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Consider the following two equation:$\frac{dx}{dt}+x+y=0$$\frac{dy}{dt}-x=0$The above set of equations is represented by$\frac{d^{2}y}{dt^{2}}-\frac{dy}{dt}-y=0$$\frac{d^...
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The area of an equilateral triangle is $\sqrt{3}$. What is the perimeter of the triangle$?$$2$$4$$6$$8$
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The reactant ($M$) is converted into product ($N$) in the presence of catalyst in a fixed bed reactor. All the flow rates ($F,\:G,\:H,\:P $ and $R$) in mol/$s$, and mole ...
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In a roll crusher, rolls of diameter $1$ $m$ each are set in such a manner that minimum clearance between the crushing surfaces is $15$ $mm$. If the angle of nip is $31^{...
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A $CSTR$ and a $PFR$ of equal volume are connected in series as shown below to carry out a first-order, isothermal, liquid phase reaction$$A{\rightarrow}P$$The rate const...
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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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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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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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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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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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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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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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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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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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For a chemical reaction, the ratio of rate constant at $500\:K$ to that at $400\:K$ is $2.5$. Given $R=8.314\:J$ mol$^{-1}$ $K^{-1}$, the value of activation energy (in $...
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A venturi meter is installed to measure the flow rate of water in a $178\:mm$ diameter ($ID$) pipe. The throat diameter is $102\:mm$. The differential pressure measured u...
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Consider the following transfer function:$$G\left ( s \right )=\frac{3}{\left ( 5s+1 \right )^{2}}$$where, the natural period of oscillation is in min. The amplitude rati...
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A set of standard stainless steel pipes, each of internal diameter $26.65\:mm$ and $6000\:mm$ length, is used to make a plug flow reactor by joining them in series to car...
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The decay ratio for a system having complex conjugate poles as $\left ( -\frac{1}{10}+j\frac{2}{15} \right )$ and $\left ( -\frac{1}{10}-j\frac{2}{15} \right )$ is $7\ti...
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For absorption of $H_{2}S$ from a mixture with hydrocarbon vapour into an aqueous alkanolamine solution, the liquid phase mass transfer resistance issignificantly higher ...
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Economy of evaporators used for concentrating sugarcane juice is$\frac{kg\:of\:concentrated\:juice\:produced}{kg\:of\:steam\:supplied}$$\frac{kg\:of\:steam\:supplied}{kg\...
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A binary distillation column is designed by McCabe-Thiele method to get a distillate mole fraction of $0.9$. The enriching section operating line has an intercept with $y...
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$G$ denotes the Gibbs free energy of a binary mixture, $n_{T}$ denotes the total number of moles present in the system, $\mu _{i}$ is the chemical potential of the $i^{th...
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A furnace installed at a cost of $Rs.\:24$ Lakh is expected to serve its useful life of $5$ years. Salvage value of the furnace is $Rs.\:8$ Lakh. The interest rate compou...
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Match the equipment in Column $A$ with the corresponding process in Column $B$$\begin{array}{|cl|cI|cI|cI|cI|cI|}\hline&\text{$Column\:A$} & \text{$Column\:B$} \\ \hline ...
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Liquid phase isomerization of $o$-xylene to $p$-xylene using a zeolite catalyst was carried out in a $CSTR$ three sets of kinetic data at different temperatures and stirr...
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In a laboratory batch setup, reaction of $P$ over a catalyst was studied at various temperature. The reactions occurring are$$P\rightarrow 2Q\:;\:P\rightarrow R$$At the e...
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An automobile travels from city $A$ to city $B$ and returns to city $A$ by the same route. The speed of the vehicle during the onward and return journeys were constant at...
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Polyvinyl chloride is produced byco-polymerizationaddition-type kineticsreacting chlorine with polyethylenereacting hydrochloric acid with polyethylene
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It is decided to extract $A$ from a feed containing $20$ mol$\%$ $A$ and $80$ mol$\%$ $B$ in two ideal cross-current stages as shown below, using equal amount of pure sol...
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Under isothermal condition, a vertical tube of length $L=100\:m$ contains a gas of molecular weight equal to $60$. The pressure and temperature at the top of the tube are...
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The fourth order Runge-Kutta ($RK4$) method to solve an ordinary differential equation $\frac{dy}{dx}=f\left ( x,y \right )$ is given as $$y\left ( x+h \right )=y\left ( ...
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Pitot tube is used to measureliquid level in a tankflow velocity at a pointangular deformationvorticity
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Two packed towers are designed for the same mass velocity of the gas. The first has liquid and gas flow rates of $30\:kg/s$ and $1.2\:kg/s$, respectively, while the corre...
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Match the items in Column $A$ with the items in Column $B$$\begin{array}{|cl|cI|}\hline&\text{$Column\:A$} & \text{$Column\:A$} \\ \hline &\text{P. Pure dead-time} & \te...
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Critical speed of a ball mill depends onthe radius of the mill (shell) and the radius of the particlesthe radius of the mill (shell) and the density of the particlesthe r...
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The elementary second-order liquid phase reaction $A+B{\rightarrow}C+D$ is carried out in an isothermal plug flow reactor of $2\:m^{3}$ volume. The inlet volumetric flow ...
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A watch uses two electronic circuits ($ECs$). Each $EC$ has a failure probability of $0.1$ in one year of operation. Both $ECs$ are required for functioning of the watch....
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According to the surface renewal theory, the unit of fractional rate of surface renewal ism$^{2}$ s$^{-2}$m$^{2}$ s$^{-1}$m s$^{-1}$$s^{-1}$
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The Annual Fixed Charges ($AFC$) and Annual Utilities Costs ($AUC$) of a distillation column being designed are expressed in terms of the reflux ratio ($R$) as $AFC$ ($Rs...