# Recent questions tagged gate2015

Choose the most appropriate word from the options given below to complete the following sentence. The principle presented the chief guest with a _______________ , as token of appreciation. momento memento momentum moment
Choose the appropriate word/phrase, out of the four options given below, to complete the following sentences: Frogs _____________________ . croak roar hiss patter
Choose the word most similar in meaning to the given word: Educe Exert Educate Extract Extend
Operators $\square$ , $\lozenge$ and ${\rightarrow}$ are defined by: $a\:\square \:b=\frac{a-b}{a+b}; \:a\:\lozenge \:b=\frac{a+b}{a-b};\:a\rightarrow b=ab.$ Find the value of $\left ( 66\:\square \:6 \right )\rightarrow \left ( 66\:\lozenge \:6\right ).$ $-2$ $-1$ $1$ $2$
If $log_{x}$ $(5/7)=-1/3$, then the value of $x$ is $343/125$ $125/343$ $-25/49$ $-49/25$
The following question presents a sentence, part of which is underlined. Beneath the sentence you find four ways of phrasing the underlined part. Following the requirements of the standard written English, select the answer that produces the most effective sentence. Tuberculosis, together ... causes of death has the rank of one of the leading causes of death are one of the leading causes of death
Read the following paragraph and choose the correct statement. Climate change has reduced human security and threatened human well being. An ignored reality of human progress is that human security largely depends upon environmental security. ... contradictory to environmental security. Human security is contradictory to environmental security. Human progress depends upon environmental security.
Fill in the missing value
A cube of side $3$ units is formed using a set smaller cubes of side $1$ unit. Find the proportion of the number of faces of the smaller cubes visible to those which are $NOT$ visible. $1:4$ $1:3$ $1:2$ $2:3$
Humpty Dumpty sits on a wall every day while having launch. The wall sometimes breaks. A person sitting on the wall falls if the wall breaks. Which one of the statements below is logically valid and can be inferred from the above sentences? Humpty Dumpty always ... while having lunch Humpty Dumpty never falls during dinner When Humpty Dumpty does not sit on the wall, the wall does not break
The following set of the three vectors $\begin{pmatrix} 1\\2\\1 \end{pmatrix}, \begin{pmatrix} x\\6\\x \end{pmatrix}\:and \:\begin{pmatrix} 3\\4 \\2 \end{pmatrix},$ is linearly dependent when $x$ is equal to $0$ $1$ $2$ $3$
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 __________ .
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 defined and have a continuous ... this equation by its integrating factor converts this into a: Homogeneous differential equation Non-linear differential equation Second order differential equation Exact differential equation
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 the following is $NOT$ ... $\frac{df}{dz}=\frac{\partial \nu }{\partial y}+i\frac{\partial \nu }{\partial x}$
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 direction of maximum increase in the value of $\phi$ at $(1,1)$ is along: $-2\hat{i}+2\hat{j}$ $2\hat{i}+2\hat{j}$ $-2\hat{i}-2\hat{j}$ $2\hat{i}-2\hat{j}$
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 liquid at $2$ bar is $320\:K$, the temperature (in $K$) at which it will boil at $1$ bar (up to one decimal place) is ____________ .
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. Which of the following is $ALWAYS \: TRUE$ for the three systems ? ($\Delta$ represents the change between the initial ... $\Delta S,\:W,\:Q$ are same $\Delta G,\:\Delta U,\:\Delta S$ are same
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 pressure is $1$ bar and the gas phase cae be assumed to be ideal. The universal gas constant $R=8.314$ $J$/mol.$K$. The fractional molar conversion of $A$ at equilibrium is : $0.44$ $0.50$ $0.64$ $0.80$
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 right columns below and choose the correct option. $\begin{array}{cc}\ &\text{P.$ ... v$} \\ &\text{S.$\left ( \partial u/\partial s \right )_{v}$} & \text{IV.$s$} \\ \\ \end{array}$
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 the second pipe, the flow is turbulent. For turbulent flow, the average velocity is $0.82$ times the centerline ... . For equal volumetric flow ates in both the pipes, the ratio $V_{max,1}/V_{max,2}$(up to two decimal places) is
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 : $\delta \left ( x \right )\alpha \:x^{-1}$ $\delta \left ( x \right )\alpha \:x$ $\delta \left ( x \right )\alpha \:x^{1/2}$ $\delta \left ( x \right )\alpha \:x^{-1/2}$
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 fraction of the bed is $0.45$. The bed is fluidized using air (density $1$ kg/$m^{3}$). If ... is $9.8\:m/s^{2}$, the pressure drop (in $Pa$) across the bed at incipient fluidization (up to one decimal place) is __________________.
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 vacuum. An infinitely large flat radiation shield $(III)$ is placed in parallel in between $I$ ... plates are equal. The ratio of the steady state radiative heat fluxes with and without the shield is : $0.5$ $0.75$ $0.25$ $0$
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 $J_{B}$ ... $N_{A}+N_{B}\neq 0\:and\:J_{A}+J_{B}\neq 0$ $N_{A}+N_{B}= 0\:and\:J_{A}+J_{B}= 0$
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 $2$ mol/min of benzene. The flow rate of wash-oil is $50$ mol/min. Vapor ... flow rates of liquid and gas phases inside the column. For this process, the value of the absorption factor (up to two decimal places) is ___________.
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 be neglected. The diffusivity of naphthalene in air at $25^{\circ}C$ is $1.1\times10^{-6}\:m^2/s$. The value of mass transfer coefficient is $B\times10^{-3}\:m/s$, where $B$ (up to one decimal place) is ____________ .
Which of the following can change if only the catalyst is changed for a reaction system? Enthalpy of reaction Activation energy Free energy of the reaction Equilibrium constant.
For which reaction order, the half-Iife of the reactant is half of the full lifetime (time for $100 \%$ conversion) of the reactant ? Zero order Half order First order Second order
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 concentration of $A$. $C_{A}$ varies in the range $0.5-50$ mol/$m^{3}$. For very high concentration of $A$, the reaction order tends to : $0$ $1$ $1.5$ $2$
Match the output signals as obtained from four measuring devices in response to a unit step change in the input signal. ... $P-IV,\:Q-I,\:R-II,\:S-III$ $P-II,\:Q-IV,\:R-III,\:S-I$
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 in a closed-loop feedback control system with proportional controller is given by $G_{d}^{closed}(s)$. Select the option ...
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 are miscible with water Steam distillation is used for mixtures that are miscible with water. Vacuum distillation columns have larger diameters as compared to atmospheric columns for the same throughput.
Match the polymer mentioned on the left with the catalyst used for its manufacture given on the right. ... $I-Q,\:II-P,\:III-S,\:IV-R$ $I-S,\:II-R,\:III-P,\:IV-Q$
Match the technologies in Group-$1$ with the entries in Group-$2$: $\begin{array}{cc}\ &\text{$Group-1$} & \text{$ ... $P-IV,\:Q-VI,\:R-I,\:S-II$ $P-IV,\:Q-I\:R-III,\:S-II$ $P-V,\:Q-VI,\:R-IV,\:S-II$
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)$} & \text{P. Rock phosphate + Sulfuric Acid + Ammonia} \\ &\text{II. Triple Superphosphate$ ... $I-R,\:II-S,\:III-P,\:IV-Q$ $I-S,\:II-R,\:III-P,\:IV-Q$
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 average diameter, in microns, (up to one decimal place) is __________________.
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 $I=\oint _{C}u.dr$ where $C$ is a closed loop formed by connecting points $(1,1),(3,1),(3,2)$ and $(1,2)$ in that order. The value of $I$ is ___________.
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 the following values: $-1$ $0$ $1$ $2$
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 $C:\left | z \right |=2$ (up to decimal places) is ___________.
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 $0.2\:m$ diameter. Both the reservoirs are open to atmosphere. The power input to the pump is $90 \:kW$ and it ... is $1000\: kg/m^{3}$. The height $H$, in meters, to which the water can be delivered (up to one decimal place) is ________.