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The value of $\underset{x\rightarrow 0}{\lim}\:\frac{\tan\left ( x \right )}{x}$ is ________________.
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The real part of $6e^{i\pi /3}$ is _______________.
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The number of positive roots of the function $f(x)$ shown below in the range $0<x<6$ is ___________________.
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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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The marks obtained by a set of students are: $38,\:84,\:45,\:70,\:75,\:60,\;48$.The mean and median marks, respectively, are$45$ and $75$$55$ and $48$$60$ and $60$$60$ an...
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The volumetric properties of two gases $M$ and $N$ are described by the generalized compressibility chart which expresses the compressibility factor $(Z)$ as a function o...
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Water is heated at atmospheric pressure from $40^{\circ}C$ to $80^{\circ}C$ using two different processes. In process $I$, the heating is done by a source at $80^{\circ}C...
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In a venturi meter. $\Delta P_{1}$ and $\Delta P_{2}$ are the pressure drops corresponding to volumetric flowrates $Q_{1}$ and $Q_{2}$. If $Q_{2}/Q_{1}=2$, then $\Delta P...
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The thickness of laminar boundary layer over a flat plate varies along the distance from the leading edge of the plate. As the distance increase, the boundary layer thic...
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Which of the following is the correct sequence of equipment for size reduction of solids?
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A gas bubble (gas density $\rho_{g} =2\:kg/m^{3}$ ; bubble diameter $D=10^{-4}\:m$ is rising vertically through water (density $\rho =1000\:kg/m^{3}$; viscosity $\mu =0.0...
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The one-dimensional unsteady heat conduction equation is $$\rho C_{p}\frac{\partial T}{\partial t}=\frac{1}{r^{n}}\frac{\partial }{\partial r}\left ( r^{n}k\frac{\partial...
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In a heat exchanger, the inner diameter of a tube is $25\:mm$ and its outer diameter is $30\:mm$. The overall heat transfer coefficient based on the inner area is $360\:W...
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Which of the following conditions are valid at the plait point?Density difference between the extract and raffinate phases is zeroInterfacial tension between the extract...
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The composition of vapour entering a tray in a distillation column is $0.47$. The average composition of the vapour leaving the tray is $0.53$. The equilibrium compositio...
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Consider steady state mass transfer of a solute $A$ from a gas phase to a liquid phase. The gas phase bilk and interface mole fractions are $y_{A,G}$ and $y_{A,i}$, respe...
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The following reaction rate curve is shown for a reaction $A{\rightarrow}P$. Here, $(-r_{A})$ and $X_{A}$ represent reaction rate and conversion, respectively. The feed i...
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Consider a first order catalytic reaction in a porous catalyst pellet.Given $R$ – characteristics length of the pellet; $D_{e}$ – effective diffusivity; $k_{c}$ – m...
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For a solid-catalyzed gas phase reversible reaction, which of the following statements is ALWAYS TRUE?Adsorption is rate-limitingDesorption is rate-limitingsolid catalyst...
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Match the variable in Group-$1$ with the instruments in Group-$2$.$\begin{array}{cc}\&\text{Group-$1$} & \text{Group-$2$} \\ &\text{P. Temperature} & \text{ I. Capacitanc...
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An $LVDT$ (Linear Variable Differential Transformation) is a transducer used for convertingdisplacement to voltagevoltage to displacementresistance to voltagevoltage to c...
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The cost of a new pump (including installation) is $24,000$ Rupees. The pump has a useful life of $10$ years. Its salvage value is $4000$ Rupees. Assuming straight line d...
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The $DCDA$ (Double Contact Double Absorption) process is used for the manufacture of ureasulphuric acidnitric acidammonia
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Match the polymerization precesses in Group-$1$ with the polymers in Group-$2$.$\begin{array}{cc}\&\text{Group-1} & \text{Group-2} \\ &\text{P. Free radical polymerizatio...
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The purpose of methanation reaction used in ammonia plants is toremove $CO$ as it is catalyst poisonincrease the amount of hydrogenremove sulphur as it is a catalyst pois...
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For the initial value problem$$\frac{dx}{dt}=\sin\left ( t \right ),\:\:\:\:x\left ( 0 \right )=0$$the value of $x$ at $t=\pi /3$ , is _____________.
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The Laplace transform of a function is $\frac{s+1}{s\left ( s+2 \right )}$The initial and final values, respectively, of the function are $0$ and $1$$1$ and $\frac{1}{2}$...
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Match the problem type in Group-$1$ with the numerical method in Group-$2$.$\begin{array}{cc}\&\text{Group-$1$} & \text{Group-$2$} \\ &\text{P. System of linear algebraic...
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A box has $6$ red balls and $4$ white balls. A ball is picked at random and replaced in the box, after which a second ball is picked.The probability of both the balls bei...
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An aqueous salt-solution enters a crystallizer operating at steady state at $25^{\circ}C$. The feed temperature is $90^{\circ}C$ and the salt concentration in the feet is...
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Reaction $A{\rightarrow}B$ is carried out in a reactor operating at steady state and $1$ mol/$s$ of pure $A$ at $425^{\circ}C$ enters the reactor. The outlet stream leave...
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The pressure of a liquid is increased isothermally. The molar volume of the liquid decreases from $50.45\times 10^{-6}$ $m^{3}$/mol to $48\times 10^{-6}$ $m^{3}$/mol duri...
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A sparingly soluble gas (solute) is in equilibrium with a solvent at $10$ bar. The mole fraction of the solvent in the gas phase is $0.01$. At the operating temperature a...
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The vapour pressure of a pure substance at a temperature $T$ is $30$ bar. The actual and ideal gas values of $g/RT$ for the saturated vapour at this temperature $T$ and $...
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Oil is being delivered at a steady flowrate through a circular pipe of radius $1.25\times10^{-2}\:m$ and $10\:m$. The pressure drop across the pipe is $500\:Pa$.The shear...
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The following table provides four sets of Fanning friction factor data, for different values of Reynolds number $(Re)$ and roughness factor $\left ( \frac{k}{D} \right )....
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A propeller (diameter $D=15\:m$) rotates at $N=1$ revolution per second $(rps)$. To understand the flow around the propeller, a lab-scale model is made. Important paramet...
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Size analysis was carried out on a sample of gravel. The data for mass fraction $(x_{i})$ and average particle diameter $(D_{pi})$ of the fraction is given in the table b...
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Let $I_{b\lambda }$ be the spectral blackbody radiation intensity per unit wavelength about the wavelength $\lambda$ . The blackbody radiation intensity emitted by a blac...
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A fluid flows over a heated horizontal plate maintain at temperature $T_{W}$. The bulk temperature of the fluid is $T_{\infty }$ . The temperature profile in the thermal...