GATE Overflow for GATE XE - Questions without answers in Classification of Materials

GATE XE 2026 | Question: 48

Tue, 24 Feb 2026 15:45:55 +0000

Consider $3$ crystals (all having FCC lattice) labelled as $\text{P, Q}$ and $\text{R}$ as described below:

Crystal $\text{P}$: Cu crystal with $4$ $\text{Cu}$ atoms per unit cell
Crystal $\text{Q}$: NaCl crystal with $4 \mathrm{Na}^{+}$ions and $4 \mathrm{Cl}^{-}$ions per unit cell
Crystal $\text{R}$: Diamond crystal with $8$ $\text{C}$ atoms per unit cell

Which of the following options is/are correct?

Only crystal $\text{P}$ is a close packed structure.
Only crystal $\text{Q}$ is a close packed structure.
Crystal $\text{R}$ has the smallest packing factor.
All the crystals $\text{P, Q}$ and $\text{R}$ are close packed structures.

GATE XE 2025 | Question: 44

Sun, 04 May 2025 19:07:33 +0000

The figure below shows a plane $\text{PQR}$ in a unit cell. The Miller indices of the plane $\text{PQR}$ is

$(432)$
$(43 \overline{2})$
$(23 \overline{4})$
$(\overline{2} \overline{3} 4)$

GATE XE 2025 | Question: 48

Sun, 04 May 2025 19:07:25 +0000

There is $\textsf{NO}$ base-centered cubic lattice among the list of $14$ Bravais lattices because of one or more of the following reasons

It does $\textsf{NOT}$ have translational symmetry
It is only compatible with the symmetry of orthorhombic crystal system
It is only compatible with the symmetry of tetragonal crystal system
It does $\textsf{NOT}$ have $3$-fold rotation axes along the body diagonals

GATE XE 2024 | Question: 38

Sun, 21 Jul 2024 16:42:16 +0000

Which one of the following unit cell parameters represents a tetragonal crystal system?

$\mathrm{a}=\mathrm{b}=\mathrm{c} ; \quad \alpha=\beta=\gamma \neq 90^{\circ}$
$\mathrm{a} \neq \mathrm{b} \neq \mathrm{c} ; \quad \alpha=\beta=\gamma=90^{\circ}$
$\mathrm{a}=\mathrm{b} \neq \mathrm{c} ; \alpha=\beta=90^{\circ}, \gamma=120^{\circ}$
$\mathrm{a}=\mathrm{b} \neq \mathrm{c} ; \quad \alpha=\beta=\gamma=90^{\circ}$

GATE XE 2023 | Question: 43

Wed, 14 Feb 2024 18:09:41 +0000

\begin{tabular}{|l|l|}
\hline Q. 53 & \begin{tabular}{l}
A student performed X-ray diffraction experiment on a FCC polycrystalline pure \\
metal. The following $\sin ^{2} \theta$ values were calculated from the diffraction peaks. \\
\\
$\sin ^{2} \theta=0.136,0.185,0.504,0.544$ \\
However, the student was negligent and missed noting one of the peaks. Which \\
one of the following Miller indices corresponds to the missing peak?
\end{tabular} \\
\hline

& $(200)$ \\
\hline
& $(220)$ \\
\hline
& $(311)$ \\
\hline
& $(222)$ \\
\hline
\end{tabular}

GATE XE 2023 | Question: 45

Wed, 14 Feb 2024 18:09:39 +0000

\begin{tabular}{|c|c|c|}
\hline \multirow[t]{6}{*}{ Q. 55} & \multicolumn{2}{|c|}{ Match the hardness test (in Column I) with its indenter type (in Column II). } \\
\hline & Column I & Column II \\
\hline & (P) Brinell & 1. Diamond pyramidal \\
\hline & (Q) Rockwell & 2. Diamond cone \\
\hline & (R) Vickers & 3. Tungsten carbide sphere \\
\hline & & 4. Steel sphere \\
\hline

& P-2, Q-4, R-1 & \\
\hline
& P-4, Q-2, R-3 & \\
\hline
& P-3, Q-4, R-2 & \\
\hline
& P-4, Q-2, R-1 & \\
\hline
\end{tabular}

GATE XE 2023 | Question: 48

Wed, 14 Feb 2024 18:09:36 +0000

\begin{tabular}{|l|l|}
\hline Q. 58 & \begin{tabular}{l}
Among the 14 Bravais lattices, there is no base centred cubic unit cell. Which of \\
the following statement(s) is/are true?
\end{tabular} \\
\hline & \\
\hline

& The base-centred cubic unit cell is same as the simple tetragonal unit cell \\
\hline
& The base-centred cubic unit cell is same as the body centred tetragonal unit cell \\
\hline
& The base-centred cubic unit cell is same as the simple orthorhombic unit cell \\
\hline
& The base-centred cubic unit cell does not have any 3-fold rotation axis \\
\hline
\end{tabular}

GATE XE 2022 | Question: 34

Fri, 17 Feb 2023 06:52:12 +0000

\begin{tabular}{|l|l|}
\hline Q.44 & Number of atoms per unit area of the (110) plane of a body centered cubic crystal, \\
with lattice parameter ' $a$ ', is \\
\hline

& $\frac{1}{a^{2}}$ \\
\hline
& $\frac{\sqrt{2}}{a^{2}}$ \\
\hline
& $\frac{1}{\sqrt{3} a^{2}}$ \\
\hline
& $\frac{1}{\sqrt{2} a^{2}}$ \\
\hline & \\
\hline
\end{tabular}

GATE XE 2022 | Question: 50

Fri, 17 Feb 2023 06:51:59 +0000

A two-phase $(\alpha+\beta)$ mixture of an $\text{A-B}$ binary system has the following properties:

Phase $\alpha$ has equal weight percentages of $\mathrm{A}$ and $\mathrm{B}$.
Phase $\beta$ has twice the mole fraction of $\mathrm{A}$ compared to $\mathrm{B}$.
The two-phase mixture has equal amounts of $\alpha$ and $\beta$.
Atomic mass of $\mathrm{A}$ is twice that of $\mathrm{B}$.

The mole fraction of $\mathrm{A}$ in the resultant two-phase mixture is

$\text{(Round off to one decimal)}$

GATE XE 2022 | Question: 52

Fri, 17 Feb 2023 06:51:57 +0000

A spherical $\beta$ particle nucleates from the $\alpha$ matrix on a non-deformable substrate \end{tabular} $\delta$, forming a contact angle of $\theta$ as shown in the schematic.

The value of $\frac{\Delta G_{\text {het }}^{*}}{\Delta G_{\text {hom }}^{*}}$ is.

$\text{(Round off to three decimal places)}$

$\Delta G_{\text {hom }}^{*}=$ Gibbs free energy change at the critical radius for homogeneous nucleation
$\Delta G_{\text {het }}^{*}=$ Gibbs free energy change at the critical radius for heterogeneous nucleation
$\alpha-\beta$ interfacial energy $=0.4 \mathrm{~J} / \mathrm{m}^{2}$
$\alpha-\delta$ interfacial energy $=0.3 \mathrm{~J} / \mathrm{m}^{2}$
$\beta-\delta$ interfacial energy $=0.02 \mathrm{~J} / \mathrm{m}^{2}$