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GATE 2015 : Chemical Engineering

42 pages, 55 questions, 6 questions with responses, 6 total responses,

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GATE 2015 CHEMICAL CH Q. 1 Q. 25 carry one mark each. Q.1 The following set of three vectors 1 2 , 1 6 and 3 4 , 2 is linearly dependent when x is equal to (A) 0 (B) Q.2 For the matrix 4 3 Q.3 1 (C) 2 (D) 3 3 1 , if is an eigenvector, the corresponding eigenvalue is ______. 4 1 Consider a linear ordinary differential equation: dy + p( x ) y = r ( x ) . Functions p( x ) and r ( x ) are dx defined and have a continuous first derivative. The integrating factor of this equation is non-zero. Multiplying this equation by its integrating factor converts this into a: (A) Homogeneous differential equation (C) Second order differential equation (B) Non-linear differential equation (D) Exact differential equation Q.4 A complex-valued function, f(z), given below is analytic in domain D: f ( z ) = u ( x, y ) + iv(x, y ) z = x + iy Which of the following is NOT correct? df v u = +i dz y y df v u = i (C) dz y y (A) df u v = +i dz x x df v v = +i (D) dz y x (B) Q.5 A scalar function in the xy-plane is given by ( , ) = 2 + 2 . If i and j are unit vectors in the x and y directions, the direction of maximum increase in the value of at (1,1) is along: + 2 (A) 2 i j + 2 (B) 2 i j (C) 2 i (D) 2 i 2 j 2 j Q.6 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 ______________. Q.7 Three identical closed systems of a pure gas are taken from an initial temperature and pressure (T1, P1) to a final state (T2, P2), each by a different path. Which of the following is ALWAYS TRUE for the three systems? ( represents the change between the initial and final states; U, S, G, Q and W are internal energy, entropy, Gibbs free energy, heat added and work done, respectively.) (A) U, S, Q are same (C) S, W, Q are same CH (B) W, U, G are same (D) G, U, S are same 1/15

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