GATE Overflow for GATE XE - Recent activity in Polymer Characterization

Edited: GATE XE 2026 | Question: 115

Thu, 02 Apr 2026 08:18:29 +0000

Select the correct option to match the Characterization technique with the Information that is obtained using these techniques.

Characterization technique		Information
$\text{P}$	Differential scanning calorimetry	$\text{I}$	Spherulite size
$\text{Q}$	Infrared spectroscopy	$\text{II}$	Loss modulus
$\text{R}$	Dynamic mechanical thermal analysis	$\text{III}$	Functional groups
$\text{S}$	Optical microscopy	$\text{IV}$	Enthalpy of crystallization

$\text{P-IV ; Q-III ; R-I ; S-II}$
$\text{P-III ; Q-IV ; R-I ; S-II}$
$\text{P-IV ; Q-III ; R-II ; S-I}$
$\text{P-III ; Q-IV ; R-II ; S-I}$

Edited: GATE XE 2026 | Question: 103

Thu, 02 Apr 2026 07:36:40 +0000

For a polydisperse polymer, the viscosity-average molecular weight $\left(\bar{M}_{v}\right)$ becomes equal to the weight-average molecular weight $\left(\bar{M}_{w}\right)$, when the Mark-Houwink constant $a$ is $\_\_\_\_$.

$0.1$
$0.5$
$0.7$
$1.0$

Edited: GATE XE 2026 | Question: 46

Tue, 31 Mar 2026 10:01:36 +0000

Match the material property in Column $\text{I}$ with the measurement technique in Column $\text{II}$.

${\text{Column I}}$		${\text{Column II}}$
$\text{P}$	Electrical conductivity	$1$	UV-Vis spectroscopy
$\text{Q}$	Band gap energy	$2$	4-Probe method
$\text{R}$	Young's modulus	$3$	Differential scanning calorimetry
$\text{S}$	Heat of fusion	$4$	Acoustic measurement

$\mathrm{P} \rightarrow 2 ; \mathrm{Q} \rightarrow 1 ; \mathrm{R} \rightarrow 4 ; \mathrm{S} \rightarrow 3$
$\mathrm{P} \rightarrow 1 ; \mathrm{Q} \rightarrow 2 ; \mathrm{R} \rightarrow 4 ; \mathrm{S} \rightarrow 3$
$\mathrm{P} \rightarrow 2 ; \mathrm{Q} \rightarrow 3 ; \mathrm{R} \rightarrow 4 ; \mathrm{S} \rightarrow 1$
$\mathrm{P} \rightarrow 1 ; \mathrm{Q} \rightarrow 4 ; \mathrm{R} \rightarrow 2 ; \mathrm{S} \rightarrow 3$

Edited: GATE XE 2025 | Question: 129

Mon, 30 Jun 2025 16:02:46 +0000

Titration was used to determine the molar mass of two linear monodisperse polymers $\text{A}$ and $\text{B}$. Both the polymers possess the same repeat unit and contain acid end-groups. First, $10 \: \mathrm{g}$ of polymer A was titrated with $5 \: \mathrm{mL}$ of a $0.1 \: \mathrm{M}$ alkali solution. In a separate experiment, $5 \: \mathrm{ g}$ of polymer $B$ was titrated with $5\: \mathrm{ mL}$ of a $0.1 \: \mathrm{M}$ alkali solution. All of the alkali solution reacted with the acid end-groups present in both polymer $\text{A}$ and polymer $\text{B}$.

The ratio of the molar mass of $\text{A}$ to the molar mass of $\text{B}$ is $\_\_\_\_\_\_\_\_$. (Round off to one decimal place)

Edited: GATE XE 2025 | Question: 128

Mon, 30 Jun 2025 16:00:59 +0000

The density of an amorphous polymer is $0.77 \mathrm{~g} \mathrm{~cm}^{-3}$ and that of its crystalline counterpart is $0.99 \mathrm{~g} \mathrm{~cm}^{-3}$. The density of a semi-crystalline sample of this polymer is found to be $0.88 \mathrm{~g} \mathrm{~cm}^{-3}$.

The degree of crystallinity (on weight basis) of this semi-crystalline sample is $\_\_\_\_\_\_\_\_$. (Round off to two decimal places)

Edited: GATE XE 2025 | Question: 111

Mon, 30 Jun 2025 15:05:55 +0000

Which one of the following permits the direct determination of intrinsic viscosity of a polymer solution for known molecular weight of the polymer?

Flory-Huggins equation
Newton's law of viscosity
Williams-Landel-Ferry equation
Mark-Houwink equation

Recategorized: GATE XE 2022 | Question: 38

Mon, 05 May 2025 12:42:40 +0000

A differential scanning calorimetry $\text{(DSC)}$ experiment tracks the heat flow into or out of a system as a function of temperature. If the experiments given in the options below are performed at 1 atmospheric pressure, then in which case will the DSC thermogram exhibit a spike, either upward or downward?

Heating $10$ mg of pure Cu from $323 \mathrm{~K}$ to $673 \mathrm{~K}$
Cooling pure water from $323 \mathrm{~K}$ to $278 \mathrm{~K}$
Heating pure ice from $263 \mathrm{~K}$ to $284 \mathrm{~K}$
Cooling a Pb-Sn alloy at the eutectic composition from $323 \mathrm{~K}$ to $273 \mathrm{~K}$

Recategorized: GATE XE 2023 | Question: 117

Mon, 05 May 2025 12:16:17 +0000

Q. 127 Polyvinylidine fluoride (PVDF) was quenched from the melt in one case and in the other case, it was slowly cooled from the melt at $10^{\circ} \mathrm{C} / \mathrm{min}$. The percentage crystallinity of the slowly cooled PVDF is $60 \%$. The heat of fusion for the quenched PVDF is $0.5 \Delta H_{m}\left(\Delta H_{m}\right.$ is the heat of fusion for the slowly cooled PVDF), and the heat of fusion for $100 \%$ crystalline PVDF is $100 \mathrm{~J} / \mathrm{g}$. The percentage crystallinity of the quenched PVDF is $\%$. (Answer in integer)

Recategorized: GATE XE 2023 | Question: 119

Mon, 05 May 2025 12:16:10 +0000

Q. 129 A polymer weighing $0.2 \mathrm{~g}$ is dissolved in $100 \mathrm{ml}$ of benzene and has a relative viscosity of 1.5 . The polymer obeys Mark-Houwink equation with constants $\mathrm{a}=0.5$ and $\mathrm{K}=0.001$. The molecular weight of the polymer is $\times 10^{10} \mathrm{~g} / \mathrm{mol}$. (Rounded off to two decimal places)

Recategorized: GATE XE 2023 | Question: 121

Mon, 05 May 2025 12:16:04 +0000

Q. 131
The molar mass distribution of a polymer is
\begin{tabular}{|l|l|}
\hline Number of molecules & Molar mass (g/mol) \\
\hline 100 & 7500 \\
\hline 50 & 5000 \\
\hline
\end{tabular}

The resulting weight average molecular weight of the polymer is $\mathrm{g} / \mathrm{mol}$. (Answer in integer)

Recategorized: GATE XE 2024 | Question: 102

Mon, 05 May 2025 10:54:50 +0000

A certain polymer synthesized in the laboratory shows that all the chains have same number of repeat units $\text{(i.e., same degree of polymerization)}$. The relationship between weight-average $\left(\bar{M}_{w}\right)$, number-average $\left(\bar{M}_{n}\right)$, and $z$-average $\left(\bar{M}_{z}\right)$ molecular weights for this polymer can be expressed as

$\bar{M}_{z}>\bar{M}_{w}>\bar{M}_{n}$
$\bar{M}_{z}=\bar{M}_{w}=\bar{M}_{n}$
${M}_{z}<\bar{M}_{w}<\bar{M}_{n}$
$\bar{M}_{z}>\bar{M}_{w}<\bar{M}_{n}$

Recategorized: GATE XE 2024 | Question: 114

Mon, 05 May 2025 10:54:14 +0000

If a given poly(ethylene) sample with specific volume, $v=1.042 \times 10^{-3} \mathrm{~m}^{3} \mathrm{~kg}^{-1}$ shows:
specific volume of the crystalline fraction, $v_{c}=0.989 \times 10^{-3} \mathrm{~m}^{3} \mathrm{~kg}^{-1}$ and specific volume of the amorphous fraction, $v_{a}=1.160 \times 10^{-3} \mathrm{~m}^{3} \mathrm{~kg}^{-1}$, then the $\%$ crystallinity (based on mass fraction) of the poly(ethylene) sample is _________ $\%$ $\text{(rounded off to the nearest integer)}$.

Recategorized: GATE XE 2024 | Question: 118

Mon, 05 May 2025 10:53:58 +0000

A monodisperse polymer sample of molecular weight $10,000 \mathrm{~g} \mathrm{~mol}^{-1}$ is mixed with another monodisperse sample of the same polymer of molecular weight $50,000 \mathrm{~g} \mathrm{~mol}^{-1}$. The total mass of the mixture is $1,000 \mathrm{~g}$ and the total number of moles of the polymer in the mixture is $0.04$ mol. The weight-average molecular weight $\left(\bar{M}_{w}\right)$ of the polymer mixture is __________ $\mathrm{g} \mathrm{mol}^{-1}$ $\text{(rounded off to the nearest integer)}$.

Recategorized: GATE XE 2024 | Question: 120

Mon, 05 May 2025 10:53:52 +0000

The dilute solution viscometry data for two samples of a polymer with two different molecular weights are shown in the figure, where $\eta_{s p} / c$ has been plotted against $c$. Here, $\eta_{s p}$ is the specific viscosity and $c$ is the mass concentration of the polymer solution. The slopes and intercepts of the plots for both the samples are shown in the figure. The plotted data for both samples are described by the Huggins equation of dilute solution. The value of the Mark-Houwink constant ' $a$ ' for both polymer samples is 0.5 .

The ratio of the viscosity-average molecular weight $\left(\bar{M}_{v}\right)$ of polymer sample 1 to that of polymer sample 2 , i.e., $\left(\bar{M}_{v}\right)_{1} /\left(\bar{M}_{v}\right)_{2}$, is _________ $\text{(rounded off to two decimal places)}$.