Recent questions tagged gateme-2020-set2

The directional derivative of $f(x,y,z) = xyz$ at point $(-1,1,3)$ in the direction of vector $\hat{i} – 2 \hat{j} +2 \hat{k}$ is$3\hat{i} – 3 \hat{j} - \hat{k} \\$$- \df...

The function $f(z)$ of complex variable $z=x+iy$, where $i=\sqrt{-1}$, is given as $f(z)=(x^3-3xy^2)+i \: v(x,y)$. For this function to be analytic, $v(x,y)$ should be$(3...

The forecast for the monthly demand of a product is given in the table below:$\begin{array}{|c|c|c|} \hline \textbf{Month} & \textbf{Forecast} & \textbf{Actual Sales} \\ ...

One kg of air in a closed system undergoes an irreversible process from an initial state of $p_1=1$ bar (absolute) and $T_1=27^\circ C$, to a final state of $p_2=3$ bar (...

For the integral $\displaystyle \int_0 ^{\pi/2} (8+4 \cos x) dx$, the absolute percentage error in numerical evaluation with the Trapezoidal rule, using only the end poin...

A hollow spherical ball of radius $20$ cm floats in still water, with half of its volume submerged. Taking the density of water as $1000 \: kg/m^3$, and the acceleration ...

Uniaxial compression test data for a solid metal bar of length $1$ m is shown in the figure.The bar material has a linear elastic response from $O$ to $P$ followed by a n...

The turning moment diagram of a flywheel fitted to a fictitious engine is shown in the figure.The mean turning moment is $2000$ Nm. The average engine speed is $1000$ rpm...

A rigid block of mass $m_1=10$ kg having velocity $v_0=2 \: m/s$ strikes a stationary block of mass $m_2=30$ kg after traveling $1$ m along a frictionless horizontal surf...

A steel spur pinion has a module $(m)$ of $1.25$ mm, $20$ teeth and $20^\circ$ pressure angle. The pinion rotates at $1200$ rpm and transmits power to a $60$ teeth gear. ...

A mould cavity of $1200 \: cm^3$ volume has to be filled through a sprue of $10$ cm length feeding a horizontal runner. Cross-sectional area at the base of the sprue is $...

A cylindrical bar with $200$ mm diameter is being turned with a tool having geometry $0 ^\circ – 9 ^\circ -7^ \circ – 8^ \circ – 15^ \circ – 30^ \circ – 0.05$ inch (coord...

There are two identical shaping machines $S_1$ and $S_2$. In machine $S_2$, the width of the workpiece is increased by $10\%$ and the feed is decreased by $10\%$, with re...

Bars of $250$ mm length and $25$ mm diameter are to be turned on a lathe with a feed of $0.2$ mm/rev. Each regrinding of the tool costs Rs. $20$. The time required for ea...

A point $‘P’$ on a CNC controlled $XY$-stage is moved to another point $‘Q’$ using the coordinate system shown in the figure below and rapid positioning command $(G00)$A ...

For a single item inventory system, the demand is continuous, which is $10000$ per year. The replenishment is instantaneous and backorders ($S$ units) per cycle are allow...

Consider a flow through a nozzle, as shown in the figure below.The air flow is steady, incompressible and inviscid. The density of air is $1.23 \: kg/m^3$. The pressure d...

Water (density $1000 \: kg/m^3$) flows through an inclined pipe of uniform diameter. The velocity, pressure and elevation at section $\textbf{A}$ are $V_A=3.2 \: m/s, \: ...

The spectral distribution of radiation from a black body at $T_1=3000 \: K$ has a maximum at wavelength $\lambda_{\text{max}}$. The body cools down to a temperature $T_2$...

Water flows through a tube of $3$ cm internal diameter and length $20$ m. The outside surface of the tube is heated electrically so that it is subjected to uniform heat f...

Air is contained in a frictionless piston-cylinder arrangement as shown in the figure.The atmosphere pressure is $100$ kPa and the initial pressure of air in the cylinder...

Moist air at $105$ kPa, $30^\circ C$ and $80\%$ relative humidity flows over a cooling coil in an insulated air-conditioning duct. Saturated air exits the duct at $100$ k...

In a steam power plant, superheated steam at $10$ MPa and $500^\circ C$, is expanded isentropically in a turbine until it becomes a saturated vapour. It is then reheated ...

Keeping all other parameters identical, the Compression Ratio (CR) of an air standard diesel cycle is increased from $15$ to $21$. Take ratio of specific heats $=1.3$ and...