# Recent questions tagged gate2017

The value of $\underset{x\rightarrow 0}{lim}\:\frac{tan\left ( x \right )}{x}$ is ________________.
The real part of $6e^{i\pi /3}$ is _______________.
The number of positive roots of the function $f(x)$ shown below in the range $0<x<6$ is ___________________.
Let $i$ and $j$ be the unit vectors in the $x$ and $y$ directions, respectively. For the function $F\left ( x,y \right )=x^{3}+y^{2}$ the gradient of the function. i.e.. $\triangledown F$ is given by $3x^{2}i-2yj$ $6x^{2}y$ $3x^{2}i+2yj$ $2yi-3x^{2}j$
The marks obtained by a set of students are: $38,\:84,\:45,\:70,\:75,\:60,\;48$. The mean and median marks, respectively, are $45$ and $75$ $55$ and $48$ $60$ and $60$ $60$ and $70$
The volumetric properties of two gases $M$ and $N$ are described by the generalized compressibility chart which expresses the compressibility factor $(Z)$ as a function of reduced pressure and reduced temperature only. The operating pressure $(P)$ and temperature $(T)$ of two gases $M$ and $N$ along with their critical ... $Z_{N}$ is $Z_{M}=8Z_{N}$ $Z_{M}=3Z_{N}$ $Z_{M}=Z_{N}$ $Z_{M}=0.333Z_{N}$
Water is heated at atmospheric pressure from $40^{\circ}C$ to $80^{\circ}C$ using two different processes. In process $I$, the heating is done by a source at $80^{\circ}C$. In process $II$, the water is first heated from $40^{\circ}C$ ... of water in process $II$ is greater than enthalpy change in process $I$ Process $I$ is closer to reversibility Process $II$ is closer to reversibility
In a venturi meter. $\Delta P_{1}$ and $\Delta P_{2}$ are the pressure drops corresponding to volumetric flowrates $Q_{1}$ and $Q_{2}$. If $Q_{2}/Q_{1}=2$, then $\Delta P_{2}/\Delta P_{1}$ equals $2$ $4$ $0.5$ $0.25$
The thickness of laminar boundary layer over a flat plate varies along the distance from the leading edge of the plate. As the distance increase, the boundary layer thickness increases decreases initially increases and the decreases initially decreases and then increases
Which of the following is the correct sequence of equipment for size reduction of solids?
A gas bubble (gas density $\rho_{g} =2\:kg/m^{3}$ ; bubble diameter $D=10^{-4}\:m$ is rising vertically through water (density $\rho =1000\:kg/m^{3}$; viscosity $\mu =0.001$ $Pa.\:s$ ... of $g=9.81\:m/s^{2}$. The terminal rising velocity of the bubble (in $cm/s$), rounded to $2$ decimal places, is ___________ $cm/s$.
The one-dimensional unsteady heat conduction equation is $\rho C_{p}\frac{\partial T}{\partial t}=\frac{1}{r^{n}}\frac{\partial }{\partial r}\left ( r^{n}k\frac{\partial T}{\partial r} \right )$ where $T$ - temperature, $t$ - time, $r$ - radial position, $k$ - ... density, and $c_{p}$ - specific heat. For the cylindrical coordinate system, the value of $n$ in the above equation is $0$ $1$ $2$ $3$
In a heat exchanger, the inner diameter of a tube is $25\:mm$ and its outer diameter is $30\:mm$. The overall heat transfer coefficient based on the inner area is $360\:W/m^{2}.^{\circ}C$. Then, the overall heat transfer coefficient based on the outer area, rounded to the nearest integer, is _______________ $W/m^{2}.^{\circ}C$.
Which of the following conditions are valid at the plait point? Density difference between the extract and raffinate phases is zero Interfacial tension between the extract and raffinate phases is zero Composition difference between the extract and raffinate phases is zero $P$ and $Q$ only $Q$ and $R$ only $P$ and $R$ only $P$, $Q$ and $R$
The composition of vapour entering a tray in a distillation column is $0.47$. The average composition of the vapour leaving the tray is $0.53$. The equilibrium composition of the vapour corresponding to the liquid leaving this tray is $0.52$. All the ... of the more volatile component. The Murphree efficiency based on the vapour phase, rounded to the nearest integer, is _____________ $\%$.
Consider steady state mass transfer of a solute $A$ from a gas phase to a liquid phase. The gas phase bilk and interface mole fractions are $y_{A,G}$ and $y_{A,i}$ ... transfer resistance is negligible in the gas phase only negligible in the liquid phase only negligible in both the phases considerable in both the phases
The following reaction rate curve is shown for a reaction $A{\rightarrow}P$. Here, $(-r_{A})$ and $X_{A}$ represent reaction rate and conversion, respectively. The feed is pure $A$ and $90\%$ conversion is desired. Which amongst the following reactor configuration gives the lowest ... volume of the reactor$(s)$? $CSTR$ followed by $PFR$ Two $CSTRs$ in series $PFR$ followed by $CSTR$ A single $PFR$
Consider a first order catalytic reaction in a porous catalyst pellet. Given $R$ - characteristics length of the pellet; $D_{e}$ - effective diffusivity; $k_{c}$ - mass transfer coefficient; $k_{1}$ - rate constant based on volume of the catalyst pellet; $C_{s}$ - concentration of reactant on the pellet surface. ... $R\sqrt{\frac{k_{1}C_{s}}{D_{e}}}$ $R\sqrt{\frac{D_{e}}{k_{1}}}$
For a solid-catalyzed gas phase reversible reaction, which of the following statements is ALWAYS TRUE? Adsorption is rate-limiting Desorption is rate-limiting solid catalyst does not affect equilibrium conversion Temperature does not effect equilibrium conversion
Match the variable in Group-$1$ with the instruments in Group-$2$. $\begin{array}{cc}\ &\text{Group-$1$} & \text{Group-$ ... $P-I,\:Q-II,\:R-IV,\:S-III$ $P-IV,\:Q-I,\:R-II,\:S-III$ $P-III,\:Q-II,\:R-I,\:S-IV$
An $LVDT$ (Linear Variable Differential Transformation) is a transducer used for converting displacement to voltage voltage to displacement resistance to voltage voltage to current
The cost of a new pump (including installation) is $24,000$ Rupees. The pump has a useful life of $10$ years. Its salvage value is $4000$ Rupees. Assuming straight line depreciation, the book value of the pump at the end of $4^{th}$ year, rounded to the nearest integer, is ____________ Rupees.
The $DCDA$ (Double Contact Double Absorption) process is used for the manufacture of urea sulphuric acid nitric acid ammonia
Match the polymerization precesses in Group-$1$ with the polymers in Group-$2$ ... $P-III,\:Q-II,\:R-I$ $P-I,\:Q-III,\:R-II$ $P-II,\:Q-I,\:R-III$
The purpose of methanation reaction used in ammonia plants is to remove $CO$ as it is catalyst poison increase the amount of hydrogen remove sulphur as it is a catalyst poison utilize methane as a catalyst for ammonia synthesis
For the initial value problem $\frac{dx}{dt}=sin\left ( t \right ),\:\:\:\:x\left ( 0 \right )=0$ the value of $x$ at $t=\pi /3$ , is _____________.
The Laplace transform of a function is $\frac{s+1}{s\left ( s+2 \right )}$ The initial and final values, respectively, of the function are $0$ and $1$ $1$ and $\frac{1}{2}$ $\frac{1}{2}$ and $1$ $\frac{1}{2}$ and $0$
Match the problem type in Group-$1$ with the numerical method in Group-$2$. $\begin{array}{cc}\ &\text{Group-$1$} & \text{Group-$ ... $P-I,\:Q-II,\:R-IV,\:S-III$ $P-IV,\:Q-III,\:R-II,\:S-I$ $P-II,\:Q-I,\:R-IV,\:S-III$
A box has $6$ red balls and $4$ white balls. A ball is picked at random and replaced in the box, after which a second ball is picked. The probability of both the balls being red, rounded to $2$ decimal places, is ___________.
An aqueous salt-solution enters a crystallizer operating at steady state at $25^{\circ}C$. The feed temperature is $90^{\circ}C$ and the salt concentration in the feet is $40$ weight $\%$. The salt crystallizes as a pentahydrate. The crystals and the mother liquor ... required for a production rate of $100\:kg/s$ of the hydrate salt, rounded to the nearest integer, is ______________ $kg/s$.
Reaction $A{\rightarrow}B$ is carried out in a reactor operating at steady state and $1$ mol/$s$ of pure $A$ at $425^{\circ}C$ enters the reactor. The outlet stream leaves the reactor at $325^{\circ}C$. The heat input to the reactor is $17\:kW$. The heat of ... are $0.1$ and $0.15$, respectively. The molar flowrate of $B$ leaving the reactor, rounded to $2$ decimal places, is ________ mol/$s$.
The pressure of a liquid is increased isothermally. The molar volume of the liquid decreases from $50.45\times 10^{-6}$ $m^{3}$/mol to $48\times 10^{-6}$ $m^{3}$/mol during this process. The isothermal compressibility of the liquid is $10^{-9}$ $Pa^{-1}$, which can be independent of pressure. The change in the molar Gibbs free energy of the liquid, rounded to nearest integer, is ________ $J$/mol.
A sparingly soluble gas (solute) is in equilibrium with a solvent at $10$ bar. The mole fraction of the solvent in the gas phase is $0.01$. At the operating temperature and pressure, the fugacity coefficient of the solute in the gas phase and the Henry's law ... liquid phase obeys Henry's law. The MOLE PERCENTAGE of the solute in the liquid phase, rounded to $2$ decimal places, is ____________.
The vapour pressure of a pure substance at a temperature $T$ is $30$ bar. The actual and ideal gas values of $g/RT$ for the saturated vapour at this temperature $T$ and $30$ bar are $7.0$ and $7.7$, respectively,. Here, $g$ is the molar ... energy and $R$ is the universal gas constant. The fugacity of the saturated liquid at these conditions, rounded to $1$ decimal place, is ________________ bar.
Oil is being delivered at a steady flowrate through a circular pipe of radius $1.25\times10^{-2}\:m$ and $10\:m$. The pressure drop across the pipe is $500\:Pa$. The shear stress at the pipe wall, rounded to $2$ decimal places, is _______________ $Pa$.
The following table provides four sets of Fanning friction factor data, for different values of Reynolds number $(Re)$ and roughness factor $\left ( \frac{k}{D} \right ).$ Which of the above sets of friction factor data is correct? Set $I$ Set $II$ Set $III$ Set $IV$
A propeller (diameter $D=15\:m$) rotates at $N=1$ revolution per second $(rps)$. To understand the flow around the propeller, a lab-scale model is made. Important parameters to study the flow are velocity of the propeller tip $(V= \pi ND)$, diameter $D$ ... $rps$.
Size analysis was carried out on a sample of gravel. The data for mass fraction $(x_{i})$ and average particle diameter $(D_{pi})$ of the fraction is given in the table below: $\begin{array}{clcI|cI|cI|cI|c}\hline &\textbf{x$_{i}$} & \textbf{D$ ... $mm$.
A fluid flows over a heated horizontal plate maintain at temperature $T_{W}$. The bulk temperature of the fluid is $T_{\infty }$ ... $\frac{k}{\delta _{t}}$ $\frac{3}{2}\frac{k}{\delta _{t}}$ $2\frac{k}{\delta _{t}}$
In nucleate boiling, the pressure inside a bubble is higher than the pressure of the surrounding liquid. Assuming that both the liquid and vapour are saturated, the temperature of the liquid will ALWAYS be at $100\:^{\circ}C$ lower than the temperature of the vapour equal to the temperature of the vapour higher than the temperature of the vapour