Recent questions tagged gate2016

Which one of the following is an iterative technique for solving a system of simultaneous linear algebraic equations? Gauss elimination Gauss-Jordan Gauss-Seidel $LU$ decomposition
The Laplace transform of $e^{at}\sin\left ( bt \right )$ is $\frac{b}{\left ( s-a \right )^{2}+b^{2}}$ $\frac{s-a}{\left ( s-a \right )^{2}+b^{2}}$ $\frac{s-a}{\left ( s-a \right )^{2}-b^{2}}$ $\frac{b}{\left ( s-a \right )^{2}-b^{2}}$
What are the modulus $\left ( r \right )$ and argument $\left ( \theta \right )$ of the complex number $3+4i$ ? $r=\sqrt{7}, \theta =tan^{-1}\left ( \frac{4}{3} \right )$ $r=\sqrt{7}, \theta =tan^{-1}\left ( \frac{3}{4} \right )$ $r={5}, \theta =tan^{-1}\left ( \frac{3}{4} \right )$ $r={5}, \theta =tan^{-1}\left ( \frac{4}{3} \right )$
A liquid mixture of ethanol and water is flowing as inlet stream $P$ into a stream splitter. It is split into two streams, $Q$ and $R$, as shown in the figure below. The flowrate of $P$, containing $30$ mass$\%$ of ethanol, is $100\:kg/h$. What is the ... additional specification$(s)$ required to determine the mass flowrates and composition (mass $\%$) of the two exit streams? $0$ $1$ $2$ $3$
The partial molar enthalpy (in $kJ$/mol) of species $1$ in a binary mixture is given by $\bar{h}_{1}=2 -60x_{2}^{2}+100x^{1}x_{2}^{2},$ where $x_{1}$ and $x_{2}$ are the mole fractions of species $1$ and $2$, respectively. The partial molar enthalpy (in $kJ$/mol, rounded off to the first decimal place) of species $1$ at infinite dilution is _________
For a flow through a smooth pipe, the Fanning friction factor $(f)$ is given by $f=mRe^{-0.2}$ in the turbulent flow regime, where $Re$ is the Reynolds number and $m$ is a constant. Water flowing through a section of this pipe with a velocity $1\:m/s$ results in a frictional ... the pressure drop across this section (in $kPa$), when the velocity of water is $\:2 m/s$? $11.5$ $20$ $34.8$ $40$
In a cyclone separator used for separation of solid particles from a dust laden gas, the separation factor is defined as the ratio of the centrifugal force to the gravitational force acting on the particle. $S_{r}$ denotes the separation factor at a location (near the wall) ... $S_{r}$ depends on tangential velocity of the particle $S_{r}$ depends on the radial location $(r)$ of the particle
A vertical cylindrical vessel has a layer of kerosene (of density $800\: kg/m^{3}$) over a layer of water (of density $1000 \:kg/m^{3}$). $L$ - shaped glass tubes are connected to the column $30\: cm$ apart. The interface between the two layers lies between ... $cm$, rounded off to the first decimal place) of the interface from the point at which the lower $L$ - tube is connected is _________
A composite wall is made of four different materials of construction in the fashion shown below. The resistance (in $K/W$) of each sections of the wall is indicated in the diagram. The overall resistance (in $K/W$, rounded off to the first decimal place) of the composite wall, in the direction of heat flow, is ________
Steam at $100^{\circ}C$ is condensing on a vertical steel plate. The condensate flow is laminar. The average Nusselt numbers are $Nu_{1}$ and $Nu_{2}$, When the plate temperatures are $10^{\circ}C$ and $55^{\circ}C$, respectively. Assume the physical properties of the fluid and steel to ... -type condensation, what is the value of the ratio $\frac{Nu_{2}}{Nu_{1}}$ ? $0.5$ $0.84$ $1.19$ $1.41$
A binary liquid mixture of benzene and toluene contains $20$ mol$\%$ of benzene. At $350 \:K$ the vapour pressures of pure benzene and pure toluene are $92\: kPa$ and $35\: KPa$, respectively. The mixture follows Raoult's law. The equilibrium vapour phase mole fraction (rounded off to the second decimal place) of benzene in contact with this liquid mixture at $350\:K$ is ________
Match the dimensionless numbers in $Group-I$ with the ratios in $Group-2$. $\begin{array}{cc}\\ &\text{Group-1} & \text{Group-2} \\ &\text{P. Biot number} & \text{ I.$\frac{buoyancy force}{viscous force}$} \\ &\text{ Q. Schmidt number} & \text{II.$\frac{internal thermal resistance of a solid}{boundary layer ... $Q-I$, $R-III$ $P-I$, $Q-III$, $R-II$ $P-III$, $Q-I$, $R-II$ $P-II$, $Q-III$, $R-I$
For what value of Lewis number, the wet-bulb temperature and adiabatic saturation temperature are nearly equal? $0.33$ $0.5$ $1$ $2$
For a non-catalytic homogeneous reaction $A\rightarrow B$, the rate expression at $300\:K$ is $-r_{A}$\left (mol\; m^{-3} s^{-1}\right )=\frac{10C_{A}}{1+5C_{A}}$, where$C_{A}$is the concentration of$A$(in$mol\;/m^{3}$). Theoretically, the upper limit for the magnitude of the reaction rate ($-r_{A}\:in\:mol\:m^{-3}s^{-1}$, rounded off to the first decimal place) at$300\:K$is _________ 0 votes 0 answers The variations of the concentration$\left ( C_{A} ,C_{R}\:and\:C_{S}\right )$for three species$\left ( A,R\:and\:S \right )$with time, in an isothermal homogeneous batch reactor are shown in the figure below. Select the reaction scheme that correctly represents the above plot. The numbers in the reaction schemes shown below, represent the first order rate constants in unit of$s^{-1}$. 0 votes 0 answers Hydrogen iodide decomposes through the reaction$2HI\leftrightharpoons H_{_{2}}+I_{2}$. The value of the universal gas constant$R$is$8.314 \:J\:mol^{-1}K^{-1}$. The activation energy for the forward reaction is$184000\:J\:mol^{-1}$. The ratio (rounded off to the first decimal place) of the forward reaction rate at$600 \:K$to that at$550\:K$is ________ 0 votes 0 answers Match the instruments in$Group-I$with process variable in$Group-2$...$Q-I$,$R-IIIP-Il$,$Q-III$,$R-IP-III$,$Q-lI$,$R-IP-IIl$,$Q-I$,$R-Il$0 votes 0 answers What is the order of response exhibited by a$U$-tube manometer? Zero order First order Second order Third order 0 votes 0 answers A system exhibits inverse response for a unit step change in the input. Which one of the following statement must necessarily be satisfied? The transfer function of the system has at least one negative pole The transfer function of the system has at least one ... transfer function of the system has at least one negative zero The transfer function of the system has at least one positive zero 0 votes 0 answers Two design options for a distillation system are being compared based on the total annual cost. Information available is as follows: ... above information, what is the total annual cost ($Rs$in lakhs/year) of the better option?$4042.492128$0 votes 0 answers Standard pipes of different schedule numbers and standard tubes of different$BWG$numbers are available in the market. For a pipe/tube of a given nominal diameter, which one the following statements is$TRUE$? Wall thickness increases with increase in both the ... the schedule number and the$BWG$number Neither the schedule number, nor the$BWG$number has any relation to wall thickness 0 votes 0 answers Terms used in engineering economics have standard definitions and interpretations. Which one of the following statements is$INCORRECT$? The profitability measure 'return on investment' does not consider the time value of money A cost index is an index value for ... different capacity Payback period is calculated based on the payback time for the sum of the fixed and the working capital investment 0 votes 0 answers India has no elemental sulphur deposits that can be economically exploited. In India, which one of the following industries produces elemental sulphur as a by-product? Coal carbonisation plants Petroleum refineries Paper and pulp industries Iron and steel making plants 0 votes 0 answers Two paper pulp plants$P$and$Q$...$P$and Plant$Q$both use the Kraft process Plant$P$uses Sulfite process Plant$P$uses Kraft process 0 votes 0 answers Match the industrial processes in$Group-I$with the catalyst materials in$Group-2$.$\begin{array}{cc}\\ \\ &\text{Group-1} & \text{Group-2} \\ &\text{P. Ethylene polymerisation} & \text{ I. Nickel} \\ &\text{ Q. Petroleum feedstock cracking} & \text{II. Vanadium pentoxide} \\ &\text{R. Oxidation of $...$R-III$,$S-IIP-I$,$Q-II$,$R-III$,$S-IVP-II$,$Q-III$,$R-IV$,$S-I$0 votes 0 answers A set of simultaneous linear algebraic equations is represented in a matrix form as shown below. ...$x_{3}$is ___________ 0 votes 0 answers The model$y=mx^{2}$is to be fit to the data given below.$\begin{array}{|cl|cI|}\hline &{x} & {1} & {\sqrt{2}} & {\sqrt{3}} \\ \hline &{y} & {2} & {5} & {8} \\ \hline \end{array}$Using linear regression, the value (rounded off to the second decimal place) of$m$is _________ 0 votes 0 answers The Lagrange mean-value theorem is satisfied for$f\left ( x \right )=x^{3}+5$, in the interval$\left ( 1,4 \right )$at a value (rounded off to the second decimal place) of$x$equal to __________ 0 votes 0 answers Values of$f\left ( x \right )$in the interval$\left [ 0,4 \right ]$...$1$, the numerical approximation (rounded off to the second decimal place) of$\int_{0}^{4}f\left ( x \right )dx$is ______________ 0 votes 0 answers An ideal gas is adiabatically and irreversibly compressed from$3$bar and$300\:K$to$6$bar in a closed system. The work required for the irreversible compression is$1.5$times the work that is required for reversible compression from the same initial ... in$K\$, rounded off to the first decimal place) of the gas at the final state in the irreversible compression case is _______________