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GATE 2017-2018 :: GATE Chemical

  1. Consider the following set of linear algebraic equations 
    x1 + 2x2 + 3x3 = 2 
    x2 + x3 = - 1 
    2x2 + 2x3 = 0
    The system has
  2. A.
    a unique solution
    B.
    no solution
    C.
    an infinite number of solutions
    D.
    only the trivial solution

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  3. If a and b are arbitrary constants, then the solution to the ordinary differential equation d2y/dx2 - 4y = 0 is
  4. A.
    y = ax + b
    B.
    y = ae-x
    C.
    y = asin 2x + bcos2x
    D.
    y = acosh 2x + bsinh 2x

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  5. For the function f(t) = e-t/T, the Taylor series approximation for t << T is
  6. A.
    1 + t/T
    B.
    1 - t/T
    C.
    1 - t2/2T2
    D.
    1 + t

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  7. A box containing 10 identical compartments has 6 red balls and 2 blue balls. If each compartment can hold only one ball, then the number of different possible arrangements are
  8. A.
    1026
    B.
    1062
    C.
    1260
    D.
    1620

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  9. Consider the following (2 * 2) matrix 

    Which one of the following vectors is NOT a valid eigenvector of the above matrix ?
  10. A.
    .

    B.
    .

    C.
    .

    D.
    .

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  11. In a throttling process, the pressure of an ideal gas reduces by 50 %. If CP and CV are the heat capacities at constant pressure and constant volume, respectively (r = CP/CV) the specific volume will change by a factor of
  12. A.
    2
    B.
    21/r
    C.
    2(r - 1)/r
    D.
    0.5

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  13. If the temperature of saturated water is increased infinitesimally at constant entropy, the resulting state of water will be
  14. A.
    Liquid
    B.
    Liquid "“ vapor coexistence
    C.
    Saturated vapor
    D.
    Solid

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  15. In a parallel flow heat exchanger operating under steady state, hot liquid enters at a temperature Th, in and leaves at a temperature Th, out. Cold liquid enters at a temperature Tc, in and leaves at a temperature Tc, out. Neglect any heat loss from the heat exchanger to the surrounding. If Th, in >> Tc, in, then for a given time interval, which ONE of the following statements is true?
  16. A.
    Entropy gained by the cold stream is GREATER than entropy lost by the hot stream
    B.
    Entropy gained by the cold stream is EQUAL to the entropy lost by the hot stream
    C.
    Entropy gained by the cold stream is LESS than the entropy lost by the hot stream
    D.
    Entropy gained by the cold stream is ZERO

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  17. For an exothermic reversible reaction, which one of the following correctly describes the dependence of the equilibrium constant ( K ) with temperature (T ) and pressure ( P ) ?
  18. A.
    K is independent of T and P
    B.
    K increases with an increase in T and P
    C.
    K increases with T and decreases with P
    D.
    K decreases with an increase in T and is independent of P

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  19. Water is flowing under laminar conditions in a pipe of length L . If the diameter of the pipe is doubled, for a constant volumetric flow rate, the pressure drop across the pipe
  20. A.
    decreases 2 times
    B.
    decreases 16 times
    C.
    increases 2 times
    D.
    increases 16 times

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