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​​​​​If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words [simmer $\rightarrow$ seethe $\rightarrow$ smolder] is analogous ...
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​​​​​In a locality, the houses are numbered in the following way:The house-numbers on one side of a road are consecutive odd integers starting from $301$, while...
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For positive integers $p$ and $q$, with $\frac{p}{q} \neq 1,\left(\frac{p}{q}\right)^{\frac{p}{q}}=p^{\left(\frac{p}{q}-1\right)}$. Then,$q^{p}=p^{q}$$q^{p}=p^{2 q}$$\sqr...
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​​​Which one of the given options is a possible value of $x$ in the following sequence?\[3,7,15, x, 63,127,255\]$35$$40$$45$$31$
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​​On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time $12:05:00$ hours to $12: 55: 00$ hours?$51...
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​​​​​​In the given text, the blanks are numbered $\text{(i)-(iv)}$. Select the best match for all the blanks.From the ancient Athenian arena to the modern Oly...
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​​​​​Three distinct sets of indistinguishable twins are to be seated at a circular table that has $8$ identical chairs. Unique seating arrangements are defined ...
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The chart given below compares the Installed Capacity $\text{(MW)}$ of four power generation technologies, $\text{T1, T2, T3}$, and $\text{T4}$, and their Electricity Gen...
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In the $4 \times 4$ array shown below, each cell of the first three columns has either a cross $(X)$ or a number, as per the given rule.\begin{array}{|l|l|l|l|}\hline 1 &...
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During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be $89.85^{\circ}$, the ratio of th...
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The first non-zero term in the Taylor series expansion of $(1-x)-e^{-x}$ about $x=0$ is$1$$-1$$\frac{x^{2}}{2}$$-\frac{x^{2}}{2}$
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Consider the normal probability distribution function\[f(x)=\frac{4}{\sqrt{2 \pi}} e^{-8(x+3)^{2}}\]If $\mu$ and $\sigma$ are the mean and standard deviation of $f(x)$ re...
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If $z_{1}=-1+i$ and $z_{2}=2 i$, where $i=\sqrt{-1}$, then $\operatorname{Arg}\left(z_{1} / z_{2}\right)$ is$\frac{3 \pi}{4}$$\frac{\pi}{4}$$\frac{\pi}{2}$$\frac{\pi}{3}$...
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​​​​​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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An infinitely long cylindrical water filament of radius $R$ is surrounded by air. Assume water and air to be static. The pressure outside the filament is $P_{\text {out }...
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​​​​​The velocity field in an incompressible flow is $\boldsymbol{v}=\alpha x y \hat{\boldsymbol{\imath}}+v_{y} \hat{\boldsymbol{\jmath}}+\beta \widehat{\boldsy...
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​​​​​Consider the steady, uni-directional diffusion of a binary mixture of $A$ and $B$ across a vertical slab of dimensions $0.2 \mathrm{~m} \times 0.1 \mathrm{...
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Consider a vapour-liquid mixture of components $A$ and $B$ that obeys Raoult's law. The vapour pressure of $A$ is half that of $B$. The vapour phase concentrations of $A$...
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The ratio of the activation energy of a chemical reaction to the universal gas constant is $1000 \mathrm{~K}$. The temperature-dependence of the reaction rate constant fo...
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​​​​​​The rate of a reaction $A \rightarrow B$ is $0.2 \mathrm{~mol} \mathrm{~m}^{-3} \mathrm{~s}^{-1}$ at a particular concentration $C_{A 1}$. The rate cons...
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​​​​​Two parallel first-order liquid phase reactions $A \xrightarrow{k_{1}} B$ and $A \xrightarrow{k_{2}} C$ are carried out in a well-mixed isothermal batch re...
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Consider the block diagram in the figure with control input $u$, disturbance $d$ and output $y$. For the feedforward controller, the ordered pair $(K, \alpha / \beta)$ is...
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​​​​​Consider the control structure for the overhead section of a distillation column shown in the figure. The composition controller (CC) controls the heavy ke...
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Which one of the given statements is correct with reference to gas-liquid contactors for mass transfer applications?A tray tower is more suitable for foaming systems than...
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​​​​​In an ammonia manufacturing facility, the necessary hydrogen is generated from methane. The facility consists of the following process units -$\text{P}$: M...
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​​​​​​Consider a linear homogeneous system of equations $\text{Ax}=0$, where $\text{A}$ is an $n \times n$ matrix, $\text{x}$ is an $n \times 1$ vector and $0...
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If the Prandtl number $\operatorname{Pr}=0.01$, which of the following statements is/are correct?The momentum diffusivity is much larger than the thermal diffusivity.The ...
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For the electrolytic cell in a chlor-alkali plant, which of the following statements is/are correct?A membrane cell operates at a higher brine concentration than a diaphr...
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​​​​​​Which of the following statements with reference to the petroleum/petrochemical industry is/are correct?Catalytic hydrocracking converts heavier hydroca...
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Consider a matrix $\text{A}=\left[\begin{array}{cc}-5 & a \\ -2 & -2\end{array}\right]$, where $a$ is a constant. If the eigenvalues of $\text{A}$ are $-1$ and $-6$, then...
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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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Consider a binary mixture of components $A$ and $B$ at temperature $T$ and pressure $P$. Let $\bar{V}_{A}$ and $\bar{V}_{B}$ be the partial molar volumes of $A$ and $B$, ...
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Consider the steady, uni-directional, fully-developed, pressure-driven laminar flow of an incompressible Newtonian fluid through a circular pipe of inner radius $5.0 \mat...
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The opposite faces of a metal slab of thickness $5 \mathrm{~cm}$ and thermal conductivity $400 \mathrm{~W} \mathrm{~m}^{-1}{ }^{\circ} \mathrm{C}^{-1}$ are maintained at ...
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The capital cost of a distillation column is Rs. $90$ lakhs. The cost is to be fully depreciated (salvage value is zero) using the double-declining balance method over $1...
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​​​​Consider a steady, fully-developed, uni-directional laminar flow of an incompressible Newtonian fluid (viscosity $\mu$ ) between two infinitely long horizonta...
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​​​​​​The temperatures of two large parallel plates of equal emissivity are $900 \mathrm{~K}$ and $300 \mathrm{~K}$. A reflection radiation shield of low emis...
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​​​​​Hot oil at $110{ }^{\circ} \mathrm{C}$ heats water from $30^{\circ} \mathrm{C}$ to $70{ }^{\circ} \mathrm{C}$ in a counter-current double-pipe heat exchang...
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​​​​​A solid slab of thickness $H_{1}$ is initially at a uniform temperature $T_{0}$. At time $t=0$, the temperature of the top surface at $y=H_{1}$ is increase...
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​​​​​​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...