GATE Mechanical Engineering Mock Test, GATE ME Test 2024

Load W produces a force of magnitude 120 kN in the member AB of the cantilever truss shown in figure. For this loading, forces in members AE and FE of the truss are

Blocks A and B of masses 40 kg and 60 kg respectively are placed on a smooth surface as shown in figure and the spring connected between them is stretched a distance 2 m. If they are released from rest, the speeds of both blocks the instant the spring becomes unstretched is (Take k = 150 N/m)

A 10 cm long and 5 cm diameter steel rod fits snugly between two rigid walls 10 cm apart at room temperature.

Young’s modulus of elasticity and coefficient of linear expansion of steel are 2 x 10⁶ kgf/cm² and 12 x 10^{– 6} /°C respectively. The stress developed in the rod due to a 100°C rise in temperature will be

A compound train consisting of spur, bevel and spiral gears is shown in the given figure along with the teeth numbers marked against the wheels. Overall speed ratio of the train is

When a system is taken from state A to state B along the path A-C-B, 180 kJ of the heat flows into the system and it does 130 kJ of work (as shown in the figure below).

How much heat will flow into the system along the path A-D-B if the work done by it along the path is 40 kJ?

A system of 100 kg mass undergoes a process in which its specific entropy increases from 0.3 kJ/kgK to 0.4 kJ/kgK. At the same time, the entropy of the surroundings decreases from 80 kJ/K to 75 kJ/K.
The process is

The internal energy of a certain system is a function of temperature alone and is given by the formula E = 25 + 0.25t kJ. If this system executes a process in which the work done by it, per degree temperature increase, is 0.75 kNm, then the heat interaction per degree temperature increase, in kJ, is

The given figure shows the Klein`s construction for acceleration of the slider- crank mechanism

Which one of the following quadrilaterals represents the required acceleration diagram?

In the epicyclic gear train shown in the given figure, A is fixed. A has 100 teeth and B has 20 teeth. If the arm C makes three revolutions, the number of revolutions made by B will be

A single block brake is shown in figure. The diameter of the drum is 250 mm and the angle of contact is 90°. If the operating force of 700 N is applied at the end of a lever and the coefficient of friction between the drum and the lining is 0.35, determine the torque that may be transmitted by the block brake.(Give your answer upto 2 decimal places)

Consider a gray and opaque surface at 0°C in an environment at 25°C. The surface has an emissivity of 0.8. If 300 W/m²is the radiation incident on the surface, the radiosity of the surface is

Consider a horizontal 0.7 m wide and 0.85 m long plate in a room at 30°C. Top side of the plate is insulated while the bottom side is maintained at 0°C. The rate of heat transfer from the room air to the plate by natural convection is
(For air, k = 0.02476 W/m °C, Pr = 0.7323, v = 1.47 x 10⁵ m²/s)

Match List I (Cycle operating between fixed temperature limits) with List II (Characteristics of cycles efficiency η temperature) and select the correct answer using the codes given below the lists:

Consider the data given in the following table:

Given the fact that production in regular and overtime is limited to 650 and 150 respectively, the balance demand of 100 units in the 4^th period can be met by

Time estimates of an activity in a PERT network are optimistic time t_o = 9 days; pessimistic time t_p = 21 days and most likely time t_m = 15 days. The approximate probability of completion of this activity in 13 days is

The design specifications of a 2 m long solid circular transmission shaft require that the angle of twist of the shaft not exceed 3° when a torque of 9 kN-m is applied.
Which of the following is the required diameter of the shaft if the shaft is made of a steel with an allowable shearing stress of 90 MPa and a modulus of rigidity of 77 GPa?(Give your answer to the nearest 1 decimal place.)

The design specifications of a 2 in long solid circular transmission shaft require that the angle of twist of the shaft not exceed 3° when a torque of 9 kN-m is applied.
Which of the following is the required diameter of the shaft if the shaft is made of a brass with an allowable shearing stress of 35 MPa and a modulus of rigidity of 42 GPa?

The pressure in an automobile tire depends on the temperature of the air in the tire. When the air temperature is 25°C, the pressure gage reads 210 kPa. The volume of the tire is 0.025 m³ and the atmospheric pressure is 100 kPa.
What will be the pressure rise in the tire when the air temperature in the tire rises to 50°C?

The pressure in an automobile tire depends on the temperature of the air in the tire. When the air temperature is 25°C, the pressure gage reads 210 kPa. The volume of the tire is 0.025 m³ and the atmospheric pressure is 100 kPa.
The amount of air that must he bled off to restore pressure to its original value at this temperature, is

A uniform rectangular rod having the cross-section of 0.17 m x 0.31 m is shown in figure:

The specific weight of the rectangular rod in kN/m³ will be
(Calculate the approximate answer upto 2 decimal places.)

A uniform rectangular rod having the cross-section of 0.17 m x 0.31 m is shown in figure.

What will be the tension in string?
(Give your answer in whole number and in newtons.)

A cold rolled steel cup with an inside radius of 30 mm and a thickness of 3 mm is to be drawn from a blank of diameter 40 mm. The shear yield stress and the maximum allowable stress of the material can be taken as 210 N/mm² and 600 N/mm² respectively.
What will be the drawing force, if the coefficient of friction µ = 0.1 and β = 0.05?

A cold rolled steel cup with an inside radius of 30 mm and a thickness of 3 mm is to be drawn from a blank of diameter 40 mm. The shear yield stress and the maximum allowable stress of the material can be taken as 210 N/mm² and 600 N/mm² respectively.
What will be the minimum possible radius of the cup which can he drawn from the given blank without causing a fracture?

Let N = 1421 x 1423 x 1425. What is the remainder when N is divided by 12?

There are 60 students in a class. These students are divided into three groups A, B and C of 15, 20 and 25 students each. The groups A and C are combined to form group D. What is the average weight of the students in group D?