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GATE201325
Choose the CORRECT set of functions, which are linearly dependent. sin $x$ , $sin^2$ $x$ and $cos^2$ $x$ cos $x$ , sin $x$ and tan $x$ cos $2x$ , $sin^2$ $x$ and $cos^2$ $x$ cos $2x$ , sin $x$ and cos $x$
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GATE201326
The following surface integral is to be evaluated over a sphere for the given steady velocity vector field $F$ = $xi$ + $yj$+ $zk$ defined with respect to a Cartesian coordinate system having $i$, $j$ and $k$ ... and n is the outward unit normal vector to the sphere. The value of the surface integral is $\pi$ $2\pi$ $3\pi/4$ $4\pi$
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GATE201327
The function $f(t)$ satisfies the differential equation $\frac{d^2f}{dt^2}+f=0$ and the auxiliary conditions, $f(0)=0$, $\frac{d(f)}{d(t)}(0)=4$. The Laplace transform of $f(t)$is given by $\frac{2}{s+1}$ $\frac{4}{s+1}$ $\frac{4}{s^2+1}$ $\frac{2}{s^4+1}$
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GATE201328
Specific enthalpy and velocity of steam at inlet and exit of a steam turbine, running under steady state, are as given below: Specific enthalpy $(kJ/kg)$ Velocity $(m/s)$ Inlet steam condition $3250$ $180$ Exit steam condition $2360$ $5$ The rate of heat loss from the turbine ... developed in $kW$ by the steam turbine per $kg$ of steam flow rate, is $901.2$ $911.2$ $17072.5$ $17082.5$
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gate2013
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GATE201329
Water is coming out from a tap and falls vertically downwards. At the tap opening, the stream diameter is $20$ $mm$ with uniform velocity of $2$ $m/s$. Acceleration due to gravity is $9.81$ $m/s^2$. Assuming steady, inviscid flow, constant atmospheric pressure everywhere ... tension effects, the diameter in mm of the stream $0.5$ $m$ below the tap is approximately $10$ $15$ $20$ $25$
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GATE201330
A steel ball of diameter $60$ $mm$ is initially in thermal equilibrium at $1030^0C$ in a furnace. It is suddenly removed from the furnace and cooled in ambient air at $30^0C$, with convective heat transfer coefficient $h = 20 W/m^2K$. The thermophysical properties of ... time required in seconds to cool the steel ball in air from $1030^0C$ to $430^0C$ is $519$ $931$ $1195$ $2144$
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GATE20135
Two threaded bolts $A$ and $B$ of same material and length are subjected to identical tensile load. If the elastic strain energy stored in bolt $A$ is $4$ times that of bolt $B$ and the mean diameter of bolt $A$ is $12$ $mm$, the mean diameter of bolt $B$ in $mm$ is $16$ $24$ $36$ $48$
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GATE20136
A link $OB$ is rotating with a constant angular velocity of $2$ $rad$/$s$ in counter clockwise direction and a block is sliding radially outward on it with an uniform velocity of $0.75$ $m$/$s$ with respect to the rod, as shown in the figure below. If $OA$ = $1$ $m$, the magnitude of the absolute acceleration of the block at location $A$ in $m$/$s^2$ is $3$ $4$ $5$ $6$
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GATE20137
For steady, fully developed flow inside a straight pipe of diameter $D$, neglecting gravity effects, the pressure drop $\Delta p$ over a length $L$ and the wall shear stress $\tau _\omega$ are related by $\tau _\omega =\frac{\Delta pD}{4L}$ $\tau _\omega =\frac{\Delta pD^2}{4L^2}$ $\tau _\omega =\frac{\Delta pD}{2L}$ $\tau _\omega =\frac{4\Delta p L}{D}$
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GATE20138
The pressure, dry bulb temperature and relative humidity of air in a room are $1$ bar, $30^0$ $C$ and $70$%, respectively. If the saturated steam pressure at $30^0$ $C$ is $4.25$ $kPa$, the specific humidity of the room air in $kg$ water $vapour$/$kg$ dry air is $0.0083$ $0.0101$ $0.0191$ $0.0232$
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GATE20139
Consider onedimensional steady state heat conduction, without heat generation, in a plane wall; with boundary conditions as shown in the figure below. The conductivity of the wall is given by $k$ = $k_0$ + $bT$ ; where $k_0$ and $b$ are positive constants, and $T$ is temperature. As $x$ increases, the temperature gradient ( $dT$/ $dx$ ) will remain constant be zero increase decrease
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GATE201310
In a rolling process, the state of stress of the material undergoing deformation is pure compression pure shear compression and shear tension and shear
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GATE201311
Match the CORRECT pairs: Process Characteristics/Applications P. Friction Welding 1. Nonconsumable electrode Q. Gas Metal Arc Welding 2. Joining of thick plates R. Tungsten Inert Gas Welding 3. Consumable electrode wire S. Electroslag Welding 4. Joining of cylindrical dissimilar materials $P4; Q3; R1; S2$ $P4; Q2; R3; S1$ $P2; Q3; R4; S1$ $P2; Q4; R1; S3$
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GATE201312
A metric thread of pitch $2$ $mm$ and thread angle $60^0$ is inspected for its pitch diameter using $3$wire method. The diameter of the best size wire in $mm$ is $0.866$ $1.000$ $1.154$ $2.000$
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GATE201313
Customers arrive at a ticket counter at a rate of $50$ per $hr$ and tickets are issued in the order of their arrival. The average time taken for issuing a ticket is $1$ $min$. Assuming that customer arrivals form a Poisson process and service times are exponentially distributed, the average waiting time in queue in $min$ is $3$ $4$ $5$ $6$
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GATE201314
In simple exponential smoothing forecasting, to give higher weightage to recent demand information, the smoothing constant must be close to $1$ zero $0.5$ $1.0$
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GATE201315
A steel bar $200$ $mm$ in diameter is turned at a feed of $0.25$ $mm$/$rev$ with a depth of cut of $4$ $mm$. The rotational speed of the workpiece is $160$ $rpm$. The material removal rate in $mm^3$/$s$ is $160$ $167.6$ $1600$ $1675.5$
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GATE201316
A cube shaped casting solidifies in $5$ $min$. The solidification time in min for a cube of the same material, which is $8$ times heavier than the original casting, will be $10$ $20$ $24$ $40$
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GATE201317
For a ductile material, toughness is a measure of resistance to scratching ability to absorb energy up to fracture ability to absorb energy till elastic limit resistance to indentation
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GATE20131
The partial differential equation $\frac{\partial u }{\partial t}+u\frac{\partial u}{\partial x}=\frac{\partial^2 u}{\partial x^2}$ is a linear equation of order $2$ nonlinear equation of order $1$ linear equation of order $1$ nonlinear equation of order $2$
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GATE20132
The eigen values of a symmetric matrix are all complex with nonzero positive imaginary part. complex with nonzero negative imaginary part. real. pure imaginary.
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GATE20133
Match the CORRECT pairs: Numerical Integration Scheme Order of Fitting Polynomial P. Simpson's 3/8 Rule 1. First Q. Trapezoidal Rule 2. Second R. Simpson's 1/3 Rule 3. Third $P2; Q1; R3$ $P3; Q2; R1$ $P1; Q2; R3$ $P3; Q1; R2$
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GATE20134
A rod of length $L$ having uniform crosssectional area $A$ is subjected to a tensile force $P$ as shown in the figure below. If the Young’s modulus of the material varies linearly from $E_1$ to $E_2$ along the length of the rod, the normal stress developed at the section$SS$ is $\frac{P}{A}$ $\frac{P(E_1E_2)}{A(E_1+E_2)}$ $\frac{PE_2}{AE_1}$ $\frac{PE_1}{AE_2}$
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