List of top Questions asked in GATE ME

Let a spherical block of ice at -7 °C be exposed to atmospheric air at 30 °C with the gravitational direction as shown in the figure below. What will be the overall direction of air flow in this situation?


 

Let \(A\) and \(B\) be real symmetric matrices of the same size. Which one of the following options is correct?
A pair of spur gears is required to maintain a velocity ratio of 1:2. The module of the gears is 10 mm and the addendum is 10 mm. If the operating pressure angle is 15°, the minimum number of teeth required on the pinion to ensure NO interference/undercutting is (answer in integer).
Two metal parts (a cylinder and a cube) of same volume are cast under identical conditions. The diameter of the cylinder is equal to its height. The ratio of the solidification time of the cube to that of the cylinder is _________ (rounded off to 2 decimal places).
Assume that solidification time follows Chvorinov’s rule with an exponent of 2.
Let \( y \) be the solution of the differential equation with the initial conditions given below. If \( y(x = 2) = A \ln 2 \), then the value of \( A \) is ___________ (rounded off to 2 decimal places). \[ x^2 \frac{d^2y}{dx^2} + 3x \frac{dy}{dx} + y = 0 \] \[ y(x = 1) = 0, \quad \frac{dy}{dx}(x = 1) = 1 \]
The endurance limit of a specific grade of steel is same as its yield strength. The ultimate strength of this grade of steel is twice of its yield strength. A component made of this steel is loaded in tension and unloaded periodically. It is required that the component does NOT fail for at least \( 10^6 \) loading cycles, as per the Soderberg law. Considering a factor of safety of 2, the maximum applied tensile principal stress is:
A block of mass 1 kg connected to a spring of stiffness 10 N m\(^{-1}\) is operating in a viscous medium such that the damping ratio (or damping factor) is equal to the ratio of the damped frequency to the natural frequency. The magnitude of the damping ratio for this system is _________ (rounded off to 2 decimal places).
The thermal efficiency of an ideal air-standard Otto cycle is 0.5. The value of specific heat ratio of air is 1.4. The compression ratio of the cycle is _________ (rounded off to 1 decimal place).
The yield stress of a metal in uniaxial tension is 200 MPa. According to von Mises yield criterion, the yield stress (in MPa) of the metal in pure shear is closest to:
Air inside a rigid, thermally-insulated tank undergoes stirring as shown in the figure below. Which one of the following options is correct?
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In a laboratory experiment using a scaled down model to measure scour at a bridge pier, the Froude number is important. The ratio of the prototype length to the model length is 100. If the velocity of the model is 1 m/s, the velocity (in m/s) of the prototype is:
For the differential equation given below, which one of the following options is correct? \[ \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0, \quad 0 \leq x \leq 1, 0 \leq y \leq 1 \]
If two unbiased coins are tossed, then what is the probability of having at least one head?
The divergence of the curl of a vector field is:
Eject : Insert : : Advance : _______ (By word meaning)
“I have not yet decided what I will do this evening; I ______ visit a friend.”
What are the number of numbers possible divisible by 3 if we choose 4 numbers from the set S = {4,5,7,8,9}