Chemical Engineering Gate 2015 Questions with Answer

Ques 14 GATE 2015

For the matrix if is an eigenvector, the corresponding eigenvalue is ______.

Ques 15 GATE 2015

Consider a linear ordinary differential equation: dy/dx + p(x)y = r(x). Functions p(x) and r(x) are 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:

Ques 16 GATE 2015

A complex-valued function, f(z), given below is analytic in domain D: f(z) = u(x, y) + i v(x, y) z = x + i y Which of the following is NOT correct?

Ques 17 GATE 2015

A scalar function in the xy-plane is given by φ(x, y) = x² + y². If î and ĵ are unit vectors in the x and y directions, the direction of maximum increase in the value of φ at (1,1) is along

Ques 18 GATE 2015

A vector u = -2y î + 2x ĵ, where î and ĵ are unit vectors in x and y directions, respectively. Evaluate the line integral I = ∮ 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 _______.

Ques 19 GATE 2015

The solution of the non-linear equation x³ - 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:

Ques 20 GATE 2015

For complex variable z, the value of the contour integral ∮ (e^-2z / (z - i) ) dz along the clockwise contour C : |z| = 2 (up to two decimal places) is _______

Ques 21 GATE 2015

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 velocity, V_max,2. For equal volumetric flow rates in both the pipes, the ratio V_max,1 / V_max,2 (up to two decimal places) is _______.

Ques 22 GATE 2015

For uniform laminar flow over a flat plate, the thickness of the boundary layer, δ, at a distance x from the leading edge of the plate follows the relation:

Ques 23 GATE 2015

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/m³. The void fraction of the bed is 0.45. The bed is fluidized using air (density 1 kg/m³). If the acceleration due to gravity is 9.8 m/s², the pressure drop (in Pa) across the bed at incipient fluidization (up to one decimal place) is _______.

Ques 24 GATE 2015

For Fanning friction factor f (for flow in pipes) and drag coefficient C_D (for flow over immersed bodies), which of the following statements are true?
P: f accounts only for the skin friction
Q: C_D accounts only for the form friction
R: C_D accounts for both skin friction and form friction
S: Both f and C_D depend on the Reynolds number
T: For laminar flow through a pipe, f doubles on doubling the volumetric flow rate

Ques 25 GATE 2015

A centrifugal pump delivers water at the rate of 0.22 m³/s from a reservoir at ground level to another reservoir at a height H, through a vertical pipe of 0.2 m diameter. Both the reservoirs are open to atmosphere. The power input to the pump is 90 kW and it operates with an efficiency of 75%. Data: Fanning friction factor for pipe flow is f = 0.004. Neglect other head losses. Take gravitational acceleration, g = 9.8 m/s² and density of water is 1000 kg/m³. The height H, in meters, to which the water can be delivered (up to one decimal place) is _______.

Ques 26 GATE 2015

A spherical solid particle of 1 mm diameter is falling with a downward velocity of 1.7 mm/s through a liquid (viscosity 0.04 Pa.s) at a low Reynolds number (Stokes regime). The liquid is flowing upward at a velocity of 1 mm/s. All velocities are with respect to a stationary reference frame. Neglecting the wall effects, the drag force per unit projected area of the particle, in Pa, (up to two decimal places) is ______.