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GATE Chemical 2024 | Question: 41
Consider the line integral $\int_{C} \boldsymbol{F}(\boldsymbol{r}) \cdot d \boldsymbol{r}$, with $\boldsymbol{F}(\boldsymbol{r})=x \hat{\boldsymbol{\imath}}+y \hat{\bold...
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GATE Chemical 2024 | Question: 42
Consider the ordinary differential equation $x^{2} \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}-3 y=0$, with the boundary conditions $y(x=1)=2$ and $y(x=2)=17 / 2$. The solu...
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GATE Chemical 2024 | Question: 43
Consider the function $f(x, y, z)=x^{4}+2 y^{3}+z^{2}$. The directional derivative of the function at the point $P(-1,1,-1)$ along $(\hat{\boldsymbol{\imath}}+\hat{\bolds...
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GATE Chemical 2024 | Question: 44
Consider the process in the figure for manufacturing $B$. The feed to the process is $90 \mathrm{~mol} \% A$ and a close-boiling inert component $I$. At a particular stea...
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GATE Chemical 2024 | Question: 45
Methane combusts with air in a furnace as $\mathrm{CH}_{4}+2 \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O}$. The heat of reaction $\Delta H_{r x ...
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GATE Chemical 2024 | Question: 46
An isolated system consists of two perfectly sealed cuboidal compartments $A$ and $B$ separated by a movable rigid wall of cross-sectional area $0.1 \mathrm{~m}^{2}$ as s...
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GATE Chemical 2024 | Question: 47
Ethylene obeys the truncated virial equation-of-state\[\frac{P V}{R T}=1+\frac{B P}{R T}\]where $P$ is the pressure, $V$ is the molar volume, $T$ is the absolute temperat...
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GATE Chemical 2024 | Question: 48
A metallic spherical particle of density $7001 \mathrm{~kg} \mathrm{~m}^{-3}$ and diameter $1 \mathrm{~mm}$ is settling steadily due to gravity in a stagnant gas of densi...
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GATE Chemical 2024 | Question: 49
Water of density $1000 \mathrm{~kg} \mathrm{~m}^{-3}$ is pumped at a volumetric flow rate of $3.14 \times 10^{-2} \mathrm{~m}^{3} \mathrm{~s}^{-1}$, through a pipe of inn...
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GATE Chemical 2024 | Question: 50
A Venturi meter with a throat diameter $d=2 \mathrm{~cm}$ measures the flow rate in a pipe of diameter $D=6 \mathrm{~cm}$, as shown in the figure. A U-tube manometer is c...
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GATE Chemical 2024 | Question: 51
Heat is available at a rate of $2 \mathrm{~kW}$ from a thermal reservoir at $400 \mathrm{~K}$. A two-stage process harnesses this heat to produce power. Stages $1$ and $2...
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GATE Chemical 2024 | Question: 52
A chemostat with cell recycle is shown in the figure. The feed flow rate and culture volume are $F=75 \mathrm{~L} \mathrm{~h}^{-1}$ and $V=200 \mathrm{~L}$, respectively....
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GATE Chemical 2024 | Question: 53
Consider the surge drum in the figure. Initially the system is at steady-state with a hold-up $\bar{V}=5 \mathrm{~m}^{3}$, which is $50 \%$ of full tank capacity, $V_{f u...
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GATE Chemical 2024 | Question: 54
A $\text{PD}$ controller with transfer function $G_{c}$ is used to stabilize an open-loop unstable process with transfer function $G_{p}$, where\[G_{c}=K_{c} \frac{\tau_{...
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GATE Chemical 2024 | Question: 55
Consider a tray-column of diameter $120 \mathrm{~cm}$. Each downcomer has a cross-sectional area of $575 \mathrm{~cm}^{2}$. For a tray, the percentage column cross-sectio...
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GATE CH 2023 | GA Question: 2
References : _______ : : Guidelines : Implement (By word meaning) Sight Site Cite Plagiarise
References : _______ : : Guidelines : Implement(By word meaning) Sight Site Cite Plagiarise
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Verbal Aptitude
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GATE CH 2023 | Question: 11
Which one of the following is the CORRECT value of $y,$ as defined by the expression given below? $y=\lim _{x \rightarrow 0} \frac{2 x}{e^x-1}$ $1$ $2$ $0$ $\infty$
Which one of the following is the CORRECT value of $y,$ as defined by the expression given below? $$y=\lim _{x \rightarrow 0} \frac{2 x}{e^x-1}$$$1$$2$$0$$\infty$
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GATE CH 2023 | Question: 12
The vector $\overrightarrow{\boldsymbol{v}}$ ... $0$ $3$ $14$ $13$
The vector $\overrightarrow{\boldsymbol{v}}$ is defined as$$\overrightarrow{\boldsymbol{v}}=z x \hat{\imath}+2 x y \hat{\jmath}+3 y z \hat{k} .$$Which one of the followin...
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GATE CH 2023 | Question: 13
Given that $F=\frac{\left|z_1+z_2\right|}{\left|z_1\right|+\left|z_2\right|},$ where $z_1=2+3 i$ and $z_2=-2+3 i$ ... $\text{CORRECT}$? $F<0$ $F<1$ $F>1$ $F=1$
Given that$$F=\frac{\left|z_1+z_2\right|}{\left|z_1\right|+\left|z_2\right|},$$where $z_1=2+3 i$ and $z_2=-2+3 i$ with $i=\sqrt{-1}$, which one of the following options i...
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GATE CH 2023 | Question: 14
For a two-dimensional plane, the unit vectors, $\left(\hat{e}_r, \hat{e}_\theta\right)$ ... $-\hat{e}_{r}+\hat{e}_{\theta}$
For a two-dimensional plane, the unit vectors, $\left(\hat{e}_r, \hat{e}_\theta\right)$ of the polar coordinate system and $(\hat{\imath}, \hat{\jmath})$ of the cartesian...
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GATE CH 2023 | Question: 15
Which one of the following statements related to octane number is NOT correct? Linear alkanes with higher carbon ... Gasoline quality is measured in terms of octane number.
Which one of the following statements related to octane number is NOT correct?Linear alkanes with higher carbon number have higher octane number.Branching in linear alkan...
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GATE CH 2023 | Question: 16
Which one of the following options represents the major components of oleum? Sulfuric acid and nitric acid ... acid and hydrochloric acid Sulfuric acid and sulfur trioxide
Which one of the following options represents the major components of oleum?Sulfuric acid and nitric acidConcentrated sulfuric acid and petroleum jellySulfuric acid and h...
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GATE CH 2023 | Question: 17
For a reversible endothermic chemical reaction with constant heat of reaction over the operating temperature range, $K$ is ... $K$ on temperature $T$?
For a reversible endothermic chemical reaction with constant heat of reaction over the operating temperature range, $K$ is the thermodynamic equilibrium constant. Which o...
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GATE CH 2023 | Question: 18
Nitrile rubber is manufactured via polymerization process. Which one of the following options is the ... and butadiene Butadiene and styrene Butadiene and isoprene
Nitrile rubber is manufactured via polymerization process. Which one of the following options is the $\text{CORRECT}$ pair of monomers used in this process?Acrylonitrile ...
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GATE CH 2023 | Question: 19
John and Jane independently performed a thermodynamic experiment, in which $\mathbf{X}$ and $\mathbf{Y}$ represent the ...
John and Jane independently performed a thermodynamic experiment, in which $\mathbf{X}$ and $\mathbf{Y}$ represent the initial and final thermodynamic states of the syste...
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GATE CH 2023 | Question: 20
For a packed-bed comprising of uniform-sized spherical particles of diameter $D_{\mathrm{p}}$, the pressure drop across the bed is given ... exponent $n$? $2$ $-1$ $-2$ $1$
For a packed-bed comprising of uniform-sized spherical particles of diameter $D_{\mathrm{p}}$, the pressure drop across the bed is given by the Kozeny-Carman equation whe...
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GATE CH 2023 | Question: 21
Match the quantities in Group $1$ with their units in Group $2$ ... $\text{P-IV, Q-I, R-III, S-II}$
Match the quantities in Group $1$ with their units in Group $2$ listed in the table below.$$\begin{array}{|l|l|} \hline \qquad \qquad \qquad \textbf{Group 1} & \textbf{Gr...
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GATE CH 2023 | Question: 22
A slab of thickness $L$, as shown in the figure below, has cross-sectional area $A$ and constant thermal conductivity $k. T_1$ ... $\frac{A}{L k}$
A slab of thickness $L$, as shown in the figure below, has cross-sectional area $A$ and constant thermal conductivity $k. T_1$ and $T_2$ are the temperatures at $x=0$ and...
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GATE CH 2023 | Question: 23
Spray dryers have many advantages. Which one of the following is NOT an advantage of a typical spray ... Has high heat efficiency Is suitable for heat sensitive materials
Spray dryers have many advantages. Which one of the following is NOT an advantage of a typical spray dryer?Has short drying timeProduces hollow spherical particlesHas hig...
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GATE CH 2023 | Question: 24
Which one of the following quantities of a flowing fluid is measured using a rotameter? Static pressure Dynamic pressure Volumetric flow rate Viscosity
Which one of the following quantities of a flowing fluid is measured using a rotameter?Static pressureDynamic pressureVolumetric flow rateViscosity
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GATE CH 2023 | Question: 25
A liquid surge tank has $F_{\text {in }}$ and $F_{\text {out }}$ as the inlet and outlet flow rates respectively, as ... (in seconds) of this system? $20$ $32$ $64$ $128$
A liquid surge tank has $F_{\text {in }}$ and $F_{\text {out }}$ as the inlet and outlet flow rates respectively, as shown in the figure below. $F_{\text {out }}$ is prop...
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GATE CH 2023 | Question: 26
A packed distillation column, with vapor having an average molecular weight of $45 \mathrm{~kg} \cdot \mathrm{kmol}^{-1}$, density ... $4 \pi$ $\frac{10}{\sqrt{\pi}}$
A packed distillation column, with vapor having an average molecular weight of $45 \mathrm{~kg} \cdot \mathrm{kmol}^{-1}$, density of $2 \mathrm{~kg} \cdot \mathrm{m}^{-3...
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GATE CH 2023 | Question: 27
An isothermal jacketed continous stirred tank reactor (CSTR) operating at $150^{\circ} \mathrm{C}$ is shown in the figure ... $H X_1$ and increase the heat duty of $H X_2$.
An isothermal jacketed continous stirred tank reactor (CSTR) operating at $150^{\circ} \mathrm{C}$ is shown in the figure below. The cold feed entering the system at $30^...
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GATE CH 2023 | Question: 28
Consider a system where a Carnot engine is operating between a source and a sink. Which of the following ... increases at the completion of each cycle of the engine.
Consider a system where a Carnot engine is operating between a source and a sink. Which of the following statements about this system is/are $\text{NOT}$ correct?This eng...
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GATE CH 2023 | Question: 29
For a fully developed turbulent flow of an incompressible Newtonian fluid through a pipe of constant diameter, ... pressure gradient in the flow direction is constant.
For a fully developed turbulent flow of an incompressible Newtonian fluid through a pipe of constant diameter, which of the following statements is/are $\text{CORRECT?}$R...
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GATE CH 2023 | Question: 30
Given that $E$ (in W. $\mathrm{m}^{-2}$ ) is the total hemispherical emissive power of a surface maintained ... . $E$ does not depend on the frequency of the emission.
Given that $E$ (in W. $\mathrm{m}^{-2}$ ) is the total hemispherical emissive power of a surface maintained at a certain temperature, which of the following statements is...
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GATE CH 2023 | Question: 31
The position $x(t)$ of a particle, at constant $\omega$ ... particle at $t=(3 \pi / \omega)$ is_______________(in integer).
The position $x(t)$ of a particle, at constant $\omega$, is described by the equation$$\frac{d^2 x}{d t^2}=-\omega^2 x.$$The initial conditions are $x(t=0)=1$ and $\left....
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GATE CH 2023 | Question: 32
Burning of methane in a combustor yields carbon monoxide, carbon dioxide, and water vapor. Methane is fed to the ... is____________(rounded off to one decimal place).
Burning of methane in a combustor yields carbon monoxide, carbon dioxide, and water vapor. Methane is fed to the combustor at $100 \mathrm{~mol} . \mathrm{hr}^{-1}$, of w...
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GATE CH 2023 | Question: 33
The viscosity of an incompressible Newtonian fluid is measured using a capillary tube of diameter ... is______________(rounded off to two decimal places).
The viscosity of an incompressible Newtonian fluid is measured using a capillary tube of diameter $0.5 \mathrm{~mm}$ and length $1.5 \mathrm{~m}$. The fluid flow is lamin...
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GATE CH 2023 | Question: 34
A liquid $\boldsymbol{L}$ containing a dissolved gas $\boldsymbol{S}$ is stripped in a countercurrent ... minimum number of ideal stages required is__________(in integer).
A liquid $\boldsymbol{L}$ containing a dissolved gas $\boldsymbol{S}$ is stripped in a countercurrent operation using a pure carrier gas $\boldsymbol{V}$. The liquid phas...
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