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121

GATE Civil 2023 Set 2 | Question: 32
The figure shows a vertical retaining wall with backfill consisting of cohesive-frictional soil and a failure plane developed due to passive earth pressure. The forces acting on the failure wedge are: $P$ as the reaction force between the wall ... that there is no adhesion between the wall and the wedge, identify the most appropriate force polygon for the wedge.

The figure shows a vertical retaining wall with backfill consisting of cohesive-frictional soil and a failure plane developed due to passive earth pressure. The forces ac...

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122

GATE Civil 2023 Set 1 | Question: 7
A group of $9$ friction piles are arranged in a square grid maintaining equal spacing in all directions. Each pile is of diameter $300 \mathrm{~mm}$ and length $7 \mathrm{~m} $ ... $ 60 \%$? $0.582$ $0.486$ $0.391$ $ 0.677$

A group of $9$ friction piles are arranged in a square grid maintaining equal spacing in all directions. Each pile is of diameter $300 \mathrm{~mm}$ and length $7 \mathrm...

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123

GATE Civil 2022 Set 1 | Question: 21
An uncompacted heap of soil has a volume of $10000\: m^{3}$ and void ratio of $1$. If the soil is compacted to a volume of $7500\: m^{3}$, then the corresponding void ratio of the compacted soil is _________________. (round off to one decimal place)

An uncompacted heap of soil has a volume of $10000\: m^{3}$ and void ratio of $1$. If the soil is compacted to a volume of $7500\: m^{3}$, then the corresponding void rat...

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124

GATE Civil 2024 Set 2 | Question: 34
Three vectors $\overrightarrow{\mathrm{p}}, \overrightarrow{\mathrm{q}}$, and $\overrightarrow{\mathrm{r}}$ are given as \[ \begin{array}{c} \overrightarrow{\mathrm{p}}=\hat{\imath}+\hat{\jmath}+\hat{k} \\ \overrightarrow{\mathrm ...

Three vectors $\overrightarrow{\mathrm{p}}, \overrightarrow{\mathrm{q}}$, and $\overrightarrow{\mathrm{r}}$ are given as\[\begin{array}{c}\overrightarrow{\mathrm{p}}=\hat...

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125

GATE Civil 2024 Set 2 | Question: 52
A horizontal curve of radius $1080 \mathrm{~m}$ (with transition curves on either side) in a Broad Gauge railway track is designed and constructed for an equilibrium speed of $70 \mathrm{kmph}$. However, a few years after construction, the Railway Authorities ... the express trains running on this track is $\_\_\_\_\_\_\_$ (rounded off to the nearest integer).

A horizontal curve of radius $1080 \mathrm{~m}$ (with transition curves on either side) in a Broad Gauge railway track is designed and constructed for an equilibrium spee...

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126

GATE Civil 2023 Set 1 | Question: 18
Which of the following statements is/are TRUE for the Refuse-Derived Fuel (RDF) in the context of Municipal Solid Waste (MSW) management? Higher Heating Value (HHV) of the unprocessed MSW is higher than the HHV of RDF processed from the ... made in the powdered form Inorganic fraction of MSW is mostly converted to RDF RDF cannot be used in conjunction with oil

Which of the following statements is/are TRUE for the Refuse-Derived Fuel (RDF) in the context of Municipal Solid Waste (MSW) management? Higher Heating Value (HHV) of th...

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127

GATE Civil 2023 Set 1 | Question: 26
A function $f(x)$, that is smooth and convex-shaped between interval $\left(x_l, x_u\right)$ is shown in the figure. This function is observed at odd number of regularly spaced points. If the area under the function is computed ... will be exactly equal to the actual with the given details, the numerical value of area cannot be obtained using trapezoidal rule

A function $f(x)$, that is smooth and convex-shaped between interval $\left(x_l, x_u\right)$ is shown in the figure. This function is observed at odd number of regularly ...

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128

GATE Civil 2022 Set 1 | Question: 28
A weld is used for joining an angle section $\text{ISA}$ $100 \:mm \times 100\:mm \times 10 \:mm$ to a gusset plate of thickness $15$ $\text{mm}$ to transmit a tensile load. The permissible stress in the angle is $150$ $\text{MPa}$ and the permissible shear stress ... $\text{mm}$ $380$ $\text{mm}$ and $151$ $\text{mm}$ $151$ $\text{mm}$ and $380$ $\text{mm}$

A weld is used for joining an angle section $\text{ISA}$ $100 \:mm \times 100\:mm \times 10 \:mm$ to a gusset plate of thickness $15$ $\text{mm}$ to transmit a tensile lo...

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129

GATE Civil 2022 Set 1 | Question: 30
The correct match between the physical states of the soils given is Group $\text{I}$ and the governing conditions given in Group $\text{II}$ ... $1-Q, 2-S, 3-P, 4-R$ $1-Q, 2-P, 3-R, 4-S$ $1-S, 2-Q, 3-P, 4-R$

The correct match between the physical states of the soils given is Group $\text{I}$ and the governing conditions given in Group $\text{II}$ is$\begin{array}{|c|c|} \hlin...

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130

GATE Civil 2022 Set 1 | Question: 34
Consider the four points $\text{P, Q, R and S}$ shown in the Greenshields fundamental speed-flow diagram. Denote their corresponding traffic densities by $k_{P}, k_{Q}, k_{R},$ and $k_{S}$ ... $k_{Q} > k_{R} > k_{S} > k_{P}$ $k_{Q} > k_{R} > k_{P} > k_{S}$

Consider the four points $\text{P, Q, R and S}$ shown in the Greenshields fundamental speed-flow diagram. Denote their corresponding traffic densities by $k_{P}, k_{Q}, k...

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131

GATE Civil 2024 Set 2 | Question: 4
The function $f(x)=x^{3}-27 x+4,1 \leq x \leq 6$ has Maxima point Minima point Saddle point Inflection point

The function $f(x)=x^{3}-27 x+4,1 \leq x \leq 6$ hasMaxima pointMinima pointSaddle pointInflection point

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132

GATE Civil 2024 Set 1 | GA Question: 5
On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time $12:05:00$ hours to $12: 55: 00$ hours? $51$ $49$ $50$ $55$

On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time $12:05:00$ hours to $12: 55: 00$ ...

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133

GATE Civil 2024 Set 2 | Question: 12
The contact pressure distribution shown in the figure belongs to a rigid footing resting on a cohesionless soil. rigid footing resting on a cohesive soil. flexible footing resting on a cohesionless soil. flexible footing resting on a cohesive soil.

The contact pressure distribution shown in the figure belongs to arigid footing resting on a cohesionless soil.rigid footing resting on a cohesive soil.flexible footing r...

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134

GATE Civil 2022 Set 2 | Question: 35
Let $y$ be a non-zero vector of size $2022 \times 1.$ Which of the following statement(s) is/are $\text{TRUE}?$ $yy^{T}$ is a symmetric matrix. $y^{T}y$ is an eigenvalue of $yy^{T}.$ $yy^{T}$ has a rank of $2022.$ $yy^{T}$ is invertible.

Let $y$ be a non-zero vector of size $2022 \times 1.$ Which of the following statement(s) is/are $\text{TRUE}?$$yy^{T}$ is a symmetric matrix.$y^{T}y$ is an eigenvalue of...

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135

GATE Civil 2022 Set 1 | Question: 32
Henry's law constant for transferring $O_{2}$ from air into water, at room temperature, is $1.3 \dfrac{\text{mmol}}{\text{liter-atm}}$. Given that the partial pressure of $O_{2}$ in the atmosphere is $0.21$ ... (Consider the molecular weight of $O_{2}$ as $32$ $\text{g/mol}$) $8.7$ $0.8$ $198.1$ $0.2$

Henry's law constant for transferring $O_{2}$ from air into water, at room temperature, is $1.3 \dfrac{\text{mmol}}{\text{liter-atm}}$. Given that the partial pressure of...

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136

GATE Civil 2024 Set 2 | Question: 32
A hypothetical multimedia filter, consisting of anthracite particles (specific gravity: $1.50$), silica sand (specific gravity: $2.60$), and ilmenite sand (specific gravity: $4.20$), is to be designed for treating water/wastewater. After backwashing, the ... than $0.64 \mathrm{~mm}$ and diameter of ilmenite particles is slightly less than $0.10 \mathrm{~mm}$.

A hypothetical multimedia filter, consisting of anthracite particles (specific gravity: $1.50$), silica sand (specific gravity: $2.60$), and ilmenite sand (specific gravi...

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137

GATE Civil 2024 Set 2 | GA Question: 6
In the given text, the blanks are numbered $\text{(i)-(iv)}$. Select the best match for all the blanks. Yoko Roi stands $\text{(i)}$ as an author for standing $\text{(ii)}$ as an honorary fellow, after she stood $\text{(iii)}$ ... $\text{(iv)}$ in $\text{(i)}$ out $\text{(ii)}$ down $\text{(iii)}$ by $\text{(iv)}$ for

In the given text, the blanks are numbered $\text{(i)-(iv)}$. Select the best match for all the blanks.Yoko Roi stands $\text{(i)}$ as an author for standing $\text{(ii)}...

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138

GATE Civil 2024 Set 2 | Question: 55
Differential levelling is carried out from point $\text{P(B M}:+200.000 \mathrm{~m})$ to point $\text{R}$. The readings taken are given in the table. Points Staff readings (m) Remarks Back Sight Fore Sight P $(-) 2.050$ BM: $+200.000 \mathrm{~m}$ ... Level (in meters) of the point $\mathrm{R}$ is $\_\_\_\_\_\_\_\_$ (rounded off to $3$ decimal places).

Differential levelling is carried out from point $\text{P(B M}:+200.000 \mathrm{~m})$ to point $\text{R}$. The readings taken are given in the table.PointsStaff readings ...

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139

GATE Civil 2022 Set 2 | Question: 36
Which of the following statements(s) is/are correct? If a linearly elastic structure is subjected to a set of loads, the partial derivative of the total strain energy with respect to the deflection at any point is equal to the load applied at that ... loaded by the $\text{M/EI}$ diagram of the real beam is equal to the corresponding deflection of the real beam.

Which of the following statements(s) is/are correct?If a linearly elastic structure is subjected to a set of loads, the partial derivative of the total strain energy with...

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140

GATE Civil 2022 Set 2 | Question: 47
A pump with an efficiency of $80\%$ is used to draw groundwater from a well for irrigating a flat field of area $108$ hectares. The base period and delta for paddy crop on this field are $120 \; \text{days}$ and $144\; \text{cm},$ respectively. Water application efficiency ... $= 9810 \; \text{N/m}^{3}$)

A pump with an efficiency of $80\%$ is used to draw groundwater from a well for irrigating a flat field of area $108$ hectares. The base period and delta for paddy crop o...

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141

GATE Civil 2022 Set 1 | Question: 3
The hoop stress at a point on the surface of a thin cylindrical pressure vessel is computed to be $30.0\text{ MPa}$. The value of maximum shear stress at this point is $7.5 \text{ MPa}$ $15.0 \text{ MPa}$ $30.0 \text{ MPa}$ $22.5\text{ MPa}$

The hoop stress at a point on the surface of a thin cylindrical pressure vessel is computed to be $30.0\text{ MPa}$. The value of maximum shear stress at this point is$7...

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142

GATE Civil 2024 Set 2 | Question: 2
The statements $\mathrm{P}$ and $\mathrm{Q}$ are related to matrices $\mathbf{A}$ and $\mathbf{B}$, which are conformable for both addition and multiplication. $\text{P}$ ... $\mathrm{P}$ is FALSE and $\mathrm{Q}$ is TRUE Both $\mathrm{P}$ and $\mathrm{Q}$ are FALSE

The statements $\mathrm{P}$ and $\mathrm{Q}$ are related to matrices $\mathbf{A}$ and $\mathbf{B}$, which are conformable for both addition and multiplication...

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143

GATE Civil 2024 Set 2 | Question: 28
A critical activity in a project is estimated to take $15$ days to complete at a cost of Rs. $30,000$. The activity can be expedited to complete in $12$ days by spending a total amount of Rs. $54,000$. Consider the statements $\text{P}$ ... $\mathrm{P}$ and $\mathrm{Q}$ are FALSE $\mathrm{P}$ is FALSE and $\mathrm{Q}$ is TRUE

A critical activity in a project is estimated to take $15$ days to complete at a cost of Rs. $30,000$. The activity can be expedited to complete in $12$ days by ...

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144

GATE Civil 2024 Set 2 | Question: 5
Consider two Ordinary Differential Equations $\text{(ODEs)}$: $\text{P}$: $\frac{d y}{d x}=\frac{x^{4}+3 x^{2} y^{2}+2 y^{4}}{x^{3} y}$ $\mathrm{Q}: \frac{d y}{d x}=\frac{-y^{2}}{x^{2}}$ Which one of the following options is ... $\mathrm{ODE}$. $\mathrm{P}$ is a nonhomogeneous $\mathrm{ODE}$ and $\mathrm{Q}$ is not an exact $\mathrm{ODE}$.

Consider two Ordinary Differential Equations $\text{(ODEs)}$:$\text{P}$: $\frac{d y}{d x}=\frac{x^{4}+3 x^{2} y^{2}+2 y^{4}}{x^{3} y}$$\mathrm{Q}: \frac{d y}{d x}=\frac{-...

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145

GATE Civil 2024 Set 2 | Question: 18
In general, the outer edge is raised above the inner edge in horizontal curves for Highways, Railways, and Taxiways Highways and Railways only Railways and Taxiways only Highways only

In general, the outer edge is raised above the inner edge in horizontal curves forHighways, Railways, and TaxiwaysHighways and Railways onlyRailways and Ta...

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146

GATE Civil 2024 Set 2 | Question: 22
To finalize the direction of a survey, four surveyors set up a theodolite at a station $\mathrm{P}$ and performed all the temporary adjustments. From the station $\mathrm{P}$, each of the surveyors observed the bearing to a tower located at station $Q$ with the same ... $30^{\circ} 30^{\prime} 00^{\prime \prime}$ $30^{\circ} 31^{\prime} 20^{\prime \prime}$

To finalize the direction of a survey, four surveyors set up a theodolite at a station $\mathrm{P}$ and performed all the temporary adjustments. From the station $\mathrm...

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147

GATE Civil 2024 Set 2 | Question: 7
Consider the statements $\text{P}$ and $\text{Q}$. $\text{P}$: In a Pure project organization, the project manager maintains complete authority and has maximum control over the project. $\text{Q}$: A Matrix organization structure facilitates quick response to ... FALSE Both $\text{P}$ and $\text{Q}$ are FALSE $\mathrm{P}$ is FALSE and $\mathrm{Q}$ is TRUE

Consider the statements $\text{P}$ and $\text{Q}$.$\text{P}$: In a Pure project organization, the project manager maintains complete authority and has maximum...

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148

GATE Civil 2023 Set 2 | Question: 36
A delivery agent is at a location $\mathrm{R}$. To deliver the order, she is instructed to travel to location P along straight-line paths of $\mathrm{RC}, \mathrm{CA}, \mathrm{AB}$ and $\mathrm{BP}$ of $5 \mathrm{~km}$ each. The direction of each path is given in the ... $\mathrm{L}=5.0 ; \mathrm{D}=2.5$ $\mathrm{L}=0.0 ; \mathrm{D}=0.0$

A delivery agent is at a location $\mathrm{R}$. To deliver the order, she is instructed to travel to location P along straight-line paths of $\mathrm{RC}, \mathrm{CA}, \m...

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149

GATE Civil 2023 Set 2 | Question: 49
A circular pile of diameter $0.6 \mathrm{~m}$ and length $8 \mathrm{~m}$ was constructed in a cohesive soil stratum having the following properties: bulk unit weight $=19~ \mathrm{kN} / \mathrm{m}^{3}$; angle of internal friction $=0^{\circ}$ ... (round off to one decimal place). [Adopt: Adhesion factor, $\alpha=1.0$ and Bearing capacity factor, $N_{c}=9.0$ ]

A circular pile of diameter $0.6 \mathrm{~m}$ and length $8 \mathrm{~m}$ was constructed in a cohesive soil stratum having the following properties: bulk unit weight $=19...

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150

GATE Civil 2022 Set 1 | Question: 37
In the context of cross-drainage structures, the correct statement(s) regarding the relative positions of a natural drain (stream/river) and an irrigation canal, is/are In an aqueduct, natural drain water goes under the irrigation canal, ... drain water goes under the irrigation canal. In a canal syphon, natural drain water goes through the irrigation canal.

In the context of cross-drainage structures, the correct statement(s) regarding the relative positions of a natural drain (stream/river) and an irrigation canal, is/areIn...

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151

GATE Civil 2024 Set 2 | GA Question: 9
Five cubes of identical size and another smaller cube are assembled as shown in Figure $\text{A}$. If viewed from direction $\text{X}$, the planar image of the assembly appears as Figure $\text{B}$. If viewed from direction $\text{Y}$, the planar image of the assembly (Figure $\text{A}$) will appear as

Five cubes of identical size and another smaller cube are assembled as shown in Figure $\text{A}$. If viewed from direction $\text{X}$, the planar image of the assembly a...

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152

GATE Civil 2024 Set 1 | GA Question: 6
In the given text, the blanks are numbered $\text{(i)-(iv)}$. Select the best match for all the blanks. From the ancient Athenian arena to the modern Olympic stadiums, athletics (i) the potential for a spectacle. The crowd (ii) with bated breath as the ... $\text{(i)}$ holds $\text{(ii)}$ waits $\text{(iii)}$ culminate $\text{(iv)}$ pivots

In the given text, the blanks are numbered $\text{(i)-(iv)}$. Select the best match for all the blanks.From the ancient Athenian arena to the modern Olympi...

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153

GATE Civil 2024 Set 1 | Question: 3
The probability that a student passes only in Mathematics is $\frac{1}{3}$. The probability that the student passes only in English is $\frac{4}{9}$. The probability that the student passes in both of these subjects is $\frac{1}{6}$. The probability that the ... one of these two subjects is $\frac{17}{18}$ $\frac{11}{18}$ $\frac{14}{18}$ $\frac{1}{18}$

The probability that a student passes only in Mathematics is $\frac{1}{3}$. The probability that the student passes only in English is $\frac{4}{9}$. Th...

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154

GATE Civil 2024 Set 2 | Question: 10
A simply supported, uniformly loaded, two-way slab panel is torsionally unrestrained. The effective span lengths along the short span $\text{(x)}$ and long span $\text{(y)}$ directions of the panel are $l_{\mathrm{x}}$ and $l_{\mathrm{y}}$, respectively. The design ... $\left(l_{\mathrm{y}} / l_{\mathrm{x}}\right)^{2}$

A simply supported, uniformly loaded, two-way slab panel is torsionally unrestrained. The effective span lengths along the short span $\text{(x)}$ and long span $\text{(y...

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155

GATE Civil 2023 Set 2 | Question: 43
A beam is subjected to a system of coplanar forces as shown in the figure. The magnitude of vertical reaction at Support $\text{P}$ is ______________________ $\text{N}$ (round off to one decimal place).

A beam is subjected to a system of coplanar forces as shown in the figure. The magnitude of vertical reaction at Support $\text{P}$ is ______________________ $\text{N}$ (...

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156

GATE Civil 2023 Set 1 | Question: 55
Trigonometric levelling was carried out from two stations $\mathrm{P}$ and $\mathrm{Q}$ to find the reduced level ($\text{R. L.}$) of the top of hillock, as shown in the table. The distance between Stations $\mathrm{P}$ and $\mathrm{Q}$ is $55 \mathrm{~m}$. ...

Trigonometric levelling was carried out from two stations $\mathrm{P}$ and $\mathrm{Q}$ to find the reduced level ($\text{R. L.}$) of the top of hillock, as shown in the ...

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157

GATE Civil 2022 Set 2 | Question: 34
A single-lane highway has a traffic density of $40 \; \text{vehicle/km}.$ If the time-mean speed and space-mean speed are $40 \; \text{kmph}$ and $30 \; \text{kmph},$ respectively, the average headway $\text{(in seconds)}$ between the vehicles is $3.00$ $2.25$ $8.33 \times 10^{-4}$ $6.25 \times 10^{-4}$

A single-lane highway has a traffic density of $40 \; \text{vehicle/km}.$ If the time-mean speed and space-mean speed are $40 \; \text{kmph}$ and $30 \; \text{kmph},$ res...

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158

GATE Civil 2022 Set 1 | Question: 8
Let $\sigma _{v}^{'}$ and $\sigma _{h}^{'}$ denote the effective vertical stress and effective horizontal stress, respectively. Which one of the following conditions must be satisfied for a soil element to reach the failure state under Rankine's passive earth pressure ... $\sigma _{v}^{'} + \sigma _{h}^{'} = 0$

Let $\sigma _{v}^{'}$ and $\sigma _{h}^{'}$ denote the effective vertical stress and effective horizontal stress, respectively. Which one of the following conditions must...

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159

GATE Civil 2024 Set 1 | GA Question: 7
Three distinct sets of indistinguishable twins are to be seated at a circular table that has $8$ identical chairs. Unique seating arrangements are defined by the relative positions of the people. How many unique seating arrangements are possible such that each person is sitting next to their twin? $12$ $14$ $10$ $28$

Three distinct sets of indistinguishable twins are to be seated at a circular table that has $8$ identical chairs. Unique seating arrangements are defined ...

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160

GATE Civil 2022 Set 2 | Question: 42
A uniform rod $KJ$ of weight $w$ shown in the figure rests against a frictionless vertical wall at the point $K$ and a rough horizontal surface at point $J.$ It is given that $w = 10 \; \text{kN}, a = 4 \; \text{m}$ ... of static friction that is required at the point $J$ to hold the rod in equilibrium is _________. (round off to three decimal places)

A uniform rod $KJ$ of weight $w$ shown in the figure rests against a frictionless vertical wall at the point $K$ and a rough horizontal surface at point $J.$ It is given ...

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