GATE Overflow for GATE XE - Recent questions and answers in Properties and Applications of Materials

GATE XE 2026 | Question: 34

Tue, 24 Feb 2026 15:47:49 +0000

The band gap of a material is $E_{g}$ and the energy of an incident photon is $E_{p}$. Optical absorption will occur in this material if,

$E_{g} < E_{p}$
$E_{g}>E_{p}$
Electron-electron recombination occurs
Electron-hole recombination occurs

GATE XE 2026 | Question: 38

Tue, 24 Feb 2026 15:46:58 +0000

Which of the following is/are polarization mechanisms in dielectric solids?

Mechanical polarization
Ionic polarization
Electronic polarization
Thermal polarization

GATE XE 2026 | Question: 50

Tue, 24 Feb 2026 15:45:48 +0000

According to quantum free electron theory, which of the following statements is/are correct regarding the behavior of valence electrons in a metal?

Valence electrons are localized to individual atoms.
Valence electrons are delocalized within the crystal.
Energy distribution of valence electrons follows Fermi-Dirac statistics.
Energy distribution of valence electrons follows Maxwell-Boltzmann statistics.

GATE XE 2026 | Question: 51

Tue, 24 Feb 2026 15:45:44 +0000

$\mathrm{Fe}$ has a density of $7.87 \mathrm{~g} . \mathrm{cm}^{-3}$, atomic mass of $55.84 \mathrm{~g} . \mathrm{mol}^{-1}$ and net magnetic moment per atom of $2.22$ Bohr magnetons ( $\mu_{B}$ ). The saturation magnetization of $\mathrm{Fe}$ in $\mathrm{A.m}^{-1}$ is $\_\_\_\_$ $\times 10^{5}$ (rounded off to one decimal place).

Given: $\mu_{B}=9.27 \times 10^{-24} \mathrm{~A} . \mathrm{m}^{2}$, Avogadro number $=6.023 \times 10^{23} \mathrm{~mol}^{-1}$

GATE XE 2026 | Question: 53

Tue, 24 Feb 2026 15:45:42 +0000

A $1 \mathrm{~cm}^{3} \mathrm{~Si}$ cube is doped with As with a concentration of $1$ atom per $10^{9} \mathrm{~Si}$ atoms. The resistance of the doped $\mathrm{Si}$ cube in $\mathrm{Ohms}$ is $\_\_\_\_$ (rounded off to one decimal place).

Given:
Atomic concentration of $\mathrm{Si}=5 \times 10^{22} \mathrm{~cm}^{-3}$
Intrinsic concentration of electrons in $\mathrm{Si}=1 \times 10^{10} \mathrm{~cm}^{-3}$
Electron mobility in $\mathrm{Si}=1350 \mathrm{~cm}^{2} \cdot \mathrm{~V}^{-1} \cdot \mathrm{~s}^{-1}$
Hole mobility in $\mathrm{Si}=450 \mathrm{~cm}^{2} \cdot \mathrm{~V}^{-1} \cdot \mathrm{~s}^{-1}$
Electronic charge $=1.6 \times 10^{-19} \mathrm{C}$

GATE XE 2026 | Question: 182

Tue, 24 Feb 2026 15:09:42 +0000

Which of the following options is/are true regarding the behaviour of a typical solar photovoltaic cell?

Ideal current source
Current limited voltage source
Voltage limited current source
Ideal power source

GATE XE 2025 | Question: 45

Sun, 04 May 2025 19:07:31 +0000

The unit of measurement for magnetic dipole moment of a body is

$\mathrm{A} \: \mathrm{m}^{2}$
$\mathrm{A} \: \mathrm{m}^{-1}$
$\mathrm{Wb} \: \mathrm{m}^{-2}$
$\mathrm{Wb} \: \mathrm{m}^{2}$

GATE XE 2025 | Question: 46

Sun, 04 May 2025 19:07:29 +0000

$B$ is the magnetic flux density and $T_{c}$ is the critical temperature. The Meissner effect is represented by

$\mathrm{B}=0$ at $\mathrm{T} \leq \mathrm{T}_{\mathrm{c}}$
$\mathrm{B}=0$ at $\mathrm{T}>\mathrm{T}_{\mathrm{c}}$
$\mathrm{B} \neq 0$ at $\mathrm{T} \leq \mathrm{T}_{\mathrm{c}}$
$\nabla \mathrm{B}=0$ at $\mathrm{T}=\mathrm{T}_{\mathrm{c}}$

GATE XE 2025 | Question: 49

Sun, 04 May 2025 19:07:22 +0000

For a conventional optical microscope, which of the following options regarding the resolution limit and the depth of field is/are correct?

Resolution limit decreases with decreasing wavelength of light
Resolution limit decreases with decreasing refractive index of the medium
Depth of field decreases with increasing value of numerical aperture of the objective lens
Resolution limit decreases with increasing value of numerical aperture of the objective lens

GATE XE 2025 | Question: 50

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

Which of the following phenomenon/phenomena contribute to intensity loss of electromagnetic radiation during transmission through a medium?

Electronic absorption
Rayleigh scattering
Photon - phonon interaction
Stimulated emission

GATE XE 2025 | Question: 59

Sun, 04 May 2025 19:07:02 +0000

On applying $10 \: \mathrm{V}$ across the two ends of a $100 \: \mathrm{cm}$ long copper wire, the average drift velocity (in $\mathrm{cm}\: \mathrm{s}^{-1}$ ) in the wire is (rounded off to two decimal places) $\_\_\_\_\_\_$

Given: Electron density of copper $=8.43 \times 10^{22} \mathrm{~cm}^{-3}$

Copper resistivity $=1.67 \times 10^{-6} \Omega \mathrm{~cm}$

Electron charge $=1.6 \times 10^{-19} \mathrm{C}$

GATE XE 2025 | Question: 61

Sun, 04 May 2025 19:07:00 +0000

An electric field is applied on a copper plate such that the electrons are displaced by $1.1 \times 10^{-18} \mathrm{~m}$ relative to the nucleus. The electronic polarization (in $\mu \mathrm{C} \: \mathrm{m}^{-2}$ ) is (rounded off to two decimal places) $\_\_\_\_\_\_\_$

Given: Atomic number of copper $=29$

Copper has FCC crystal structure with lattice parameter $=0.362 \mathrm{~nm}$

Electron charge $=1.6 \times 10^{-19} \mathrm{C}$

GATE XE 2024 | Question: 39

Sun, 21 Jul 2024 16:42:15 +0000

Which of the following types of materials exhibit(s) positive magnetic susceptibility?

Paramagnetic
Diamagnetic
Ferrimagnetic
Ferromagnetic

GATE XE 2024 | Question: 44

Sun, 21 Jul 2024 16:42:11 +0000

Which one of the following figures corresponds to the density of states $g(E)$ of a typical intrinsic semiconductor? $\text{(E represents the energy level of a charge carrier)}$.

GATE XE 2024 | Question: 46

Sun, 21 Jul 2024 16:42:10 +0000

Which one of the following curves best represents the $E$ vs. $f(E)$ behavior of the hot end of a metal rod demonstrating Seebeck Effect? $\text{$( f(E)$ is the probability of electron occupancy at an energy state $\mathrm{E} ; \mathrm{E}_{\mathrm{F}}$ is the Fermi energy)}$.

GATE XE 2024 | Question: 47

Sun, 21 Jul 2024 16:42:09 +0000

In a typical light emitting diode (LED), which of the following type(s) of materials is/are used?

Indirect bandgap semiconductor with transition metal impurities
Direct bandgap semiconductor
Indirect bandgap semiconductor with isoelectronic impurities
Indirect bandgap semiconductor without any impurity

GATE XE 2024 | Question: 52

Sun, 21 Jul 2024 16:42:04 +0000

At room temperature, the electrical conductivity and electron mobility for aluminium are $3.8 \times 10^{7}(\Omega \mathrm{m})^{-1}$ and $0.0012 \mathrm{~m}^{2}(\mathrm{~V} \mathrm{~s})^{-1}$, respectively. Density of free electrons for aluminium at room temperature is $\text{(in units of $\mathrm{m}^{-3}$ )}$ __________ $\times 10^{27}$ $\text{(rounded off to nearest integer)}$.

Given: Electrical charge on an electron is $1.6 \times 10^{-19} \mathrm{C}$.

GATE XE 2023 | Question: 42

Wed, 14 Feb 2024 18:09:42 +0000

Q. 52 In a semiconductor, the ratio of electronic mobility to hole mobility is 10 . The density of electrons and holes are $10^{15} \mathrm{~m}^{-3}$ and $10^{16} \mathrm{~m}^{-3}$, respectively. If the conductivity of the material is $1.6 \Omega^{-1} \mathrm{~m}^{-1}$, then the mobility of holes is (in $m^{2} V^{-1} s^{-1}$ ) : (rounded off to nearest integer)
Given: Charge of an electron: $1.6 \times 10^{-19} \mathrm{C}$

GATE XE 2023 | Question: 47

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

\begin{tabular}{l|l}
Q. 57 & Which of the following statement(s) is/are true for an optical microscope? \\
\hline

& Increasing the aperture of the objective lens deteriorates the resolution \\
\hline
& Reducing the wavelength of illuminating light improves the resolution \\
\hline
& \begin{tabular}{l}
Increasing the refractive index of the medium in between the sample and the \\
objective lens improves the resolution
\end{tabular} \\
\hline
& Reducing the wavelength of illuminating light decreases the depth of field
\end{tabular}

GATE XE 2023 | Question: 51

Wed, 14 Feb 2024 18:09:33 +0000

\begin{tabular}{l|l}
Q. 61 & \begin{tabular}{l}
The Young's modulus of a quartz piezoelectric crystal is $100 \mathrm{GPa}$. The uniaxial \\
stress required to change its polarization by $1 \%$ is (give absolute value in GPa) \\
(rounded off to nearest integer)
\end{tabular} \\
\hline
\end{tabular}

GATE XE 2023 | Question: 52

Wed, 14 Feb 2024 18:09:33 +0000

Q. 62 A one-dimensional nanowire has a linear electron density of $10^{8}$ electrons $\mathrm{cm}^{-1}$. The Fermi energy of the system is (in $\mathrm{eV}$ ) (rounded off to two decimal places)
Given: $\frac{\hbar^{2}}{2 m}=0.24(\mathrm{eV})^{2} \mathrm{~s}^{2} \mathrm{~kg}^{-1}$ where ' $m$ ' is the mass of an electron

GATE XE 2023 | Question: 55

Wed, 14 Feb 2024 18:09:30 +0000

\begin{tabular}{l|l|}
\hline Q. 65 & \begin{tabular}{l}
In a Raman spectroscopy experiment done at $300 \mathrm{~K}$, a Raman line is observed at \\
$200 \mathrm{~cm}^{-1}(\sim 25 \mathrm{meV})$. The ratio of the intensity of the Stokes line to that of the \\
Anti-Stokes line is $\quad$ (rounded off to two decimal places) \\
Given: Boltzmann constant, $k=8.62 \times 10^{-5} \mathrm{eV} \mathrm{K}$
\end{tabular} \\
\hline
\end{tabular}

GATE XE 2022 | Question: 37

Fri, 17 Feb 2023 06:52:10 +0000

Which one of the following statements is true for an intrinsic semiconductor?

Electrical conductivity increases with increasing temperature and pressure
Electrical conductivity increases with increasing temperature and decreasing pressure
Electrical conductivity increases with decreasing temperature and increasing pressure
Electrical conductivity increases with decreasing temperature and pressure

GATE XE 2022 | Question: 42

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

An electrochemical reaction is known to occur at $+4.50 \mathrm{~V}$ against a $\mathrm{Li}^{+} / \mathrm{Li}$ reference electrode. The potential of the same reaction against a $\mathrm{Zn}^{2+} / \mathrm{Zn}$ reference electrode is V.

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

Given:
$\mathrm{E}^0\left(\mathrm{Li}^{+} / \mathrm{Li}\right)=-3.04 \mathrm{~V}$ versus Standard Hydrogen Electrode
$\mathrm{E}^0\left(\mathrm{Zn}^{2+} / \mathrm{Zn}\right)=-0.77 \mathrm{~V}$ versus Standard Hydrogen Electrode

GATE XE 2022 | Question: 53

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

The resistivity of a pure semiconductor at $298 \mathrm{~K}$ is $3000 \Omega \mathrm{m}$. Assume that the number of electrons excited $\left(n_{e}\right)$ across the band gap is given by the relation
\[
n_{e}=N_{A} \exp \left(-\frac{E_{g}}{k_{B} T}\right)
\]

$N_{A}$ : Avogadro's number $=6.02 \times 10^{23} \mathrm{~mole}^{-1}$

$k_{B}$ : Boltzmann's constant $=8.62 \times 10^{-5} \mathrm{eV} / \mathrm{K}$

Mobility of electrons in the semiconductor $=0.14 \mathrm{~m}^{2} /(\mathrm{V} \mathrm{s})$

Mobility of holes in the semiconductor $=0.06 \mathrm{~m}^{2} /(\mathrm{V} \mathrm{s})$

Absolute charge of an electron $=1.60 \times 10^{-19} \mathrm{C}$

The band gap $\text{(E_g)}$ of semiconductor

$\text{(Round off to decimals)}$

GATE XE 2022 | Question: 55

Fri, 17 Feb 2023 06:51:55 +0000

The third peak in the X-ray diffraction pattern of a face-centered cubic crystal is at $2 \theta$ value of $45^{\circ}$, where $2 \theta$ is the angle between the incident and reflected rays.
The wavelength of the monochromatic X-ray beam is $1.54 A^{\circ}$. Considering first-order reflection, the lattice parameter of the crystal is $A^{\circ}$.

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

GATE XE 2022 | Question: 54

Fri, 17 Feb 2023 06:51:55 +0000

A new glass material is developed to minimize the transmission of the light through the window with glass panel of thickness $5 \mathrm{~mm}$. The refractive index of the glass material is $1.5$ and the absorption coefficient can be changed from $0.3 \mathrm{~cm}^{-1}$ to $1 \mathrm{~cm}^{-1}$. In the given range of absorption coefficients, the ratio of the maximum to the minimum fraction of the light coming out of the other side of the glass panel is.

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