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GATE Mechanical Mcq Set-2

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1. The partial differential equation is a




2. The eigenvalues of a symmetric matrix are all




3. Two threaded bolts A and B of same material and length are subjected to identical tensile load. If the elastic strain energy stored in bolt A is 4 times that of bolt B and the mean diameter of bolt A is 12 mm, the mean diameter of bolt B in mm is




4. For steady, fully developed flow inside a straight pipe of diameter D, neglecting gravity effects, the pressure drop ∆p over a length L and the wall shear stress tw are related by




5. The pressure, dry bulb temperature and relative humidity of air in a room are 1 bar, 30°C and 70%, respectively. If the saturated steam pressure at 30°C is 4.25 kPa, the specific humidity of the room air in kg water vapour/kg dry air is




6. In a rolling process, the state of stress of the material undergoing deformation is




7. A metric thread of pitch 2 mm and thread angle 60° is inspected for its pitch diameter using 3-wire method. The diameter of the best size wire in mm is




8. Customers arrive at a ticket counter at a rate of 50 per hr and tickets are issued in the order of their arrival. The average time taken for issuing a ticket is 1 min. Assuming that customer arrivals form a Poisson process and service times are exponentially distributed, the average waiting time in queue in min is




9. In simple exponential smoothing forecasting, to give higher weightage to recent demand information, the smoothing constant must be close to




10. In simple exponential smoothing forecasting, to give higher weightage to recent demand information, the smoothing constant must be close to




11. A steel bar 200 mm in diameter is turned at a feed of 0.25 mm/rev with a depth of cut of 4 mm. The rotational speed of the workpiece is 160 rpm. The material removal rate in mm3/s is




12. For a ductile material, toughness is a measure of




13. In order to have maximum power from a Pelton turbine, the bucket speed must be




14. Consider one-dimensional steady state heat conduction along x-axis(0 ≤ x ≤ L) through a plane wall with the boundary surfaces (x=0 and x=L) maintained at temperatures of 0°C and 100°C. Heat is generated uniformly throughout the wall. Choose the CORRECT statement.




15. A cylinder contains 5 m3 of an ideal gas at a pressure of 1 bar. This gas is compressed in a reversible isothermal process till its pressure increases to 5 bar. The work in kJ required for this process is




16. A long thin walled cylindrical shell, closed at both the ends, is subjected to an internal pressure. The ratio of the hoop stress (circumferential stress) to longitudinal stress developed in the shell is




17. If two nodes are observed at a frequency of 1800 rpm during whirling of a simply supported long slender rotating shaft, the first critical speed of the shaft in rpm is




18. Let X be a normal random variable with mean 1 and variance 4. The probability P{X < 0} is




19. Choose the CORRECT set of functions, which are linearly dependent.




20. 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




21. pecific 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 180 Exit steam condition 2360 5 The 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 flow rate, is




22. pecific 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 180 Exit steam condition 2360 5 The 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 flow rate, is




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




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




25. 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




26. 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




27. Two cutting tools are being compared for a machining operation. The tool life equations are: Carbide tool: VT1.6 = 3000 HSS tool: VT0.6 = 200 where V is the cutting speed in m/min and T is the tool life in min. The carbide tool will provide higher tool life if the cutting speed in m/min exceeds




28. In a CAD package, mirror image of a 2D point P(5,10) is to be obtained about a line which passes through the origin and makes an angle of 45° counterclockwise with the X-axis. The coordinates of the transformed point will be




29. A linear programming problem is shown below. Maximize 3x + 7y Subject to 3x + 7y ≤ 10 4x + 6y ≤ 8 x, y ≥ 0 It has




30. During the electrochemical machining (ECM) of iron (atomic weight = 56, valency = 2) at current of 1000 A with 90% current efficiency, the material removal rate was observed to be 0.26 gm/s. If Titanium (atomic weight = 48, valency = 3) is machined by the ECM process at the current of 2000 A with 90% current efficiency, the expected material removal rate in gm/s will be




31. During the electrochemical machining (ECM) of iron (atomic weight = 56, valency = 2) at current of 1000 A with 90% current efficiency, the material removal rate was observed to be 0.26 gm/s. If Titanium (atomic weight = 48, valency = 3) is machined by the ECM process at the current of 2000 A with 90% current efficiency, the expected material removal rate in gm/s will be




32. A single degree of freedom system having mass 1 kg and stiffness 10 kN/m initially at rest is subjected to an impulse force of magnitude 5 kN for 10-4 seconds. The amplitude in mm of the resulting free vibration is




33. A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The material has yield strength of 240 MPa and endurance limit in reversed bending is 160 MPa. According to the Soderberg principle, the area of cross-section in mm2 of the bar for a factor of safety of 2 is




34. A simply supported beam of length L is subjected to a varying distributed load sin(3 π x/L) Nm-1, where the distance x is measured from the left support. The magnitude of the vertical reaction force in N at the left support is




35. Two large diffuse gray parallel plates, separated by a small distance, have surface temperatures of 400 K and 300 K. If the emissivities of the surfaces are 0.8 and the Stefan-Boltzmann constant is 5.67 * 10-8W/m2K4, the net radiation heat exchange rate in kW/m2 between the two plates is




36. The pressure, temperature and velocity of air flowing in a pipe are 5 bar, 500 K and 50 m/s, respectively. The specific heats of air at constant pressure and at constant volume are 1.005 kJ/kgK and 0.718 kJ/kgK, respectively. Neglect potential energy. If the pressure and temperature of the surroundings are 1 bar and 300 K, respectively, the available energy in kJ/kg of the air stream is




37. The probability that a student knows the correct answer to a multiple choice question is 2/3. If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is 1/4. Given that the student has answered the question correctly, the conditional probability that the student knows the correct answer is




38. The solution to the differential equation d2u/dx2 - k du/dx = 0 where k is a constant, subjected to the boundary conditions u(0) = 0 and u(L) = U, is




39. Water (specific heat, cp = 4.18 kJ/kgK) enters a pipe at a rate of 0.01 kg/s and a temperature of 20°C. The pipe, of diameter 50 mm and length 3 m, is subjected to a wall heat flux qnw in W/m2: If qnw = 2500x, where x is in m and in the direction of flow (x = 0 at the inlet), the bulk mean temperature of the water leaving the pipe in °C is




40. Water (specific heat, cp = 4.18 kJ/kgK) enters a pipe at a rate of 0.01 kg/s and a temperature of 20°C. The pipe, of diameter 50 mm and length 3 m, is subjected to a wall heat flux qnw in W/m2: If qnw = 5000 and the convection heat transfer coefficient at the pipe outlet is 1000 W/m2K, the temperature in °C at the inner surface of the pipe at the outlet is