Question 21. The function f (t ) satisfies the differential equation d2f/dt2 + f = 0 and the auxiliary conditions, f(0) = 0, df/dt(0) = 4. The Laplace transform of f (t) is given by

Question 22. A flywheel connected to a punching machine has to supply energy of 400 Nm while running at a mean angular speed of 20 rad/s. If the total fluctuation of speed is not to exceed ± 2%, the mass moment of inertia of the flywheel in kg-m2 is

Question 23. Water is coming out from a tap and falls vertically downwards. At the tap opening, the stream diameter is 20 mm with uniform velocity of 2 m/s. Acceleration due to gravity is 9.81 m/s2. Assuming steady, inviscid flow, constant atmospheric pressure everywhere and neglecting curvature and surface tension effects, the diameter in mm of the stream 0.5 m below the tap is approximately

Question 24. A steel ball of diameter 60 mm is initially in thermal equilibrium at 1030°C in a furnace. It is suddenly removed from the furnace and cooled in ambient air at 30°C, with convective heat transfer coefficient h = 20 W/m2K. The thermo-physical properties of steel are: density ρ = 7800 kg/m3, conductivity k = 40 W/mK and specific heat c = 600 J/kgK. The time required in seconds to cool the steel ball in air from 1030°C to 430°C is

Question 25. Specific enthalpy and velocity of steam at inlet and exit of a steam turbine, running under steady state, are as given below:                                  Specific enthalpy (kJ/kg)  Velocity (m/s)Inlet steam condition        3250                          180Exit steam condition          2360                             5The rate of heat loss from the turbine per kg of steam flow rate is 5 kW. Neglecting changes in potential energy of steam, the power developed in kW by the steam turbine per kg of steam flowrate, is

Question 26. The area enclosed between the straight line y = x and the parabola y = x2 in the x-y plane is

Question 27. Which one of the following is NOT a decision taken during the aggregate production planning stage?

Question 28. Consider the function f(x) = |x| in the interval -1 ≤ x ≤ 1. At the point x = 0, f(x) is

Question 29. A CNC vertical milling machine has to cut a straight slot of 10 mm width and 2 mm depth by a
cutter of 10 mm diameter between points (0, 0) and (100, 100) on the XY plane (dimensions in mm).
The feed rate used for milling is 50 mm/min. Milling time for the slot (in seconds) is

Question 30. An ideal gas of mass m and temperature T1 undergoes a reversible isothermal process from an initial pressure P1 to final pressure P2. The heat loss during the process is Q. The entropy change ∆S of the gas is