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41

GATE Civil 2024 Set 2 | Question: 38
Consider two matrices $\mathbf{A}=\left[\begin{array}{lll}2 & 1 & 4 \\ 1 & 0 & 3\end{array}\right]$ and $\mathbf{B}=\left[\begin{array}{cc}-1 & 0 \\ 2 & 3 \\ 1 & 4\end{array}\right]$. The determinant of the matrix $\mathbf{AB}$ is $\_\_\_\_\_\_\_$ (in integer).

Consider two matrices $\mathbf{A}=\left[\begin{array}{lll}2 & 1 & 4 \\ 1 & 0 & 3\end{array}\right]$ and $\mathbf{B}=\left[\begin{array}{cc}-1 & 0 \\ 2 & 3 \\ 1 & 4\end{ar...

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42

GATE Civil 2024 Set 2 | Question: 26
In a sample of $100$ heart patients, each patient has $80 \%$ chance of having a heart attack without medicine $\mathrm{X}$. It is clinically known that medicine $\mathrm{X}$ reduces the probability of having a heart attack by $50 \%$. Medicine $\text{X}$ is ... $\mathrm{X}$ and has a heart attack is $40 \%$ $60 \%$ $20 \%$ $30 \%$

In a sample of $100$ heart patients, each patient has $80 \%$ chance of having a heart attack without medicine $\mathrm{X}$. It is clinically known that medicine $\mathrm...

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43

GATE Civil 2024 Set 2 | Question: 16
Which one of the following products is NOT obtained in anaerobic decomposition of glucose? $\mathrm{CO}_{2}$ $\mathrm{CH}_{4}$ $\mathrm{H}_{2} \mathrm{~S}$ $\mathrm{H}_{2} \mathrm{O}$

Which one of the following products is NOT obtained in anaerobic decomposition of glucose?$\mathrm{CO}_{2}$$\mathrm{CH}_{4}$$\mathrm{H}_{2} \mathrm{~S}$$\mathrm{H}_{2} \m...

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44

GATE Civil 2024 Set 2 | Question: 33
The consolidated data of a spot speed study for a certain stretch of a highway is given in the table. Speed range $(\mathrm{kmph})$ Number of observations $0-10$ $7$ $10-20$ $31$ $20-30$ $76$ $30-40$ $129$ $40-50$ $104$ $50-60$ $78$ ... $13$ $90-100$ $9$ The "upper speed limit" (in $\mathrm{kmph}$) for the traffic sign is $50$ $55$ $65$ $70$

The consolidated data of a spot speed study for a certain stretch of a highway is given in the table.Speed range $(\mathrm{kmph})$Number of observations...

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45

GATE Civil 2024 Set 2 | Question: 19
Various stresses in jointed plain concrete pavement with slab size of $3.5 \mathrm{~m} \times 4.5 \mathrm{~m}$ are denoted as follows: Wheel load stress at interior $=S_{w l}^{i}$ Wheel load stress at edge $=S_{w l}^{e}$ Wheel load stress at corner $=S_{w l}^{c}$ Warping stress at ... $S_{w l}^{e}+S_{t}^{e}-S_{f}$ $S_{w l}^{c}+S_{t}^{c}+S_{f}$

Various stresses in jointed plain concrete pavement with slab size of $3.5 \mathrm{~m} \times 4.5 \mathrm{~m}$ are denoted as follows:Wheel load stress at interior $=S_{w...

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46

GATE Civil 2024 Set 2 | Question: 27
A linearly elastic beam of length $2 l$ with flexural rigidity $E I$ has negligible mass. A massless spring with a spring constant $k$ and a rigid block of mass $m$ ... $\sqrt{\frac{48 E I k}{\left(k l^{3}+48 E I\right) m}}$

A linearly elastic beam of length $2 l$ with flexural rigidity $E I$ has negligible mass. A massless spring with a spring constant $k$ and a rigid block of...

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47

GATE Civil 2024 Set 2 | Question: 6
A $3 \mathrm{~m}$ long, horizontal, rigid, uniform beam $\mathrm{PQ}$ has negligible mass. The beam is subjected to a $3 \mathrm{kN}$ concentrated vertically downward force at $1 \mathrm{~m}$ from $\mathrm{P}$, as shown in the figure. The beam is resting on ... (in $\mathrm{kN} / \mathrm{m}$ ) for the spring at the end $\mathrm{Q}$ is $150$ $100$ $50$ $200$

A $3 \mathrm{~m}$ long, horizontal, rigid, uniform beam $\mathrm{PQ}$ has negligible mass. The beam is subjected to a $3 \mathrm{kN}$ concentrated vertically downward for...

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48

GATE Civil 2024 Set 2 | Question: 9
Consider the following data for a project of $300$ days duration. Budgeted Cost of Work Scheduled (BCWS) = Rs. $200$ Budgeted Cost of Work Performed (BCWP) = Rs. $150$ Actual Cost of Work Performed (ACWP) = Rs. $190$ The 'schedule variance' for the project is (-)Rs. $50$ (-)$50$ days (+)Rs. $50$ (+)$50$ days

Consider the following data for a project of $300$ days duration.Budgeted Cost of Work Scheduled (BCWS) = Rs. $200$Budgeted Cost of Work Performed (BCWP) =...

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49

GATE Civil 2024 Set 1 | Question: 15
If the number of sides resulting in a closed traverse is increased from three to four, the sum of the interior angles increases by $90^{\circ}$ $180^{\circ}$ $270^{\circ}$ $360^{\circ}$

If the number of sides resulting in a closed traverse is increased from three to four, the sum of the interior angles increases by$90^{\circ}$$180^{\circ}$...

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50

GATE Civil 2024 Set 2 | Question: 42
The table shows the activities and their durations and dependencies in a project. \begin{array}{|c|c|c|} \hline \text{Activity} & \text{Duration (Days)} & \text{Depends on} \\ \hline \text{A} & 8 & - \\ \hline \text{B} & 4 & \text{ ... , K} \\ \hline \end{array} The total duration (in days) of the project is $\_\_\_\_\_\_\_$ (in integer).

The table shows the activities and their durations and dependencies in a project.\begin{array}{|c|c|c|}\hline \text{Activity} & \text{Duration (Days)} & \text{Depends on}...

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51

GATE Civil 2024 Set 2 | Question: 44
The in-situ percentage of voids of a sand deposit is $50 \%$. The maximum and minimum densities of sand determined from the laboratory tests are $1.8 \mathrm{~g} / \mathrm{cm}^{3}$ and $1.3 \mathrm{~g} / \mathrm{cm}^{3}$, respectively. Assume the ... $\_\_\_\_\_\_\_$ (rounded off to $2$ decimal places).

The in-situ percentage of voids of a sand deposit is $50 \%$. The maximum and minimum densities of sand determined from the laboratory tests are $1.8 \mathrm{~g} / \mathr...

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52

GATE Civil 2024 Set 1 | Question: 9
Consider the statements $\text{P}$ and $\text{Q}$. $\text{P}$: Soil particles formed by mechanical weathering, and close to their origin are generally subrounded. $\text{Q}$: Activity of the clay physically signifies its swell potential. Which one of the following ... $\mathrm{\text{P}}$ and $\mathrm{Q}$ are FALSE $\mathrm{P}$ is FALSE and $\mathrm{Q}$ is TRUE

Consider the statements $\text{P}$ and $\text{Q}$.$\text{P}$: Soil particles formed by mechanical weathering, and close to their origin are generally subrounded.$\text{Q}...

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53

GATE Civil 2024 Set 1 | Question: 5
Concrete of characteristic strength $30 \mathrm{MPa}$ is required. If $40$ specimens of concrete cubes are to be tested, the minimum number of specimens having at least $30 \mathrm{MPa}$ strength should be $35$ $37$ $38$ $39$

Concrete of characteristic strength $30 \mathrm{MPa}$ is required. If $40$ specimens of concrete cubes are to be tested, the minimum number of specimens having at least $...

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54

GATE Civil 2024 Set 2 | Question: 24
A reinforced concrete pile of $10 \mathrm{~m}$ length and $0.7 \mathrm{~m}$ diameter is embedded in a saturated pure clay with unit cohesion of $50 \mathrm{kPa}$. If the adhesion factor is $0.5$, the net ultimate uplift pullout capacity (in $\mathrm{kN}$ ) of the pile is $\_\_\_\_\_\_\_$ (rounded off to the nearest integer).

A reinforced concrete pile of $10 \mathrm{~m}$ length and $0.7 \mathrm{~m}$ diameter is embedded in a saturated pure clay with unit cohesion of $50 \mathrm{kPa}$. If the ...

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55

GATE Civil 2024 Set 2 | Question: 53
A vertical summit curve on a freight corridor is formed at the intersection of two gradients, $+3.0 \%$ and $-5.0 \%$. Assume the following: Only large-sized trucks are allowed on this corridor Design speed $=80 \mathrm{kmph}$ Eye height of truck drivers ... ) to accommodate the stopping sight distance is $\_\_\_\_\_\_\_\_\_$ (rounded off to $2$ decimal places).

A vertical summit curve on a freight corridor is formed at the intersection of two gradients, $+3.0 \%$ and $-5.0 \%$.Assume the following:Only large-sized trucks are all...

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56

GATE Civil 2024 Set 2 | Question: 17
The longitudinal sections of a runway have gradients as shown in the table. \begin{array}{|c|c|} \hline \text{End to end for sections of runway (m)} & \text{Gradient} (\%) \\ \hline 0 \text{to} 200 & +1.0 \\ \hline 200 \text{to} 600 & -1.0 \\ ... as $100 \mathrm{~m}$. The effective gradient of the runway is $0.02 \%$ $0.35 \%$ $0.28 \%$ $0.18 \%$

The longitudinal sections of a runway have gradients as shown in the table.\begin{array}{|c|c|}\hline \text{End to end for sections of runway (m)} & \text{Gradient} (\%) ...

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57

GATE Civil 2024 Set 2 | Question: 25
A $2 \mathrm{~m}$ wide rectangular channel is carrying a discharge of $30 \mathrm{~m}^{3} / \mathrm{s}$ at a bed slope of $1$ in $300$. Assuming the energy correction factor as $1.1$ and acceleration due to gravity as $10 \mathrm{~m} / \mathrm{s}^{2}$, the critical depth of flow (in meters) is $\_\_\_\_\_\_\_$ (rounded off to $2$ decimal places).

A $2 \mathrm{~m}$ wide rectangular channel is carrying a discharge of $30 \mathrm{~m}^{3} / \mathrm{s}$ at a bed slope of $1$ in $300$. Assuming the energy correction fac...

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58

GATE Civil 2024 Set 2 | Question: 20
For a reconnaissance survey, it is necessary to obtain vertical aerial photographs of a terrain at an average scale of $1: 13000$ using a camera. If the permissible flying height is assumed as $3000 \mathrm{~m}$ above a datum and the average terrain ... above the datum, the required focal length (in $\mathrm{mm}$ ) of the camera is $100$ $150$ $125$ $200$

For a reconnaissance survey, it is necessary to obtain vertical aerial photographs of a terrain at an average scale of $1: 13000$ using a camera. If the...

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59

GATE Civil 2024 Set 2 | Question: 49
A rectangular channel is $4.0 \mathrm{~m}$ wide and carries a discharge of $2.0 \mathrm{~m}^{3} / \mathrm{s}$ with a depth of $0.4 \mathrm{~m}$. The channel transitions to a maximum width contraction at a downstream location, without influencing the ... . The width (in meters) at the maximum contraction is $\_\_\_\_\_\_\_$ (rounded off to $2$ decimal places).

A rectangular channel is $4.0 \mathrm{~m}$ wide and carries a discharge of $2.0 \mathrm{~m}^{3} / \mathrm{s}$ with a depth of $0.4 \mathrm{~m}$. The channel transitions t...

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60

GATE Civil 2024 Set 1 | Question: 7
The following figure shows the arrangement of formwork for casting a cantilever $\mathrm{RC}$ ...

The following figure shows the arrangement of formwork for casting a cantilever $\mathrm{RC}$ beam.The correct sequence of removing the Shores/Props is$\mathrm{S} 1 \righ...

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61

GATE Civil 2024 Set 1 | Question: 6
Consider the statements $\text{P}$ and $\text{Q}$. $\text{P}$: Client's Preliminary Estimate is used for budgeting costs toward the end of planning and design phase. $\text{Q}$: Client's Detailed Estimate is used for controlling costs during the execution ... Both $\mathrm{P}$ and $\mathrm{Q}$ are FALSE $\mathrm{P}$ is FALSE and $\mathrm{Q}$ is TRUE

Consider the statements $\text{P}$ and $\text{Q}$.$\text{P}$: Client's Preliminary Estimate is used for budgeting costs toward the end of planning and design phase.$\text...

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62

GATE Civil 2024 Set 2 | Question: 29
A homogeneous, prismatic, linearly elastic steel bar fixed at both the ends has a slenderness ratio $(l / r)$ of $105$, where $l$ is the bar length and $r$ ... $298^{\circ} \mathrm{C}$ $85^{\circ} \mathrm{C}$ $400^{\circ} \mathrm{C}$ $250^{\circ} \mathrm{C}$

A homogeneous, prismatic, linearly elastic steel bar fixed at both the ends has a slenderness ratio $(l / r)$ of $105$, where $l$ is the bar length and $r$ is the radius ...

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63

GATE Civil 2024 Set 2 | Question: 3
The second derivative of a function $f$ is computed using the fourth-order Central Divided Difference method with a step length $h$. The CORRECT expression for the second derivative is $\frac{1}{12 h^{2}}\left[-f_{i+2}+16 f_{i+1}-30 f_{i}+16 f_{i-1}-f_{i-2}\right]$ ... $\frac{1}{12 h^{2}}\left[-f_{i+2}-16 f_{i+1}+30 f_{i}-16 f_{i-1}-f_{i-2}\right]$

The second derivative of a function $f$ is computed using the fourth-order Central Divided Difference method with a step length $h$.The CORRECT expression ...

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64

GATE Civil 2024 Set 1 | Question: 55
A bird is resting on a point $\mathrm{P}$ at a height of $8 \mathrm{~m}$ above the Mean Sea Level (MSL). Upon hearing a loud noise, the bird flies parallel to the ground surface and reaches a point $\mathrm{Q}$ ... the horizontal distance (in meters) between points $\mathrm{P}$ and $\mathrm{Q}$ is $\_\_\_\_\_\_$ (in integer).

A bird is resting on a point $\mathrm{P}$ at a height of $8 \mathrm{~m}$ above the Mean Sea Level (MSL). Upon hearing a loud noise, the bird flies parallel to the ground ...

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65

GATE Civil 2024 Set 1 | Question: 4
The three-dimensional state of stress at a point is given by \[ \sigma=\left(\begin{array}{ccc} 10 & 0 & 0 \\ 0 & 40 & 0 \\ 0 & 0 & 0 \end{array}\right) \mathrm{MPa} . \] The maximum shear stress at the point is $20 \mathrm{MPa}$ $15 \mathrm{MPa}$ $5 \mathrm{MPa}$ $25 \mathrm{MPa}$

The three-dimensional state of stress at a point is given by\[\sigma=\left(\begin{array}{ccc}10 & 0 & 0 \\0 & 40 & 0 \\0 & 0 & 0\end{array}\right) \mathrm{MPa} .\]The max...

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66

GATE Civil 2024 Set 2 | GA Question: 7
Seven identical cylindrical chalk-sticks are fitted tightly in a cylindrical container. The figure below shows the arrangement of the chalk-sticks inside the cylinder. The length of the container is equal to the length of the chalk-sticks. The ratio of the occupied space to the empty space of the container is $5 / 2$ $7 / 2$ $9 / 2$ $3$

Seven identical cylindrical chalk-sticks are fitted tightly in a cylindrical container. The figure below shows the arrangement of the chalk-sticks inside the cylinder.The...

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67

GATE Civil 2024 Set 2 | Question: 54
A child walks on a level surface from point $\text{P}$ to point $\text{Q}$ at a bearing of $30^{\circ}$, from point $\mathrm{Q}$ to point $\mathrm{R}$ at a bearing of $90^{\circ}$ ... degrees, the straight-line path length $\text{RP}$ (in meters) is $\_\_\_\_\_\_\_$ (rounded off to the nearest integer).

A child walks on a level surface from point $\text{P}$ to point $\text{Q}$ at a bearing of $30^{\circ}$, from point $\mathrm{Q}$ to point $\mathrm{R}$ at a bearing of $90...

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68

GATE Civil 2024 Set 1 | Question: 38
A $2 \mathrm{~m} \times 2 \mathrm{~m}$ tank of $3 \mathrm{~m}$ height has inflow, outflow and stirring mechanisms. Initially, the tank was half-filled with fresh water. At $t=0$ ... grams) in the tank at $75 \%$ of its capacity is $\_\_\_\_\_\_\_$ (rounded off to $2$ decimal places).

A $2 \mathrm{~m} \times 2 \mathrm{~m}$ tank of $3 \mathrm{~m}$ height has inflow, outflow and stirring mechanisms. Initially, the tank was half-filled with fresh water. A...

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69

GATE Civil 2024 Set 1 | Question: 21
The primary air pollutant(s) is/are Sulfur dioxide Lead Ozone Sulphuric acid

The primary air pollutant(s) is/areSulfur dioxideLeadOzoneSulphuric acid

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70

GATE Civil 2024 Set 1 | Question: 20
Consider a balanced doubly-reinforced concrete section. If the material and other sectional properties remain unchanged, for which of the following cases will the section becomes under-reinforced? Area of tension reinforcement ... compression reinforcement is increased. Area of tension reinforcement is decreased. Area of compression reinforcement is decreased.

Consider a balanced doubly-reinforced concrete section. If the material and other sectional properties remain unchanged, for which of the following cases will the section...

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71

GATE Civil 2024 Set 1 | Question: 19
The elements that DO NOT increase the strength of structural steel are Carbon Manganese Sulphur Chlorine

The elements that DO NOT increase the strength of structural steel areCarbonManganeseSulphurChlorine

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72

GATE Civil 2024 Set 2 | Question: 15
What is the CORRECT match between the air pollutants and treatment techniques given in the table? \begin{array}{|l|l|} \hline \text{Air pollutants} & \text{Treatment techniques} \\ \hline \mathrm{P}-\mathrm{NO}_{2} & \text{i - Flaring} \\ \mathrm{Q}-\mathrm{SO}_{2} & ... $\text{P-ii, Q-iii, R-iv, S-i}$ $\text{P-iv, Q-iii, R-i, S-ii}$

What is the CORRECT match between the air pollutants and treatment techniques given in the table?\begin{array}{|l|l|}\hline \text{Air pollutants} & \text{Treatment techni...

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73

GATE Civil 2024 Set 2 | Question: 51
An organic waste is represented as $\mathrm{C}_{240} \mathrm{O}_{200} \mathrm{H}_{180} \mathrm{~N}_{5} \mathrm{~S}$. (Atomic weights: $\mathrm{S}-32, \mathrm{H}-1, \mathrm{C}-12, \mathrm{O}-16, \mathrm{~N}-14$ ... $\mathrm{kg}$ of this waste is $\_\_\_\_\_\_\_$ (rounded off to $1$ decimal place).

An organic waste is represented as $\mathrm{C}_{240} \mathrm{O}_{200} \mathrm{H}_{180} \mathrm{~N}_{5} \mathrm{~S}$.(Atomic weights: $\mathrm{S}-32, \mathrm{H}-1, \mathrm...

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74

GATE Civil 2024 Set 2 | Question: 39
For the $6 \mathrm{~m}$ long horizontal cantilever beam $\mathrm{PQR}$ shown in the figure, $\mathrm{Q}$ is the midpoint. Segment $\mathrm{PQ}$ of the beam has flexural rigidity $\mathrm{EI}=2 \times 10^{5} \mathrm{kN. \textrm {m } ^ { 2 }}$ whereas the ... (in $\mathrm{mm}$ ) at point $\mathrm{Q}$ is $\_\_\_\_\_\_\_$ (rounded off to $3$ decimal places).

For the $6 \mathrm{~m}$ long horizontal cantilever beam $\mathrm{PQR}$ shown in the figure, $\mathrm{Q}$ is the midpoint. Segment $\mathrm{PQ}$ of the beam has flexural r...

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75

GATE Civil 2024 Set 1 | Question: 30
A homogeneous shaft $\text{PQR}$ with fixed supports at both ends is subjected to a torsional moment $\mathrm{T}$ at point $\mathrm{Q}$, as shown in the figure. The polar moments of inertia of the portions $\text{PQ}$ and $\text{QR}$ of the shaft with circular ... the ratio of the lengths $\mathrm{L}_{1} / \mathrm{L}_{2}$ is $0.50$ $0.25$ $4.00$ $2.00$

A homogeneous shaft $\text{PQR}$ with fixed supports at both ends is subjected to a torsional moment $\mathrm{T}$ at point $\mathrm{Q}$, as shown in the fi...

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76

GATE Civil 2024 Set 1 | Question: 23
The plane frame shown in the figure has fixed support at joint $\text{A}$, hinge support at joint $\text{F}$, and roller support at joint $\text{I}$. In the figure, $\text{A}$ to $\text{I}$ indicate joints of the frame. If the axial deformations are neglected, the degree of kinematic indeterminacy is $\_\_\_\_\_\_$. (in integer).

The plane frame shown in the figure has fixed support at joint $\text{A}$, hinge support at joint $\text{F}$, and roller support at joint $\text{I}$. In the figure, $\tex...

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77

GATE Civil 2024 Set 1 | Question: 31
A vertical smooth rigid retaining wall is supporting horizontal ground with dry cohesionless backfill having a friction angle of $30^{\circ}$. The inclinations of failure planes with respect to the major principal plane for Rankine's active and passive earth pressure conditions, ... $30^{\circ}$ and $60^{\circ}$ $60^{\circ}$ and $30^{\circ}$

A vertical smooth rigid retaining wall is supporting horizontal ground with dry cohesionless backfill having a friction angle of $30^{\circ}$. The inclinations of failure...

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78

GATE Civil 2024 Set 1 | Question: 36
Which of the following statement(s) is/are CORRECT? Swell potential of soil decreases with an increase in the shrinkage limit. Both loose and dense sands with different initial void ratios can attain similar void ... other corrections. In electrical resistivity tomography, the depth of current penetration is half of the spacing between the electrodes.

Which of the following statement(s) is/are CORRECT?Swell potential of soil decreases with an increase in the shrinkage limit.Both loose and dense sands ...

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79

GATE Civil 2024 Set 1 | Question: 22
Consider the data of $f(x)$ given in the table. \begin{array}{|c|c|c|c|} \hline i & 0 & 1 & 2 \\ \hline x_{i} & 1 & 2 & 3 \\ \hline f\left(x_{i}\right) & 0 & 0.3010 & 0.4771 \\ \hline ... value of $f(1.5)$ estimated using second-order Newton's interpolation formula is $\_\_\_\_\_\_$. (rounded off to $2$ decimal places).

Consider the data of $f(x)$ given in the table.\begin{array}{|c|c|c|c|}\hline i & 0 & 1 & 2 \\\hline x_{i} & 1 & 2 & 3 \\\hline f\left(x_{i}\right) & 0 & 0.3010 & 0.4771 ...

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80

GATE Civil 2024 Set 1 | Question: 34
The free mean speed is $60 \mathrm{~km} / \mathrm{hr}$ on a given road. The average space headway at jam density on this road is $8 \mathrm{~m}$. For a linear speed-density relationship, the maximum flow (in veh/hr/lane) expected on the road is $1875$ $938$ $2075$ $1038$

The free mean speed is $60 \mathrm{~km} / \mathrm{hr}$ on a given road. The average space headway at jam density on this road is $8 \mathrm{~m}$. For a linear speed-densi...

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