Recent questions tagged gateme-2017-set1

Moist air is treated as an ideal gas mixture of water vapour and dry air (molecular weight of air$= 28.84$ and molecular weight of water $=18$). At a location, the total ...

$P(0, 3), Q (0.5, 4)$ and $R(1, 5)$ are three points on the curve defined by $f(x)$. Numerical integration is carried out using both Trapezoidal rule and Simpson's rule w...

For a steady flow, the velocity field is $\vec{V}=(-x^{2}+3y)\hat{i}+(2xy)\hat{j}$. The magnitude of the acceleration of a particle at $(1, -1)$ is$2$$1$$2\sqrt{5}$$0$

A parametric curve defined by $x= \cos \left ( \dfrac{\Pi u}{2} \right ), y= \sin \left ( \dfrac{\Pi u}{2} \right )$ in the range $0 \leq u \leq 1$ is rotated about the $...

For the vector $\vec{V}=2yz\hat{i}+3xz \hat{j}+4xy \hat{k}$, the value of $\bigtriangledown$. $(\bigtriangledown \times \vec{V})$ is ________.

Consider the matrix $P=\begin{bmatrix} \dfrac{1}{\sqrt{2}} & 0 &\dfrac{1}{\sqrt{2}} \\ 0 & 1 & 0\\ -\dfrac{1}{\sqrt{2}} &0 & \dfrac{1}{\sqrt{2}}\end{bmatrix}$ Which one ...

The pressure ratio across a gas turbine (for air, specific heat at constant pressure, $c_{p}=1040 J/kg.K$ and ratio of specific heats, $\gamma=1.4$) is $10$. If the inlet...

One kg of an ideal gas (gas constant, $R= 400 J/kg.K$; specific heat at constant volume, $c_{v}=1000 J/kg.K$) at $1$ bar, and $300$ K is contained in a sealed rigid cylin...

Consider steady flow of an incompressible fluid through two long and straight pipes of diameters $d_{1}$ and $d_{2}$ arranged in series. Both pipes are of equal length an...

The velocity profile inside the boundary layer for flow over a flat plate is given as $\dfrac{u}{U_{\infty }}= \sin \left ( \dfrac{\Pi }{2}\dfrac{y}{\delta } \right )$, w...

Metric thread of $0.8$ mm pitch is to be cut on a lathe. Pitch of the lead screw is $1.5$ mm. If the spindle rotates at $1500$ rpm, the speed of rotation of the lead scre...

In an arc welding process, welding speed is doubled. Assuming all other process parameters to be constant, the cross-sectional area of the weld bead will Increase by $25\...

Match the processes with their characteristics:$\begin{array}{|l|l|l|} \hline & \textbf{Process} & & \textbf{Characteristics} \\ \hline P. & \text{Electrical Discharge Ma...

Cylindrical pins of diameter $15^{\pm0.020}$ mm are being produced on a machine. Statistical quality control tests show a mean of $14.995$ mm and standard deviation of $0...

In a metal forming operation when the material has just started yielding. the principal stresses are $\sigma_{1}=+180 MPa, \sigma_{2}=-100 MPa, \sigma_{3}=0$. Following v...

Consider the schematic of a riveted lap joint subjected to tensile load $F$, as shown below. Let $d$ be the diameter of the rivets, and $S_{f}$ be the maximum permissible...

The damping ratio for a viscously damped spring-mass system, governed by the relationship $m \dfrac{d^{2}x}{dt^{2}}+c\dfrac{dx}{dt}+kx=F(t)$, is given by$\sqrt{\dfrac{c}{...

The following figure shows the velocity-time plot for a particle travelling along a straight line. The distance covered by the particle from $t=0$ to $t=5$s is __________...

Consider a beam with circular cross-section of diameter $d$. The ratio of the second moment of area about the neutral axis to the section modulus of the area is$\dfrac{d}...

A motor driving a solid circular steel shaft transmits $40$ kW of power at $500$ rpm. If the diameter of the shaft is $40$ mm, the maximum shear stress in the shaft is __...

A particle of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by $r(t)=t^{2}, \theta (t)=t$, where $t$ is time. The Kinetic energy of the p...

A heat pump absorbs $10$kW of heat from outside environment at $250$ K while absorbing $15$ kW of work. It delivers the heat to a room that must be kept warm at $300$ K. ...

The molar specific heat at constant volume of an ideal gas is equal to $2.5$ times the universal gas constant ($8.314$ J/mol.K). When the temperature increases by $100$K,...

A six-face fair dice is rolled a large number of times. The mean value of the outcomes is ________.

The differential equation $\dfrac{d^{2}y}{dx^{2}}+16y=0$ for $y(x)$ with the two boundary conditions $\dfrac{dy}{dx}\bigg \vert _{x=0}=1$ and $\dfrac{dy}{dx}\bigg \vert_{...

Consider the following partial differential equation for $u(x, y)$, with the constant $c 1$:$\dfrac{\partial u}{\partial y}+c\dfrac{\partial u}{\partial x}=0$Solution of...

The value of $\displaystyle{}\lim_{x \rightarrow 0}\dfrac{x^{3}-\sin(x)}{x}$ is$0$$3$$1$$-1$

The product of eigenvalues of the matrix $P$ is$P=\begin{bmatrix}2 & 0 & 1\\ 4& -3 &3 \\ 0 & 2 & -1\end{bmatrix}$$-6$$2$$6$$-2$