GATE Examination

YEAR 2013

  • Q.1

    The effectiveness of a heat exchanger in the \(\epsilon\)-NTU method is defined as 

    (A) 

    \(\frac{increase\space in\space temperature\space of\space the \space cold \space fluid}{decrease\space in \space temperature \space of \space the \space hot \space fluid}\)

    (B) 

    \(\frac{actual \space exit \space temperature \space attained \space by \space the \space cold \space fluid}{maximum \space exit \space temperature \space attained \space by \space the \space cold \s (C) 

    \(\frac{actual \space exit \space temperature \space attained \space by \space the \space hot \space fluid}{maximum \space exit \space temperature \space attained \space by \space the \space hot \spa (D) 

    \(\frac{actual \space heat \space transfer \space rate }{maximum \space possible \space heat \space transfer \space rate \space from \space hot \space fluid \space to \space cold\space fluid}\)

    Marks:1 Explanation
    • Answer:

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  • Q.2

    In a pool boiling experiment, the following phenomena were observed.

    P. Natural convection

    Q. Film boiling

    R. Transition boiling

    S. Nucleate boiling

    What was the CORRECT sequence of their occurrence?

    (A) 

    P, Q, R, S

    (B) 

    S, R, Q, P

    (C) 

    Q, R, P, S

    (D) 

    P, S, R, Q

    Marks:1 Explanation
    • Answer:

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  • Q.3

    A hole of area 1 cm\(^2\) is opened on the surface of a large spherical cavity whose inside temperature is maintained at 727 °C. The value of Stefan-Boltzmann constant is 5.67×10-8 W/m\(^2\) .K\(^4\) . Assuming black body radiation, the rate at which the energy is emitted (in W) by the cavity through the hole, up to 3 digits after the decimal point, is_______.

    Marks:1 Explanation
    • Answer:

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  • Q.4

    The packing of an existing absorption tower is replaced with a new type of packing. The height of the packing and the inlet conditions are maintained the same as before. Tests reveal that the number of transfer units is lower than before. This indicates that the tower with the new packing, when compared to that with the old packing, will

    (A) 

    have a higher rate of absorption of the solute from the gas stream

    (B) 

    have a lower rate of absorption of the solute from the gas stream

    (C) 

    have the same rate of absorption of the solute from the gas stream

    (D) 

    have a lower height of transfer unit

    Marks:1 Explanation
    • Answer:

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  • Q.5

    A wet solid is dried over a long period of time by unsaturated air of nonzero constant relative humidity. The moisture content eventually attained by the solid is termed as the

    (A) 

    unbound moisture content

    (B) 

    bound moisture content

    (C) 

    free moisture content

    (D) 

    equilibrium moisture content

    Marks:1 Explanation
    • Answer:

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  • Q.6

    The exit age distribution for a reactor is given by E(t) = \(\delta\)(t - 4), where t is in seconds. A first order liquid phase reaction (k = 0.25 s\(^{-1}\) ) is carried out in this reactor under steady state and isothermal conditions. The mean conversion of the reactant at the exit of the reactor, up to 2 digits after the decimal point, is_________.

    Marks:1 Explanation
    • Answer:

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  • Q.7

    An isothermal liquid phase zero order reaction A \(\rightarrow\) B (k = 0.5 mol/m3 -s) is carried out in a batch reactor. The initial concentration of A is 2 mol/m\(^3\) . At 3 seconds from the start of the reaction, the concentration of A in mol/m\(^3\) is ______.

    Marks:1 Explanation
    • Answer:

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  • Q.8

    The overall rates of an isothermal catalytic reaction using spherical catalyst particles of diameters 1 mm and 2 mm are r\(_A\)\(_1\) and r\(_{A2}\) (in mol (kg-catalyst)\(^{-1}\)1 h\(^{-1}\) ), respectively. The other physical properties of the catalyst particles are identical. If pore diffusion resistance is very high, the ratio r\(_{A2}\)/r\(_{A1}\) is _______.

    Marks:1 Explanation
    • Answer:

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  • Q.9

    In the manufacture of sulphuric acid by the contact process, the catalytic oxidation of SO\(_2\) is carried out in multiple stages mainly to

    (A) 

    increase the reaction rate by providing inter-stage heating

    (B) 

    increase the overall conversion by providing inter-stage heating

    (C) 

    increase the overall conversion by providing inter-stage cooling

    (D) 

    decrease the overall conversion by removing sulphur trioxide between stages

    Marks:1 Explanation
    • Answer:

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  • Q.10

    Match the following.

    Group 1

    Group 2

    (P) Viscosity

    (1) Pyrometer

    (Q) Pressure

    (2) Hot wire anemometer

    (R) Velocity

    (3) Rheometer

    (S) Temperature

    (4) Piezoelectric element

     

    (A) 

    P-4, Q-3, R-1, S-2

    (B) 

    P-3, Q-4, R-2, S-1

    (C) 

    P-3, Q-4, R-1, S-2

    (D) 

    P-4, Q-3, R-2, S-1

    Marks:1 Explanation
    • Answer:

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  • Q.11

    For the function

    \(f(z)=\frac{1}{(2-z)(2+z)}\) the residue at z=2 is ________.

    Marks:2 Explanation
    • Answer:

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  • Q.12

    The solution of the differential equation

    \(\frac{dy}{dx}-y^2=0\), given y=1 at x=0 is,

    (A) 

    \(\frac{1}{1+x}\)

    (B) 

    \(\frac{1}{1-x}\)

    (C) 

    \(\frac{1}{(1-x)^2}\)

    (D) 

    \(\frac{x^3}{3}+1\)

    Marks:2 Explanation
    • Answer:

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  • Q.13

    The solution of the differential equation

    \(\frac{d^2y}{dx^2}-\frac{dy}{dx}+0.25y=0,\) given y=0 at x=0 and \(\frac{dy}{dx}=1\) at x=0 is

    (A) 

    \(xe^{0.5x}-xe^{-0.5x}\)

    (B) 

    \(0.5xe^x-0.5xe^{-x}\)

    (C) 

    \(xe^{0.5x}\)

    (D) 

    \(-xe^{0.5x}\)

    Marks:2 Explanation
    • Answer:

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  • Q.14

    The value of the integral \(\int_{0.1}^{0.5}e^{-x^3}dx\)  evaluated by Simpson’s rule using 4 subintervals (up to 3 digits after the decimal point) is__________.

    Marks:2 Explanation
    • Answer:

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  • Q.15

    In a process occurring in a closed system F, the heat transferred from F to the surroundings E is 600 J. If the temperature of E is 300 K and that of F is in the range 380 - 400 K, the entropy changes of the surroundings (ΔS\(_E\)) and system (ΔS\(_F\)), in J/K, are given by

    (A) 

    \(\Delta S_E=2,\Delta S_F=-2\)

    (B) 

    \(\Delta S_E=-2,\Delta S_F=2\)

    (C) 

    \(\Delta S_E=2,\Delta S_F<-2\)

    (D) 

    \(\Delta S_E=2,\Delta S_F>-2\)

    Marks:2 Explanation
    • Answer:

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  • Q.16

    A binary liquid mixture is in equilibrium with its vapor at a temperature T = 300 K. The liquid mole fraction x\(_1\) of species 1 is 0.4 and the molar excess Gibbs free energy is 200 J/mol. The value of the universal gas constant is 8.314 J/mol-K, and \(\gamma\)i denotes the liquid-phase activity coefficient of species i. If ln(\(\gamma _1\)) = 0.09, then the value of ln(\(\gamma _2\)), up to 2 digits after the decimal point, is _________.

    Marks:2 Explanation
    • Answer:

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  • Q.17

    Water (density 1000 kg/m\(^3\) ) is flowing through a nozzle, as shown below and exiting to the atmosphere. The relationship between the diameters of the nozzle at locations 1 and 2 is D\(_1\) = 4D\(_2\). The average velocity of the stream at location 2 is 16 m/s and the frictional loss between location 1 and location 2 is 10000 Pa. Assuming steady state and turbulent flow, the gauge pressure in Pa, at location 1 is ________

                   

    Marks:2 Explanation
    • Answer:

      ..

  • Q.18

    The number of emails received on six consecutive days is 11, 9, 18, 18, 4 and 15, respectively. What are the median and the mode for these data?

    (A) 

    18 and 11, respectively

    (B) 

    13 and 18, respectively

    (C) 

    13 and 12.5, respectively

    (D) 

    12.5 and 18, respectively

    Marks:1 Explanation
    • Answer:

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  • Q.19

    For two rolls of a fair die, the probability of getting a 4 in the first roll and a number less than 4 in the second roll, up to 3 digits after the decimal point, is ____________.

    Marks:1 Explanation
    • Answer:

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  • Q.20

    Which of the following statements are TRUE?

    P. The eigenvalues of a symmetric matrix are real

    Q. The value of the determinant of an orthogonal matrix can only be +1

    R. The transpose of a square matrix A has the same eigenvalues as those of A

    S. The inverse of an ‘n × n’ matrix exists if and only if the rank is less than ‘n’

    (A) 

    P and Q only

    (B) 

    P and R only

    (C) 

    Q and R only

    (D) 

    P and S only

    Marks:1 Explanation
    • Answer:

      .

  • Q.21

    Evaluate   \(\int \frac{dx}{e^x-1}\)  ( Note: C is a constant of integration.)

    (A) 

    \(\frac{e^x}{e^x-1}+C\)

    (B) 

    \(\frac{ln(e^x-1)}{e^x}+C\)

    (C) 

    \(ln(\frac{e^x}{e^x-1})+C\)

    (D) 

    \(ln(1-e^{-x})+C\)

    Marks:1 Explanation
    • Answer:

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  • Q.22

    A gaseous system contains H\(_2\), I\(_2\), and HI, which participate in the gas-phase reaction

                                           \(2HI\rightleftharpoons H_2+I_2\)

    At a state of reaction equilibrium, the number of thermodynamic degrees of freedom is _________.

    Marks:1 Explanation
    • Answer:

      .

  • Q.23

    The thermodynamic state of a closed system containing a pure fluid changes from (T\(_1\), p\(_1\)) to (T\(_2\), p\(_2\)), where T and p denote the temperature and pressure, respectively. Let Q denote the heat absorbed (> 0 if absorbed by the system) and W the work done (> 0 if done by the system). Neglect changes in kinetic and potential energies. Which one of the following is CORRECT?

    (A) 

    Q is path-independent and W is path-dependent

    (B) 

    Q is path-dependent and W is path-independent

    (C) 

    (Q − W) is path-independent

    (D) 

    (Q + W) is path-independent

    Marks:1 Explanation
    • Answer:

      .

  • Q.24

    An equation of state is explicit in pressure p and cubic in the specific volume v. At the critical point ‘c’, the isotherm passing through ‘c’ satisfies

    (A) 

    \(\frac{\partial p}{\partial v}<0,\frac{\partial^2 p}{\partial ^2v}=0\)

    (B) 

    \(\frac{\partial p}{\partial v}>0,\frac{\partial^2 p}{\partial ^2v}<0\)

    (C) 

    \(\frac{\partial p}{\partial v}=0,\frac{\partial^2 p}{\partial ^2v}>0\)

    (D) 

    \(\frac{\partial p}{\partial v}=0,\frac{\partial^2 p}{\partial ^2v}=0\)

    Marks:1 Explanation
    • Answer:

      .

  • Q.25

    The units of the isothermal compressibility are

    (A) 

    \(m^{-3}\)

    (B) 

    \(Pa^{-1}\)

    (C) 

    \(m^3Pa^{-1}\)

    (D) 

    \(m^{-3}Pa^{-1}\)

    Marks:1 Explanation
    • Answer:

      .

  • Q.26

    An open tank contains two immiscible liquids of densities (800 kg/m\(^3\) and 1000 kg/m\(^3\) ) as shown in the figure. If g = 10 m/s\(^2\) , under static conditions, the gauge pressure at the bottom of the tank in Pa is_________.

                                     

    Marks:1 Explanation
    • Answer:

      .

  • Q.27

    The apparent viscosity of a fluid is given by \(0.07|\frac{dV}{dy}|^{0.3}\)   where \((\frac{dV}{dy})\) is the velocity gradient . The fluid is

    (A) 

    Bingham plastic

    (B) 

    dilatent

    (C) 

    pseudoplastic

    (D) 

    thixotropic

    Marks:1 Explanation
    • Answer:

      .

  • Q.28

    The mass balance for a fluid with density \(\rho\) and velocity vector \((\overrightarrow V)\) is

    (A) 

    \(\frac{\partial \rho}{\partial t}+\bigtriangledown.(\rho \overrightarrow {V})=0\)

    (B) 

    \(\frac{\partial \rho}{\partial t}+\overrightarrow {V}.(\bigtriangledown\rho )=0\)

    (C) 

    \(\frac{\partial \rho}{\partial t}+\rho(\bigtriangledown.\overrightarrow {V} )=0\)

    (D) 

    \(\frac{\partial \rho}{\partial t}-\overrightarrow {V}.(\bigtriangledown\rho )=0\)

    Marks:1 Explanation
    • Answer:

      .

  • Q.29

    An incompressible Newtonian fluid, filled in an annular gap between two concentric cylinders of radii R1 and R2 as shown in the figure, is flowing under steady state conditions. The outer cylinder is rotating with an angular velocity of \(\Omega\) while the inner cylinder is stationary. Given that \((R_2-R_1)\ll R_1\) , the profile of the \(\theta\)-component of the velocity V\(_{\theta}\) can be approximated by,

    (A) 

    \(R_2\Omega\)

    (B) 

    \(\frac{(r-R_2)}{(R_2-R_1)}r\Omega\)

    (C) 

    \(\frac{(r+R_1)}{(R_2+R_1)}R_1\Omega\)

    (D) 

    \(\frac{(r-R_1)}{(R_2-R_1)}R_2\Omega\)

    Marks:1 Explanation
    • Answer:

      .

  • Q.30

    For a Newtonian fluid flowing in a circular pipe under steady state conditions in fully developed laminar flow, the Fanning friction factor is

    (A) 

    \(0.046Re^{-0.2}\)

    (B) 

    \(0.014+\frac{0.125}{Re^{0.32}}\)

    (C) 

    \(\frac{16}{Re}\)

    (D) 

    \(\frac{24}{Re}\)

    Marks:1 Explanation
    • Answer:

      .

  • Q.31

    In the Tyler standard screen scale series, when the mesh number increases from 3 mesh to 10 mesh, then

    (A) 

    the clear opening decreases

    (B) 

    the clear opening increases

    (C) 

    the clear opening is unchanged

    (D) 

    the wire diameter increases

    Marks:1 Explanation
    • Answer:

      .

  • Q.32

    Taking the acceleration due to gravity to be 10 m/s\(^2\) , the separation factor of a cyclone 0.5 m in diameter and having a tangential velocity of 20 m/s near the wall is__________.

    Marks:1 Explanation
    • Answer:

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