GATE Overflow for GATE XE - Recent questions in Polymer Science and Engineering

GATE XE 2026 | Question: 36

Tue, 24 Feb 2026 15:47:34 +0000

Which one of the following polymer processing techniques involves shaping a heated sheet?

Thermoforming
Injection molding
Blow molding
Extrusion

GATE XE 2026 | Question: 39

Tue, 24 Feb 2026 15:46:54 +0000

Which of these methods is/are used for the synthesis of ceramic powders?

Sol-gel
Hydromechanical
Thermomechanical
Hydrothermal

GATE XE 2026 | Question: 46

Tue, 24 Feb 2026 15:46:05 +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

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

GATE XE 2026 | Question: 100

Tue, 24 Feb 2026 15:38:46 +0000

Which one of the following polymerization methods is used for the synthesis of butyl rubber?

Ring opening polymerization
Condensation polymerization
Cationic polymerization
Anionic polymerization

GATE XE 2026 | Question: 101

Tue, 24 Feb 2026 15:38:28 +0000

The stress-strain profiles in the figure were obtained following longitudinal tensile loading for a brittle polymer, glass fibre, and a composite lamina consisting of unidirectional continuous glass fibres and the polymer matrix. Assume that the matrix is free of voids, there is perfect bonding between glass fibres and the matrix, and there are no residual stresses in the composite lamina.

Identify the correct stress-strain profile for the polymer matrix, glass fibre, and their composite lamina from the above figure.

$\mathrm{P}$ - Matrix ; $\mathrm{Q}$ - Glass Fibre ; $\mathrm{R}$ - Composite
$\mathrm{P}$ - Glass fibre ; $\mathrm{Q}$ - Composite ; $\mathrm{R}$ - Matrix
$\mathrm{P}$ - Glass fibre ; $\mathrm{Q}$ - Matrix ; $\mathrm{R}$ - Composite
$\mathrm{P}$ - Composite ; $\mathrm{Q}$ - Glass fibre ; $\mathrm{R}$ - Matrix

GATE XE 2026 | Question: 102

Tue, 24 Feb 2026 15:38:09 +0000

Norrish-Smith effect or Trommsdorff effect during free radical bulk polymerization at high conversion is characterized by $\_\_\_\_$.

increase in rate of polymerization with time due to increase in viscosity
decrease in rate of polymerization with time due to increase in viscosity
decrease in rate of polymerization with time due to reduction in viscosity
increase in rate of polymerization with time due to reduction in viscosity

GATE XE 2026 | Question: 103

Tue, 24 Feb 2026 15:37:50 +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 $\_\_\_\_$.

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

GATE XE 2026 | Question: 104

Tue, 24 Feb 2026 15:37:35 +0000

Which one of the following is NOT a rotational rheometer?

Cone and plate rheometer
Parallel plate rheometer
Capillary rheometer
Cylindrical Couette rheometer

GATE XE 2026 | Question: 105

Tue, 24 Feb 2026 15:36:50 +0000

Select the correct option to match the Product with the most appropriate Processing technique from the table given below:

Product		Processing technique
$\text{P}$	Fibre-reinforced pressure vessel	$1$	Rotomoulding
$\text{Q}$	Overhead water tank	$2$	Thermoforming
$\text{R}$	Blister package for medicine	$3$	Filament winding
$\text{S}$	Plastic carry bag	$4$	Blown film extrusion

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

GATE XE 2026 | Question: 106

Tue, 24 Feb 2026 15:36:45 +0000

Which of the following is/are the most appropriate compatibilizer(s) for the ploypropylene/Nylon $66$ blend?

Maleic anhydride grafted polystyrene
Maleic anhydride grafted polypropylene
Polypropylene-$b$-polystyrene
Glycidyl methacrylate grafted polypropylene

GATE XE 2026 | Question: 108

Tue, 24 Feb 2026 15:35:55 +0000

An insulating polymer is used as a dielectric medium between two capacitor plates. The dielectric constant of the polymer is $5.0$ and the permittivity of vacuum is $8.85 \times 10^{-12} \mathrm{~F} / \mathrm{m}$. The permittivity of the polymer is $\_\_\_\_$ $\times 10^{-12} \mathrm{~F} / \mathrm{m}$ (rounded off to two decimal places).

GATE XE 2026 | Question: 109

Tue, 24 Feb 2026 15:35:53 +0000

Select the correct option to match the Polymer to its Major polymeric constituent from the table given below:

Polymer		Major polymeric constituent
$\text{P}$	Natural rubber	$\text{I}$	Polyisobutylene
$\text{Q}$	Gutta percha	$\text{II}$	Polychloroprene
$\text{R}$	Neoprene	$\text{III}$	trans-$1$, $4$-polyisoprene
$\text{S}$	Butyl rubber	$\text{IV}$	cis-$1$, $4$-polyisoprene

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

GATE XE 2026 | Question: 110

Tue, 24 Feb 2026 15:35:19 +0000

Resol is produced by reaction of $\_\_\_\_\_\_$.

phenol with an excess of formaldehyde in presence of a base catalyst
formaldehyde with an excess of phenol in presence of a base catalyst
phenol with an excess of formaldehyde in presence of an acid catalyst
an equimolar mixture of phenol and formaldehyde at neutral $\text{pH}$

GATE XE 2026 | Question: 111

Tue, 24 Feb 2026 15:35:01 +0000

Select the correct option to match the Polymer to its most suitable Monomer(s) from the table given below:

Polymer		Monomer(s)
$\text{P}$	Poly($p$-phenylene sulfide)	$\text{I}$
$\text{Q}$	Poly(ether sulfone)	$\text{II}$
$\text{R}$	Poly(ether ether ketone)	$\text{III}$
$\text{S}$	Polycarbonate	$\text{IV}$

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

GATE XE 2026 | Question: 112

Tue, 24 Feb 2026 15:34:28 +0000

Select the correct option to match the Compound/Additive to its most suitable Function from the table given below:

Compound/Additive		Function
$\text{P}$	Azocarbonamide	$\text{I}$	Flame retardant
$\text{Q}$	$2$-($2$-hydroxyphenyl)-benzotriazole	$\text{II}$	Coupling agent
$\text{R}$	($3$-Aminopropyl)triethoxysilane	$\text{III}$	Blowing agent
$\text{S}$	Ammonium polyphosphate	$\text{IV}$	UV-absorber

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

GATE XE 2026 | Question: 113

Tue, 24 Feb 2026 15:34:09 +0000

The variation of steady shear viscosity $(\eta)$ of a polymer melt with shear rate $(\dot{\gamma})$ is shown in the figure, where $\dot{\gamma}_{s}$ is the upper limit of the applied shear rate.

Which one of the following figures, labeled $\mathrm{P}, \mathrm{Q}, \mathrm{R}$ and $\mathrm{S}$, shows the most appropriate variation of shear stress $(\tau)$ with shear rate for the same polymer melt?

$\mathrm{P}$
$\mathrm{Q}$
$\mathrm{R}$
$\mathrm{S}$

GATE XE 2026 | Question: 114

Tue, 24 Feb 2026 15:33:50 +0000

Select the correct option to match the Initiator(s) with the Method of polymerization from the table given below:

Initiator(s)		Method of polymerization
$\text{P}$	$\mathrm{BF}_{3} / \mathrm{H}_{2} \mathrm{O}$	$\text{I}$	Anionic polymerization
$\text{Q}$	$n-\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{Li}$	$\text{II}$	Cationic polymerization
$\text{R}$	$\mathrm{FeCl}_{2}$ / $\mathrm{K}_{2}$ $\mathrm{~S}_{2}$ $\mathrm{O}_{8}$	$\text{III}$	Coordination addition
$\text{S}$	Metallocene/methylaluminoxane	$\text{IV}$	Free radical addition polymerization

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

GATE XE 2026 | Question: 115

Tue, 24 Feb 2026 15:33:16 +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

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

GATE XE 2026 | Question: 116

Tue, 24 Feb 2026 15:33:04 +0000

Which of the following options is/are used to plasticize poly(vinyl chloride) (PVC)?

Addition of vinyl acetate comonomer during the synthesis of PVC
Chlorination of PVC
Addition of di-iso-octyl phthalate during processing of PVC
Addition of dicumyl peroxide during processing of PVC

GATE XE 2026 | Question: 117

Tue, 24 Feb 2026 15:33:00 +0000

A certain amount of plasticizer with a glass transition temperature $\left(T_{g}\right)$ of $-50^{\circ} \mathrm{C}$ was added to a polymer to reduce its $T_{g}$ from $70^{\circ} \mathrm{C}$ to $30^{\circ} \mathrm{C}$. Using the Fox equation, the weight fraction of the plasticizer used is $\_\_\_\_\_\_$ (rounded off to two decimal places).

GATE XE 2026 | Question: 119

Tue, 24 Feb 2026 15:32:57 +0000

Equimolar mixture of terephthalic acid and butylene glycol was taken to synthesize a polyester. The reaction was stopped at $99.6 \%$ conversion of the acid monomer. The weight-average molecular weight ( $\bar{M}_{w}$) of the synthesized polyester is $\_\_\_\_$ $\mathrm{g} / \mathrm{mol}$ (rounded off to the nearest integer).

GATE XE 2026 | Question: 120

Tue, 24 Feb 2026 15:32:54 +0000

A viscoelastic polymer is subjected to a constant strain of $0.3$. The behaviour of the polymer follows Maxwell model of linear viscoelasticity. Elastic modulus of the polymer is $5$ $\text{MPa}$ and the relaxation time is $200$ days. The stress in the polymer after $100$ days from the initial application of the strain is $\_\_\_\_\_\_$ $\text{MPa}$ (rounded off to two decimal places).

GATE XE 2026 | Question: 121

Tue, 24 Feb 2026 15:32:48 +0000

A single-screw extruder is operated at $12$ $\mathrm{rpm}$ under open discharge condition (i.e., without a die).

The screw has a diameter of $10$ $\mathrm{cm}$, a distance of $2.5$ $\mathrm{cm}$ between the adjacent flights, a gap of $0.25$ $\mathrm{cm}$ between the screw and the inner wall of the barrel, and a helix angle (i.e., angle between the flights and the plane perpendicular to the screw axis) of $8^{\circ}$.

If the flow of the molten polymer in the metering zone through the extruder is assumed isothermal, Newtonian and incompressible, the volumetric flow rate of the polymer melt is $\_\_\_\_\_\_$ $\mathrm{cm}^{3} / \mathrm{min}$ (rounded off to the nearest integer).

GATE XE 2026 | Question: 132

Tue, 24 Feb 2026 15:29:19 +0000

Match the vitamins in Column I with their respective coenzyme forms listed in Column II.

$$\begin{array}{|ll|ll|} \hline & \textbf{Column I} & & \textbf{Column II} \\ \hline \text{P.} & \text{Vitamin } B_{1} & 1.& \text{Tetrahydrofolate} \\ \hline Q. & \text{Vitamin } B_{2} & 2.& \text{Methylcobalamin} \\
\hline R. & \text{Pantothenic acid} & 3. & \text{Thiamine pyrophosphate} \\ \hline S. & \text{Vitamin } B_{12} & 4. &\text{Flavin adenine dinucleotide} \\ \hline T. & \text{Folic acid} & 5.& \text{Coenzyme A} \\ \hline
\end{array}$$

$\text{P-3; Q-4; R-5; S-2; T-1}$
$\text{P-4; Q-3; R-1; S-5; T-2}$
$\text{P-1; Q-5; R-4; S-2; T-3}$
$\text{P-5; Q-2; R-4; S-3; T-1}$

GATE XE 2026 | Question: 183

Tue, 24 Feb 2026 15:08:41 +0000

A $75$ $\mathrm{kWh}$ electric vehicle battery pack made of lithium-ion batteries has $4,800$ individual cells in a series-parallel combination, with $120$ cells in series. The nominal voltage of the individual cell is $3.7$ $\mathrm{V}$. The capacity in $\mathrm{Ah}$ (rounded off to two decimal places) of the individual cell is $\_\_\_\_$.

A certain polymer synthesized in the laboratory shows that all the chains have the same number

Tue, 03 Jun 2025 02:42:55 +0000

GATE XE 2025 | Question: 54

Sun, 04 May 2025 19:07:13 +0000

Match the detector for a scanning electron microscope $\textsf{(SEM)}$ in $\textbf{Column I}$ with the resulting output in $\textbf{Column II}$.

$\textsf{SE}$: Secondary electrons; $\textsf{BSE}$: Backscattered electrons;

$\textsf{EDS}$: Energy Dispersive Spectroscopy; $\textsf{EBSD}$: Electron Backscatter Diffraction

$\begin{array}{ll} \textbf{Column I} & \textbf{Column II} \\ (P) \text{SE Detector} & (1) \: \text{Elemental composition analysis} \\ (Q) \text{BSE Detector} & (2) \: \text{Kikuchi lines} \\ (R) \text{EDS Detector} & (3) \:\text{Topographic image} \\ (S) \text{EBSD Detector} & (4) \: \text{Compositional contrast image} \end{array}$

$\text{P}-4; \text{Q}-3; \text{R}-1; \text{S}-2$
$\text{P}-2 ; \text{Q}-4 ; \text{R}-1 ; \text{S}-3$
$\text{P}-3; \text{Q}-4; \text{R}-2; \text{S}-1$
$\text{P}-3; \text{Q}-4; \text{R}-1; \text{S}-2$

GATE XE 2025 | Question: 110

Sun, 04 May 2025 19:05:25 +0000

Which one of the following measures of viscosity is dimensionless?

Inherent viscosity
Reduced viscosity
Zero-shear viscosity
Specific viscosity

GATE XE 2025 | Question: 111

Sun, 04 May 2025 19:05:23 +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

GATE XE 2025 | Question: 112

Sun, 04 May 2025 19:05:21 +0000

Under which combination of conditions does the glass transition of a polymer increase?

Increase in molecular weight and increase in plasticizer content
Increase in plasticizer content and decrease in cross-linking
Increase in branching and decrease in inter-chain interactions
Increase in chain length and decrease in plasticizer content

GATE XE 2025 | Question: 113

Sun, 04 May 2025 19:05:18 +0000

In a polymer recycling plant, polymer " $\mathbf{X}$ " was depolymerized by glycolysis in the presence of ethylene glycol and a suitable catalyst. The glycolysis reaction yielded the following compound:

Identify the polymer " $\mathbf{X}$ " from the following options.

Poly(ethylene terephthalate)
Polystyrene
Acrylonitrile butadiene styrene
Poly(vinyl chloride)

GATE XE 2025 | Question: 114

Sun, 04 May 2025 19:05:16 +0000

Polymer " $\mathbf{Z}$ " has a high melting point and it decomposes even before it melts. Hence, it is usually dissolved and subsequently regenerated. Rayon is one such regenerated form. Identify the polymer "$\mathbf{Z}$" from the following options.

Urea formaldehyde
Poly(vinyl carbazole)
Cellulose
Poly(vinyl acetate)

GATE XE 2025 | Question: 115

Sun, 04 May 2025 19:05:14 +0000

Match the Product with the most appropriate Processing Technique employed.

$$\begin{array}{|l|l|l|l|} \hline & \textbf{Product} & & \textbf{Processing Technique} \\ \hline P & \text{Rainboots} & 1 & \text{Blow molding} \\ \hline Q & \text{Disposable plastic cups} & 2 & \text{Calendering} \\ \hline R & \text{Soft drink bottles} & 3 & \text{Rotational molding} \\
\hline S & \text{Flexible films} & 4 & \text{Thermoforming} \\ \hline \end{array}$$

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

GATE XE 2025 | Question: 116

Sun, 04 May 2025 19:05:11 +0000

Crystallization is favored in polymer melts when the chain entanglement is $\_\_\_\_\_$ and only polymers with $\_\_\_\_\_$ molecular arrangement can crystallize.

maximum, ordered
minimum, random
maximum, random
minimum, ordered

GATE XE 2025 | Question: 117

Sun, 04 May 2025 19:05:08 +0000

Match the $\textbf{Polymer}$ with the most suitable $\textbf{Monomer combinations}$ from which it is synthesized.

$\begin{array}{|l|l|l|l|} \hline& \textbf{Polymer} && \textbf{Monomer combinations} \\ \hline P & \text{Polyurethane } & 1 & \text{Maleic acid and propylene glycol } \\
\hline Q & \text{Epoxy } & 2 & \text{Pyromellitic anhydride and } p, p^{\prime} \text{-diamino diphenyl ether} \\ \hline R & \text{Polyimide} & 3 & \text{Epichlorohydrin and bisphenol A} \\ \hline S & \text{Polyester} & 4 & \text{Hexamethylene diisocyanate and tetramethylene glycol } \\ \hline \end{array}$

$\text{P}-4; \text{Q}-3; \text{R}-2; \text{S}-1$
$\text{P}-4; \text{Q}-2; \text{R}-3; \text{S}-1$
$\text{P}-2; \text{Q}-1; \text{R}-4; \text{S}-3$
$\text{P}-2; \text{Q}-3; \text{R}-1; \text{S}-4$

GATE XE 2025 | Question: 118

Sun, 04 May 2025 19:05:04 +0000

Thermoplastic Polyurethane and Polyamide $6$ both contain amide linkages, but when compared to Polyurethane, Polyamide $6$ shows higher melting point due to $\_\_\_\_\_\_\_$.

Higher molecular rigidity
Higher degree of branching
Lower molecular rigidity
Lower degree of crosslinking

GATE XE 2025 | Question: 119

Sun, 04 May 2025 19:05:02 +0000

Injection molding is typically used to make plastic parts. If the pressure at the gate is monitored as a function of time during the injection of a thermoplastic polymer, identify the profile that best describes this event.

$\text{Q}$
$\text{R}$
$\text{P}$
$\text{S}$

GATE XE 2025 | Question: 120

Sun, 04 May 2025 19:05:00 +0000

The 'unperturbed dimension' of the polymer chain is represented as,

$$\left(\overline{r_{o}^{2}}\right)^{1 / 2} \propto \bar{l}(n)^{1 / 2}$$

where,
$\left(\overline{r_{o}^{2}}\right)^{1 / 2}=$ root-mean square end-to-end distance\

$\bar{l}=$ average length of a segment

$n=$ number of segments in the chain

Using the above information, root-mean square end-to-end distance of a branched polyethylene would be $\_\_\_\_\_\_\_\_$ when compared with that of the linear polyethylene of the same molecular weight and the same number of segments.

Same
Higher
Lower
Exactly $\sqrt{2}$ times

GATE XE 2025 | Question: 121

Sun, 04 May 2025 19:04:57 +0000

Choose the option(s) that correctly match(es) the $\textbf{Zones}$ with their typical $\textbf{Functions}$ in an industrial extruder

$$\begin{array}{|l|l|l|l|} \hline & \textbf{Zones} && \textbf{Functions} \\ \hline P & \text{Feed zone} & 1 & \text{The melt acquires a constant flow rate} \\ \hline Q & \text{Compression zone} & 2 & \text{No heating takes place} \\ \hline R & \text{Metering zone} & 3 & \text{Polymer melts due to heat transferred} \\ &&& \text{from the heating element} \\ \hline & & 4 & \text{The helical flight of the screw imparts} \\ &&& \text{constant flow of the melt} \\ \hline & & 5 & \text{Polymer melts due to shear forces} \\ &&& \text{imparted by the screw} \\ \hline \end{array}$$

$\text{P-2; Q-5; R-1}$
$\text{P-2; Q-3; R-4}$
$\text{P-5; Q-1; R-2}$
$\text{P-2; Q-1; R-3}$

GATE XE 2025 | Question: 123

Sun, 04 May 2025 19:04:51 +0000

Which option(s) correctly match(es) the $\textbf{Polymer property}$ with its appropriate $\textbf{Units}$?

$$\begin{array}{|l|l|l|l|}\hline & \textbf{Polymer property} & & \textbf{Units} \\ \hline \text{P} & \text{Hildebrand solubility parameter} & 1 & \mathrm{Pa} \\ \hline \text{Q} & \text{Loss modulus} & 2 & \mathrm{J} \mathrm{m}^{-3} \\ \hline \text{R} & \text{Toughness} & 3 & (\mathrm{MPa})^{1 / 2} \\ \hline \text{S} & \text{Flexural strength} & 4 & \mathrm{Kg} \mathrm{m}^{-1} \mathrm{~s}^{-2} \\ \hline \end{array}$$

$\text{P-2; Q-1; R-3; S-4}$
$\text{P-2; Q-4; R-3; S-1}$
$\text{P-3; Q-1; R-2; S-4}$
$\text{P-3; Q-4; R-2; S-1}$

GATE XE 2025 | Question: 124

Sun, 04 May 2025 19:04:48 +0000

Which option(s) correctly match(es) the $\textbf{Class of additives}$ used during polymer compounding with the corresponding $\textbf{Chemicals}$?

$$\begin{array}{|l|l|l|l|} \hline & \textbf{Class of additives} & & \textbf{Chemicals} \\ \hline \text{P} & \text{Antioxidant} & 1 & \text{Phthalocyanine} \\ \hline \text{Q} & \text{Flame retardant} & 2 & \text{Di(2-ethylhexyl) phthalate} \\ \hline \text{R} & \text{Plasticizer} & 3 & \text{Tricresyl phosphate} \\ \hline \text{S} & \text{Colorant} & 4 & \text{Phenyl } \beta \text{-napthyl amine} \\ \hline \end{array}$$

$\text{P-4; Q-3; R-2; S-1}$
$\text{P-4; Q-3; R-3; S-1}$
$\text{P-1; Q-2; R-4; S-2}$
$\text{P-2; Q-3; R-1; S-2}$

GATE XE 2025 | Question: 125

Sun, 04 May 2025 19:04:45 +0000

In a set of copolymerization reactions, the following monomer reactivity ratios ($\textbf{r 1}$ and $\textbf{r 2}$) were found for different cases.

$$\begin{array}{|c|c|c|} \hline \textbf{Case} & \textbf{r1} &\textbf{r2} \\
\hline \text{I} & 0.1 & 10 \\ \hline \text{II} & 0.003 & +0.02 \\ \hline \text{III} & 3.4 & 5.6 \\ \hline \text{IV} & 51 & 0.01 \\ \hline
\end{array}$$

Which option(s) correctly identify/identifies the type of copolymerization corresponding to each $\textbf{Case}$?

$\text{I}$ - Ideal copolymerization
$\text{II}$ - Azeotropic copolymerization
$\text{III}$ - Block copolymerization
$\text{IV}$ - Alternating copolymerization

GATE XE 2025 | Question: 126

Sun, 04 May 2025 19:04:41 +0000

The crystallization of a polymer can only proceed in a temperature range limited to glass transition temperature ( $T_{g}$ ) on the lower side, and the equilibrium melting point $\left(T_{m}^{o}\right)$ on the higher side. Around $T_{g}$, the mobility of the polymer chains is lower, while in the proximity of $T_{m}^{o}$, crystal nucleation is inhibited.

In a miscible polymer blend with only one component being crystalline, which option(s) correctly match(es) the Temperature conditions with Events?

$$\begin{array}{|l|l|l|l|} \hline & \textbf{Temperature conditions} & & \textbf{Events} \\ \hline P & \text{The } T_{g} \text{ of the amorphous} & 1 & \text{The temperature range over} \\ & \text{component is lower than } \\ & \text{which crystallization can occur} \\ & \text{the crystallizable one} && \text{the crystallizable onebecomes smaller} \\ \hline Q & \text{The } T_{g} \text{ of the amorphous} & 2 & \text{Crystallization is inhibited} \\ & \text{component is higher than} \\ & \text{the crystallizable one} \\ \hline R & \text{The blend } T_{g} \text{ is higher than the} & 3 & \text{The crystallization envelope} \\ & (T_{m}^{o} \text{ of the crystalisable one} && (T_{m}^{o}-T_{g}) is widened \\ \hline & & 4 & \text{Crystallization is favored} \\
\hline \end{array}$$

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

GATE XE 2025 | Question: 127

Sun, 04 May 2025 19:04:37 +0000

The heat of polymerization of ethylene is $25 \mathrm{kcal} / \mathrm{mol}$. The amount of heat generated during the polymerization of $5.6$ $\textsf{kg}$ polyethylene is $\_\_\_\_\_\_\_ \: \mathrm{kcal}$. (Round off to the nearest integer)

GATE XE 2025 | Question: 128

Sun, 04 May 2025 19:04:36 +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)

GATE XE 2025 | Question: 129

Sun, 04 May 2025 19:04:34 +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)

GATE XE 2025 | Question: 130

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

A unidirectional composite of a resin is prepared with continuous fibers, wherein the volume fraction of the fiber in the composite is $0.7$. Assume that the resin has a modulus of $9 \: \mathrm{GPa}$ and the fiber has a modulus of $90 \: \mathrm{GPa}$. A sample of this composite, possessing a breadth of $4 \: \mathrm{mm}$ and a thickness of $1 \: \mathrm{ mm}$, is subjected to a uniaxial tensile test along the direction of the fiber.

Corresponding to a strain of $0.5 \%$, the force applied on the sample is $\_\_\_\_\_\_\_ \: \mathrm{N}$. (Round off to the nearest integer)

GATE XE 2025 | Question: 131

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

A rubber contains $70 \mathrm{wt} \%$ butadiene (molar mass $=54 \mathrm{~g} / \mathrm{mol})$, $20 \: \mathrm{wt} \%$ isoprene (molar mass $=68 \mathrm{~g} / \mathrm{mol})$, $5 \: \mathrm{wt} \%$ sulfur and $5 \: \mathrm{wt} \%$ carbon black. Assume that all the sulfur is present in crosslinks.

If each sulfide crosslink contains an average of two sulfur atoms, the percentage of possible crosslinks that are joined by vulcanization is $\_\_\_\_\_ \: \%$. (Round off to one decimal place)

GATE XE 2025 | Question: 144

Sun, 04 May 2025 15:30:34 +0000

Which of the following is the most suitable flexible packaging laminate for dry fruits?

$\textsf{PET/LDPE}$
$\textsf{PS/LDPE}$
$\textsf{BOPP/LDPE}$
$\textsf{Nylon/LDPE}$

GATE XE 2024 | Question: 37

Sun, 21 Jul 2024 16:42:17 +0000

In ball milling of ceramic powder, selection of grinding media depends on the __________ difference between grinding media and powder particles.

thermal conductivity
dielectric constant
hardness
density