GATE Overflow for GATE XE - Questions without answers in Others

GATE XE 2026 | GA | Question: 9

Tue, 24 Feb 2026 16:01:07 +0000

Circles $C_{1}, C_{2}$, and $C_{3}$, with centers $O_{1}, O_{2}$, and $O_{3}$, and radii $r_{1}, r_{2}$, and $r_{3}$, respectively, touch each other as shown in the following figure. Given $r_{1}=2 \mathrm{~cm}$, $r_{2}=1 \mathrm{~cm}$ and the angle $\angle O_{1} O_{3} O_{2}$ is $90^{\circ}, r_{3}=$ $\_\_\_\_$ cm.

$\dfrac{1}{2}(-3+\sqrt{17})$
$\dfrac{1}{2}(3+\sqrt{17})$
$\dfrac{1}{2}(-2+\sqrt{17})$
$\dfrac{1}{2}(-3+2 \sqrt{17})$

GATE XE 2026 | Question: 31

Tue, 24 Feb 2026 15:48:06 +0000

For a steady, laminar, and incompressible flow over a flat plate, the local skin friction coefficient is given as $C_f = \dfrac{0.664}{\sqrt{Re_x}}$ where $\mathrm{Re}_{x}$ is the local Reynolds number. The density and kinematic viscosity of the fluid are $1.2 \mathrm{kg}·\mathrm{m}^{-3}$ and $1.5 \times 10^{-5} \mathrm{m}^{2}·\mathrm{s}{-1}$, respectively. If the freestream velocity is $3$ $\mathrm{m}·{s}^{-1}$, then the local shear stress (in $\mathrm{N}·\mathrm{m}^{-2}$) at $x = 0.05$ $\mathrm{m}$ is ________ (rounded off to three decimal places).

GATE XE 2026 | Question: 54

Tue, 24 Feb 2026 15:45:40 +0000

A circular disk-shaped ceramic green body has a relative density of $50 \%$. On sintering, both the height and the diameter of the disk shrink by $20 \%$. The sintered disk's relative density in $\%$ is $\_\_\_\_$ (rounded off to one decimal place).

GATE XE 2026 | Question: 58

Tue, 24 Feb 2026 15:45:30 +0000

Identify the zero-force member in the truss structure as shown in the figure.

$\text{ST}$
$\text{SR}$
$\text{SP}$
$\text{SQ}$

GATE XE 2026 | Question: 72

Tue, 24 Feb 2026 15:42:54 +0000

A motorized pulley of diameter $200$ mm is used to transfer a block of mass $100$ kg from platform $1$ to platform $2$ using a ramp kept at an inclination of $30^{\circ}$ as shown in the figure. The coefficient of static friction between the block and the ramp is $0.2$. The acceleration due to gravity is $10$ $\mathrm{m}$/ $\mathrm{s}^2$.

Assume the rope to be parallel to the ramp surface.

The minimum torque required by the motor to transport the block uphill is $\_\_\_\_\_$ $\mathrm{Nm}$ (rounded off to two decimal places).

GATE XE 2026 | Question: 141

Tue, 24 Feb 2026 15:24:52 +0000

Hot fluid is being cooled in a countercurrent, double-pipe heat exchanger from $410$ $\mathrm{K}$ to $340$ $\mathrm{K}$ by chilled water entering at $290$ $\mathrm{K}$ and exiting the exchanger at $330$ $\mathrm{K}$. The Log Mean Temperature Difference (LMTD) for this heat transfer is $\_\_\_\_\_\_$ $\mathrm{K}$. (Round off to one decimal place)

GATE XE 2026 | Question: 142

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

A cold-storage room has a double-layered wall. The inner layer is $10$ $\mathrm{cm}$ thick, made of fiber insulation board $(\text{k} = 0.048 \text{W m}^{-1} \text{K}^{-1})$, and the outer layer is $15$ $\mathrm{cm}$ thick, made of concrete $(\text{k} = 0.762 \text{W m}^{-1} \text{K}^{-1})$. The surface temperature of the wall inside the cold room is $260$ $\text{K}$ and the ambient temperature outside is $300$ $\text{K}$. The steady state heat flux into the cold room is $\_\_\_\_\_\_\_\_$ $\text{W/m}^{2}$. (Round off to two decimal places)

GATE XE 2026 | Question: 143

Tue, 24 Feb 2026 15:24:21 +0000

A tubular centrifuge separates $5$ micron particles of density $1500 \mathrm{~kg/m}^{3}$ from a slurry. The slurry is fed at a volumetric flow rate of $0.5 \mathrm{~m}^{3}/s$. The equivalent clarification area of the centrifuge is ________ $\mathrm{~m}^{2}$. (Answer in integer)

Assume $\text{g}=10 \mathrm{~m/s}^{2}$ and for water, density = $1000 \mathrm{~kg/m}^{3}$, coefficient of viscosity $(μ)=10^{-3} \mathrm{~Pa-s}$

GATE XE 2026 | Question: 151

Tue, 24 Feb 2026 15:21:28 +0000

The required magnitude of heat transfer to reduce the temperature of $10$ $\mathrm{kg}$ of dry air by $5^{\circ} \mathrm{~C}$ is __________ kilo Joules. (rounded off to one decimal place)

[Specific heat capacity of dry air is $1004$ $\text{J kg}^{-1} \text{K}^{-1}]$

GATE XE 2026 | Question: 153

Tue, 24 Feb 2026 15:21:11 +0000

In a two-layered fluid system, temperature and salinity values are given for cases $\text{P, Q}$ and $\text{R}$. Which of the following options indicates that the process of 'salt fingering' is likely to occur?

Only $\text{P}$
Only $\text{Q}$
$\text{Q}$ and $\text{R}$
$\text{P}$ and $\text{R}$

GATE XE 2026 | Question: 164

Tue, 24 Feb 2026 15:16:32 +0000

Using the dispersion relation for deep water small amplitude wave, the wavelength (in $\mathrm{m}$) for a $20$ second gravity wave is $\_\_\_\_\_\_\_$. (Answer in integer)

[Take accelaration due to gravity as $9.81$ $\text{m s}^{-2}$]

GATE XE 2026 | Question: 165

Tue, 24 Feb 2026 15:16:17 +0000

A two-layered fluid system in an estuarine environment has a total water depth of $10$ $\mathrm{m}$. The difference in densities between the two layers is $15$ $\text{kg m}^{-3}$ and thickness of the less dense upper layer is $3$ $\mathrm{m}$.

If complete mixing occurs in $3$ hours, then intensity (in $\mathrm{W m}^{-2}$) of mixing process is __________. (rounded off to three decimal places)

[Acceleration due to gravity is $9.81$ $\mathrm{m s}^{-2}$]

GATE XE 2026 | Question: 167

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

Which one of the following biomass treatment processes occurs in an oxygen limited condition approximately between $450^{\circ} \mathrm{~C}$ and $600^{\circ}\mathrm{~C}$, and produces biochar and bio-oil as primary products?

Gasification
Pyrolysis
Anaerobic Digestion
Steam Reforming

GATE XE 2026 | Question: 169

Tue, 24 Feb 2026 15:15:07 +0000

A part of the blowdown energy losses in a boiler can be recovered by which one of the following ways?

Completely avoiding the blowdown
Recycling the blowdown to the steam drum
Flashing the blowdown to generate low-pressure steam
Mixing the blowdown with the boiler feedwater

GATE XE 2026 | Question: 171

Tue, 24 Feb 2026 15:14:17 +0000

Which of the following is/are step(s) followed in energy audit?

Walkthrough
Collection of past energy consumption data
Evaluation of energy conservation measures
Preparation of historic profit and loss statement

GATE XE 2026 | Question: 173

Tue, 24 Feb 2026 15:13:42 +0000

The open circuit voltage, short circuit current, and the fill factor of a solar photovoltaic module are $45 \mathrm{~V}$, $9 \mathrm{~A}$, and $0.8$, respectively. The maximum output power (in Watt) of the solar photovoltaic module is $\_\_\_\_\_$ (Answer in integer)

GATE XE 2026 | Question: 174

Tue, 24 Feb 2026 15:13:27 +0000

Energy is extracted from a fully charged supercapacitor bank and the voltage of this system drops to $25 \%$ of its initial value. The energy extracted with respect to initial energy (in $\%$ rounded off to two decimal places) is ________.

GATE XE 2026 | Question: 175

Tue, 24 Feb 2026 15:13:12 +0000

A grid-connected induction generator is used to generate electricity from a wind turbine. Which one of the following statements is true while the generator is feeding power to the grid?

The slip of the induction generator is zero
The slip of the induction generator is one
The slip of the induction generator is less than zero
The slip of the induction generator is greater than one

GATE XE 2026 | Question: 181

Tue, 24 Feb 2026 15:10:14 +0000

Which of the following statements is/are FALSE concerning a wind turbine generation system?

The rotor power coefficient, $C_{p}$, of a multi-blade turbine is a monotonically increasing function of tip-speed ratio
Maximum power point tracking algorithms are typically employed in wind turbine generators for enhancing energy yield
The theoretical maximum value of rotor power coefficient, $C_{p}$, is $0.65$
Speed control of wind turbine generator is carried out to ensure rotor speed varies in response to wind speed

GATE XE 2026 | Question: 184

Tue, 24 Feb 2026 15:08:40 +0000

A nonlinear load connected to a sinusoidal voltage source (of peak value $V_{m}$ and $50$ $\mathrm{Hz}$ frequency) draws a quasi-square wave shaped current (of maximum value $I_{m}$ ) as shown in the figure below. The power factor of the nonlinear load (rounded off to two decimal places) is $\_\_\_\_$.

GATE XE 2026 | Question: 185

Tue, 24 Feb 2026 15:08:39 +0000

A resident has ₹ $50,000$ to purchase a $5$-star rated air conditioner with a life of $10$ years. The annual energy cost savings (in ₹) needed to recover this investment in $6$ years assuming a discount rate of $10 \%$ per annum is $\_\_\_\_$ (Answer in integer)

GATE XE 2026 | Question: 186

Tue, 24 Feb 2026 15:08:37 +0000

A country’s annual crude oil production in the year $2024$ was $150$ million tons and that in $2022$ was $141$ million tons. The proven crude oil resources in $2024$ of the country are $12,000$ million tons. Consider an exponential growth rate model with a growth rate as compound annual growth rate during $2022–2024$. The crude oil reserve will last for ________ years. (rounded off to nearest integer)

GATE XE 2025 | Question: 60

Sun, 04 May 2025 19:07:01 +0000

An aluminum transmission line of $7 \: \mathrm{km}$ length is designed to carry $100 \: \mathrm{A}$ current with no more than $2 \: \mathrm{MW}$ power loss. The required minimum diameter (in mm ) of the transmission line is (rounded to the two decimal places) $\_\_\_\_\_\_\_$

Given: Aluminum conductivity $=3.77 \times 10^{5} \Omega^{-1} \mathrm{~cm}^{-1}$

GATE XE 2025 | Question: 63

Sun, 04 May 2025 19:06:57 +0000

The slopes of reduction potential versus pH plots for the two reactions, $\mathrm{NiO}+2 \mathrm{H}^{+}+2 \mathrm{e}^{-} \rightleftharpoons \mathrm{Ni}+\mathrm{H}_{2} \mathrm{O}$ and $2 \mathrm{H}^{+}+2 \mathrm{e}^{-} \rightleftharpoons \mathrm{H}_{2}$, at $298 \: \mathrm{K}$ and one atmospheric pressure are $\mathrm{S} 1$ and $\mathrm{S} 2$, respectively. The ratio $\frac{\mathrm{S} 1}{\mathrm{S} 2}$ is (rounded off to one decimal place) $\_\_\_\_\_\_$

GATE XE 2025 | Question: 141

Sun, 04 May 2025 15:30:42 +0000

Identify the gas composition (in percent) suitable for packaging cured meat under $\textsf{MAP}$ conditions.

$\mathrm{O}_{2}=0 ; \mathrm{CO}_{2}=50 ; \mathrm{N}_{2}=50$
$\mathrm{O}_{2}=50 ; \mathrm{CO}_{2}=0 ; \mathrm{N}_{2}=50$
$\mathrm{O}_{2}=0 ; \mathrm{CO}_{2}=0 ; \mathrm{N}_{2}=100$
$\mathrm{O}_{2}=50 ; \mathrm{CO}_{2}=50 ; \mathrm{N}_{2}=0$

GATE XE 2024 | Question: 41

Sun, 21 Jul 2024 16:42:14 +0000

In thermogravimetric analysis (TGA), weight change of a material sample during decomposition with temperature is shown in the figure below.

$\mathrm{W}_{\mathrm{i}}$ and $\mathrm{W}_{\mathrm{f}}$ represent the weight of the material, corresponding to temperatures $T_{i}$ and $T_{f}$, respectively. Which of the following factor(s) can influence $T_{i}$ and $T_{f}$ ?

Heating rate
Particle size of the material
Atmosphere in the sample chamber
Initial weight of the sample

GATE XE 2024 | Question: 54

Sun, 21 Jul 2024 16:42:03 +0000

In X-ray powder diffraction pattern obtained from a face centered cubic $\text{(FCC)}$ metal, the first five reflections are at $\theta=21.65^{\circ}, 25.21^{\circ}, 37.06^{\circ}, \boldsymbol{x}$ and $47.58^{\circ}$. The Bragg angle, $\theta$ of the fourth reflection is missed out and is represented by $\boldsymbol{x}$. The value of $\boldsymbol{x}$ is $\text{(in degree)}$ _________ $\text{(rounded off to one decimal place)}$.

GATE XE 2024 | Question: 65

Sun, 21 Jul 2024 16:41:53 +0000

A $0-45-90$ strain gauge rosette is mounted on an aircraft wing. The co-ordinate system is placed such that the strain gauges $\mathrm{p}, \mathrm{q}$ and r are oriented at angles $0^{\circ}, 45^{\circ}$ and $90^{\circ}$, respectively, from the $x$ axis $\text{(see figure)}$. The strain readings associated to $\mathrm{p}, \mathrm{q}$ and r are denoted by $\varepsilon_{p}, \varepsilon_{q}$, and $\varepsilon_{r}$, respectively. While conducting a test the strain gauges show the following readings.
\[
\varepsilon_{p}=150 \times 10^{-6}, \varepsilon_{q}=180 \times 10^{-6}, \varepsilon_{r}=-90 \times 10^{-6}
\]

The developed engineering shear strain $\gamma_{x y}$ associated to the strain gauge data is

$120 \times 10^{-6}$
$180 \times 10^{-6}$
$300 \times 10^{-6}$
$240 \times 10^{-6}$

GATE XE 2024 | Question: 130

Sun, 21 Jul 2024 16:40:59 +0000

Thermal resistance constant ( $z$-value) is defined as the change in temperature required to reduce the decimal reduction time of a microorganism by _________ percent $\text{(Answer in integer)}$.

GATE XE 2023 | Question: 75

Wed, 14 Feb 2024 18:09:10 +0000

GATE XE 2023 | Question: 81

Wed, 14 Feb 2024 18:09:04 +0000

GATE XE 2023 | Question: 82

Wed, 14 Feb 2024 18:09:03 +0000

GATE XE 2023 | Question: 90

Wed, 14 Feb 2024 18:08:55 +0000

GATE XE 2023 | Question: 105

Wed, 14 Feb 2024 18:08:41 +0000

\begin{tabular}{|l|l|}
Q.115 & \begin{tabular}{l}
Polymer wetting is improved by the addition of fillers with functional groups. In a \\
typical case-study, natural-clay was modified with hydroxyl groups and \\
compounded with Nylon 6 along with an antioxidant. The resulting composite \\
exhibited poor mechanical properties. Which one among the options given \\
explains this observation?
\end{tabular} \\
\hline

& The surface functional groups of the filler reacted with Nylon 6 \\
\hline
& The antioxidant degraded during the processing \\
\hline
& \begin{tabular}{l}
The surface functional groups of the filler formed hydrogen bonds with the \\
antioxidant
\end{tabular} \\
\hline
& The antioxidant reacted with Nylon 6 \\
\hline
\end{tabular}

GATE XE 2023 | Question: 128

Wed, 14 Feb 2024 18:08:20 +0000

Q. 138 Calculate the efficiency in percent (rounded off to 1 decimal place) of an oil expeller which yields $37 \mathrm{~kg}$ oil containing $5 \%$ solid impurities from $100 \mathrm{~kg}$ mustard seeds. The oil content of the mustard seed is $38 \%$.

GATE XE 2023 | Question: 130

Wed, 14 Feb 2024 18:08:18 +0000

Q. 140 The weight of $10 \mathrm{~kg}$ dried cauliflower containing 5\% moisture (wet basis) after rehydration is $60 \mathrm{~kg}$. If the fresh cauliflower contained $87 \%$ moisture (wet basis), calculate the coefficient of rehydration (rounded off to 2 decimal places).

GATE XE 2023 | Question: 138

Wed, 14 Feb 2024 18:08:10 +0000

GATE XE 2023 | Question: 143

Wed, 14 Feb 2024 18:08:05 +0000

Q. 153 Cow milk is pasteurized at a flow rate of $1 \mathrm{~kg} . \mathrm{s}^{-1}$ in a counter-current heat exchanger using hot water as the heating medium. The milk enters the heat exchanger at $15^{\circ} \mathrm{C}$ and exits at $50^{\circ} \mathrm{C}$. The specific heat of cow milk is $3.5 \mathrm{~kJ} . \mathrm{kg}^{-}$ ${ }^{1} .{ }^{\circ} \mathrm{C}^{-1}$ and remains constant at the inlet and exit of the heat exchanger. The inlet and exit temperatures of the hot water are $75^{\circ} \mathrm{C}$ and $60^{\circ} \mathrm{C}$ respectively. If the overall heat transfer coefficient is $1800 \mathrm{~W} \cdot \mathrm{m}^{-2} .{ }^{\circ} \mathrm{C}^{-1}$, the heat transfer surface area in $\mathrm{m}^{2}$ is (rounded off to 2 decimal places). Assume steady state conditions.

GATE XE 2022 | Question: 32

Fri, 17 Feb 2023 06:52:14 +0000

GATE XE 2022 | Question: 33

Fri, 17 Feb 2023 06:52:13 +0000