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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 Chemical 2020 | Question: 6
In a laboratory experiment, a unit pulse input of tracer is given to an ideal plug flow reactor operating at steady state with a recycle ratio, $R=1$. The exit age distri...
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GATE Chemical 2018 | Question: 5
The terminal velocity of a spherical particle in gravitational settling under Stokes’ regime varieslinearly with the particle diameterlinearly with the viscosity of the...
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GATE CH 2022 | Question: 19
$5$ moles of liquid benzene, $8$ moles of liquid toluene and $7$ moles of liquid xylene are mixed at $25^{\circ}C$ ... $J\:K^{-1}$ (rounded off to one decimal place).
$5$ moles of liquid benzene, $8$ moles of liquid toluene and $7$ moles of liquid xylene are mixed at $25^{\circ}C$ and $1$ bar. Assuming the formation of an ideal solutio...
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GATE CH 2022 | Question: 30
Consider a bare long copper wire of $1$ $\text{mm}$ diameter. Its surface temperature is $T_{s}$ ... places, is $0.02$ $0.04$ $0.10$ $0.01$
Consider a bare long copper wire of $1$ $\text{mm}$ diameter. Its surface temperature is $T_{s}$ and the ambient temperature is $T_{a}\:(T_{s} T_{a})$. The wire is to be...
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GATE CH 2021 | Question: 2
The function $\cos(x)$ is approximated using Taylor series around $x=0$ as $\cos(x) \approx 1 + ax + bx^2 + cx^3 + dx^4$. The values ... $a=-0.5, \: b=0,\: c=0.042, \: d=0$
The function $\cos(x)$ is approximated using Taylor series around $x=0$ as $\cos(x) \approx 1 + ax + bx^2 + cx^3 + dx^4$. The values of $a,b,c$ and $d$ are$a=1, \: b=-0....
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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 2022 | Question: 6
Consider turbulent flow in a pipe under isothermal conditions. Let $r$ denote the radial coordinate ... Decreases and then increases Remains unchanged Only increases
Consider turbulent flow in a pipe under isothermal conditions. Let $r$ denote the radial coordinate and $z$ denote the axial flow direction. On moving away from the wall ...
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GATE CH 2022 | Question: 29
Consider a horizontal rod of radius $aR (a < 1)$ in a stationary pipe of radius $R$. The rod is pulled coaxially at a constant ... $0$ $-\frac{\pi \mu V} {\text{ln}(a)}$
Consider a horizontal rod of radius $aR (a < 1)$ in a stationary pipe of radius $R$. The rod is pulled coaxially at a constant velocity $V$ as shown in the figure. The an...
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GATE Chemical 2019 | Question: 32
$100$ $kg$ of a feed containing $50$ $wt.\%$ of a solute $C$ is contacted with $80$ $kg$ of a solvent containing $0.5$ $wt.\%$ of $C$ is a mixer-settler unit. From the op...
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GATE Chemical 2019 | Question: 47
The elementary liquid-phase irreversible reactions$A\overset{k_{1}=0.4\: min^{-1}}{\rightarrow}B\overset{k_{2}=0.1\:min^{-1}}{\rightarrow}C$take place in an isothermal id...
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GATE CH 2022 | Question: 9
The chemical formula of Glauber’s salt, used in the Kraft process, is $Na_{2}CO_{3}.10H_{2}O$ $Na_{2}S_{2}O_{4}.2H_{2}O$ $Na_{2}HPO_{4}.2H_{2}O$ $Na_{2}SO_{4}.10H_{2}O$
The chemical formula of Glauber’s salt, used in the Kraft process, is$Na_{2}CO_{3}.10H_{2}O$$Na_{2}S_{2}O_{4}.2H_{2}O$$Na_{2}HPO_{4}.2H_{2}O$$Na_{2}SO_{4}.10H_{2}O$
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GATE Chemical 2015 | Question: 31
The transfer function for the disturbance response in an open-loop process is given by $G_{d}^{open}(s)$. The corresponding transfer function for the disturbance response...
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GATE CH 2021 | Question: 17
Feed solution $\textbf{F}$ is contacted with solvent $\textbf{B}$ in an extraction process. Carrier liquid ... raffinate composition if the mixture composition is at $M$
Feed solution $\textbf{F}$ is contacted with solvent $\textbf{B}$ in an extraction process. Carrier liquid in the feed if $\textbf{A}$ and the solute is $\textbf{C}$. The...
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GATE Chemical 2018 | Question: 30
A person is drowning in sea at location $R$ and the lifeguard is standing at location $P$. The beach boundary is straight and horizontal, as shown in the figure.The lifeg...
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GATE Chemical 2018 | GA Question: 7
A set of $4$ parallel lines intersect with another set of $5$ parallel lines. How many parallelograms are formed?$20$$48$$60$$72$
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GATE CH 2023 | Question: 49
Wet air containing $10$ mole percent water vapor is dried by continuously passing it through a column of ... the column is_______________(rounded off to two decimal places).
Wet air containing $10$ mole percent water vapor is dried by continuously passing it through a column of $\mathrm{CaCl}_2$ pellets. The pellets remove $50$ percent of wat...
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GATE CH 2022 | Question: 5
For a single component system at vapor-liquid equilibrium, the extensive variables $\text{A,V, S and N}$ denote the Helmholtz free ...
For a single component system at vapor-liquid equilibrium, the extensive variables $\text{A,V, S and N}$ denote the Helmholtz free energy, volume, entropy, and number of ...
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GATE Chemical 2019 | Question: 16
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_...
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GATE Chemical 2016 | Question: 8
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 c...
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GATE Chemical 2012 | Question: 32
A bed of spherical glass beads (density $3000 \text{ kg/m$^3$}$, diameter $1\:\text{mm}$, bed porosity $0.5$) is to be fluidized by a liquid of density $1000 \text{ kg/m$...
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GATE CH 2023 | Question: 38
Match the products in Group $1$ with the manufacturing processes in Group $2$ ... $\text{P-I, Q-IV, R-II, S-III}$
Match the products in Group $1$ with the manufacturing processes in Group $2$ listed in the table below.$$\begin{array}{|l|l|} \hline \quad \; \textbf{Group 1} & \; \qqua...
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GATE CH 2022 | Question: 2
Given matrix $A = \begin{bmatrix} x & 1 & 3\\ y & 2 & 6\\ 3 & 5 & 7 \end{bmatrix}$ ... is $(1, 1)$ $(1, 2)$ $(2, 2)$ $(2, 1)$
Given matrix $A = \begin{bmatrix} x & 1 & 3\\ y & 2 & 6\\ 3 & 5 & 7 \end{bmatrix}$, the ordered pair $(x, y)$ for which $\text{det}(A) = 0 $ is$(1, 1)$$(1, 2)$$(2, 2)$$(2...
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GATE CH 2021 | Question: 29
In a solvent regeneration process, a gas is used to strip a solute from a liquid in a countercurrent packed tower operating ...
In a solvent regeneration process, a gas is used to strip a solute from a liquid in a countercurrent packed tower operating under isothermal condition. Pure gas is used i...
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GATE Chemical 2020 | Question: 1
Which one of the following methods requires specifying an initial interval containing the root (i.e., bracketing) to obtain the solution of $f(x) =0$, where $f(x)$ is a c...
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GATE Chemical 2024 | Question: 4
​​​​​A homogeneous azeotropic distillation process separates an azeotropic $AB$ binary feed using a heavy entrainer, $E$, as shown in the figure. The loss of $E...
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GATE CH 2023 | Question: 60
An irreversible liquid-phase second-order reaction ... is______________ (rounded off to the nearest integer).
An irreversible liquid-phase second-order reaction$$\boldsymbol{A} \stackrel{k}{\longrightarrow} \boldsymbol{B}$$with rate constant $k=0.2$ liter. $\mathrm{mol}^{-1} \mat...
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GATE Chemical 2020 | Question: 27
The maximum value of the function $f(x)=-\dfrac{5}{3} x^3 +10x^2-15x+16$ in the interval $(0.5,3.5)$ is$0$$8$$16$$48$
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GATE Chemical 2019 | Question: 26
The solution of the ordinary differential equation$\frac{dy}{dx}+3y=1$, subjects to the initial condition $y=1$ at $x=0$, is$\frac{1}{3}\left ( 1+2e^{-x/3} \right )$$\fra...
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GATE Chemical 2019 | Question: 36
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 iterat...
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GATE Chemical 2017 | Question: 4
Let $i$ and $j$ be the unit vectors in the $x$ and $y$ directions, respectively. For the function $F\left ( x,y \right )=x^{3}+y^{2}$ the gradient of the function. i.e.. ...
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GATE Chemical 2015 | Question: 48
In the figure below, the temperature profiles of cold and hot fluids in counter double pipe heat exchangers (in different modes of operation) are shown on the left. For e...
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GATE Chemical 2013 | Question: 61
Velocity of an object fired directly in upward direction is given by $V = 80 – 32\: t$, where $t$ (time) is in seconds. When will the velocity be between $32\: m/sec$ a...
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GATE Chemical 2012 | Question: 42
The block diagram of a system with a proportional controller is shown below A unit step is introduced in the set point. Th...
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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 Chemical 2018 | Question: 50
In a closed piston-cylinder system, methane was observed to obey the following equation of state$$P\left ( V-nb \right )=nRT$$where $b=0.029\:m^{3}$/mol. The temperature ...
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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 | 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 2022 | Question: 17
In an enzymatic reaction, an inhibitor $(I)$ competes with the substrate $(S)$ to bind with the enzyme $(E)$, thereby reducing the rate ... A. B. C. D.
In an enzymatic reaction, an inhibitor $(I)$ competes with the substrate $(S)$ to bind with the enzyme $(E)$, thereby reducing the rate of product $(P)$ formation. The co...
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GATE Chemical 2014 | Question: 43
A cash flow of Rs. $12,000$ per year is received at the end year (uniform periodic payment) for $7$ consecutive years. The rate of interest is $9\%$ per year compounded a...
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