List of top Questions asked in GATE ME- 2026

A closely coiled helical compression spring of mean coil diameter \(D\) and wire diameter \(d\), is loaded by an axial force \(F\).
The maximum shear stress developed in the wire is

In a single degree of freedom vibrating system with only viscous damping, the critical damping coefficient is 350 N s/m and the damping coefficient is 35 N s/m.
The logarithmic decrement of the vibrating system is

Consider the following statements about four numbers:
(S1) The average of the four numbers is 25
(S2) Each number is at most 40
(S3) Each number is at least 20
Choose the option that is necessarily correct.

A steel plate having yield strength of \( 550 \) MPa is subjected to a biaxial state of stress as \( \sigma_x = \sigma \) and \( \sigma_y = -2\sigma \). Using the distortion energy theory (von Mises criterion) and taking the factor of safety as \( 2 \), find the permissible value of \( \sigma \) that can be applied to the plate. Give the answer in MPa, rounded off to 1 decimal place.

If \( w = \log_e z = \log_e(x+iy) \), where \( i = \sqrt{-1} \), then which one of the following statements is correct?

For an ideal gas, starting from state point 1, two different processes take place. The corresponding final states in these two processes are 2 and 3, lying on same isotherm. If \(P\) and \(h\) represent pressure and enthalpy, respectively, then which one of the following options is correct?

Consider a string P of length \(l\) that is laid out as a straight line segment. Another string K is laid out as a semicircular arc with string P as its diameter, as represented in Figure (i). When both the strings are shortened by a length \(x\) they can be re-arranged such that the shortened string K forms a full circle with the shortened string P as its diameter, as represented in Figure (ii).

The value of \(x/l\) is ____________

For an ideal regenerative Rankine cycle, as shown in the figure below, which one of the following options is the correct representation of temperature-entropy (T-s) diagram?

Consider the following differential equation: \[ \frac{\partial y}{\partial x} = 3\frac{\partial y}{\partial t} + y \] If \( y(x,0) = 10e^{-2x} \), then the solution of the differential equation is

A rigid closed vertical cylindrical vessel of 15 cm diameter contains 5 kg water at 80 °C with 10% quality. The water is heated till its temperature reaches 130 °C. Considering only a horizontal separated interface between liquid and vapor, the dip in the liquid level after the heating process is ________ cm (rounded off to 2 decimal places).
Properties of water at various saturation temperatures are given in the table below.

T (°C)	vf (m3/kg)	vg (m3/kg)	uf (kJ/kg)	ug (kJ/kg)
80	0.001029	3.4053	334.97	2481.60
130	0.001070	0.66808	546.10	2539.50

T, v, and u are temperature, specific volume, and specific internal energy, respectively. Subscripts f and g represent saturated liquid and saturated vapor, respectively.

A simply supported beam is subjected to an external point load P as shown in the figure below. The beam has a rectangular cross-section of 20 mm \(\times\) 45 mm. A is a pin support and B is a roller support. The shear stress developed at point C, lying on the neutral axis of the beam, is 3 MPa. Neglecting the mass of the beam, the magnitude of the applied load is _______ kN (rounded off to 1 decimal place).

A very long fin of a uniform square cross-section is replaced by another very long fin of a uniform circular cross-section of the same material. Assume uniform and identical heat transfer coefficient for both the fins. If the diameter of the circular fin is equal to the side length of the square fin, then the ratio of heat transfer rates before and after the replacement is

"The team ______ more than 300 runs in 20 overs ___________ rains. However, some players needed to improve their batting skills." Choose the option with the correct sequence of words to fill the blanks.

Convective heat transfer coefficients for Fluid 1 and Fluid 2 in a heat exchanger, as shown in the figure below, are 50 W/(m²K) and 80 W/(m²K), respectively. The inner tube is made of a material which has a thermal conductivity 386 W/(m K) for the given range of temperatures in the heat exchanger. The length of the heat exchanging surface, the inside radius of the inner tube, and thickness of the inner tube are 1 m, 10 mm, and 1 mm, respectively. Considering no heat exchange between the outer tube and the surrounding, the heat transfer rate for the heat exchanger is ________ W (rounded off to 1 decimal place).

A welded square plate of 1 m \(\times\) 1 m is subjected to biaxial stress of magnitude 6.5 MPa and 25 MPa, as shown in the figure below. The ratio of the normal stress acting in the perpendicular direction of the weld to the shear stress of the weld is ________ (rounded off to 2 decimal places).

An inward flow reaction turbine, having an outer diameter of \(1\) m, runs at \(600\) RPM. The normal component of absolute velocity at the inlet is \(10\) m/s. If the guide blade angle is \(15^{\circ}\), then the inlet vane angle of the runner is ________ degree (rounded off to 1 decimal place).

The exact solution of \( \displaystyle\int_0^4 \frac{dx}{1+x} \) is represented as \( n \).
If \( m \) represents the numerically evaluated value of the above integral using the Trapezoidal rule by considering four equal subintervals in the range of \( x \), then \( (m-n) \) is

An ideal gas passes isothermally through a long horizontal uniform cross-section pipe under steady flow. Consider that the pressure gradient in the pipe is sufficient for a finite change in the density of the gas. If the flow of the gas is purely pressure driven and subsonic throughout, then the average flow velocity

A horizontal disk has a radial frictionless slot in which a small block is confined to slide. The disk turns anticlockwise about its centre with a constant angular velocity of 3 rad/s.
If the block slides along the slot with a constant speed of 0.2 m/s relative to the slot, then the magnitude of Coriolis acceleration in \( \text{m/s}^2 \) is

Water with a density of 1000 kg/m³ comes out of an industrial condenser through a horizontal pipe of 15 cm radius at the flow rate of 4.5 m³/min. The outlet of the pipe is connected to a coaxial diffuser of 0.5 m length using a flange to raise the pressure of water to atmospheric condition without any backflow. The inner radius (\(r\), in m) of the diffuser cross-section is expressed as
\[ r = 0.15 + 0.4x^2 \]
where, \(x\) represents the axial distance of the diffuser in m, from its inlet. Considering frictionless flow, the magnitude of the force exerted by the diffuser on the flange is ________ N (rounded off to 2 decimal places).

Which one of the patterns labelled P, Q, R, and S is used to generate the following figure?

Newton-Raphson method for solving algebraic equations is based on

Let \( \varphi \) be a scalar function. Then, \( \nabla \varphi \) is

Let \( f(t) \) be a function of \( t \) defined for all positive values of \( t \). The Laplace transform of \( f(t) \), denoted by \( L\{f(t)\} = \int_0^{\infty} e^{-st}f(t)\,dt \), exists for a parameter \( s \) that may be real or complex, provided the integral exists. The Laplace transform of \( f(t) = \sin 2t\sin 4t \) is

"All the mangoes in the basket are good." If the above statement is false, then which one of the following statements is necessarily true?