List of top Questions asked in GATE Metallurgical Engineering

Match the phenomena in Column I with the typical observations in Column II. 

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).

Consider the gas phase reaction: \[ CO + \frac{1}{2} O_2 \rightleftharpoons CO_2 \] At equilibrium for a particular temperature, the partial pressures of \( CO \), \( O_2 \), and \( CO_2 \) are found to be \( 10^{-6} \, {atm} \), \( 10^{-6} \, {atm} \), and \( 16 \, {atm} \), respectively. The equilibrium constant for the reaction is ......... \( \times 10^{10} \) (rounded off to one decimal place).

For an application where the Reynolds number is to be kept constant, a liquid with a density of 1 g cm\(^-3\) and viscosity of 0.01 Poise results in a characteristic speed of 1 cm s\(^-1\). If this liquid is replaced by another with a density of 1.25 g cm\(^-3\) and viscosity of 0.015 Poise, the characteristic velocity will be ......... cm s\(^-1\) (rounded off to one decimal place).

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

Consider a fully developed, steady, one-dimensional, laminar flow of a Newtonian liquid through a pipe. The maximum velocity in the pipe is proportional to which of the following quantities? 
Given: \( \Delta P \) is the difference between the outlet and inlet pressure, \( \mu \) is the dynamic viscosity of the liquid, and \( R \) and \( L \) are the radius and length of the pipe, respectively.

Match the following elements in Column I with their respective ores in Column II. 

Match each crystal defect in Column I with the corresponding type in Column II. 

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?