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Recent questions tagged numerical-answers

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GATE Chemical 2026 | GA | Question: 5
In a group of students, $10$ students like Mathematics, $12$ students like English, $4$ students like both Mathematics and English, and $6$ students like neither Mathemat...
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GATE Chemical 2026 | GA | Question: 10
As shown in the figure, circle $C_{1}$ with center $O_{1}$ and radius $r_{1}$ touches the square $V W X Y$ at points $P$ and $Q$ while circle $C_{2}$ with center $O_{2}$ ...
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GATE Chemical 2026 | Question: 4
Which one of the following ratios does Grashof number represent?buoyancy force to inertia forcebuoyancy force to viscous forceviscous force to capillary forceviscous forc...
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GATE Chemical 2026 | Question: 5
Consider a closed system of one mole of an ideal gas undergoing a polytropic process. The process follows $P V^{n}=$ constant, where $P$ is the pressure, $V$ is the volum...
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GATE Chemical 2026 | Question: 10
A binary mixture of butane and butadiene is to be separated in an extractive distillation using furfural. Furfural lowers the activity of butadiene more than it does for ...
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GATE Chemical 2026 | Question: 12
Which one of the following is the value of $\lim _{x \rightarrow 0} \dfrac{e^{x}-x-1}{\cos x-1}?$$-1$$0$$1$$\infty$
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GATE Chemical 2026 | Question: 20
Consider two successive screen sizes in the Tyler standard screen scale, viz. $150$ meshes per inch and $200$ meshes per inch. Their linear sizes of the openings are $\ma...
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GATE Chemical 2026 | Question: 21
Consider a homogeneous gas phase reaction, $\mathrm{A}+2 \mathrm{~B} \rightarrow 2 \mathrm{C}+3 \mathrm{D}$, occurring at constant temperature and pressure in a varying v...
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GATE Chemical 2026 | Question: 22
Water is discharged from vertical side of a tank through a circular orifice of diameter $2$ cm under laminar flow conditions. The water surface in the tank is maintained ...
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GATE Chemical 2026 | Question: 23
Consider a non-reactive binary mixture of two ideal gases $\text{A}$ and $\text{B}$ in an isothermal horizontal closed tube. Due to the concentration difference at the tw...
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GATE Chemical 2026 | Question: 24
An experiment is performed by rolling an unbiased die once. Events A and B are defined as follows:Event A: The outcome of the rolled die is a prime number.Event B: The ou...
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GATE Chemical 2026 | Question: 25
Using single step trapezoidal rule, the value of\[\int_{0}^{0.5}\left(1+16 x-20 x^{2}\right) d x\]is $\_\_\_\_$ (rounded off to two decimal places).
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GATE Chemical 2026 | Question: 26
$K$ value is defined as the ratio of mole fraction of a component in the vapor phase to that in the liquid phase. The $K$ values of propane and iso-butane at $293$ $K$ ar...
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GATE Chemical 2026 | Question: 28
 Vapor pressure of water at various temperature is given in the table.\[\begin{array}{|l|c|c|c|c|c|}\hline\text{Temperature (in K)} & 284 & 289 & 294 & 299 & 310 \\\hline...
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GATE Chemical 2026 | Question: 29
A volatile organic compound $\text{(VOC)}$ is to be adsorbed from air onto a bed of activated carbon. The equilibrium capacity of activated carbon at the feed conditions ...
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GATE Chemical 2026 | Question: 31
Consider the following curve in polar coordinates.\[r=2-2 \sin \theta\]Which one of the following is the area enclosed by the curve for $0 \leq \theta \leq 2 \pi$?$3 \pi$...
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GATE Chemical 2026 | Question: 34
A control valve with hyperbolic characteristics has a turndown ratio (ratio of maximum flow to minimum controllable flow) of $50$. The flow rate through the valve at $70 ...
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GATE Chemical 2026 | Question: 35
The gross energy requirement, to reduce a very large feed of coal to such a size that $80 \%$ of the product passes through a $100 ~\mu \mathrm{m}$ screen, is $13 \text{k...
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GATE Chemical 2026 | Question: 36
In a certain project, $15 \%$ of the total investment is the working capital. The minimum acceptable rate of return is $4.95 \%$ and the period of evaluation is $15$ year...
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GATE Chemical 2026 | Question: 37
A continuous distillation column is used to separate an equimolar mixture of diethylamine (DEA) and methanol. The feed enters the column as saturated liquid at a flow rat...
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GATE Chemical 2026 | Question: 38
A gas stream with $2.01 \mathrm{~mol} \%$ ammonia is to be scrubbed in a counter-current isothermal packed bed absorber using pure water to reduce its concentration to $0...
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GATE Chemical 2026 | Question: 39
Laboratory filtration is conducted at constant pressure drop of $200 \text{ kPa}$ on a slurry of $\mathrm{CaCO}_{3}$ in water at room temperature. The time taken to colle...
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GATE Chemical 2026 | Question: 41
A thermometer initially at a steady temperature of $30^{\circ} \mathrm{C}$ is inserted in a water bath maintained at $90^{\circ} \mathrm{C}$. The initial rate of temperat...
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GATE Chemical 2026 | Question: 42
In a double pipe cocurrent heat exchanger, operating at steady state, oil (specific heat capacity $=2100 \mathrm{~J} \mathrm{~kg}^{-1}{ }^{\circ} \mathrm{C}^{-1}$ ) enter...
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GATE Chemical 2026 | Question: 43
A pipe with outer diameter of $0.02 \text{ m},$ carries hot water. The temperature at the outer surface of the pipe is $70^{\circ} \mathrm{C}$. This pipe is covered with ...
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GATE Chemical 2026 | Question: 44
Methanol is formed by the following gas phase homogeneous reaction:\[\mathrm{CO}(\mathrm{~g})+2 \mathrm{H}_{2}(\mathrm{~g}) \leftrightharpoons \mathrm{CH}_{3} \mathrm{OH}...
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GATE Chemical 2026 | Question: 45
A first-order homogeneous liquid-phase reaction ( $\mathrm{A} \rightarrow \mathrm{B}$ ) occurs in an adiabatic, ideal mixed flow reactor operating at steady state. The vo...
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GATE Chemical 2026 | Question: 46
A first-order homogeneous liquid-phase reaction ( $\mathrm{A} \rightarrow \mathrm{B}$ ) occurs in a non-ideal isothermal reactor operating at steady state. The variance (...
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GATE Chemical 2026 | Question: 47
A feed containing $10 \mathrm{~mol} \%$ propylene, $15 \mathrm{~mol} \%$ ammonia and rest air is charged into a reactor to produce acrylonitrile $\left(\mathrm{C}_{3} \ma...
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GATE Chemical 2026 | Question: 48
A gas mixture of $50 \mathrm{wt} . \%$ argon and $50 \mathrm{wt} . \%$ helium flowing through a horizontal tube of uniform diameter at a rate of $1 \mathrm{~kg} \mathrm{~...
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GATE Chemical 2026 | Question: 49
When a cylindrical capillary glass tube, open at both ends, is vertically inserted in a pool of water, the water level in the tube rises to $7 \mathrm{~cm}$ relative to t...
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GATE Chemical 2026 | Question: 50
Consider a two-dimensional, steady, laminar flow of an incompressible fluid with zero pressure gradient, over a thin horizontal flat plate of length $2 \text{ m}$. The fr...
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GATE Chemical 2026 | Question: 51
The flooding velocity curves for two different structured packings are shown in the figure. The ratio of mass velocities of liquid $\left(G_{x}\right)$ to that of the gas...
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GATE Chemical 2026 | Question: 52
Consider a differential equation:\[\begin{array}{c}x^{2} \dfrac{d^{2} y}{d x^{2}}+3 x \dfrac{d y}{d x}-3 y=0 \\\left.\begin{array}{r}y=3 \\\dfrac{d y}{d x}=-5\end{array}\...
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GATE Chemical 2026 | Question: 53
The data given in the table are fitted to the equation $y=m x$ using the method of least squares. The value of $m$ is $\_\_\_\_$ (rounded off to one decimal place).\[\beg...
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GATE Chemical 2026 | Question: 54
Cyclohexane $\left(\mathrm{C}_{6} \mathrm{H}_{12}\right)$ is produced from benzene $\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)$ and hydrogen $\left(\mathrm{H}_{2}\right)$...
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GATE Chemical 2026 | Question: 55
The velocity profile for a fully developed laminar flow of an incompressible Newtonian fluid, at steady state, through a horizontal infinitely wide and long slit of gap $...
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GATE Chemical 2025 | Question: 2
​​​​Consider a Cartesian coordinate system defined over a $3$-dimensional vector space with orthogonal unit basis vectors $\hat{\imath}, \hat{\jmath}$ and $\hat{k}$. Let ...
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GATE Chemical 2025 | Question: 3
​​​​Consider two complex numbers $z_{1}=1-i$ and $z_{2}=i$. The argument of $z_{1} z_{2}$ is$0$$\frac{\pi}{4}$$\frac{\pi}{2}$$\pi$
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GATE Chemical 2025 | Question: 4
​​​​A box contains $3$ identical green balls and $7$ identical blue balls. Two balls are randomly drawn without replacement from the box. The probability of drawing $1$ g...
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