $m/s$) at the end B is __________

A rigid rod $(AB)$ of length $L=\sqrt{2} \: m$ is undergoing translational as well as rotational motion in the $x-y$ plane (see the figure). The point $A$ has the velocit...

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GATE2016-3-31
A circular disc of radius $100 \: mm$ and mass $1 \: kg$, initially at rest at position $A$, rolls without slipping down a curved path as shown in figure. The speed $v$ of the disc when it reaches position $B$ is _________ $m/s$. Acceleration due to gravity $g = 10 \: m/s^2$.

A circular disc of radius $100 \: mm$ and mass $1 \: kg$, initially at rest at position $A$, rolls without slipping down a curved path as shown in figure. The speed $v$ o...

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GATE2016-3-30
An inextensible massless string goes over a frictionless pulley. Two weights of $100$ $N$ and $200$ $N$ are attached to the two ends of the string. The weights are released from rest, and start moving due to gravity. The tension in the string (in $N$) is __________

An inextensible massless string goes over a frictionless pulley. Two weights of $100$ $N$ and $200$ $N$ are attached to the two ends of the string. The weights are releas...

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GATE2016-3-27
The value of the line integral $\oint_{c}^{ }\overline{F}.{\overline{r}}'ds$ ,where $C$ is a circle of radius $\dfrac{4}{\sqrt{\pi }}$ units is ________ Here, $\overline{F}(x,y)=y\hat{i}+2x\hat{j}$ ... $x-y$ Cartesian reference. In evaluating the line integral, the curve has to be traversed in the counter-clockwise direction.

The value of the line integral $\oint_{c}^{ }\overline{F}.{\overline{r}}'ds$ ,where $C$ is a circle of radius $\dfrac{4}{\sqrt{\pi }}$ units is ________Here, $\overline{F...

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GATE2016-3-26
The number of linearly independent eigenvectors of matrix $A=\begin{bmatrix} 2 & 1 & 0\\ 0 &2 &0 \\ 0 & 0 & 3 \end{bmatrix}$ is _________

The number of linearly independent eigenvectors of matrix $A=\begin{bmatrix} 2 & 1 & 0\\ 0 &2 &0 \\ 0 & 0 & 3 \end{bmatrix}$ is _________

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