List of top Questions asked in GATE Mechanical Engineering- 2025

Identify the option that has the most appropriate sequence such that a coherent paragraph is formed:
Statement:
P. At once, without thinking much, people rushed towards the city in hordes with the sole aim of grabbing as much gold as they could.
Q. However, little did they realize about the impending hardships they would have to face on their way to the city: miles of mud, unfriendly forests, hungry beasts, and inimical local lords—all of which would reduce their chances of getting gold to almost zero.
R. All of them thought that easily they could lay their hands on gold and become wealthy overnight.
S. About a hundred years ago, the news that gold had been discovered in Kolar spread like wildfire and the whole State was in raptures.
 

Consider two identical tanks with a bottom hole of diameter \( d \). One tank is filled with water and the other tank is filled with engine oil. The height of the fluid column \( h \) is the same in both cases. The fluid exit velocity in the two tanks are \( V_1 \) and \( V_2 \). Neglecting all losses, which one of the following options is correct?

Fish : Shoal :: Lion : _________
Select the correct option to complete the analogy.

P and Q play chess frequently against each other. Of these matches, P has won 80% of the matches, drawn 15% of the matches, and lost 5% of the matches.
If they play 3 more matches, what is the probability of P winning exactly 2 of these 3 matches?

The given figure is reflected about the horizontal dashed line and then rotated clockwise by 90° about an axis perpendicular to the plane of the figure.
Which one of the following options correctly shows the resultant figure?
Note: The figures shown are representative

A heat pump, operating in reversed Carnot cycle, maintains a steady air temperature of 300 K inside an auditorium. The heat pump receives heat from the ambient air. The ambient air temperature is 280 K. Heat loss from the auditorium is 15 kW. The power consumption of the heat pump is _________ kW (rounded off to 2 decimal places).

A project involves eight activities with the precedence relationship and duration as shown in the table below. The slack for the activity D is __________ hours (answer in integer). 

A company uses 3000 units of a part annually. The units are priced as given in the table below. It costs ₹150 to place an order. Carrying costs are 40 percent of the purchase price per unit on an annual basis. The minimum total annual cost is ₹ _________ (rounded off to 1 decimal place).

Cylindrical workpieces of diameter 60 mm and length 400 mm are machined on a lathe at a cutting speed of 25 m/min and a feed of 0.2 mm/rev. The Taylor’s tool life parameters \(C\) and \(n\) for this setup are 75 and 0.25, respectively. The tool changing time is 3 minutes. With a labor and overhead cost of ₹5 per minute, the tool changing cost per piece is ₹_________ (rounded off to 2 decimal places).

Two plates of thickness 10 mm each are to be joined by a transverse fillet weld on one side and the resulting structure is loaded as shown in the figure below. If the ultimate tensile strength of the weld material is 150 MPa and the factor of safety to be used is 3, the minimum length of the weld required to ensure that the weld does NOT fail is ____________ mm (rounded off to 2 decimal places).

An offset slider-crank mechanism is shown in the figure below. The length of the stroke of the slider is __________ mm (rounded off to nearest integer).

An isotropic brittle material is tested in the universal testing machine. The stress-strain diagram for the material shows a bi-linear elastic behavior as shown in the figure given below. The strain energy density is _________ MJ m\(^{-3}\) (rounded off to 2 decimal places).

A simply supported beam of length 1 m is subjected to a uniformly distributed bending moment of 1 N m per meter throughout the length as shown in the figure. The bending moment at the mid-point of the beam is __________ N m (rounded off to the nearest integer).

The state of stress at a point is shown in the figure given below. Under plane stress assumption, the normal strain along the thickness direction (\(\epsilon_{zz}\)) is _________ (rounded off to 2 decimal places).

A thermodynamically closed system contains 1 kg of hydrogen. The system undergoes a reversible polytropic process with polytropic index 1.3. The work output during the process is 400 kJ. During the process, hydrogen behaves as an ideal gas with constant specific heats. The absolute value of heat transfer during the process is _________ kJ (rounded off to 1 decimal place). Specific heat of hydrogen at constant pressure = 14.56 kJ kg\(^{-1}\) K\(^{-1}\)
Specific heat of hydrogen at constant volume = 10.4 kJ kg\(^{-1}\) K\(^{-1}\)

Consider a Pelton wheel of 1 m diameter. The magnitude of relative velocity of water at the bucket inlet is the same as the magnitude of relative velocity of water at the bucket exit. The absolute speed of water at the bucket inlet is 125.66 m/s\(^{-1}\). For maximum power output from the Pelton wheel, the rpm of the Pelton wheel is (rounded off to 1 decimal place).

A thermal power plant is running with no reheat or regeneration. The specific enthalpy and specific entropy of steam at the turbine inlet are 3344 kJ/kg and 6.5 kJ/kg·K, respectively. The turbine isentropic efficiency is 0.9, and the mass flow rate of steam at the turbine inlet is 102 kg/s. The turbine power output is _________ MW (rounded off to 1 decimal place).

Consider a velocity field \( \vec{V} = 3z \hat{i} + 0 \hat{j} + Cx \hat{k} \), where \( C \) is a constant. If the flow is irrotational, the value of \( C \) is (rounded off to 1 decimal place).

Water enters a tube of diameter, \( D = 60 \, {mm} \) with mass flow rate of 0.01 kg/s\(^{-1}\) as shown in the figure below. The inlet mean temperature is \( T_{{in},i} = 293 \, {K} \) and the uniform heat flux at the surface of the tube is 2000 W/m\(^{-2}\). For the exit mean temperature of \( T_{{m},o} = 353 \, {K} \), the length of the tube, \( L \) is _________m (rounded off to 1 decimal place).
Use the specific heat of water as 4181 J kg\(^{-1}\) K\(^{-1}\).