GATE 2024 Question Paper for Textile Engineering and Fibre Science (TF)

GATE
2024
Question Paper | Answer Key
Graduate Aptitude Test in Engineering
(GATE) is a prestigious national-level exam
that assesses candidates for
comprehensive understanding in various
undergraduate-level subjects in
Engineering, Technology, Science,
Architecture, and Humanities.

General Aptitude (GA)
Q.1 – Q.5 Carry ONE mark Each

Q.1 If ‘→’ denotes increasing order of intensity, then the meaning of the words

[dry → arid → parched] is analogous to [diet → fast → ________ ].

Which one of the given options is appropriate to fill the blank?

(A) starve

(B) reject

(C) feast

(D) deny

Q.2 If two distinct non-zero real variables 𝑥 and 𝑦 are such that (𝑥 + 𝑦) is proportional
𝑥
to (𝑥 − 𝑦) then the value of
𝑦

(A) depends on 𝑥𝑦

(B) depends only on 𝑥 and not on 𝑦

(C) depends only on 𝑦 and not on 𝑥

(D) is a constant

Page 1 of 34

Q.3 Consider the following sample of numbers:

9, 18, 11, 14, 15, 17, 10, 69, 11, 13

The median of the sample is

(A) 13.5

(B) 14

(C) 11

(D) 18.7

Q.4 The number of coins of ₹1, ₹5, and ₹10 denominations that a person has are in the
ratio 5:3:13. Of the total amount, the percentage of money in ₹5 coins is

(A) 21%

(B) 2
14 7%

(C) 10%

(D) 30%

Page 2 of 34

Q.5 For positive non-zero real variables 𝑝 and 𝑞, if

log (𝑝2 + 𝑞 2 ) = log 𝑝 + log 𝑞 + 2 log 3 ,

𝑝4 +𝑞4
then, the value of is
𝑝2 𝑞 2

(A) 79

(B) 81

(C) 9

(D) 83

Page 3 of 34

Q.6 – Q.10 Carry TWO marks Each

Q.6 In the given text, the blanks are numbered (i)−(iv). Select the best match for all the
blanks.

(i) (ii)
Steve was advised to keep his head before heading to bat;
(iii)
for, while he had a head batting, he could only do so with a cool head
(iv)
s his shoulders.

(A) (i) down (ii) down (iii) on (iv) for

(B) (i) on (ii) down (iii) for (iv) on

(C) (i) down (ii) out (iii) for (iv) on

(D) (i) on (ii) out (iii) on (iv) for

Page 4 of 34

Q.7 A rectangular paper sheet of dimensions 54 cm × 4 cm is taken. The two longer
edges of the sheet are joined together to create a cylindrical tube. A cube whose
surface area is equal to the area of the sheet is also taken.

Then, the ratio of the volume of the cylindrical tube to the volume of the cube is

(A) 1/π

(B) 2/π

(C) 3/π

(D) 4/π

Page 5 of 34

Q.8 The pie chart presents the percentage contribution of different macronutrients to a
typical 2,000 kcal diet of a person.

Macronutrient energy contribution

Trans
fat
5%
Saturated fat
20% Carbohydrates
35%

Unsaturated fat
20%
Proteins
20%

The typical energy density (kcal/g) of these macronutrients is given in the table.

Macronutrient Energy density (kcal/g)
Carbohydrates 4
Proteins 4
Unsaturated fat 9
Saturated fat 9
Trans fat 9

The total fat (all three types), in grams, this person consumes is

(A) 44.4

(B) 77.8

(C) 100

(D) 3,600

Page 6 of 34

Q.9 A rectangular paper of 20 cm × 8 cm is folded 3 times. Each fold is made along the
line of symmetry, which is perpendicular to its long edge. The perimeter of the final
folded sheet (in cm) is

(A) 18

(B) 24

(C) 20

(D) 21

Q.10 The least number of squares to be added in the figure to make AB a line of
symmetry is

(A) 6

(B) 4

(C) 5

(D) 7

Page 7 of 34

Q.11 – Q.35 Carry ONE mark Each

Q.11 The approximate value of the integral
3
𝑑𝑥
∫
𝑥
2

using Simpson’s rule with ℎ = 0.5 is

(A) 0.12

(B) 0.19

(C) 0.41

(D) 0.58

Page 8 of 34

Q.12 The differential equation

𝑑𝑦 𝑀(𝑥, 𝑦)
=
𝑑𝑥 𝑁(𝑥, 𝑦)

is exact if

(A) 𝜕𝑀 𝜕𝑁
=
𝜕𝑦 𝜕𝑥

(B) 𝜕𝑀 𝜕𝑁
=
𝜕𝑥 𝜕𝑦

(C) 𝜕𝑀 𝜕𝑁
+ =0
𝜕𝑦 𝜕𝑥

(D) 𝜕𝑀 𝜕𝑁
× =0
𝜕𝑦 𝜕𝑥

Page 9 of 34

Q.13 The value of the integral
∞
𝑑𝑥
∫
𝑒 𝑥 + 𝑒 −𝑥
0

is

(A) 0

(B) 𝜋
4

(C) 𝜋
2

(D) 𝜋

Q.14 Amongst the following polymers, the one with the lowest glass transition
temperature is

(A) Polyethylene

(B) Polypropylene

(C) Polystyrene

(D) Poly(ethylene terephthalate)

Page 10 of 34

Q.15 Amongst the following fibre forming polymers, the one which is synthesised by
chain growth polymerisation is

(A) Poly(ethylene terephthalate)

(B) Nylon 6,6

(C) Polyacrylonitrile

(D) Poly(p-phenylene terephthalamide)

Q.16 The purpose of opening in blowroom is

(A) Individualisation of fibres in tufts

(B) Parallelisation of fibres in tufts

(C) Separation of short fibres from tufts

(D) Creation of more voluminous tufts

Page 11 of 34

Q.17 Amongst the following, forward as well as reverse rotary motion in cotton combing
is given to

(A) Feed roller

(B) Cylinder comb

(C) Detaching rollers

(D) Drawing rollers in comber drawbox

Q.18 A circular weft knitting machine with 24 inch gauge and 20 inch diameter needle
bed is used to make a tubular knitted fabric. If the fabric shrinks by 35 % in course-
wise direction upon withdrawal from the machine, the circumference (inch) of the
shrunk tubular fabric is approximately

(A) 40.9

(B) 56.2

(C) 68.6

(D) 72.2

Page 12 of 34

Q.19 A winder operates at 750 m/min with 93 % efficiency. Time (min) taken for the
winder to wind 1.2 kg of 20 tex yarn is approximately

(A) 68

(B) 74

(C) 86

(D) 90

Q.20 With reference to Shirley stiffness tester, the relationship between the fabric
bending length (C) and the overhanging length (L) at the standard angle of
deflection of 41.5° is approximately

(A) C = 0.25 L

(B) C = 0.5 L

(C) C=L

(D) C=2L

Page 13 of 34

Q.21 An evenness tester, working on capacitance principle, provides

(A) Mass per unit length of yarn

(B) Standard deviation of mass per unit length of yarn

(C) Coefficient of variation of mass per unit length of yarn

(D) Coefficient of variation of diameter of yarn

Q.22 Amongst the following, the chemical used for bleaching of cotton fabric in acidic
medium is

(A) NaClO2

(B) NaOCl

(C) NaClO3

(D) MgCl2

Page 14 of 34

Q.23 In a discharge printing process, two dyes of different colours, one with high
dischargeability (HD) and another with low dischargeability (LD), are to be
considered. The correct statement regarding the selection of dyes is

(A) LD can be used only as illuminant colour but HD cannot be used either as ground
or as illuminant colour

(B) HD can be used only as ground colour but LD cannot be used either as ground or
as illuminant colour

(C) LD can be used only as ground colour and HD can be used only as illuminant colour

(D) HD can be used only as ground colour and LD can be used only as illuminant colour

Q.24 Amongst the following, the nitrogen containing fibre(s) is/are

(A) Nylon 6

(B) Kevlar

(C) Acrylic

(D) Polyester

Page 15 of 34

Q.25 As the package builds up in a roving frame, the component(s) whose speed DOES
NOT remain constant, amongst the following, is/are

(A) Spindle

(B) Bobbin

(C) Bobbin rail

(D) Drafting rollers

Q.26 Amongst the following, the correct condition(s) that will reduce bumping during
weaving is/are

(A) Higher warp tension

(B) Reduction in sweep of the sley

(C) Higher pick density

(D) Reduction of shed height

Page 16 of 34

Q.27 With reference to the principles of yarn hairiness measurement, the correct
statement(s), amongst the following, is/are

(A) Light scattering principle is used to measure length of hairs

(B) Light scattering principle is used to measure number of hairs

(C) Photocells are used to measure length of hairs

(D) Photocells are used to measure number of hairs

Q.28 A fluorocarbon-based soil release finish consists of alternating hydrophobic blocks
and hydrophilic blocks arranged side by side on fabric surface. The correct
statement(s) amongst the following is/are

(A) In dry state, the hydrophobic blocks shield the hydrophilic blocks to repel soil

(B) During washing, the hydrophilic blocks swell and facilitate release of soil

(C) In dry state, the hydrophilic blocks shield the hydrophobic blocks to repel soil

(D) During washing, the hydrophobic blocks swell and facilitate release of soil

Page 17 of 34

Q.29 If 𝑔(𝑥) is a continuous function such that
𝑏

∫ 𝑔(𝑥)𝑑𝑥 = 𝛽
𝑎
then the correct statement(s), amongst the following, is/are

(A) 𝑏+1

∫ 𝑔(𝑥 − 1)𝑑𝑥 = 𝛽
𝑎+1

1−𝑏
(B) 2

∫ 2 𝑔(1 − 2𝑥)𝑑𝑥 = 𝛽
1−𝑎
2

(C) 𝑏−𝑎

∫ 𝑔(𝑥 + 𝑎)𝑑𝑥 = 𝛽
0

(D) 𝑎−𝑏

∫ 𝑔(𝑎 − 𝑥)𝑑𝑥 = 𝛽
0

Page 18 of 34

Q.30 A continuous random variable X has the following probability density function

𝑘𝑥 2 (1 − 𝑥 3 ), 0 ≤ 𝑥 ≤ 1
𝑓(𝑥) = {
0, elsewhere

If mean of X is 0.64, then the value of k (rounded off to 2 decimal places) is
_________________.

Q.31 Poly(ethylene terephthalate) has a number average molecular weight of 25000. The
degree of polymerisation (rounded off to the nearest integer) is
__________________.

Q.32 A cotton yarn of 20 tex count is replaced by a polyester yarn such that both the yarns
have same diameter and same packing density. Assuming densities of cotton and
polyester fibres as 1.52 g/cm3 and 1.38 g/cm3, respectively, the count (tex) of the
polyester yarn (rounded off to 2 decimal places) is ______________________.

Q.33 A knitted fabric is prepared from a yarn of 15 tex count. The fabric has 16
courses/cm, 17 wales/cm and 2.6 mm loop length. The areal density (g/m2) of the
fabric (rounded off to the nearest integer) is _________________.

Q.34 A 59.05 Ne cotton yarn, a 20 tex polyester/cotton blended yarn and a 90 denier
polyester filament are twisted together to obtain a 3-ply yarn. Assuming there is no
twist contraction, the resultant count (Ne) of the 3-ply yarn (rounded off to 2
decimal places) is _________________.

Page 19 of 34

Q.35 One kg bone-dry cotton fabric is padded with water to obtain 80 % wet pick up. The
temperature of the wet fabric after padding is 30 oC. Assume the specific heat of
water to be 1 cal/(goC); the latent heat of evaporation of water to be 540 cal/g and
the specific heat of cotton to be 0.3 cal/(goC). The energy (kcal) required to dry the
fabric completely (in integer) is ______________________.

Page 20 of 34

Q.36 – Q.65 Carry TWO marks Each

Q.36 The three eigenvalues of the matrix

−2 𝑥 −3
[ 2 1 −6 ]
−1 −2 𝑦

are 1 = 5 and 2 = 3 = −3. The value of 𝑥 is

(A) −2

(B) 0

(C) 2

(D) 4

Q.37 A scientist wants to find the root of the equation 2𝑥 3 + 𝑥 2 − 1 = 0 lying in (0,1).
He applies Secant method only once by taking two initial guesses 0.5 and 0.7. The
value of the root is approximately

(A) 0.17

(B) 0.52

(C) 0.65

(D) 0.75

Page 21 of 34

Q.38 Determine the correctness or otherwise of the following Assertion [a] and
Reason [r]:

[a]: Nylon 6 should be thoroughly dried before melt spinning

[r]: The glass transition temperature of Nylon 6 decreases in presence of moisture

(A) Both [a] and [r] are true and [r] is the correct reason for [a]

(B) Both [a] and [r] are true and [r] is not the correct reason for [a]

(C) Both [a] and [r] are false

(D) [a] is true but [r] is false

Q.39 Determine the correctness or otherwise of the following Assertion [a] and
Reason [r]:

[a]: Cotton does not exhibit melting behaviour when exposed to flame

[r]: Cotton is not crystalline enough to exhibit melting behaviour

(A) Both [a] and [r] are true and [r] is the correct reason for [a]

(B) Both [a] and [r] are true and [r] is not the correct reason for [a]

(C) Both [a] and [r] are false

(D) [a] is true but [r] is false

Page 22 of 34

Q.40 Amongst the different zones in a carding machine, if

P = draft between feed roller and taker-in

Q = draft between taker-in and cylinder

R = draft between cylinder and doffer

then the drafts follow the order

(A) Q<R<P

(B) Q<P<R

(C) R<Q<P

(D) R<P<Q

Page 23 of 34

Q.41 Group I lists yarn manufacturing technologies and Group II contains typical
structural features of the yarns. Match the manufacturing technology with the
structural features of the yarn.

Group I Group II

P. Rotor spinning 1. Twistless parallel fibres in core and helically
arranged filament on surface

Q. Air-jet spinning 2. Helically twisted core and distinct wrappers on
surface

R. Wrap spinning 3. Multifilament core covered by staple fibres stuck
to molten polymer

S. Bobtex spinning 4. Twistless core wrapped regularly and helically
by thin fibre ribbons

(A) P-1, Q-3, R-4, S-2

(B) P-1, Q-4, R-3, S-2

(C) P-2, Q-4, R-1, S-3

(D) P-2, Q-1, R-4, S-3

Page 24 of 34

Q.42 Group I lists weaving machine related parameters and Group II contains the
shortcomings of these parameters. Match the machine related parameter with its
shortcoming.

Group I Group II

P. Variable heald staggering 1. Not favourable for heavy fabric

Q. High eccentricity ratio 2. Reduction in shed height

R. Fixed heald staggering 3. Reduction of sley dwell

S. Late shedding 4. Higher vibration in weaving machine

(A) P-1, Q-3, R-2, S-4

(B) P-1, Q-3, R-4, S-2

(C) P-3, Q-4, R-2, S-1

(D) P-3, Q-4, R-1, S-2

Page 25 of 34

Q.43 Determine the correctness or otherwise of the following Assertion [a] and
Reason [r]:

[a]: The variability of fibre diameter in melt-blown nonwoven fabric is remarkably
higher than that in spunbond nonwoven fabric

[r]: Hot air attenuation in melt-blown process is responsible for high variation in
fibre diameter

(A) Both [a] and [r] are true and [r] is the correct reason for [a]

(B) Both [a] and [r] are true and [r] is not the correct reason for [a]

(C) Both [a] and [r] are false

(D) [a] is true but [r] is false

Q.44 A print paste for pigment printing of cotton fabric is prepared by using a synthetic
thickener. The suitable chemical, amongst the following, to build the viscosity of
the print paste is

(A) HCOOH

(B) NH4OH

(C) CH3COOH

(D) MgCl2

Page 26 of 34

Q.45 Consider the following diagram where an oil droplet is formed on a fabric immersed
in water. At equilibrium, the balance of various interfacial forces acting on the
droplet is given by the following equation

𝛾𝐹𝑊 = 𝛾𝐹𝑂 + 𝛾𝑂𝑊 𝑐𝑜𝑠𝜃

When a surfactant is added to water, assuming that 𝛾𝑂𝑊 and 𝛾𝐹𝑂 remain unchanged,
the following happens

(A) 𝛾𝐹𝑊 decreases and the oil droplet tends to become rounder

(B) 𝛾𝐹𝑊 increases and the oil droplet tends to become flatter

(C) 𝛾𝐹𝑊 decreases and the oil droplet tends to become flatter

(D) 𝛾𝐹𝑊 increases and the oil droplet tends to become rounder

Q.46 Polymer melt flowing through a capillary exhibits die-swell. The correct
statement(s), amongst the following, is/are

(A) Die-swell is due to entropic effect

(B) Die-swell is dependent on capillary length

(C) Die-swell is independent of processing temperature

(D) Die-swell is dependent on shear rate

Page 27 of 34

Q.47 Amongst the given options, the spinning technology(ies) in which the concept of
spinning triangle exists is/are

(A) Ring spinning

(B) Rotor spinning

(C) Friction spinning

(D) Compact spinning

Q.48 Consider the following equation

𝐶 = 𝐶1 + 𝐶2 − 𝐶1 𝐶2

where 𝐶 stands for fractional cover of a fabric, 𝐶1 denotes the fractional cover of
warp and 𝐶2 refers to the fractional cover of weft. Amongst the given options, the
fabric structure(s) in which the aforesaid equation is valid is/are

(A) Plain woven fabric

(B) Double cloth

(C) Terry fabric

(D) Leno fabric

Page 28 of 34

Q.49 With reference to the KES FB-1 system, the correct statement(s) amongst the
following is/are

(A) Tensile strain is measured by angle of drum rotation

(B) Tensile strain is measured by crosshead movement

(C) Tensile force is measured by tensile load cell

(D) Tensile force is measured by torque sensor

Q.50 With reference to cotton fibre testing systems, the correct statement(s) amongst the
following is/are

(A) Image processing principle is used to measure nep count in HVI

(B) Image processing principle is used to measure trash count in HVI

(C) Air flow principle is used to measure fibre fineness in HVI

(D) Air flow principle is used to measure fibre fineness in AFIS

Page 29 of 34

Q.51 Amongst the given options, the condition(s) which will increase the equilibrium
wicking height of water in a yarn is/are

(A) Higher contact angle between fibre and water

(B) Lower contact angle between fibre and water

(C) Higher capillary diameter

(D) Lower capillary diameter

Q.52 Consider the following equilibrium dyeing isotherms for dyeing of polyester with a
disperse dye at 100 oC and 120 oC. Amongst the following, the correct statement(s)
is/are

(A) Rate of dyeing at 100 oC is higher than that at 120 oC

(B) Saturation dye-uptake at 120 oC is higher than that at 100 oC

(C) Dye solubility at 120 oC is higher than that at 100 oC

(D) Dye solubility at 120 oC is lower than that at 100 oC

Page 30 of 34

Q.53 Amongst the following, the property(ies) of a disperse dye that allow(s) it to be
applied on polyester by thermofixation method is/are

(A) Sublimation tendency

(B) High extinction coefficient

(C) Low extinction coefficient

(D) High molecular weight

Q.54 Consider the following function

𝑘, 𝑥=1
𝑓(𝑥) = {
√3𝑥 + 1 − √2𝑥 + 2 1
, 𝑥 > − ,𝑥 ≠ 1
𝑥−1 3
If 𝑓(𝑥) is continuous at 𝑥 = 1, the value of 𝑘 (correct up to 2 decimal places)
is__________________.

Q.55 A textile company decides to find the coefficient of correlation (r) between fibre
quality (𝑋) and yarn quality (𝑌). The company randomly selects 10 samples and
observes the following: ∑ 𝑋 = 50, ∑ 𝑌 = 40, ∑ 𝑋 2 = 260, ∑ 𝑌 2 = 228,
∑ 𝑋𝑌 = 222 and 𝑟(𝑋, 𝑌) = 0.84. If the correct pairs (𝑋 = 4, 𝑌 = 11) and
(𝑋 = 6, 𝑌 = 9) are taken wrongly as (𝑋 = 6, 𝑌 = 15) and (𝑋 = 4, 𝑌 = 5),
respectively, then the correct value of 𝑟(𝑋, 𝑌) (rounded off to 2 decimal places) is
__________________.

Page 31 of 34

Q.56 Three melt-spun fibre samples A, B and C produced from same polymer under
different conditions are found to have densities 1.10 g/cm3, 1.15 g/cm3 and
1.20 g/cm3, respectively. If the mass fraction based degree of crystallinity (xc)
of A and C is 0.45 and 0.75, respectively, then xc for B (rounded off to 2 decimal
places) is _________________.

Q.57 A 200 m long bone-dry Nylon fibre with circular cross-section and density of
1.2 g/cm3, absorbs 0.003 g moisture. If the moisture content of the fibre becomes
4 % after moisture absorption, then the diameter (µm) of bone-dry Nylon fibre
(rounded off to 1 decimal place) is _________________.

Q.58 A parallel fibre strand of 30 tex count is coming out from the nip of the front
delivery rollers of a ring spinning machine. This strand is given twist to produce a
yarn such that the length of the yarn becomes 0.95 times the length of the parallel
fibre strand. If 600 turns are present in 1 m length of the yarn, then the twist factor
(tpmtex0.5) of the yarn (rounded off to the nearest integer) is _______________.

Q.59 A plied yarn is prepared by twisting two single yarns (A and B). Yarn A has a mean
count of 20 tex and a coefficient of variation (CV) of count of 20 %. Yarn B has a
mean count of 30 tex and a CV of count of 10 %. Neglecting twist contraction during
plying, the CV (%) of the count of the plied yarn (in integer) is
___________________.

Q.60 A plain woven fabric with square construction, prepared from yarns of 0.2 mm
diameter, has a fractional cover of 0.7. The distance (mm) between the two adjacent
ends (rounded off to 2 decimal places) is ________________.

Page 32 of 34

Q.61 Two shuttle looms (A and B), running at same picks per minute, have same mass
of sley and associated system for beat up. The crank radius (r) and the eccentricity
ratio (e) of the looms are

𝑟A = 10 cm; 𝑒A = 0.5; 𝑟B = 6 cm; 𝑒B = 0.4

The ratio of the beat up force of loom A to that of loom B (rounded off to 1 decimal
place) is _________________.

Q.62 A polyester fibre of circular cross-section has density of 1.38 g/cm3 and diameter
of 20 µm. The fineness (denier) of the fibre (rounded off to 1 decimal place) is
_____________________.

Q.63 The relationship between tensile stress (σ) and tensile strain (ε) of a yarn is

σ = 1.5√ε

If the breaking strain of the yarn is 1.2, the work factor of the yarn (rounded off to
2 decimal places) is __________________.

Page 33 of 34

Q.64 A ballistic type impact tester is shown below. The test specimen is connected to the
bob of the pendulum of 10 N weight. The pendulum is released from a height of 1
m from the base, and this results in rupture of test specimen. Considering no
frictional losses and neglecting the weight of the connecting rod, if the work of
rupture of the specimen is 10 Nm, then the total swing angle (degree) that the
pendulum makes during its travel (in integer) is ___________________.

Q.65 A cotton fabric is given crease resist finish with 60 g/L DMDHEU (molecular
weight = 178) aqueous solution by continuous method. The density of the padding
liquor is 1.1 g/cm3 and the wet pick up is 110 %. Assuming that the entire
DMDHEU on the fabric is consumed during cross-linking reaction with cellulose,
the nitrogen content (%) of the finished fabric (rounded off to 2 decimal places) is
____________________.

Page 34 of 34

Entrance Exams
Agricultural Entrance Exams
Architecture Entrance Exam
Arts and Humanities Entrance Exams
Commerce Entrance Examinations
Common Entrance Examinations
Computer Application Entrance Exams
Design Entrance Exams
Education Entrance Exams
Engineering Entrance Exams
Hotel Management Entrance Exams
Law Entrance Exams
MBA Entrance Exams
Media & Journalism Entrance Exams
Medical Entrance Exams
Nursing Entrance Exams
Pharmacy Entrance Exams
Science Entrance Exams
Diploma & Polytechnic
Lateral Entry