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GATE CH 2021 | GA Question: 6
We have $2$ rectangular sheets of paper, $M$ and $N$, of dimensions $6$ cm $\times$ $1$ cm each. Sheet $M$ is rolled to form an ... $\frac{9}{\pi} \\$ $3 \pi$
We have $2$ rectangular sheets of paper, $M$ and $N$, of dimensions $6$ cm $\times$ $1$ cm each. Sheet $M$ is rolled to form an open cylinder by bringing the short edges ...
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GATE CH 2021 | GA Question: 7
... its marked price, is ___________ $25$ $12.5$ $10$ $5$
$$\begin{array}{|c|c|c|c|} \hline \textbf{Items} & \textbf{Cost} & \textbf{Profit} \% & \textbf{Marked Price} \\ & (₹) && (₹) \\ \hline P & 5,400 & \dots & 5,860 \\ ...
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GATE CH 2021 | GA Question: 8
There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag. The probability ... $0.4235$ $0.6976$ $0.8125$
There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag. The probability that at least two chocolates are ide...
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GATE CH 2021 | GA Question: 9
Given below are two statements $1$ and $2$, and two conclusions $\text{I}$ and $\text{II}$ ... Neither conclusion $\text{I}$ nor $\text{II}$ is correct
Given below are two statements $1$ and $2$, and two conclusions $\text{I}$ and $\text{II}$.$\text{Statement 1}$: All bacteria are microorganisms.$\text{Statement 2}$: All...
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GATE CH 2021 | GA Question: 10
Some people suggest anti-obesity measures $\text{(AOM)}$ such as displaying calorie information in restaurant menus. Such measures sidestep addressing the core problems t...
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GATE CH 2021 | Question: 1
An ordinary differential equation $\text{(ODE)}, \: \dfrac{dy}{dx}=2y$, with an initial condition $y(0)=1$, has the analytical ... $0.06$ $0.8$ $4.0$ $8.0$
An ordinary differential equation $\text{(ODE)}, \: \dfrac{dy}{dx}=2y$, with an initial condition $y(0)=1$, has the analytical solution $y=e^{2x}$.Using Runge-Kutta secon...
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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 2021 | Question: 3
The heat of combustion of methane, carbon monoxide and hydrogen are $P$, $Q$ and $R$ ... $Q+3R-P$ $P-Q-R$ $Q+R-P$
The heat of combustion of methane, carbon monoxide and hydrogen are $P$, $Q$ and $R$ respectively. For the reaction below, $$CH_4+H_2O \rightarrow CO+3H_2$$ the heat of r...
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GATE CH 2021 | Question: 4
A batch settling experiment is performed in a long column using a dilute dispersion containing equal number of particles of ... $A$ particles on top of type $B$ particles
A batch settling experiment is performed in a long column using a dilute dispersion containing equal number of particles of type $A$ and type $B$ in water (density $1000 ...
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GATE CH 2021 | Question: 5
A three-dimensional velocity field is given by $V=5x^2y \: i + Cy \: j-10xyz \: k$, where $i,j,k$ are the unit vectors in ... fluid flow, the value of $C$ is $-1$ $0$ $1$ $5$
A three-dimensional velocity field is given by $V=5x^2y \: i + Cy \: j-10xyz \: k$, where $i,j,k$ are the unit vectors in $x,y,z$ directions, respectively, describing a c...
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GATE CH 2021 | Question: 6
Heat transfer coefficient for a vapor condensing as a film on a vertical surface is given by Dittus- ... equation Nusselt theory Chilton-Colburn analogy Sieder-Tate equation
Heat transfer coefficient for a vapor condensing as a film on a vertical surface is given byDittus-Boelter equationNusselt theoryChilton-Colburn analogySieder-Tate equati...
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GATE CH 2021 | Question: 7
In a double-pipe heat exchanger of $10 \: m$ length, a hot fluid flows in the annulus and a cold fluid flows in the inner pipe. The ... $24.6$ $27.9$ $30.0$ $50.0$
In a double-pipe heat exchanger of $10 \: m$ length, a hot fluid flows in the annulus and a cold fluid flows in the inner pipe. The temperature profiles of the hot $(T_h)...
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GATE CH 2021 | Question: 8
For a shell-and-tube heat exchanger, the clean overall heat transfer coefficient is calculated as $\text{250 W m$^{-2}$ ... 2}$ K}^{-1})$. $100$ $150$ $200$ $250$
For a shell-and-tube heat exchanger, the clean overall heat transfer coefficient is calculated as $\text{250 W m$^{-2}$ K}^{-1}$ for a specific process condition. It is e...
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GATE CH 2021 | Question: 9
In reverse osmosis, the hydraulic pressure and osmotic pressure at the feed side of the membrane are $P_1$ and $\pi_1$, ... $P_1 - \pi_1 = P_2-\pi_2$
In reverse osmosis, the hydraulic pressure and osmotic pressure at the feed side of the membrane are $P_1$ and $\pi_1$, respectively. The corresponding values are $P_2$ a...
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GATE CH 2021 | Question: 10
Ethylene adsorbs on the vacant active sites $V$ ... $N_T=N_V+0.5N_{C_2H_4}$
Ethylene adsorbs on the vacant active sites $V$ of a transition metal catalyst according to the following mechanism.If $N_T, N_V$ and $N_{C_2H_4}$ denote the total number...
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GATE CH 2021 | Question: 11
Which of the following is $\text{NOT}$ a standard to transmit measurement and control signals? $4-20 \: \text{mA}$ $3-15 \text{ psig}$ $0-100\: \%$ $1-5 \text{ VDC}$
Which of the following is $\text{NOT}$ a standard to transmit measurement and control signals?$4-20 \: \text{mA}$$3-15 \text{ psig}$$0-100\: \%$$1-5 \text{ VDC}$
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GATE CH 2021 | Question: 12
A feedforward controller can be used only if the disturbance variable can be measured the disturbance variable ... variable can be ignored regulatory control is not required
A feedforward controller can be used only ifthe disturbance variable can be measuredthe disturbance variable can be manipulatedthe disturbance variable can be ignoredregu...
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GATE CH 2021 | Question: 13
Turnover ratio is defined as $\dfrac{\text{Fixed capital investment}}{\text{Gross annual sales}} \\$ ...
Turnover ratio is defined as$\dfrac{\text{Fixed capital investment}}{\text{Gross annual sales}} \\$$\dfrac{\text{Gross annual sales}}{\text{Fixed capital investment}} \\$...
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GATE CH 2021 | Question: 14
A principal amount is charged a nominal annual interest rate of $10 \%$. If the interest rate is compounded continuously ... using an effective interest rate of $27.18 \%$
A principal amount is charged a nominal annual interest rate of $10 \%$. If the interest rate is compounded continuously, the final amount at the end of the one year woul...
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GATE CH 2021 | Question: 15
Match the common name of chemicals in $\text{Group-1}$ with their chemical formulae in $\text{Group-2}$ ... $\text{P-II, Q-I, R- III}$
Match the common name of chemicals in $\text{Group-1}$ with their chemical formulae in $\text{Group-2}$$\begin{array}{|l|l|l|l|} \hline & \textbf{Group – 1} & & \textbf...
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GATE CH 2021 | Question: 16
For the function $f(x) = \begin{cases} -x, & x<0 \\ x^2, & x \geq 0 \end{cases}$ ... $x=0$ $f(x)$ is differentiable at $x=0$
For the function $f(x) = \begin{cases} -x, & x<0 \\ x^2, & x \geq 0 \end{cases}$ the $\text{CORRECT}$ statement(s) is/are$f(x)$ is continuous at $x=1$$f(x) $ is different...
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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 CH 2021 | Question: 18
The inherent characteristics of the three control valves $P$, $Q$ and $R$ ... is an equal percentage valve $R$ is an equal percentage valve
The inherent characteristics of the three control valves $P$, $Q$ and $R$ are shown in the figure.The $\text{CORRECT}$ option(s) is/are$P$ is a quick opening valve$Q$ is ...
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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: 26
Let $A$ be a square matrix of size $n \times n (n>1)$. The elements of $A=\{a_{ij}\}$ ... $A$ is $0$ $1$ $n!$ $(n!)^2$
Let $A$ be a square matrix of size $n \times n (n>1)$. The elements of $A=\{a_{ij}\}$ are given by $$a_{ij} = \begin{cases} i \times j, & \text{if } i \geq j \\ 0, & \tex...
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GATE CH 2021 | Question: 27
Consider a fluid confined between two horizontal parallel plates and subjected to shear flow. In the ... is ___________ Newtonian Pseudoplastic Dilatant Ideal and inviscid
Consider a fluid confined between two horizontal parallel plates and subjected to shear flow.In the first experiment, the plates are separated by a distance of $1 \: mm$....
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GATE CH 2021 | Question: 28
Water of density $1000 \text{ kg m}^{-3}$ flows in a horizontal pipe of $10 \: cm$ diameter at an average velocity of ... $0.0012$ $0.0074$ $0.0082$ $0.0106$
Water of density $1000 \text{ kg m}^{-3}$ flows in a horizontal pipe of $10 \: cm$ diameter at an average velocity of $0.5 \: m \: s^{-1}$. The following plot shows the p...
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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 CH 2021 | Question: 30
Which of these symbols can be found in piping and instrumentation diagrams? $(Q)$ and $(S)$ only $(P)$, $(Q)$ and $(R)$ ... $(P)$, $(Q)$, $(R)$ and $(S)$
Which of these symbols can be found in piping and instrumentation diagrams?$(Q)$ and $(S)$ only$(P)$, $(Q)$ and $(R)$ only$(P)$, $(R)$ and $(S)$ only$(P)$, $(Q)$, $(R)$ a...
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GATE CH 2021 | Question: 31
It is required to control the volume of the contents in the jacketed reactor shown in the figure. Which one of the ... $V-3$ Measure $F101$ and manipulate valve $V-1$
It is required to control the volume of the contents in the jacketed reactor shown in the figure.Which one of the following schemes can be used for feedback control?Measu...
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GATE CH 2021 | Question: 32
Which of the following is $\text{NOT}$ a necessary condition for a process under closed-loop control to be ... an amplitude ratio less than $1$ at the critical frequency
Which of the following is $\text{NOT}$ a necessary condition for a process under closed-loop control to be stable?Dead-time term(s) must be absent in the open-loop transf...
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GATE CH 2021 | Question: 33
Match the reaction in $\textbf{Group - 1}$ with the reaction type in $\textbf{Group - 2}$ ... $\text{P-I, Q-IV, R-III, S-II}$
Match the reaction in $\textbf{Group – 1}$ with the reaction type in $\textbf{Group – 2}$.$\begin{array}{|c|l|c|l|} \hline & \textbf{Group – 1} && \textbf{Group –...
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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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