# Recent questions tagged gate2019

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A system of $n$ homogeneous linear equations containing $n$ unknowns will have non-trivial solutions if and only if the determinant of the coefficient matrix is $1$ $-1$ $0$ $\infty$
The value of the expression $\underset{x\rightarrow \frac{\pi }{2}}{lim}\:\left | \frac{tan\:x}{x} \right |$ is $\infty$ $0$ $1$ $-1$
Consider a rigid, perfectly insulated, container partitioned into two unequal parts by a thin membrane (see figure). One part contains one mole of an ideal gas at pressure $P_{i}$ and temperature $T_{i}$ while the other part is evacuated. The membrane ruptures, the gas fills the entire volume and the equilibrium pressure is ... $C_{p}$In$2$ +$R$In$4$ $-C_{v}$In$2$ +$R$In$4$ $R$In$4$ $C_{p}$In$2$
For a single component system, vapor (subscript $g$) and liquid (subscript $f$) coexist in mechanical, thermal and phase equilibrium when $u_{g}=u_{f}$ (equality of specific internal energy) $h_{g}=h_{f}$ (equality of specific enthalpy) $s_{g}=s_{f}$ (equality of specific entropy) $g_{g}=g_{f}$ (equality of specific Gibbs free energy)
For a binary nonideal $A-B$ mixture exhibiting a minimum boiling azeotrope, the activity coefficients, $\gamma_{i} \left ( i=A, B \right )$, must satisfy $\gamma _{A}> 1,\gamma _{B}> 1$ $\gamma _{A}< 1,\gamma _{B}> 1$ $\gamma _{A}= 1,\gamma _{B}= 1$ $\gamma _{A}< 1,\gamma _{B}< 1$
For a fully-developed turbulent hydrodynamic boundary layer for flow past a flat plate, the thickness of the boundary layer increases with distance $x$ from the leading edge of the plate, along the free-stream flow direction, as $x^{0.5}$ $x^{1.5}$ $x^{0.4}$ $x^{0.8}$
Consider a cylinder (diameter $D$ and length $D$), a sphere (diameter $D$) and a cube (side length $D$). Which of the following statements concerning the sphericity $\left ( \Phi \right )$ of the above objects is true: $\Phi _{sphere}> \Phi _{cylinder}> \Phi _{cube}$ ... $\Phi _{sphere}< \Phi _{cylinder}< \Phi _{cube}$ $\Phi _{cylinder}> \Phi _{sphere}= \Phi _{cube}$
Prandtl number signifies the ratio of $\frac{Momentum \: Diffusivity}{Thermal \: Diffusivity}$ $\frac{Mass \: Diffusivity}{Thermal \: Diffusivity}$ $\frac{Thermal \: Diffusivity}{Momentum \: Diffusivity}$ $\frac{Thermal \: Diffusivity}{Mass \: Diffusivity}$
Pool boiling equipment operating above ambient temperature is usually designed to operate far above the critical heat flux near the critical heat flux far above the Leidenfrost point near the Leidenfrost point
The desired liquid-phase reaction $D+E\overset{k_{1}}{\rightarrow}F \:\:\:\:\:\:\:\:\:r_{F}=k_{1}\:C_{D}^{2}\:C_{E}^{0.3}$ ... molar feed rates of $D$ and $E$ are shown in figure. Each scheme is designed for the same conversion. The scheme that gives the most favorable product distribution is:
For a first order reaction in a porous spherical catalyst pellet, diffiusional effects are most likely to lower the observed rate of reaction for slow reaction in a pellet of small diameter slow reaction in a pellet of large diameter fast reaction in a pellet of small diameter fast reaction in a pellet of large diameter
A thermocouple senses temperature based on the Nernst Effect Maxwell Effect Seebeck Effect Peltier Effect
The correct expression for the Colburn $j$-factor for mass transfer that relates Sherwood number ($Sh$), Reynolds number ($Re$) and Schmidt number ($Sc$) is $\frac{Sh}{\left ( Re \right )\left ( Sc \right )^{1/3}}$ $\frac{Sh}{\left ( Re \right )^{1/2}\left ( Sc \right )}$ $\frac{Sh}{\left ( Re \right )^{1/2}\left ( Sc \right )^{1/3}}$ $\frac{Sh}{\left ( Re \right )\left ( Sc \right )}$
In the drying of non-dissolving solids at constant drying conditions, the internal movement of moisture in the solid has a dominant effect on the drying rate during the initial adjustment period only the constant rate period only the falling rate period only both the initial adjustment and constant rate periods
Three distillation schemes for separating an equimolar, constant relative volatility $ABC$ mixture into nearly pure components are shown. The usual simplifying assumptions such as constant molal overflow, negligible heat loss, ideal trays are valid. All the schemes are designed for minimum total reboiler duty. Given ... of total reboiler duty is $I, II, III$ $III, I, II$ $II,I, III$ $III, II, I$
Consider the two countercurrent heat exchanger designs for heating a cold stream from $t_{in}$ to $t_{out}$ as shown in figure. The hot process stream is available at $T_{in}$. The inlet stream conditions and overall heat transfer coefficients are identical in both the designs. The heat transfer area in Design $I$ and ... $A_{HX}^{I}< A_{HX}^{II}\:\:\:\:T_{out}^{I}= T_{out}^{II}$
Producer gas is obtained by passing air through red hot coke thermal cracking of naphtha passing steam through red hot coke passing air and steam through red hot coke
In Kraft process, the essential chemical reagents used in the digester are caustic soda, mercaptans and ethylene oxide caustic soda, sodium sulphide and soda ash quick lime, salt cake and dimethyl sulphide baking soda, sodium sulphide and mercaptans
The most common catalyst used for oxidation of $o$-xylene to phthalic anhydride is $V_{2}O_{5}$ $Pd$ $Pt$ $Ag$
In petroleum refining operations, the process used for converting paraffins and naphthenes to aromatics is alkylation catalytic reforming hydrocracking isomerization
The combination that correctly matches the polymer in Group-$1$ with the polymerization reaction type in Group-$2$ ... $R-III$ $P-I$, $Q-III$, $R-II$ $P-III$, $Q-II$, $R-I$ $P-II$, $Q-III$, $R-I$
The product of the eigenvalues of the matrix $\begin{pmatrix} 2 &3 \\ 0& 7 \end{pmatrix}$ is ______________________ (rounded off to one decimal place).
For a hydraulic lift with dimensions shown in figure, assuming $g=10\:m/s^{2}$, the maximum diameter $D_{left}$ (in $m$) that lifts a vehicle of mass $1000 \:kg$ using a force of $100 \:N$ is ____________________ (rounded off to two decimal places).
The liquid flow rate through an equal percentage control valve, when fully open, is $150$ gal/min and the corresponding pressure drop is $50$ psi. If the specific gravity of the liquid is $0.8$, then the valve coefficient, $C_{V}$, in gal/(min $psi^{0.5}$) is _________________ (rounded off to two decimal places).
Consider a sealed rigid bottle containing $CO_{2}$ and $H_{2}O$ at $10$ bar and ambient temperature. Assume that the gas phase in the bottle is pure $CO_{2}$ and follows the ideal gas law. The liquid phase in the bottle contains $CO_{2}$ ... $CO_{2}$ dissolved in $H_{2}O$ is __________________ (rounded off to three decimal places).
The solution of the ordinary differential equation $\frac{dy}{dx}+3y=1$, subjects to the initial condition $y=1$ at $x=0$, is $\frac{1}{3}\left ( 1+2e^{-x/3} \right )$ $\frac{1}{3}\left ( 5-2e^{-x/3} \right )$ $\frac{1}{3}\left ( 5-2e^{-3x} \right )$ $\frac{1}{3}\left ( 1+2e^{-3x} \right )$
The value of the complex number $i^{-1/2}$ (where $i=\sqrt{-1}$) is $\frac{1}{\sqrt{2}}\left ( 1-i \right )$ $-\frac{1}{\sqrt{2}}i$ $\frac{1}{\sqrt{2}}i$ $\frac{1}{\sqrt{2}}\left ( 1+i \right )$
Two unbiased dice are thrown. Each dice can show any number between $1$ and $6$. The probability that the sum of the outcomes of the two dice is divisible by $4$ is ____________ (rounded off to two decimal places).
The Newton-Raphson method is used to determine the root of the equation $f(x)=e^{-x}-x$. If the initial guess for the root is 0, the estimate of the root after two iterations is _______ (rounded off to three decimal places).
Carbon monoxide $(CO)$ reacts with hydrogen sulphide $(H_2S)$ at a constant temperature of $800\:K$ and a constant pressure of 2 bar as: $CO+H_2S\leftrightharpoons COS+H_2$ The Gibbs free energy of the reaction ${\Delta g^\circ}_{rxn}=22972.3\:J/mol$ and ... only $4\:mol$ of CO are present, the extent of the reaction (in mol) at equilibrium is _________ (rounded off to two decimal places).