List of top Metallurgical Engineering Questions on Metallurgical asked in GATE MT

The hydrostatic stress for the stress tensor provided below is __________ MPa (in integer).

\[ \begin{bmatrix} 150 & 0 & 0 \\ 0 & -100 & 100 \\ 0 & 100 & 250 \end{bmatrix} \ \text{MPa} \]
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).
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.
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 \( k = 400 \, {W m}^{-1} {K}^{-1} \).
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 \( k_B = 8.6 \times 10^{-5} \, {eV K}^{-1} \)
A linear regression model was fitted to a set of \( (x, y) \) data. The total sum of squares and sum of squares of error are 1200 and 120, respectively. The coefficient of determination \( R^2 \) of the fit is ......... (rounded off to one decimal place).
A cylindrical Al alloy billet of 300 mm diameter is hot extruded to produce a cylindrical rod of 75 mm diameter at a constant true strain rate of 10 s$^{-1$. The flow stress of the alloy at the extrusion temperature is given by $\sigma = 10 \, (\dot{\epsilon})^{0.3}$ MPa. Assume the alloy is perfectly plastic and there is no temperature rise during the extrusion process. The ideal plastic work of deformation per unit volume is ............ × 10$^6$ J m$^{-3}$ (rounded off to one decimal place).}
Front tension is applied during cold rolling of a thin metal sheet. Which of the following statements is/are TRUE?
Match the casting defects in Column I with the characteristic features in Column II. Column I:
P. Misrun
Q. Expansion scab
R. Pin holes
S. Hot tearing
Column II:
1. Penetration of liquid metal behind surface layer of sand moulds
2. Metal solidifies prematurely in the mould and some sections of the casting are not filled
3. Cracking because of restraint to contraction in certain areas during solidification and cooling
4. Evolution of gases during solidification resulting in porosity
Which of the following techniques can be used to detect an internal defect in a metal casting?
In metal casting, which sprue:runner:gate \emph{area ratio represents a non-pressurized gating system?}

Radiative heat flux \( \dot{q} \) at a hot surface at a temperature \( T_s \) can be expressed as \[ \dot{q} = A f(T_s, T_\infty) (T_s - T_\infty) \] where \( A \) is a constant and \( T_\infty \) is the temperature of the surroundings (temperatures are expressed in K). The function \( f(T_s, T_\infty) \) is given by ______.

Match the steel plant related processes in Column I with the associated information in Column II.

Consider the phase diagram of a one-component system given below. \( V_{\alpha} \), \( V_{\beta} \), and \( V_{{Liquid}} \) are the molar volumes of \( \alpha \), \( \beta \), and liquid phases, respectively. Which one of the following statements is TRUE? Given: The change in molar enthalpies, \( \Delta H_{\alpha \to \beta} \) and \( \Delta H_{\beta \to {Liquid}} \), are positive.

For two continuous functions \( M(x, y) \) and \( N(x, y) \), the relation \( M dx + N dy = 0 \) describes an exact differential equation if

A linear regression model was fitted to a set of \( (x, y) \) data. The total sum of squares and sum of squares of error are 1200 and 120, respectively. The coefficient of determination \( R^2 \) of the fit is ......... (rounded off to one decimal place).

The hydrostatic stress for the stress tensor provided below is ......... MPa (in integer). \[ \begin{bmatrix} 150 & 0 & 0 \\ 0 & -100 & 100 \\ 0 & 100 & 250 \end{bmatrix} \, \text{MPa} \]

Which of the following statements is/are CORRECT with respect to the initial stage of GP zone formation in a precipitation-hardenable Al - 4.5 wt.% Cu alloy?
With reference to edge and screw dislocations, which of the following statements is/are CORRECT?
Which of the following functions is/are expandable using the Maclaurin series?
Which one of the following is an intensive property?

Two randomly oriented polycrystalline copper samples with average grain sizes of 10 $\mu$m (Sample A) and 100 $\mu$m (Sample B) were tested at room temperature. 
Given: $E_A$ = Young's modulus of Sample A $E_B$ = Young's modulus of Sample B $Y_{SA}$ = Yield strength of Sample A $Y_{SB}$ = Yield strength of Sample B 
Which one of the following statements is CORRECT?

Which one of the following slag components is responsible for the oxidizing power of steelmaking slags?