GATE Mechanical Engineering Test 1 Online Question Answers

1. 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 0⁰ C and 100⁰C. Heat is generated uniformly throughout the wall. Choose the correct statement.

2. During the electrochemical machining (ECM) of iron (atomic weight = 56, valency = ) 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 2000 A with 90% current efficiency, the expected material removal rate in gm/s will be:

3. A cube shaped casting solidifies in 5 minutes. The solidification time in minutes for a cube of the same material, which is 8 times heavier than the original casting will be:

4. The probability that a student knows the correct answer to a multiple choice question in 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 known the correct answer is:

5. What will be the maximum sum of 44, 42, 40, ____ ?

6. The eigen values of symmetric matrix area all:

7. Let X be a nominal variable with mean 1 and variance 4. The probability P (X < 0) is:

8. For a ductile material, toughness is a measure of:

9. A tourist covers half of his journey by train at 60 km/h, half of the remainder by bus at 30 km/h and the rest by cycle at 10 km/h. The average speed of the tourist in km/h during his entire journey is:

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

11. Water is coming out from a tap and falls vertically downwards. At the tap opening, the stream diameter i 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 0.5m below the tap is approximately:

12. 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 surface are 0.8 and the Stefan-Boltzmann constant is 5.67 x 10^-8 W/m²K⁴, the net radiation heat exchange rate in kW/m² between the two plates is:

13. The partial difference equation

14. A planar closed kinematic chain is formed with rigid links PQ = 2.0 m, QR = 3.0 m, RS = 2.5 m and SP = 2.7 m with all revolute joints. The link to be fixed to obtain a double rocker (rocker-rocker) mechanism is:

15.

16. 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:

17. Consider one-dimensional steady state heat conduction, without heat generation, in a plane wall; with boundary conditions as shown in the figure below. The conductivity of the wall is given by k = k₀ +bT; where k₀ and b are positive constants and T is temperature.

As x increases, the temperature gradient (dT/dx) will:

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

19. A link OB is rotating with a constant angular velocity of 2 rad/s in counter clockwise direction and a block is sliding radially outward on it with an uniform velocity of 0.75 m/s with respect to the rod, as shown in the figure below. If OA = 1m, the magnitude of the absolute acceleration of the block at location A in m/s² is:

20. Find the sum of the expression:

21. The 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 the bolt B and the mean diameter of bolt A is 12 mm, the mean diameter of bolt B in mm is:

22. Which one of the following options is closest in meaning to the word 'Nadir'.

23. Universalism is to particularism as diffuseness is to:

24. 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^o counterclockwise with the x-axis. The coordinated of the transformed point will be:

25.

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

27. Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at random. What is the probability that the selected number is not divisible by 7?

28. A pin jointed uniform rigid rod of weight W and Length L is supported horizontally by an external force F as shown in the figure below. The force F is suddenly removed, At the instant of force removal, the magnitude of vertical reaction developed at the support is:

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

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

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

32. Choose the correct set of functions which are linearly dependent.

A. sin x, sin²x and cos²x

B. cos x, sin x and tan x

C. cos2x, sin²x and cos²x

D. cos2x, sin x and cos x

33. A compound gear train with gears P, Q, R and S has number of teeth 20, 40, 15 and 20, respectively. Gears Q and R are mounted on the same shaft as shown in the figure below. The diameter of the gear Q is twice that of the gear R. If the module of gear R is 2 mm, the centre distance in mm between gears P and S is:

34. 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:

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

36. Two cutting tools are being compared for a machining operation. The tool life equations are:

Carbide tool: VT^1.6 = 3000

HSS tool: VT^0.6 = 200

Where V is the cutting speed in m/min and T is the tool life in min. The carbide toll will provide higher tool life if the cutting speed in m/min exceeds:

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

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

39. 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:

40. The current erection cost of a structure is र 13,200. If the labor wages per day increase by 1/5 of the current wages and the working hours decrease by 1/24 of the current period, then the new cost of erection in र is: