Recent questions tagged gateme-2021-set2

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GATE Mechanical 2021 Set 2 | Question: 1
Consider an $n \times n$ matrix $\text{A}$ and a non-zero $n \times 1$ vector $p.$ Their product $Ap=\alpha ^{2}p$, where $\alpha \in \Re$ and $\alpha \notin \left \{ -1,0,1 \right \}$. Based on the given information, the eigen value of $A^{2}$ is: $\alpha$ $\alpha ^{2}$ $\surd{\alpha }$ $\alpha ^{4}$

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GATE Mechanical 2021 Set 2 | Question: 2
If the Laplace transform of a function $f(t)$ is given by $\frac{s+3}{\left ( s+1 \right )\left ( s+2 \right )}$, then $f(0)$ is $0$ $\frac{1}{2}$ $1$ $\frac{3}{2}$

go_editor asked in Differential Equations Mar 1, 2021

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GATE Mechanical 2021 Set 2 | Question: 3
The mean and variance, respectively, of a binomial distribution for $n$ independent trails with the probability of success as $p$, are $\sqrt{np},np\left ( 1-2p \right )$ $\sqrt{np},\sqrt{np\left ( 1-p \right )}$ $np,np$ $np, np\left ( 1-p \right )$

go_editor asked in Probability and Statistics Mar 1, 2021

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GATE Mechanical 2021 Set 2 | Question: 4
The Cast Iron which possesses all the carbon in the combined form as cementite is known as Grey Cast Iron Spheroidal Cast Iron Malleable Cast Iron White Cast Iron

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GATE Mechanical 2021 Set 2 | Question: 5
The size distribution of the powder particles used in Powder Metallurgy process can be determined by Laser scattering Laser reflection Laser absorption Laser penetration

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GATE Mechanical 2021 Set 2 | Question: 6
In a $\text{CNC}$ machine tool, the function of an interpolator is to generate signal for the lubrication pump during machining error signal for tool radius compensation during machining $\text{NC}$ code from the part drawing during post processing reference signal prescribing the shape of the part to be machined

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GATE Mechanical 2021 Set 2 | Question: 7
The machining process that involves ablation is Abrasive Jet Machining Chemical Machining Electrochemical Machining Laser Beam Machining

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GATE Mechanical 2021 Set 2 | Question: 8
A $\text{PERT}$ network has $9$ activities on its critical path. The standard deviation of each activity on the critical path is $3$. The standard deviation of the critical path is $3$ $9$ $27$ $81$

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GATE Mechanical 2021 Set 2 | Question: 9
The allowance provided in between a hole and a shaft is calculated from the difference between lower limit of the shaft and the upper limit of the hole upper limit of the shaft and the upper limit of the hole upper limit of the shaft and the lower limit of the hole lower limit of the shaft and the lower limit of the hole

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GATE Mechanical 2021 Set 2 | Question: 10
In forced convective heat transfer, Stanton number $\text{(St)}$, Nusselt number $\text{(Nu)}$, Reynolds number $\text{(Re)}$ and Prandtl number $\text{(Pr)}$ are related as $St=\frac{Nu}{Re\:Pr}$ $St=\frac{Nu\:Pr}{Re}$ $\text{St = Nu Pr Re}$ $St=\frac{Nu\:Re}{Pr}$

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GATE Mechanical 2021 Set 2 | Question: 11
For a two-dimensional, incompressible flow having velocity components $u$ and $v$ in the $x$ and $y$ directions, respectively, the expression $\frac{\partial \left ( u^{2} \right )}{\partial x}+\frac{\partial \left ( uv \right )}{\partial y}$ can ... $u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}$

go_editor asked in Calculus Mar 1, 2021

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GATE Mechanical 2021 Set 2 | Question: 12
Which of the following is responsible for eddy viscosity (or turbulent viscosity) in a turbulent boundary layer on a flat plate? Nikuradse stresses Reynolds stresses Boussinesq stresses Prandtl stresses

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GATE Mechanical 2021 Set 2 | Question: 13
A two dimensional flow has velocities in $x$ and $y$ directions given by $u = 2xyt$ and $v = -y^{2}t$, where $\text{t}$ denotes time. The equation for streamline passing through $x=1,\:y=1$ is $x^{2}y=1$ $xy^{2}=1$ $x^{2}y^{2}=1$ $x/y^{2}=1$

go_editor asked in Calculus Mar 1, 2021

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GATE Mechanical 2021 Set 2 | Question: 14
A plane truss $\text{PQRS}$ ($\text{PQ=RS}$, and $\angle PQR=90^{\circ}$) is shown in the figure. The forces in the members $\text{PR}$ and $\text{RS}$, respectively, are _____________________ $F\sqrt{2}$ (tensile) and $\text{F}$ (tensile ... (compressive) $\text{F}$ (compressive) and $F\sqrt{2}$ (compressive) $\text{F}$ (tensile) and $F\sqrt{2}$ (tensile)

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GATE Mechanical 2021 Set 2 | Question: 15
Consider the mechanism shown in the figure. There is rolling contact without slip between the disc and ground. Select the correct statement about instantaneous centers in the mechanism. Only points $\text{P, Q}$, and $\text{S}$ are instantaneous centers of ... mechanism All points $\text{P, Q, R, S, T}$ and $\text{U}$ are instantaneous centers of mechanism

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GATE Mechanical 2021 Set 2 | Question: 16
The controlling force curves $\text{P, Q,}$ and $\text{R}$ for a spring controlled governor are shown in the figure, where $r_{1}$ and $r_{2}$ are any two radii of rotation. The characteristics shown by the curves are $\text{P}$ ... $\text{R}$ - Unstable $\text{P}$ - Stable; $\text{Q}$ - Unstable; $\text{R}$ - Isochronous

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GATE Mechanical 2021 Set 2 | Question: 17
The von Mises stress at a point in a body subjected to forces is proportional to the square root of the total strain energy per unit volume plastic strain energy per unit volume dilatational strain energy per unit volume distortional strain energy per unit volume

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GATE Mechanical 2021 Set 2 | Question: 18
Value of $\int_{4}^{5.2} \ln x\: dx$ using Simpson’s one-third rule with interval size $0.3$ is $1.83$ $1.60$ $1.51$ $1.06$

go_editor asked in Numerical Methods Mar 1, 2021

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GATE Mechanical 2021 Set 2 | Question: 19
Value of $\left ( 1+i \right )^{8}$, where $i=\sqrt{-1}$, is equal to $4$ $16$ $4i$ $16i$

go_editor asked in Calculus Mar 1, 2021

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GATE Mechanical 2021 Set 2 | Question: 20
Consider adiabatic flow of air through a duct. At a given point in the duct, velocity of air is $\text{300 m/s}$, temperature is $\text{330 K}$ and pressure is $\text{180 kPa}$. Assume that the air behaves as a perfect gas with constant ... $\text{K} (\textit{round off to two decimal places}$).

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GATE Mechanical 2021 Set 2 | Question: 21
Consider an ideal vapour compression refrigeration cycle working on $\text{R-134a}$ refrigerant. The $\text{COP}$ of the cycle is $10$ and the refrigeration capacity is $\text{150 kJ/kg}$. The heat rejected by the refrigerant in the condenser is __________ $\text{kJ/kg} (\textit{round off to the nearest integer}$).

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GATE Mechanical 2021 Set 2 | Question: 22
A rigid tank of volume $50 \text{ m}^{3}$ contains a pure substance as a saturated liquid vapour mixture at $\text{400 kPa}$. Of the total mass of the mixture, $20\%$ mass is liquid and $80\%$ ... $\text{kg } (\textit{round off to the nearest integer}$).

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GATE Mechanical 2021 Set 2 | Question: 23
An object is moving with a Mach number of $0.6$ in an ideal gas environment, which is at a temperature of $\text{350 K}$. The gas constant is $\text{320 J/kg.K}$ and ratio of specific heats is $1.3$. The speed of object is _________ $\text{m/s} (\textit{round off to the nearest integer}$).

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GATE Mechanical 2021 Set 2 | Question: 24
A column with one end fixed and one end free has a critical buckling load of $\text{100 N}$. For the same column, if the free end is replaced with a pinned end then the critical buckling load will be _______ $\text{N}\; (\textit{round off to the nearest integer}$).

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GATE Mechanical 2021 Set 2 | Question: 25
A steel cubic block of side $\text{200 mm}$ is subjected to hydrostatic pressure of $\text{250 N/mm}^{2}$. The elastic modulus is $2 \times 10^{5}\:\text{N/mm}^{2}$ and Poisson ratio is $0.3$ for steel. The side of the block is reduced by _________ $\text{mm}\: (\textit{round off to two decimal places}$).

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GATE Mechanical 2021 Set 2 | Question: 26
The value of $\int_{0}^{^{\pi }/_{2}}\int_{0}^{\cos\theta }r\sin\theta \:dr\:d\theta$ is $0$ $\frac{1}{6}$ $\frac{4}{3}$ $\pi$

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GATE Mechanical 2021 Set 2 | Question: 27
Let the superscript $\text{T}$ represent the transpose operation. Consider the function $f(x)=\frac{1}{2}x^TQx-r^Tx$, where $x$ and $r$ are $n \times 1$ vectors and $\text{Q}$ is a symmetric $n \times n$ matrix. The stationary point of $f(x)$ is $Q^{T}r$ $Q^{-1}r$ $\frac{r}{r^{T}r}$ $r$

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GATE Mechanical 2021 Set 2 | Question: 28
Consider the following differential equation $\left ( 1+y \right )\frac{dy}{dx}=y.$ The solution of the equation that satisfies condition $y(1)=1$ is $2ye^{y}=e^{x}+e$ $y^{2}e^{y}=e^{x}$ $ye^{y}=e^{x}$ $\left ( 1+y \right )e^{y}=2e^{x}$

go_editor asked in Differential Equations Mar 1, 2021

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GATE Mechanical 2021 Set 2 | Question: 29
A factory produces $m (i= 1,2,\cdots, m)$ products, each of which requires processing on $n(j = 1,2,\cdots, n)$ workstations. Let $a_{ij}$ be the amount of processing time that one unit of the $i^{th}$ product requires on the $j^{th}$ workstation. Let the revenue ... $I_{it}=I_{i,t-1}+S_{it}-X_{it}\:\forall \:i,t$

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GATE Mechanical 2021 Set 2 | Question: 30
Ambient pressure, temperature, and relative humidity at a location are $\text{101 kPa}$, $\text{300 K}$, and $60\%$, respectively. The saturation pressure of the water at $\text{300 K}$ is $\text{3.6 kPa}$. The specific humidity of ambient air is ____________________ $\text{g/kg}$ of dry air. $21.4$ $35.1$ $21.9$ $13.6$

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GATE Mechanical 2021 Set 2 | Question: 31
A plane frame $\text{PQR}$ (fixed at $\text{P}$ and free at $\text{R}$) is shown in the figure. Both members ($\text{PQ}$ and $\text{QR}$) have length, $\text{L}$, and flexural rigidity, $\text{EI}$. Neglecting the effect of axial stress and transverse shear, the ... , is $\frac{5FL^{3}}{3EI}$ $\frac{4FL^{3}}{3EI}$ $\frac{2FL^{3}}{3EI}$ $\frac{FL^{3}}{3EI}$

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GATE Mechanical 2021 Set 2 | Question: 32
A power transmission mechanism consists of a belt drive and a gear train as shown in the figure. Diameters of pulleys of belt drive and number of teeth $\text{(T)}$ on the gears $2$ to $7$ are indicated in the figure. The speed and ... $\text{255.68 rpm}$; anticlockwise $\text{575.28 rpm}$; clockwise $\text{575.28 rpm}$; anticlockwise

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GATE Mechanical 2021 Set 2 | Question: 33
A machine of mass $\text{100 kg}$ is subjected to an external harmonic force with a frequency of $\text{40 rad/s}$. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination ... the force transmitted to the foundation. $1-3-4-2$ $1-3-2-4$ $4-3-1-2$ $3-1-2-4$

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GATE Mechanical 2021 Set 2 | Question: 34
Consider the system shown in the figure. A rope goes over a pulley. A mass, $\text{m}$, is hanging from the rope. A spring of stiffness, $\text{k}$, is attached at one end of the rope. Assume rope is inextensible, massless and there is no slip between pulley and rope. The ... $\sqrt{\frac{kr^{2}}{J + mr^{2}}}$ $\sqrt{k/m}$ $\sqrt{\frac{kr^{2}}{J}}$

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GATE Mechanical 2021 Set 2 | Question: 35
Find the positive real root of $x^3-x-3=0$ using Newton-Raphson method. lf the starting guess $(x_{0})$ is $2,$ the numerical value of the root after two iterations $(x_{2})$ is ______ ($\textit{round off to two decimal places}$).

go_editor asked in Numerical Methods Mar 1, 2021

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GATE Mechanical 2021 Set 2 | Question: 36
Daily production capacity of a bearing manufacturing company is $30000$ bearings. The daily demand of the bearing is $15000$. The holding cost per year of keeping a bearing in the inventory is $₹20$. The setup cost for the production of a ... $\textit{in integer}$).

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GATE Mechanical 2021 Set 2 | Question: 37
A cast product of a particular material has dimensions $75\: \text{mm} \times 125\: \text{mm} \times 20 \:\text{mm}$. The total solidification time for the cast product is found to be $2.0$ minutes as calculated using Chvorinov's rule ... = $\text{50 mm}$, the total solidification time will be ______ minutes ($\textit{round off to two decimal places}$).

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GATE Mechanical 2021 Set 2 | Question: 43
The demand and forecast of an item for five months are given in the table. ... Mean Absolute Percent Error $\text{(MAPE)}$ in the forecast is __________________ $\% (\textit{round off to two decimal places}$)

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GATE Mechanical 2021 Set 2 | Question: 44
A shell and tube heat exchanger is used as a steam condenser. Coolant water enters the tube at $300 \text{ K}$ at a rate of $100 \text{ kg/s}$ ... temperature of the coolant water coming out of the condenser is __________________ $\text{K} (\textit{round off to the nearest integer}$).

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GATE Mechanical 2021 Set 2 | Question: 45
Ambient air flows over a heated slab having flat, top surface at $y = 0$. The local temperature (in Kelvin) profile within the thermal boundary layer is given by $\text{T(y)} = 300 + 200 \exp (-5y)$, where $\text{y}$ is the distance ... $y=0$ is ____________________ $\text{K/m} (\textit{round off to the nearest integer}$).

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