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GATE Chemical 2024 | Question: 2
Consider the normal probability distribution function\[f(x)=\frac{4}{\sqrt{2 \pi}} e^{-8(x+3)^{2}}\]If $\mu$ and $\sigma$ are the mean and standard deviation of $f(x)$ re...
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GATE Chemical 2024 | Question: 34
A first-order heterogenous reaction $A \rightarrow B$ is carried out using a porous spherical catalyst. Assume isothermal conditions, and that intraphase diffusion contro...
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GATE Chemical 2024 | Question: 33
​​​Alumina particles with an initial moisture content of $5 \mathrm{~kg}$ per $\mathrm{kg}$ dry solid are dried in a batch dryer. For the first two hours, the measu...
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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: 1
The first non-zero term in the Taylor series expansion of $(1-x)-e^{-x}$ about $x=0$ is$1$$-1$$\frac{x^{2}}{2}$$-\frac{x^{2}}{2}$
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GATE Chemical 2024 | Question: 46
An isolated system consists of two perfectly sealed cuboidal compartments $A$ and $B$ separated by a movable rigid wall of cross-sectional area $0.1 \mathrm{~m}^{2}$ as s...
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GATE Chemical 2024 | Question: 21
Consider the reaction $\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$ in a continuous flow reactor under steady-state conditions...
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GATE Chemical 2024 | Question: 52
A chemostat with cell recycle is shown in the figure. The feed flow rate and culture volume are $F=75 \mathrm{~L} \mathrm{~h}^{-1}$ and $V=200 \mathrm{~L}$, respectively....
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GATE Chemical 2024 | Question: 31
​​​​​Sulfur dioxide $\left(\mathrm{SO}_{2}\right)$ gas diffuses through a stagnant air-film of thickness $2 \mathrm{~mm}$ at 1 bar and $30^{\circ} \mathrm{C}$. ...
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GATE Chemical 2024 | Question: 10
​​​​​​The rate of a reaction $A \rightarrow B$ is $0.2 \mathrm{~mol} \mathrm{~m}^{-3} \mathrm{~s}^{-1}$ at a particular concentration $C_{A 1}$. The rate cons...
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GATE Chemical 2024 | Question: 22
Consider a binary mixture of components $A$ and $B$ at temperature $T$ and pressure $P$. Let $\bar{V}_{A}$ and $\bar{V}_{B}$ be the partial molar volumes of $A$ and $B$, ...
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GATE Chemical 2024 | Question: 3
If $z_{1}=-1+i$ and $z_{2}=2 i$, where $i=\sqrt{-1}$, then $\operatorname{Arg}\left(z_{1} / z_{2}\right)$ is$\frac{3 \pi}{4}$$\frac{\pi}{4}$$\frac{\pi}{2}$$\frac{\pi}{3}$...
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GATE Chemical 2024 | Question: 11
​​​​​Two parallel first-order liquid phase reactions $A \xrightarrow{k_{1}} B$ and $A \xrightarrow{k_{2}} C$ are carried out in a well-mixed isothermal batch re...
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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: 18
For the electrolytic cell in a chlor-alkali plant, which of the following statements is/are correct?A membrane cell operates at a higher brine concentration than a diaphr...
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GATE Chemical 2024 | Question: 26
​​​​Consider a steady, fully-developed, uni-directional laminar flow of an incompressible Newtonian fluid (viscosity $\mu$ ) between two infinitely long horizonta...
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GATE Chemical 2024 | Question: 20
Consider a matrix $\text{A}=\left[\begin{array}{cc}-5 & a \\ -2 & -2\end{array}\right]$, where $a$ is a constant. If the eigenvalues of $\text{A}$ are $-1$ and $-6$, then...
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GATE Chemical 2024 | Question: 23
Consider the steady, uni-directional, fully-developed, pressure-driven laminar flow of an incompressible Newtonian fluid through a circular pipe of inner radius $5.0 \mat...
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GATE Chemical 2024 | Question: 29
​​​​​A solid slab of thickness $H_{1}$ is initially at a uniform temperature $T_{0}$. At time $t=0$, the temperature of the top surface at $y=H_{1}$ is increase...
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GATE Chemical 2024 | Question: 19
​​​​​​Which of the following statements with reference to the petroleum/petrochemical industry is/are correct?Catalytic hydrocracking converts heavier hydroca...
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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: 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: 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: 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 CH 2023 | Question: 57
Distillation of a non-reactive binary mixture with components $A$ and $B$ is carried out in a batch ... the vessel is____________(rounded off to three decimal places).
Distillation of a non-reactive binary mixture with components $A$ and $B$ is carried out in a batch still as shown in the figure below. The initial charge of the mixture ...
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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: 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: 36
An exhibition was held in a hall on $15$ August $2022$ between $\text{3 PM}$ and $\text{4 PM}$ during which any person was ... $\frac{2}{9}$ $\frac{7}{9}$
An exhibition was held in a hall on $15$ August $2022$ between $\text{3 PM}$ and $\text{4 PM}$ during which any person was allowed to enter only once. Visitors who entere...
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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: 64
The purchase cost of a new distillation column is $\text{Rs. 10 lakhs}$ with an installation factor ... capital is________________ (rounded off to one decimal place).
The purchase cost of a new distillation column is $\text{Rs. 10 lakhs}$ with an installation factor of $5.8.$ The cost of the capital is to be annualized over a period of...
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GATE CH 2023 | Question: 40
Water in a container at $290 \mathrm{~K}$ is exposed to air containing $3 \% ~ \mathrm{CO}_2$ by volume. Air behaves like an ... $0.5 \times 10^{-4}$
Water in a container at $290 \mathrm{~K}$ is exposed to air containing $3 \% ~ \mathrm{CO}_2$ by volume. Air behaves like an ideal gas and is maintained at $100 ~ \mathrm...
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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: 65
Pumps $A$ and $B$ are being considered for purchase in a chemical plant. Cost details for these two pumps are given in the ...
Pumps $A$ and $B$ are being considered for purchase in a chemical plant. Cost details for these two pumps are given in the table below. The interest rate is $10 \%$ per a...
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GATE CH 2023 | Question: 61
The outlet concentration $C_A$ of a plug flow reactor $\text{(PFR)}$ is controlled by manipulating the ... this system is______________ (rounded off to one decimal place).
The outlet concentration $C_A$ of a plug flow reactor $\text{(PFR)}$ is controlled by manipulating the inlet concentration $C_{A 0}$. The following transfer function desc...
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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: 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: 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: 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: 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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