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GATE Chemical 2018 | Question: 46
If $y=e^{-x^{2}}$ then the value of $\underset{x\rightarrow \infty }{\lim}\frac{1}{x}\frac{dy}{dx}$ is __________
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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 $$a_{ij} = \begin{cases} i \times j, & \text{if } i \geq j \\ 0, & \tex...
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GATE Chemical 2020 | Question: 25
Sum of the eigenvalues of the matrix $\begin{bmatrix} 2 & 4 & 6 \\ 3 & 5 & 9 \\ 12 & 1 & 7 \end{bmatrix}$ is ______ (round off to nearest integer).
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GATE Chemical 2014 | Question: 37
A homogenous reaction $(R{\rightarrow}P)$ occurs in a batch reactor. The conversion of the reactant $R$ is $67\%$ after $10$ minutes and $80\%$ after $20$ minutes. The ra...
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GATE Chemical 2018 | Question: 55
A hot liquid is to be cooled in a $1-1$ shell and tube heat exchanger from $80^{\circ}C$ to $50^{\circ}C$. Cooling water enters the tube side at $30^{\circ}C$, and exits ...
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GATE Chemical 2018 | Question: 38
At a shear rate of $10\:s^{-1}$, the apparent viscosity of a non-Newtonian liquid was found to be $1\: Pa\:s$. At a shear rate of $100\:s^{-1}$, the apparent viscosity of...
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GATE Chemical 2018 | Question: 36
Vapour bubbles are formed in the nucleate boiling regime at a frequency of $10$ bubbles per second per nucleation site. There are $100$ nucleation sites per $m^{2}$ of he...
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GATE Chemical 2018 | Question: 25
The inital water level in a tank is $4\:m$. When the value located at the bottom is opened, the rate of change of water level ($L$) with respect to time ($t$) is, $\frac{...
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GATE Chemical 2018 | Question: 24
The ammonia ($NH_{3}$) oxidation process occurs over a catalyst as$$4NH_{3}+5O_{2}\rightarrow 6H_{2}O+4NO$$Air is supplied such that oxygen ($O_{2}$) is $20\%$ in excess ...
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GATE CH 2021 | GA Question: 1
The ratio of boys to girls in a class is $7$ to $3$. Among the options below, an acceptable value for the total number of students in the class is: $21$ $37$ $50$ $73$
The ratio of boys to girls in a class is $7$ to $3$.Among the options below, an acceptable value for the total number of students in the class is:$21$$37$$50$$73$
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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 Chemical 2020 | Question: 4
Consider the following unit step function.The Laplace transform of this function is$\dfrac{e^{-3s}}{s} \\ $$\dfrac{e^{-3s}}{s^2} \\$$\dfrac{e^{-3s}}{3s} \\$$\dfrac{e^{-6s...
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GATE Chemical 2019 | GA Question: 6
The police arrested four criminals – $P, Q, R$ and $S.$ The criminals knew each other. They made the following statements:$P$ says “Q committed the crime.”$Q$ says ...
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GATE Chemical 2019 | Question: 20
In petroleum refining operations, the process used for converting paraffins and naphthenes to aromatics isalkylationcatalytic reforminghydrocrackingisomerization
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GATE Chemical 2019 | Question: 42
A solid sphere of radius $1$ $cm$ and initial temperature of $25^{\circ}\:C$ is exposed to a gas stream at $100^{\circ}\:C$. For the solid sphere, the density is $10^{4}$...
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GATE Chemical 2012 | Question: 29
If $i = \sqrt{-1}$, the value of the integral $$\oint_{c}\dfrac{7z + i}{z(z^2 + 1)}dz \quad\quad\quad\quad|z|<2$$,u...
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GATE Chemical 2018 | Question: 34
An insulted storage tank contains $1000\:kg$ liquid of specific heat $10\:kJ\:kg^{-1}\:K^{-1}$. The liquid is heated by saturated steam, condensing in a helical coil at a...
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GATE Chemical 2024 | Question: 30
​​​​​​A gas stream containing $95 \mathrm{~mol} \% \mathrm{CO}_{2}$ and $5 \mathrm{~mol} \%$ ethanol is to be scrubbed with pure water in a counter-current, i...
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GATE Chemical 2019 | Question: 29
A disk turbine is used to stir a liquid in a baffled tank. To design the agitator, experiments are performed in a lab-scale model with a turbine diameter of $0.05 \:m$ an...
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GATE Chemical 2016 | GA Question: 7
A smart city integrates all modes of transport, uses clean energy and promotes sustainable use of resources. It also uses technology to ensure safety and security of the ...
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GATE Chemical 2013 | Question: 65
All professors are researchersSome scientists are professorsWhich of the given conclusions is logically valid and is inferred from the above arguments:All scientists are ...
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GATE Chemical 2012 | Question: 48
A counter-current extraction column is designed to remove 99% of solute C from a solution of solvent A and solute C using pure solvent B. The initial concentration of sol...
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GATE Chemical 2018 | Question: 43
A fiberboard sheet $\left ( 1.5\:m\times 2.0\:m\times 15\:mm \right )$ is being dried by suspending it horizontally in a current of hot, dry air. The edges are insulted s...
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GATE Chemical 2018 | Question: 18
A first-order process having a transfer function, $G_{p}=\frac{2}{7s+1}$ is controlled by a proportional controller with gain of $3.2$. The process time constant is in mi...
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GATE CH 2021 | GA Question: 2
A polygon is convex if, for every pair of points, $P$ and $Q$ ... following is $\underline{ \text{NOT}}$ a convex polygon?
A polygon is convex if, for every pair of points, $P$ and $Q$ belonging to the polygon, the line segment $PQ$ lies completely inside or on the polygon. Which one of the f...
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GATE CH 2021 | GA Question: 3
Consider the following sentences: Everybody in the class is prepared for the exam. Babu invited Danish to his ... grammatically incorrect and $\text{(ii)}$ is ambiguous
Consider the following sentences:Everybody in the class is prepared for the exam.Babu invited Danish to his home because he enjoys playing chess.Which of the following is...
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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 Chemical 2019 | GA Question: 4
Ten friends planned to share equally the cost of buying a gift for their teacher. When two of them decided not to contribute, each of the other friends had to pay Rs. $15...
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GATE Chemical 2019 | Question: 8
Prandtl number signifies the ratio of$\frac{Momentum \: Diffusivity}{Thermal \: Diffusivity}$$\frac{Mass \: Diffusivity}{Thermal \: Diffusivity}$$\frac{Thermal \: Diffusi...
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GATE Chemical 2019 | Question: 46
A first-order irreversible liquid phase reaction $A\rightarrow B\left ( k=0.1\:min^{-1} \right )$ is carried out under isothermal, steady state conditions in the followin...
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GATE Chemical 2013 | Question: 62
In a factory, two machines $M1$ and $M2$ manufacture $60\%$ and $40\%$ of the autocomponents respectively. Out of the total production, $2\%$ of $M1$ and $3\%$ of $M2$ ar...
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GATE Chemical 2012 | Question: 62
A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation $y = 2x – 0.1...
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GATE Chemical 2012 | Question: 58
The cost function for a product in a firm is given by $5q^{2}$, where q is the amount of production. The firm can sell the product at a market price of $₹50$ per unit. ...
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GATE Chemical 2018 | Question: 42
A binary distillation column is designed by McCabe-Thiele method to get a distillate mole fraction of $0.9$. The enriching section operating line has an intercept with $y...
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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 2020 | Question: 22
Consider two Carnot engines $C_1$ and $C_2$ as shown in the figure.The efficiencies of the engines $C_1$ and $C_2$ are $0.40$ and $0.35$, respectively. If the temperature...
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GATE Chemical 2020 | Question: 26
In a box, there are $5$ green balls and $10$ blue balls. A person picks $6$ balls randomly. The probability that the person has picked $4$ green balls and $2$ blue balls ...
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GATE Chemical 2017 | Question: 6
The volumetric properties of two gases $M$ and $N$ are described by the generalized compressibility chart which expresses the compressibility factor $(Z)$ as a function o...
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GATE Chemical 2016 | Question: 9
A composite wall is made of four different materials of construction in the fashion shown below. The resistance (in $K/W$) of each sections of the wall is indicated in th...
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GATE Chemical 2014 | Question: 38
A vapour phase catalytic reaction $(Q+R{\rightarrow}S)$ follows Rideal mechanism ($R$ and $S$ are not absorbed). Initially, the mixture contains only the reactants in equ...
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