GATE 20172018 :: GATE Chemical

Consider the following set of linear algebraic equations x_{1} + 2x_{2} + 3x_{3} = 2x_{2} + x_{3} =  12x_{2} + 2x_{3} = 0The system has
 If a and b are arbitrary constants, then the solution to the ordinary differential equation d^{2}y/dx^{2}  4y = 0 is
 For the function f(t) = e^{t/T}, the Taylor series approximation for t << T is
 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

Consider the following (2 * 2) matrix Which one of the following vectors is NOT a valid eigenvector of the above matrix ?
 In a throttling process, the pressure of an ideal gas reduces by 50 %. If C_{P} and C_{V} are the heat capacities at constant pressure and constant volume, respectively (r = C_{P}/C_{V}) the specific volume will change by a factor of
 If the temperature of saturated water is increased infinitesimally at constant entropy, the resulting state of water will be
 In a parallel flow heat exchanger operating under steady state, hot liquid enters at a temperature T_{h, in} and leaves at a temperature T_{h, out}. Cold liquid enters at a temperature T_{c, in} and leaves at a temperature T_{c, out}. Neglect any heat loss from the heat exchanger to the surrounding. If T_{h, in} >> T_{c, in}, then for a given time interval, which ONE of the following statements is true?
 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 ) ?
 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