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Recent questions tagged gateme-2018-set2

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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...
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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...
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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).
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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 $N$ ...
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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...
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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).
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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. $75$...
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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
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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
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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...
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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. & ...
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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...
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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...
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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 ...
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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 ...
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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 ...
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GATE2018-2-4
If $y$ is the solution of the differential equation $y^3 \dfrac{dy}{dx}+x^3 = 0, \: y(0)=1,$ the value of $y(-1)$ is $-2$ $-1$ $0$ $1$
If $y$ is the solution of the differential equation $y^3 \dfrac{dy}{dx}+x^3 = 0, \: y(0)=1,$ the value of $y(-1)$ is$-2$$-1$$0$$1$
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GATE2018-2-2
The divergence of the vector field $\overrightarrow{u}=e^x(\cos \: y\hat{i}+\sin \: y \hat{j})$ is $0$ $e^x \cos y + e^x \sin y$ $2e^x \cos y$ $2e^x \sin y$
The divergence of the vector field $\overrightarrow{u}=e^x(\cos \: y\hat{i}+\sin \: y \hat{j})$ is$0$$e^x \cos y + e^x \sin y$$2e^x \cos y$$2e^x \sin y$
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GATE2018-2-6
A frictionless gear train is shown in the figure. The leftmost $12$-teeth gear is given a torque of $100 \: N-m$. The output torque from the $60$-teeth gear on the right in $N-m$ is $5$ $20$ $500$ $2000$
A frictionless gear train is shown in the figure. The leftmost $12$-teeth gear is given a torque of $100 \: N-m$. The output torque from the $60$-teeth gear on the right ...
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GATE2018-2-5
The minimum axial compressive load, $P$, required to initiate buckling for a pinned-pinned slender column with bending stiffness $EI$ and length $L$ is $P=\dfrac{\pi^2 EI}{4L^2} \\$ $P=\dfrac{\pi^2 EI}{L^2} \\$ $P=\dfrac{3\pi^2 EI}{4L^2} \\$ $P=\dfrac{4\pi^2 EI}{L^2}$
The minimum axial compressive load, $P$, required to initiate buckling for a pinned-pinned slender column with bending stiffness $EI$ and length $L$ is$P=\dfrac{\pi^2 EI}...
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GATE2018-2-1
The Fourier cosine series for an even function $f(x)$ is given by $ f(x)=a_0 + \Sigma_{n=1}^\infty a_n \cos (nx).$ The value of the coefficient $a_2$ for the function $f(x)=\cos ^2 (x)$ in $[0, \pi]$ is $-0.5$ $0.0$ $0.5$ $1.0$
The Fourier cosine series for an even function $f(x)$ is given by $$ f(x)=a_0 + \Sigma_{n=1}^\infty a_n \cos (nx).$$ The value of the coefficient $a_2$ for the function $...
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