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GATE Chemical 2015 | Question: 12
For the matrix $\begin{pmatrix} 4 & 3\\ 3& 4 \end{pmatrix}$, if $\begin{pmatrix} 1\\ 1 \end{pmatrix}$ is an eigenvector, the corresponding eigenvalue is __________ .
Milicevic3306
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Milicevic3306
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Mar 26, 2018
Linear Algebra
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numerical-answers
linear-algebra
matrices
eigen-values
eigen-vectors
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GATE Chemical 2015 | Question: 13
Consider a linear ordinary differential equation: $\frac{dy}{dx}+p\left ( x \right )y=r\left ( x \right )$. Functions $p\left ( x \right )$ and $r\left ( x \right )$ are...
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Milicevic3306
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Differential equations
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differential-equations
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GATE Chemical 2015 | Question: 14
A complex-valued function, $f(z)$, given below is analytic in domain $D$:$$f\left ( z \right )=u\left ( x,y\right )+i\nu \left ( x,y\right )\:\:\:\:\:\:\:z=x+iy$$Which of...
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7.9k
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Milicevic3306
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Complex variables
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complex-variables
complex-valued-function
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GATE Chemical 2015 | Question: 15
A scalar function in the $xy$-plane is given by $\phi \left ( x,y \right )=x^{2}+y^{2}$. If $\hat{i}$ and $\hat{j}$ are unit vectors in the $x$ and $y$ directions, the d...
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7.9k
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Milicevic3306
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Calculus
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calculus
vector-calculus
unit-vectors
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GATE Chemical 2015 | Question: 16
For a pure liquid, the rate of change of vapour pressure with temperature is $0.1$ bar/$K$ in the temperature range of $300$ to $350\:K$. If the boiling point of the liqu...
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Milicevic3306
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Others
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GATE Chemical 2015 | Question: 17
Three identical closed systems of a pure gas are taken from an initial temperature and pressure $(T_{1},P_{1})$ to a final state $(T_{2},P_{2})$, each by a different path...
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GATE Chemical 2015 | Question: 18
For a gas phase cracking reaction $A{\rightarrow}B+C$ at $300^{\circ}$, the Gibbs free energy of the reaction at this temperature is $\Delta G^{\circ}=-2750$ $J$/mol. The...
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GATE Chemical 2015 | Question: 19
If $v,\:u,\:s$ and $g$ represent respectively the molar volume, molar internal energy, molar entropy and molar Gibbs free energy, then match the entries in the left and r...
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GATE Chemical 2015 | Question: 20
Two different liquids are flowing through different pipes of the same diameter. In the first pipe, the flow is laminar with centerline velocity, $V_{max,1}$, whereas in t...
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Milicevic3306
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GATE Chemical 2015 | Question: 21
For uniform laminar flow over a flat plate, the thickness of the boundary layer, $\delta$ at a distance $x$ from the leading edge of the plate follows the reaction :$\del...
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GATE Chemical 2015 | Question: 22
A cylindrical packed bed of height $1\:m$ is filled with equal sized spherical particles. The particles are nonporous and have a density of $1500$ kg/$m^{3}$. The void fr...
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Milicevic3306
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Others
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GATE Chemical 2015 | Question: 23
Two infinitely large parallel plates ($I$ and $II$) are held at temperatures $T_{I}$ and $T_{II}$ $(T_{I}>T_{II})$ respectively, and placed at a distance $2d$ apart in va...
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GATE Chemical 2015 | Question: 24
For a binary mixture of components $A$ and $B$, $N_{A}$ and $N_{B}$ denote the total molar fluxes of components $A$ and $B$, respectively. $J_{A}$ and $J_{B}$ are the cor...
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GATE Chemical 2015 | Question: 25
Benzene is removed from air by absorbing it n a non-volatile wash-oil at $100$ $kPa$ in a counter- current gas absorber. Gas flow rate is $100$ mol/min , which includes $...
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Milicevic3306
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Others
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GATE Chemical 2015 | Question: 26
A spherical naphthalene ball of $2\:mm$ diameter is subliming very slowly in stagnant air at $25^{\circ}C$. The change in the size of the ball during the sublimation can ...
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Others
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GATE Chemical 2015 | Question: 27
Which of the following can change if only the catalyst is changed for a reaction system?Enthalpy of reactionActivation energyFree energy of the reactionEquilibrium consta...
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GATE Chemical 2015 | Question: 28
For which reaction order, the half-Iife of the reactant is half of the full lifetime (time for $100 \%$ conversion) of the reactant ?Zero orderHalf orderFirst orderSecond...
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GATE Chemical 2015 | Question: 29
An irreversible, homogeneous reaction $A{\rightarrow}$ products, has the rate expression:Rate = $\frac{2C_{A}^{2}+0.1C_{A}}{1+50C_{A}}$, where $C_{A}$ is the concentratio...
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GATE Chemical 2015 | Question: 30
Match the output signals as obtained from four measuring devices in response to a unit step change in the input signal.$\begin{array}{cc}\&\text{P. Gas chromatograph, wit...
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GATE Chemical 2015 | Question: 31
The transfer function for the disturbance response in an open-loop process is given by $G_{d}^{open}(s)$. The corresponding transfer function for the disturbance response...
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GATE Chemical 2015 | Question: 32
Identify the $WRONG$ statement amongst the following:Steam distillation is used for mixtures that are immiscible with water.Vacuum distillation is used for mixtures that ...
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GATE Chemical 2015 | Question: 33
Match the polymer mentioned on the left with the catalyst used for its manufacture given on the right.$\begin{array}{cc}\&\text{I. Low density Polyethylene} & \text{P. Zi...
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GATE Chemical 2015 | Question: 34
Match the technologies in Group-$1$ with the entries in Group-$2$:$\begin{array}{cc}\&\text{$Group-1$} & \text{$Group-2$} \\ &\text{P. Urea manufacture} & \text{ I. Micro...
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GATE Chemical 2015 | Question: 35
Match the chemicals written on the left with the raw materials required to produce them mentioned on the right.$\begin{array}{cc}\&\text{I. Single Superphosephate $(SSP)$...
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GATE Chemical 2015 | Question: 36
The diameters of sand particles in a sample range from $50$ to $150$ microns. The number of particles of diameter x in the sample is proportional to $\frac{1}{50+x}$. The...
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Milicevic3306
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Others
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numerical-answers
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GATE Chemical 2015 | Question: 37
A vector $u=-2y\hat{i}+2x\hat{j}$, where $\hat{i}$ and $\hat{j}$ are unit vectors in $x$ and $y$ directions, respectively. Evaluate the line integral$$I=\oint _{C}u.dr$$w...
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7.9k
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Milicevic3306
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Mar 26, 2018
Calculus
gate2015
numerical-answers
calculus
line-integral
vector-identities
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GATE Chemical 2015 | Question: 38
The solution of the non-linear equation$$x^{3}-x=0$$is to be obtained using Newton-Raphson method. If the initial guess is $x=0.5$, the method converges to which one of t...
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7.9k
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Milicevic3306
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Mar 26, 2018
Numerical Methods
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numerical-methods
newton-raphson-method
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GATE Chemical 2015 | Question: 39
For complex variable $z$, the value of the contour integral $\frac{1}{2\pi i} \underset{C}{\int }\frac{e^{-2z}}{z(z-3)}dz$ along the clockwise contour $C:\left | z \right...
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7.9k
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Milicevic3306
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Mar 26, 2018
Complex variables
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numerical-answers
complex-variables
contour-integral
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GATE Chemical 2015 | Question: 40
The schematic diagram of a steady state process is shown below. The fresh feed $(F)$ to the reactor consists ot $96$ mol$\%$ reactant $A$ and $4$ mol$\%$ inert $I$. The s...
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Others
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numerical-answers
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GATE Chemical 2015 | Question: 41
An ideal gas is initially at a pressure of $0.1\:MPa$ and a total volume of $2\:m^{3}$. It is first compressed to $1\:MPa$ by a reversible adiabatic process and then cool...
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numerical-answers
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GATE Chemical 2015 | Question: 42
Given that molar residual Gibbs free energy, $g^{R}$, and molar residual volume, $v^{R}$, are related as $\frac{g^{R}}{RT}=\int _{0}^{P}\left ( \frac{v^{R}}{RT} \right )d...
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Milicevic3306
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GATE Chemical 2015 | Question: 43
A binary mixture of components $(1)$ and $(2)$ forms an azeotrope at $130^{\circ}C$ and $X_{1}=0.3$. The liquid phase non-ideality is described by In $\gamma _{1}=Ax{_{2}...
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numerical-answers
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GATE Chemical 2015 | Question: 44
For Fanning friction factor $f$ (for flow in pipes) and drag coefficient $C_{D}$ (for flow over immersed bodies), which of the following statements are true?$P.$ $f$ acco...
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GATE Chemical 2015 | Question: 45
A centrifugal pump delivers water at the rate of $0.22 m^{3}/s$ from a reservoir at ground level to another reservoir at a height $H$,through a vertical pipe ot $0.2\:m$ ...
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Others
gate2015
numerical-answers
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GATE Chemical 2015 | Question: 46
A typical batch filtration cycle consists of filtration followed by washing. One such filtration unit operating at constant pressure difference first filters a slurry dur...
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Milicevic3306
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Others
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GATE Chemical 2015 | Question: 47
A spherical solid particle of $1\: mm$ diameter is falling with a downward velocity of $1.7\:mm/s$ through a liquid (viscosity $0.04\: Pa.s$) at a low Reynolds number Sto...
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GATE Chemical 2015 | Question: 48
In the figure below, the temperature profiles of cold and hot fluids in counter double pipe heat exchangers (in different modes of operation) are shown on the left. For e...
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GATE Chemical 2015 | Question: 49
A heated solid copper sphere (of surface area $A$ and volume $V$) is immersed in a large body of cold fluid. Assume the resistance to heat transfer inside the sphere to b...
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GATE Chemical 2015 | Question: 50
Air is flowing at a velocity of $3\:m/s$ perpendicular to a long pipe as shown in the figure below. The outer diameter of the pipe is $d=6\:cm$ and temperature at the out...
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numerical-answers
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GATE Chemical 2015 | Question: 51
Consider a solid block of unit thickness for which the thermal conductivity decreases with an increase in temperature. The opposite faces of the block are maintained at c...
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