GATE Mechanical Engineering Test Online

1. If y = f (x) is the solution of d²y/dx² = 0 with the boundary conditions y = 5  at x= 0, and dy/dx = 2 at x = 10, f (15) = ___________

2. For a completely submerged body with centre of gravity 'G' and centre of buoyancy 'B', the condition of stability will be:

3. You are given three coins; one has head on both faces, second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it and it comes up head. The probability that the other face is tails is:

4. Which one of the following is a CFC refrigerant?

5. A circular object of radius r rolls without slipping on a horizontal level floor with the center having velocity V. The velocity at the point of contact between the object and the floor is:

6. The argument of the complex number 1 + ί/1 - ί, where ί = √-1, is

7. A train that is 280 metres long, traveling at a uniform speed, crosses a platform in 60 seconds and passes a man standing on the platform in 20 seconds. What is the length of the platform in metres?

8. The jobs arrive at a facility, for service in a random manner. The probability distribution of number of arrivals of jobs in a fixed time interval is:

9. The exports and imports (in crores and र) of a country from 2000 to 2007 are given in the following bar chart. If the trade deficit is defined as excess of imports over exports, in which year is the trade deficit 1/5th of the exports?

10. Choose the most appropriate phrase from the options given below to complete the following sentence:

The aircraft __________ take off as soon as its flight plan was filed.

11. Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length 0.01 m. The frequency of vibration of the beam with a 0.5 kg mass attached at the free tip, is 100 Hz. The flexural rigidity (in N.m²) of the beam is _________.

12. A circular rod of length 'L' and area of cross-section 'A' has a modulus of elasticity 'E' and coefficient of thermal expansion 'α'. One end of the rod is fixed and other end is free. If the temperature of the rod is increased by ΔT, then

13. An ideal water jet with volume flow rate of 0.05 m³/s strikes a flat plate placed normal to its path and exerts a force of 1000 N. Considering the density of water as 1000 kg/m³, the diameter (in mm) of the water jet is:

14. Consider a two dimensional laminar flow over a long cylinder as shown in the figure below.

The free stream velocity is U_∞ and the free stream temperature T_∞ is lower than the cylinder surface temperature T_s. The local heat transfer coefficient is minimum at point:

15. For the given statement:

1. Mating spur gear teeth is an example of higher pair.
2. A revolute joint is an example of lower pair

Indicate the correct answer.

16. Which one of the following instruments is widely used to check and calibrate geometric features of machine tools during their assembly?

17. The matrix form of the linear system dx/dt =3x - 5y and dy/dt = 4x + 8y is

18.

19. The main cutting force acting on a tool during the turning (orthogonal cutting) operation of a metal is 400 N. The turning was performed using 2 mm depth of cut and 0.1 mm/rev feed rate. The specific cutting pressure (in N/mm²) is:

20. The process of reheating the martensitic steel to reduce its brittleness without any significant loss in its hardness is:

21. Biot number signifies the ratio of:

22. Jobs arrive at a facility at an average a\rate of 5 in an 8 hour shift. The arrival of the hobs follows Poisson distribution. The average service time of a job on the facility is 40 minutes. The service time follows exponential distribution. Idle time (in hour) at the facility per shift will be

23. A pair of spur gears with module 5 mm and a center distance of 450 mm is used for a speed reduction of 5:1. The number of teeth on pinion is _________.

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

Many ancient cultures attributed disease to supernatural causes. However, modern science has largely helped _________ such notions.

25. For machining a rectangular island represented by coordinates P(0,0), Q(100, 0), R(100, 50) and S(0,50) on a casting using CNC milling machine, an end mill with a diameter of 16 mm us used. The trajectory of the cutter centre to machine the island PQRS is:

26. A block weighing 200 N is in contact with a level plane whose coefficients of static and kinetic friction are 0.4 and 0.2, respectively. The block is acted upon by a horizontal force (in newton) P = 10t, where t denotes the time in seconds. The velocity (in m/s) of the block attained after 10 seconds is __________.

27. What is the next number in the series?

12 35 81 173 357 _____

28. A rigid link PQ is 2 m long and oriented at 20^o to the horizontal as shown in the figure. The magnitude and direction of velocity V_Q, and the direction of velocity V_P are given. The magnitude of V_P (in m/s) at this instant is:

29. In exponential smoothening method, which one of the following is true?

30. A slider crank mechanism has slider mass of 10 kg, stroke of 0.2 m and rotates with a uniform angular velocity of 10 rad/s. The primary inertia forces of the slider are partially balanced by a revolving mass of 6 kg at the crank, placed at a distance equal to crank radius. Neglect the mass of connecting rod and crank. When the crank angle (with respect to slider axis) is 30^o, the unbalanced force (in newton) normal to the slider axis is _________.

31. Read the statements:

All women are entrepreneurs.

Some women are doctors.

Which of the following conclusion can be logically inferred from the above statements?

32. Find the odd one from the following group:

1. W, E, K, O
2. F, N, T, X
3. I, Q, W, A
4. N, V, B, D

33. A reversible heat engine receives 2 kJ of heat from a reservoir at 1000 K and a certain amount of heat from a reservoir at 800 K. It rejects 1 kJ of heat to a reservoir  at 400 K. The net work output (in kJ) of the cycle is

34. A rigid  uniform rod AB of length L and mass m is hinged at C such that AC = L/3, CB = 2L/3. Ends A and B are supported by springs of spring constant k. The natural frequency of the system is given by:

35. In solid-state welding, the contamination layers between the surfaces to be welded are removed by:

36. In the following table, x is a discrete random variable and p(x) is the probability density. The standard deviation of x is:

37. A block R of mass 100 kg is placed on a block S of mass 150 kg as shown in the figure. Block R is tied to the wall by a massless and inextensible string PQ. If the coefficient of static friction for all surfaces is 0.4, the minimum force F (in  kN) needed to move the block S is:

38. The statistics of runs scored in a series by four batsman are provided in the following table. Who is the most consistent batsman of these four?

39. Critical damping is the:

40. The maximum theoretical work obtainable, when a system interacts to equilibrium with a reference environment, is called: