Recent questions tagged gateme-2014-set3

A force $P$ is applied at a distance $x$ from the end of the beam as shown in the figure. What would be the value of $x$ so that the displacement at ‘$A$’ is equal to zer...

An annular disc has a mass $m$, inner radius $R$ and outer radius $2R$. The disc rolls on a flat surface without slipping. If the velocity of the center of mass is $v$, t...

An analytic function of a complex variable $z = x + i y$ is expressed as $f (z) = u(x, y) + i v(x, y)$ , where $i=\sqrt{-1}$ . If $u(x, y) = x^2 − y^2$ , then expression...

The real root of the equation $5x − 2 \cos x −1 = 0$ (up to two decimal accuracy) is _______

Consider two solutions $x(t)=x_1(t)$ and $x(t)=x_2(t)$ of the differential equation $\dfrac{d^2x(t)}{dt^2}+x(t)=0, \: t>0$ such that $x_1(0)=1, \dfrac{dx_1(t)}{dt} \bigg ...

The damping ratio of a single degree of freedom spring-mass-damper system with mass of $1 kg$, stiffness $100 N/m$ and viscous damping coefficient of $25 N.s/m$ is ______...

Consider a simply supported beam of length, $50h$, with a rectangular cross-section of depth, $h$, and width, $2h$. The beam carries a vertical point load, P, at its mid-...

A body of mass (M) $10$ $kg$ is initially stationary on a $45^{\circ}$ inclined plane as shown in figure. The coefficient of dynamic friction between the body and the pla...

A drum brake is shown in the figure. The drum is rotating in anticlockwise direction. The coefficient of friction between drum and shoe is $0.2$. The dimensions shown in ...

A machine produces $0$, $1$ or $2$ defective pieces in a day with associated probability of $1/6$, $2/3$ and $1/6$, respectively. The mean value and the variance of the n...

The hot tearing in a metal casting is due tohigh fluidityhigh melt temperaturewide range of solidification temperaturelow coefficient of thermal expansion

The stress-strain curve for mild steel is shown in the figure given below. Choose the correct option referring to both figure and table.$\begin{array}{|l|l|}\hline \textb...

Cutting tool is much harder than the workpiece. Yet the tool wears out during the tool-work interaction, becauseextra hardness is imparted to the workpiece due to coolant...

Match the casting defects (Group A) with the probable causes (Group B):$\begin{array}{|l|l|}\hline \textbf{Group A} & \textbf{Group B} \\ \hline \text{P: Hot tears} & ...

A minimal spanning tree in network flow models involvesall the nodes with cycle/loop allowedall the nodes with cycle/loop not allowedshortest path between start and end n...

A straight turning operation is carried out using a single point cutting tool on an AISI $1020$ steel rod. The feed is $0.2$ $mm/rev$ and the depth of cut is $0.5$ $mm$. ...

Which one of the following pairs of equations describes an irreversible heat engine?$\oint \delta Q 0$ and $\oint \dfrac{\delta Q}{T} < 0 \\$$\oint \delta Q< 0$ and $\oin...

The process utilizing mainly thermal energy for removing material isUltrasonic MatchingElectrochemical Matching Abrasive Jet MatchingLaser Beam Matching

The actual sales of a product in different months of a particular year are given below:$$\begin{array}{|c|c|c|c|c|c|c|}\hline \text{September} & \text{October} & \text{...

A sample of moist air at a total pressure of $85$ $kPa$ has a dry bulb temperature of $30^oC$ (saturation vapour pressure of water = $4.24$ $kPa$). If the air sample has ...

A source at a temperature of $500$ $K$ provides $1000$ $kJ$ of heat. The temperature of environment is $27^oC$. The maximum useful work (in $kJ$) that can be obtained fro...

For a gas turbine power plant, identify the correct pair of statements.P. Smaller in size compared to steam power plant for same power outputQ. Starts quickly compared to...

Consider the turbulent flow of a fluid through a circular pipe of diameter, D. Identify the correct pair of statements.The fluid is well-mixedThe fluid is unmixed$Re_D$ <...

Consider a long cylindrical tube of inner and outer radii, $r_i$ and $r_o$ , respectively, length, $L$ and thermal conductivity, $k$. Its inner and outer surfaces are mai...

Gear $2$ rotates at $1200$ $rpm$ in counter clockwise direction and engages with Gear $3$. Gear $3$ and Gear $4$ are mounted on the same shaft. Gear $5$ engages with Gear...

Which one of following is NOT correct?Intermediate principal stress is ignored when applying the maximum principal stress theoryThe maximum shear stress theory gives the ...

A mass $m_1$ of $100$ $kg$ traveling with a uniform velocity of $5$ $m/s$ along a line collides with a stationary mass $m_2$ of $1000$ $kg$. After the collision, both the...

Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase angle (in degree) of the displacement with respect to...

Two solid circular shafts of radii $R_1$ and $R_2$ are subjected to same torque. The maximum shearstresses developed in the two shafts are $\tau _1$ and $\tau _2$. If $R_...

A rotating steel shaft is supported at the ends. It is subjected to a point load at the center. The maximum bending stress developed is $100$ $MPa$. If the yield, ultimat...