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Recent questions tagged numerical-answers

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GATE CH 2022 | Question: 44
A cylindrical fin of diameter $24$ $\text{mm}$ is attached horizontally to a vertical planar wall. The heat transfer ... $\text{mm}$ (rounded off to the nearest integer).
A cylindrical fin of diameter $24$ $\text{mm}$ is attached horizontally to a vertical planar wall. The heat transfer rate from the tin to the surrounding ar is $60\%$ of ...
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GATE CH 2022 | Question: 45
A single-effect evaporator with a heat transfer area of $70\:m^{2}$ concentrates a salt solution using steam. The salt ... (rounded off to the nearest integer).
A single-effect evaporator with a heat transfer area of $70\:m^{2}$ concentrates a salt solution using steam. The salt solution feed rate and temperature are $10000\:kg\:...
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GATE CH 2022 | Question: 46
An equimolar binary mixture is to be separated in a simple tray-distillation column. The feed rate is ... ratio is __________ (rounded off to two decimal places).
An equimolar binary mixture is to be separated in a simple tray-distillation column. The feed rate is $50\text{ kmol min}^{-1}$ . The mole fractions of the more volatile ...
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GATE CH 2022 | Question: 47
The dry-bulb temperature of air in a room is $30^{\circ}C$ ... = ____________ (rounded off to one decimal place).
The dry-bulb temperature of air in a room is $30^{\circ}C$. The Antoine equation for wateris given as $$\text{ln} P^{sat} = 12.00 -\frac{4000}{T - 40}$$ where $T$ is the ...
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GATE CH 2022 | Question: 48
In the block diagram shown in the figure, the transfer function ... remains stable is ___________________ (rounded off to two decimal places).
In the block diagram shown in the figure, the transfer function $G = \dfrac{K}{\left ( \tau s + 1 \right )}$ with $K 0$ and $\tau 0$. The maximum value of $K$ below whi...
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GATE CH 2022 | Question: 49
Consider the tank level control system shown in the figure, where the cross-section area of the tank is ... is _____________________ (rounded off to the nearest integer).
Consider the tank level control system shown in the figure, where the cross-section area of the tank is $A$. Assume perfect flow controllers $\text{(FC)}$. The level cont...
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GATE CH 2022 | Question: 50
Consider a single-input-single-output $\text{(SISO)}$ ... is ______________ minutes (rounded off to two decimal places).
Consider a single-input-single-output $\text{(SISO)}$ system with the transfer function $$G_{P}\left ( s \right ) =\frac{2\left ( s + 1 \right )}{\left ( \dfrac{1}{2} s +...
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GATE CH 2022 | Question: 51
Information for a proposed greenfield project is provided in the table. The discounted cash flow for the fourth year is Rs ...
Information for a proposed greenfield project is provided in the table. The discounted cash flow for the fourth year is Rs ___________________ crores (rounded off to one ...
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GATE CH 2022 | Question: 52
Consider the process in the figure. The liquid phase elementary reactions ... fresh feeds, process exit streams and recycle streams are pure
Consider the process in the figure. The liquid phase elementary reactions $$A + B \rightarrow P \:\:\:\: -r_{B1} = k_{1}\:x_{A}\:x_{B}$$ $$P + B \rightarrow S \:\:\:\: -r...
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GATE CH 2022 | Question: 53
An elementary irreversible liquid-phase reaction, $2A \rightarrow B$ ... $\%$ (rounded off to one decimal place).
An elementary irreversible liquid-phase reaction, $2A \rightarrow B$, is carried out under isothermal conditions in a $1\:m^{3}$ ideal plug flow reactor $\text{(PFR)}$ as...
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GATE CH 2022 | Question: 54
An elementary irreversıble gas-phase reaction, $A \rightarrow B + C$, is carried out at fixed temperature and pressure in ... (rounded off to one decimal place).
An elementary irreversıble gas-phase reaction, $A \rightarrow B + C$, is carried out at fixed temperature and pressure in two separate ideal reactors: $(i)$ a $10\:m^{3}...
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GATE CH 2022 | Question: 55
An elementary irreversible liquid-phase reaction, $2P \overset{k}{\rightarrow}Q$ ... is _____________ $\%$ (round off to the nearest integer)
An elementary irreversible liquid-phase reaction, $2P \overset{k}{\rightarrow}Q$, where the rate constant $k = 2\:L\:\text{mol}^{-1}\:\text{min} ^{-1}$, takes place in an...
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GATE CH 2021 | Question: 19
A source placed at the origin of a circular sample holder (radius $r=1 \: m$) emits particles ... total number of particles emitted during the experiment is ___________.
A source placed at the origin of a circular sample holder (radius $r=1 \: m$) emits particles uniformly in all directions. A detector of length $l=1 \: cm$ has been place...
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GATE CH 2021 | Question: 20
$\textbf{A, B, C}$ and $\textbf{D}$ are vectors of length $4$ ... is __________
$\textbf{A, B, C}$ and $\textbf{D}$ are vectors of length $4$. $$\textbf{A} = \begin{bmatrix} a_1 & a_2 & a_3 & a_4 \end{bmatrix} \\ \textbf{B} = \begin{bmatrix}b_1 & b_2...
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GATE CH 2021 | Question: 21
The van der Waals equation of the state is given by $P_r = \dfrac{8T_r}{3v_r-1} - \dfrac{3}{v_r^2}$ ... equation of state is __________ (round off to $2$ decimal places).
The van der Waals equation of the state is given by$$P_r = \dfrac{8T_r}{3v_r-1} – \dfrac{3}{v_r^2}$$where $P_r$, $T_r$ and $v_r$ represent reduced pressure, reduced tem...
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GATE CH 2021 | Question: 22
Consider a steady flow of an incompressible, Newtonian fluid through a smooth circular pipe. Let ... is ______ (round off to $2$ decimal places).
Consider a steady flow of an incompressible, Newtonian fluid through a smooth circular pipe. Let $\alpha_{\textit{laminar}}$ and $\alpha_{\textit{turbulent}}$ denote the ...
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GATE CH 2021 | Question: 23
The molar heat capacity at constant pressure $C_p$ (in $\text{J mol}^{-1} K^{-1}$) for $n$-pentane as a function of ... $2$ decimal places).
The molar heat capacity at constant pressure $C_p$ (in $\text{J mol}^{-1} K^{-1}$) for $n$-pentane as a function of temperature $(T$ in $K)$ is given by$ \dfrac{C_p}{R} =...
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GATE CH 2021 | Question: 24
The following homogeneous liquid phase reactions are at equilibrium, The values of rate constants are given by: ... $s^{-1}$ (round off to $1$ decimal place)
The following homogeneous liquid phase reactions are at equilibrium,The values of rate constants are given by: $k_1 = 0.1 s^{-1}$, $k_{-1}=0.2 s^{-1}, k_2 = 1 s^{-1}, k_{...
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GATE CH 2021 | Question: 25
A company invests in a recovery unit to separate valuable metals from effluent streams. The total initial capital ... lakhs of rupees (correct to $1$ decimal place)
A company invests in a recovery unit to separate valuable metals from effluent streams. The total initial capital investment of this unit is Rs. $10$ lakhs. The recovered...
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GATE CH 2021 | Question: 34
To solve an algebraic equation $f(x)=0$, an iterative scehme of the type $x_{n+1} = g(x_n)$ ... order of convergence for this iterative scheme near the solution is ________
To solve an algebraic equation $f(x)=0$, an iterative scehme of the type $x_{n+1} = g(x_n)$ is proposed, where $g(x)=x-\dfrac{f(x)}{f’(x)}$.At the solution $x=s,\: g’...
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GATE CH 2021 | Question: 35
The probability distribution function of a random variable $X$ is shown in the following figure. From this distribution, ... is _______ (round off to $3$ decimal places)
The probability distribution function of a random variable $X$ is shown in the following figure.From this distribution, random samples with sample size $n=68$ are taken. ...
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GATE CH 2021 | Question: 36
For the ordinary differential equation $\dfrac{d^3y}{dt^3}+6 \dfrac{d^2y}{dt^2}+11 \dfrac{dy}{dt}+6y=1$ with ... $3$ decimal places).
For the ordinary differential equation $$\dfrac{d^3y}{dt^3}+6 \dfrac{d^2y}{dt^2}+11 \dfrac{dy}{dt}+6y=1$$ with initial conditions $y(0)=y’(0) = y’’(0)=y’’’(0)...
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GATE CH 2021 | Question: 37
Formaldehyde is produced by the oxidation of methane in a reactor. The following two parallel reactions occur. ... reactor is _______ $\text{mol s}^{-1}$
Formaldehyde is produced by the oxidation of methane in a reactor. The following two parallel reactions occur.$$CH_4+O_2 \rightarrow HCHO+H_2O \\ CH_4 +2O_2 \rightarrow C...
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GATE CH 2021 | Question: 38
The combustion of carbon monoxide is carried out in a closed, rigid and insulated vessel. $1 \text{ mol}$ ... is ___________ bar (round off to $1$ decimal place).
The combustion of carbon monoxide is carried out in a closed, rigid and insulated vessel. $1 \text{ mol}$ of $CO$, $0.5 \text{ mol}$ of $O_2$ and $2 \text{ mol}$ of $N_2$...
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GATE CH 2021 | Question: 39
A gaseous mixture at $1$ bar and $300 \: K$ consists of $20 \text{ mol } \% \: CO_2$ ... and pressure is ________ $\text{kJ}$ (round off to nearest integer)
A gaseous mixture at $1$ bar and $300 \: K$ consists of $20 \text{ mol } \% \: CO_2$ and $80 \text{ mol } \%$ inert gas.Assume the gases to be ideal. Take $R=8.314 \text{...
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GATE CH 2021 | Question: 40
A binary liquid mixture consists of two species $1$ and $2$. Let $\gamma$ and $x$ represent the activity ... mole fraction is ___________ ( correct to $3$ decimal places)
A binary liquid mixture consists of two species $1$ and $2$. Let $\gamma$ and $x$ represent the activity coefficient and the mole fraction of the species, respectively. U...
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GATE CH 2021 | Question: 41
Consider a tank filled with $3$ immiscible liquid $A$, $B$ and $C$ at static equilibrium, as shown in the figure. At ... that is wetted by liquid $B$ is _______ $\text{cm}$
Consider a tank filled with $3$ immiscible liquid $A$, $B$ and $C$ at static equilibrium, as shown in the figure. At $2 \: cm$ below the liquid $A$- liquid $B$ interface,...
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GATE CH 2021 | Question: 42
Seawater is passed through a column containing a bed of resin beads. Density of seawater $=1025 \: \text{ kg m}^{-3}$ ... (round off to nearest integer).
Seawater is passed through a column containing a bed of resin beads.Density of seawater $=1025 \: \text{ kg m}^{-3}$Density of resin beads $=1330 \text{ kg m}^{-3}$Diame...
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GATE CH 2021 | Question: 43
A straight fin of uniform circular cross section and adiabatic tip has an aspect ratio (length/diameter) of $4$. If ... is ___________ $\%$ (round off to nearest integer).
A straight fin of uniform circular cross section and adiabatic tip has an aspect ratio (length/diameter) of $4$. If the Biot number (based on the radius of the fin as the...
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GATE CH 2021 | Question: 44
A double-effect evaporator is used to concentrate a solution. Steam is sent to the first effect at ... is _________$^\circ C$ (round off to nearest integer)
A double-effect evaporator is used to concentrate a solution. Steam is sent to the first effect at $110\:^{\circ} C$ and the boiling point of the solution in the second e...
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GATE CH 2021 | Question: 45
Consider a solid slab of thickness $2L$ and uniform cross section $A$. The volumetric rate of heat generation within ... slab is _______ $K$ (round off to nearest integer).
Consider a solid slab of thickness $2L$ and uniform cross section $A$. The volumetric rate of heat generation within the slab is $\dot{g} \: (W \: m^{-3})$. The slab lose...
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GATE CH 2021 | Question: 46
A distillation column handling a binary mixture of $A$ and $B$ is operating at total reflux. It has two ideal stages ... $2$ decimal places).
A distillation column handling a binary mixture of $A$ and $B$ is operating at total reflux. It has two ideal stages including the reboiler. The mole fraction of the more...
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GATE CH 2021 | Question: 47
In a batch drying experiment, a solid with a critical moisture content of $0.2 \: kg$ $H_2O/kg$ dry solid is dried ... is _______ $kg/m^2$ (round off to nearest integer).
In a batch drying experiment, a solid with a critical moisture content of $0.2 \: kg$ $H_2O/kg$ dry solid is dried from an initial moisture content of $0.35 \: kg$ $H_2O/...
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GATE CH 2021 | Question: 48
As shown in the figure below, air flows in parallel to a freshly painted solid surface of width $10 \: m$, along ... $2$ decimal places).
As shown in the figure below, air flows in parallel to a freshly painted solid surface of width $10 \: m$, along the $z$-direction.The equilibrium vapor concentration of ...
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GATE CH 2021 | Question: 49
The following isothermal autocatalytic reaction ... time of the $\text{CSTR}$ is _________ seconds.
The following isothermal autocatalytic reaction $$ A +B \longrightarrow 2B \quad\quad\quad(-r_A)=0.1C_AC_B(\text{mol } L^{-1} s^{-1})$$is carried out in an ideal continuo...
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GATE CH 2021 | Question: 50
Reactant $A$ decomposes to products $B$ and $C$ in the presence of an enzyme in a well-stirred batch reactor. The ... $\text{min}$ (round off to $2$ decimal places).
Reactant $A$ decomposes to products $B$ and $C$ in the presence of an enzyme in a well-stirred batch reactor. The kinetic rate expression is given by$$-r_A = \dfrac{0.01C...
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GATE CH 2021 | Question: 51
The following homogeneous, irreversible reaction involving ideal gases, ... meter. (round off to $2$ decimal places).
The following homogeneous, irreversible reaction involving ideal gases, $$A \longrightarrow B+C \quad\quad\quad(-r_A)=0.5C_A (\text{mol L}^{-1} s^{-1})$$ is carried out i...
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GATE CH 2021 | Question: 52
A system has a transfer function $G(s)= \dfrac{3e^{-4s}}{12s+1}$. When a step change of magnitude $M$ is ... is measured to be $120$. The value of $M$ is ____________.
A system has a transfer function $G(s)= \dfrac{3e^{-4s}}{12s+1}$. When a step change of magnitude $M$ is given to the system input, the final value of the system output i...
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GATE CH 2021 | Question: 53
A person has a transfer function $G(s)= \dfrac{Y(s)}{X(s)} = \dfrac{20}{90000s^2+240s+1}$. Initially ... new steady state is __________ (round off to $1$ decimal place).
A person has a transfer function $G(s)= \dfrac{Y(s)}{X(s)} = \dfrac{20}{90000s^2+240s+1}$. Initially the process is at steady state with $x(t=0)=0.4$ and $y(t=0)=100$. If...
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GATE CH 2021 | Question: 54
Operating labor requirements $L$ ... is _______(round off to nearest integer).
Operating labor requirements $L$ in the chemical process industry is described in terms of the plant capacity $C ( \text{kg day}^{-1})$ over a wide range $(10^3-10^6)$ by...
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