GATE Mechanical Engineering Online Test 4 Question Answers

1. A phenomenon is modeled using n dimensional variables with k primary dimensions. The number of non-dimensional variables is:

2. Modern warfare has changed from large scale crashes of armies to suppression of civilian population. Chemical agents that do their work silently appear to be suited to such warfare; and regretfully, there exit people in military establishments who think that chemical agents are useful tools for their cause.

Which of the following statement best sums up the meaning of the above passage.

3. Simplex method of solving linear programming problem uses:

4. A lightly loaded ful journal bearing has journal diameter of 50 mm, bush bore of 50.05 mm and bush length of 20 mm. If rotational speed of journal is 1200 rom and average viscosity of liquid lubricant is 0.03 Pa s, the power loss (in W) will be:

5. A bracket (shown in figure) is rigidly mounted on wall using four rivets. Each rivet is 6 mm in diameter and has an effective length of 12 mm.

Direct Shear stress (in MPa) in the most heavily loaded rivet is:

6. A mass m attached to a spring is subjected to a harmonic force as shown in figure. The amplitude of the forced motion is observed to be 50 mm. The value of m (in kg) is:

7. Tooth interference in an external involute spurgear pair can be reduced by:

8. For Tool A, Taylor's tool life exponent (n) is 0.45 and constant (K) is 90. Similarly for tool B, n = 0.3 and K = 60. The cutting speed (in m/min) above which tool A will have a higher tool life than tool B is:

9. The state of plain-stress at a point is given by σ_x = - 200 MPa, σ_y = 100 MPa and τ_xy = 100 MPa. The maximum shear stress (in MPa) is:

10. In a CNC program block, N002 G02 G91 X40 Z40..., G02 and G91 refer to:

11. For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?

12. 25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is:

13. The material property which depends only on the basic crystal structure is:

14. The project activities, precedence relationships and durations are described in table. The critical path of the project is:

15. A smooth pipe of diameter 200 mm carries water. The pressure in the pipe at section S1 (elevation: 10 m) is 50 kPa. At section S2 (elevation: 12 m) the pressure is 20 kPa and velocity is 2 ms^-1. Density of water is 1000 kgm^-3 and acceleration due to gravity is 9.8 ms^-2. Which of the following is TRUE?

16. 5 skilled workers can built a wall in 20 days; 8 semi-skilled workers can build a wall in 15 days; 10 unskilled workers can build a wall in 30 days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall?

17. Two pipes of inner diameter 100 mm and outer diameter 110 mm each are joined by flash-butt welding using 30 V power supply. At the interface, 1 mm of material melts from each pipe which has a resistance of 42.4 Ω. If the unit melt energy is 64.4 MJ m^-3, then time required for welding (in s) is:

18. There are two points P and Q on a planar rigid body. The relative velocity between the two points:

19. A turbo-charged four-stroke direct injection diesel engine has a displacement volume of 0.0259 m³ (25.9 litres). The engine has an output of 950 kW at 2200 rpm. The mean effective pressure (in MPa) is closest to:

20. A hydraulic turbine develops 1000 kW power for a head of 40 m. If the head is reduced to 20 m, the power developed (in kW) is:

21. The question below consists of a pair of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair.

Unemployed: Worker

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

23. Which of the following statements is INCORRECT?

24. Choose the most appropriate word from the options given below to complete the following sentence:

His rather casual remarks on politics _________ his lack of seriousness about the subject.

25. Little's law is a relationship between:

26. In a gating system, the ratio 1 : 2 : 4 represents:

27. Torque exerted on a flywheel over a cycle is listed in the table. Flywheel energy (in J per unit cycle) using Simpson's rule is:

28. The demand and forecast for February are 12000 and 10275, respectively. Using single exponential smoothening method (smoothening coefficient = 0.25), forecast for the month of March is:

29. A moist air sample has dry bulb temperature of 30^oC and the specific humidity of 11.5 g water wapour per kg dry air. Assume molecular weight of air as 28.93. If the saturation vapor pressure of water at 30^oC is 4.24 kPa and the total pressure in 90 kPa, then the relative (in %) of air sample is:

30. Mobility of a statically indeterminate structure is:

31. A tapper hole is inspected using a CMM, with a probe of 2 mm diameter. At a height, Z = 10 mm from the bottom, 5 points are touched and a diameter of circle (not compensated for probe size) is obtained as 20 mm. Similarly, a 40 mm diameter is obtained at a height Z = 40 m. The smaller diameter (in mm) of hole at Z = 0 is

32. A mono-atomic ideal gas (γ = 1.67, molecular weight = 40) is compressed adiabatically from 0.1 MPA, 300 K to 0.2 MPa. The universal gas constant is 8.314 kJ kmol^-1 K^-1. The work of compression of the gas (in kJ kg^-1) is:

33. Consider the following two processes:

1. A heat source at 1200 K loses 2500 kJ of heat to sink at 800 K
2. A heat source at 800 K loses 2000 kJof heat to sink at 500 K

Which of the following statements is true?

34. A box contains 2 washers, 3 nuts and 4 bolts. Items are drawn from the box at random one at a time without replacement. The probability of drawing 2 washers first followed by 3 nuts and subsequently the 4 bolts is:

35. One kilogram of water at room temperature is brought into contact with a high temperature thermal reservoir. The entropy change of the universe is:

36. Given digits 2, 2, 3, 3, 3, 4, 4, 4, 4 how many distinct 4 digit numbers greater than 3000 can be formed?

37. The maximum velocity of a one-dimensional incompressible fully developed viscous flow, between two fixed parallel plates, is 6 ms^-1. The mean velocity (in ms^-1) of the flow is:

38. Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings. All were born on 1st January. The age difference between any two successive siblings is less than 3 years. Given the following facts:

1. Hari's age + Gita's age > Irfan's age + Saira's age
2. The age difference between Gita and Saira is 1 year. However Gita is not the oldest and Saira is not the youngest.
3. There are no twins.

In what order were they born (oldest first)?

39. Vehicle manufacturing assembly line is an example of:

40. Annual demand for window frames is 10000. Each frame costs (Rs. 200 and ordering cost is Rs. 300 per order. Inventory holding cost is Rs. 40 per frame per year. The supplier is willing to offer 2% discount it the order quantity is 1000 or more, and 4% if order quantity is 2000 or more. If the total cost is to be minimized, the retailer should: