List of top Metallurgical Engineering Questions asked in GATE MT

The value of \[ \lim_{x \to 0} \frac{6(x - \sin x)}{x^3} \] is ........ (in integer).

The diameter of spherical galena particles that have the same settling velocity as spherical quartz particles of diameter 25 μm (both settling in water) is _________ μm (rounded off to one decimal place). Assume Stokes law of settling to be valid. Given: Density of galena = 7400 kg m\(^{-3}\), Density of quartz = 2600 kg m\(^{-3}\), Density of water = 1000 kg m\(^{-3}\).

An intrinsic semiconductor has conductivity of 100 Ω\(^{-1}\) m\(^{-1}\) at 300 K and 300 Ω\(^{-1}\) m\(^{-1}\) at 500 K. The band gap of the semiconductor is _________ eV (rounded off to two decimal places). Given: Boltzmann constant \( k_B = 8.6 \times 10^{-5} \, {eV K}^{-1} \)

Temperatures at two sides of a 0.4 m thick copper plate are 1000°C and 500°C. Assuming steady state, one-dimensional conductive heat transfer through the wall and ignoring end-effects, the magnitude of the heat flux through the wall is _________ \( \times 10^5 \, {W m}^{-2} \) (in integer). Given: Thermal conductivity of copper \( k = 400 \, {W m}^{-1} {K}^{-1} \).

In polycrystalline Ni, Nabarro-Herring diffusion creep was found to be the rate controlling creep mechanism at a certain temperature. At that temperature, if the steady state strain rate is \( 10^{-8} \, {s}^{-1} \) at a stress of 10 MPa, the steady state strain rate of \( 10^{-9} \, {s}^{-1} \) will be obtained at a stress value of _________ MPa (in integer). Assume that the same creep mechanism is rate controlling during the creep deformation.

Two consecutive estimates of the root of a function \( f(x) \) obtained using the Newton-Raphson method are \( x_i = 8.5 \) and \( x_{i+1} = 13.5 \), and the value of the function at \( x_i \) is 15. The numerical value of the first derivative of the function evaluated at \( x_i \) is _________ (in integer).

A specimen containing maximum initial surface crack of size 1.5 mm is subjected to cyclic loading with \( \sigma_{max} = 300 \) MPa and \( \sigma_{min} = 0 \) MPa. Assuming specimen geometric factor of 1, and referring to the given figure, the crack growth rate in \(\mu\)m cycle\(^{-1}\) is ................... (round off to nearest integer). 

The alloy A (given in the phase diagram) is cooled slowly from the liquid state to just below the eutectic temperature. The ratio of weight fractions of pro-eutectic \(\alpha\) to eutectic \(\alpha\) is ................... (round off to 1 decimal place). 

 

For the given schematic TTT diagram of an eutectoid steel, the following statement(s) is/are true for the heat treatment schedules HT-1, HT-2, and HT-3. 

The mechanism of creep for a single crystal as depicted in the schematic is 

 

An elutriator is used to separate particles based on their sizes in flowing air as shown in the figure. Assuming spherical particles, the diameter (\(D_{50}\)) of the suspended particles which have 50% chance to report to overflow by turbulent air flow is expressed as