# Recent questions tagged gateme-2022-set2

Parts $P1 - P7$ are machined first on a milling machine and then polished at a separate machine. Using the information in the following table, the minimum total completion time required tor carrying out both the operations for all $7$ ... $31$ $33$ $30$ $32$
A manufacturing unit produces two products $P1$ and $P2$. For each piece of $P1$ and $P2$, the table below provides quantities of materials $\text{M1, M2}$ and $M3$ required, and also the profit earned. The maximum quantity available per day for $\text{M1, M2}$ and $M3$ is also ... $5000$ $4000$ $3000$ $6000$
A tube of uniform diameter $D$ is immersed in a steady flowing inviscid liquid stream of velocity $V$, as shown in the figure. Gravitational acceleration is represented by $g$. The volume flow rate through the tube is __________________. $\dfrac{\pi}{4}D^{2}V$ $\dfrac{\pi}{4}D^{2}\sqrt{2gh_{2}}$ $\dfrac{\pi}{4}D^{2}\sqrt{2g\left ( h_{1} + h_{2}\right )}$ $\dfrac{\pi}{4}D^{2}\sqrt{V^{2} - 2gh_{2}}$
The steady velocity field in an inviscid fluid of density $1.5$ is given to be $\vec{V} = \left ( y^{2}-x^{2} \right )\hat{i} + \left ( 2xy \right )\hat{j}.$ Neglecting body forces, the pressure gradient at $(x = 1, y = 1)$ is _________________. $10\hat{j}$ $20\hat{i}$ $-6\hat{i} - 6\hat{j}$ $-4\hat{i} - 4\hat{j}$
In a vapour compression refrigeration cycle, the refrigerant enters the compressor in saturated vapour state at evaporator pressure, with specific enthalpy equal to $250$ $\text{kJ/kg}$ ... the dryness fraction of the refrigerant at entry to evaporator is _______________. $0.2$ $0.25$ $0.3$ $0.35$
$A$ is a $3 \times 5$ real matrix of rank $2$. For the set ot homogeneous equations $Ax = 0$, where $0$ is a zero vector and $x$ is a vector of unknown variables, which of the following is/are true? The given set of equations will have ... of appropriate size. The given set of equations will have infinitely many solutions. The given set of equations will have many but a finite number of solutions.
The lengths of members $\text{BC}$ and $\text{CE}$ in the frame shown in the figure are equal. All the members are rigid and lightweight, and the friction at the joints is negligible. Two forces of magnitude $Q> 0$ are applied as shown, each at the mid-length of the respective ... or more of the following members do not carry any load (force)? $\text{AB}$ $\text{CD}$ $\text{EF}$ $\text{GH}$
If the sum and product of eigenvalues of a $2 \times 2$ real matrix $\begin{bmatrix} 3 & p\\ p & q \end{bmatrix}$ are $4$ and $-1$ respectively, then $\left | p \right |$ is ______________ (in integer).
Given $z = x + iy, i = \sqrt{-1}$. $C$ is a circle of radius $2$ with the centre at the origin. If the contour $C$ is traversed anticlockwise, then the value of the integral $\dfrac{1}{2\pi}\int _{C}\dfrac{1}{\left ( z-i \right )\left ( z+4i \right )}dz$ is __________________ (round off to one decimal place).
A shaft of length $L$ is made of two materials, one in the inner core and the other in the outer rim, and the two are perfectly joined together (no slip at the interface) along the entire length of the shaft. The diameter of the inner core is $d_{i}$ and the ... range and stress-strain relations are linear. Then the ratio $\tau_{i}/ \tau_{o}$ is ______________ (round off to $2$ decimal places).
A rigid beam $\text{AD}$ of length $3a = 6\:m$ is hinged at frictionless pin joint $A$ and supported by two strings as shown in the figure. String $\text{BC}$ passes over two small frictionless pulleys of negligible radius. All the strings are made of the ... . Assuming small deflections, the tension developed in the string at $C$ is _______________ $\text{kN}$ (round off to $2$ decimal places).
In the configuration of the planar four-bar mechanism at a certain instant as shown in the figure, the angular velocity of the $2$ $\text{cm}$ long link is $w_{2} = 5$ $\text{rad/s}$. Given the dimensions as shown, the magnitude of the angular velocity $w_{4}$ of the $4$ $\text{cm}$ long link is given by ______________ $\text{rad/s}$ (round off to $2$ decimal places).
A shaft $\text{AC}$ rotating at a constant speed carries a thin pulley of radius $r= 0.4\:m$ at the end $C$ which drives a belt. A motor is coupled at the end $A$ of the shaft such that it applies a torque $M_{z}$ about the shaft axis ... and fatigue loading and assuming maximum shear stress theory, the minimum required shaft diameter is _____________ $\text{mm}$ (round off to $2$ decimal places).
A straight-teeth horizontal slab milling cutter is shown in the figure. It has $4$ teeth and diameter $(D)$ of $200$ $\text{mm}$. The rotational speed of the cutter is $100$ $\text{rpm}$ and the linear feed given to the workpiece is $1000$ $\text{mm}$/minute. The ... of $\frac{d}{D}< < 1$ is invalid. The maximum cutting force required is _____________ $\text{kN}$ (round off to one decimal place).
ln an orthogonal machining operation, the cutting and thrust forces are equal in magnitude. The uncut chip thickness is $0.5$ $\text{mm}$ and the shear angle is $15^{\circ}$. The orthogonal rake angle of the tool is $0^{\circ}$ and the width of cut is $2$ ... and its yield shear strength is $500$ $\text{MPa}$. The cutting force is ___________________ $\text{N}$ (round off to the nearest integer).
The best size wire is fitted in a groove of a metric screw such that the wire touches the flanks of the thread on the pitch line as shown in the figure. The pitch $(p)$ and included angle of the thread are $4$ $\text{mm}$ and $60^{\circ}$, respectively. The diameter of the best size wire is _______________ $\text{mm}$ (round off to $2$ decimal places).
In a direct current arc welding process, the power source has an open circuit voltage of $100\: V$ and short circuit current of $1000 \:A$. Assume a linear relationship between voltage and current. The arc voltage $(V)$ varies with the arc length $(l)$ ... volts and $l$ is in $\text{mm}$. The maximum available arc power during the process is ________________ $\text{kVA}$ (in integer).
A cylindrical billet of $100$ $\text{mm}$ diameter and $100$ $\text{mm}$ length is extruded by a direct extrusion process to produce a bar of $L$-section. The cross sectional dimensions of this $L$-section bar are shown in the figure. The total extrusion pressure ... $1.05$, then the maximum force required at the start of extrusion is ________________ $\text{kN}$ (round off to one decimal place).
A project consists of five activities $\text{(A, B, C, D and E)}$. The duration of each activity follows beta distribution. The three time estimates (in weeks) of each activity and immediate predecessor$(s)$ are listed in the table. The expected time of the project completion is ________________ weeks (in integer ... time Pessimistic time A 4 5 6 None B 1 3 5 A C 1 2 3 A D 2 4 6 C E 3 4 5 B, D
A rigid tank of volume of $8 \:m^{3}$ is being filled up with air from a pipeline connected through a valve. Initially the valve is closed and the tank is assumed to be completely evacuated. The air pressure and temperature inside the pipeline are maintained ... The final temperature of the tank after the completion of the filling process is _______________ $K$ (round off to the nearest integer).
At steady state, $500$ $\text{kg/s}$ of steam enters a turbine with specific enthalpy equal to $3500$ $\text{kJ/kg}$ and specific entropy equal to $6.5$ ${kJ \cdot kg^{-1} \cdot K^{-1}}$. It expands reversibly in the turbine to the condenser pressure. Heat loss occurs ... ${kJ \cdot kg^{-1} \cdot K^{-1}}$, respectively, the work output from the turbine is ______________ $\text{MW}$ (in integer).
A uniform wooden rod (specific gravity = $0.6$, diameter = $4$ $\text{cm}$ and length = $8\:m$) is immersed in the water and is hinged without friction at point $A$ on the waterline as shown in the figure. A solid spherical ball made of lead (specific gravity = $11.4$) is ... $\pi = 3.14$. Radius of the ball is _____________ $\text{cm}$ (round off to $2$ decimal places).
Consider steady state, one-dimensional heat conduction in an infinite slab of thickness $2L (L = 1\:m)$ as shown in the figure. The conductivity $(k)$ of the material varies with temperature as $\text{k = CT}$, where $T$ is the temperature in $K$, and $C$ is a ... slab. If both faces of the slab are maintained at $600\: K$, then the temperature at $X = 0$ is _______________ $K$ (in integer).
Saturated vapor at $200\: ^{\circ}C$ condenses to saturated liquid at the rate of $150$ $\text{kg/s}$ on the shell side of a heat exchanger (enthalpy of condensation $h_{fg} = 2400$ $\text{kJ/kg}$ ... effectiveness of the heat exchanger is $0.9$, then the mass flow rate of the fluid in the tube side is ____________ $\text{kg/s}$ (in integer).
Consider a hydrodynamically and thermally fully-developed, steady fluid flow of $1$ $\text{kg/s}$ in a uniformly heated pipe with diameter of $0.1\: m$ and length of $40 \:m$. A constant heat flux of magnitude $15000\: W/m^{2}$ is imposed on the outer ... on the basis of the pipe diameter. The pipe surface temperature at the exit is _______________ $^{\circ}C$ (round off to the nearest integer).