List of top Questions asked in GATE CE- 2022

At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively. The probability of observing at least 2 vehicles in 30 minutes is \(\underline{\hspace{2cm}}\) . (round off to two decimal places)

Two reservoirs are connected by two parallel pipes of equal length and of diameters 20 cm and 10 cm, as shown in the figure (not drawn to scale). When the difference in the water levels of the reservoirs is 5 m, the ratio of discharge in the larger diameter pipe to the discharge in the smaller diameter pipe is \(\underline{\hspace{2cm}}\) (round off to two decimal places). 

For the dual-wheel carrying assembly shown in the figure, \( P \) is the load on each wheel, \( a \) is the radius of the contact area of the wheel, \( s \) is the spacing between the wheels, and \( d \) is the clear distance between the wheels. Assuming that the ground is an elastic, homogeneous, and isotropic half space, the ratio of Equivalent Single Wheel Load (ESWL) at depth \( z = \frac{d}{2} \) to the ESWL at depth \( z = 2s \) is \(\underline{\hspace{1cm}}\) (round off to one decimal place). 

The vehicle count obtained in every 10 minute interval of a traffic volume survey done in peak one hour is given below. \[ \begin{array}{|c|c|} \hline \text{Time Interval (in minutes)} & \text{Vehicle Count} \\ \hline 0 - 10 & 10 \\ 10 - 20 & 11 \\ 20 - 30 & 12 \\ 30 - 40 & 15 \\ 40 - 50 & 13 \\ 50 - 60 & 11 \\ \hline \end{array} \] The peak hour factor (PHF) for 10 minute sub-interval is \(\underline{\hspace{1cm}}\) (round off to one decimal place).

A horizontal force of P kN is applied to a homogeneous body of weight 25 kN, as shown in the figure. The coefficient of friction between the body and the floor is 0.3. Which of the following statement(s) is/are correct? 

The plane truss shown in the figure is subjected to an external force \( P \). It is given that \( P = 70 \, \text{kN} \), \( a = 2 \, \text{m} \), and \( b = 3 \, \text{m} \). 

The magnitude (absolute value) of force in member EF is \(\underline{\hspace{1cm}}\) (round off to the nearest integer).

A semi-circular bar of radius R m, in a vertical plane, is fixed at the end G, as shown in the figure. A horizontal load of magnitude P kN is applied at the end H. The magnitude of the axial force, shear force, and bending moment at point Q for \(\theta = 45^\circ\), respectively, are 
 

A weld is used for joining an angle section ISA 100 mm \(\times\) 100 mm \(\times\) 10 mm to a gusset plate of thickness 15 mm to transmit a tensile load. The permissible stress in the angle is 150 MPa and the permissible shear stress on the section through the throat of the fillet weld is 108 MPa. The location of the centroid of the angle is represented by \( C_{yy} \) in the figure, where \( C_{yy} = 28.4 \, \text{mm} \). The area of cross-section of the angle is 1903 mm\(^2\). Assuming the effective throat thickness of the weld to be 0.7 times the given weld size, the lengths \( L_1 \) and \( L_2 \) (rounded off to the nearest integer) of the weld required to transmit a load equal to the full strength of the tension member are, respectively 
 

Consider the four points 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 \( k_S \), respectively. The correct order of these densities is: 
 

Let max {a, b} denote the maximum of two real numbers a and b. Which of the following statement(s) is/are TRUE about the function \( f(x) = \text{max}\{3 - x, x - 1\}? \)

Henry's law constant for transferring \( O_2 \) from air into water, at room temperature, is 1.3 \( \frac{\text{mmol}}{\text{liter-atm}} \) . Given that the partial pressure of \( O_2 \) in the atmosphere is 0.21 atm, the concentration of dissolved oxygen (mg/liter) in water in equilibrium with the atmosphere at room temperature is \[ \text{(Consider the molecular weight of O}_2 \text{ as 32 g/mol)} \]

The correct match between the physical states of the soils given in Group I and the governing conditions given in Group II is 

The project activities are given in the following table along with the duration and dependency. \[ \begin{array}{|c|c|c|} \hline \text{Activities} & \text{Duration (days)} & \text{Depends on} \\ \hline P & 10 & - \\ Q & 12 & - \\ R & 5 & P \\ S & 10 & Q \\ T & 10 & P, Q \\ \hline \end{array} \] Which one of the following combinations is correct?

Consider the cross-section of a beam made up of thin uniform elements having thickness \( t \) (where \( t \ll a \)) shown in the figure. The (x, y) coordinates of the points along the center-line of the cross-section are given in the figure. The coordinates of the shear center of this cross-section are: 

With respect to fluid flow, match the following in Column X with Column Y: 

Which one of the following combinations is correct?

A water treatment plant has a sedimentation basin of depth 3 m, width 5 m, and length 40 m. The water inflow rate is 500 m\(^3\)/h. The removal fraction of particles having a settling velocity of 1.0 m/h is \(\underline{\hspace{2cm}}\) . (round off to one decimal place)
(Consider the particle density as 2650 kg/m\(^3\) and liquid density as 991 kg/m\(^3\))
A two-phase signalized intersection is designed with a cycle time of 100 s. The amber and red times for each phase are 4 s and 50 s, respectively. If the total lost time per phase due to start-up and clearance is 2 s, the effective green time of each phase is \(\underline{\hspace{2cm}}\) s. (in integer)
A reinforced concrete beam with rectangular cross section (width = 300 mm, effective depth = 580 mm) is made of M30 grade concrete. It has 1% longitudinal tension reinforcement of Fe 415 grade steel. The design shear strength for this beam is 0.66 N/mm\(^2\). The beam has to resist a factored shear force of 440 kN. The spacing of two-legged, 10 mm diameter vertical stirrups of Fe 415 grade steel is \(\underline{\hspace{2cm}}\) mm. (round off to the nearest integer)
A square concrete pile of 10 m length is driven into a deep layer of uniform homogeneous clay. Average unconfined compressive strength of the clay, determined through laboratory tests on undisturbed samples extracted from the clay layer, is 100 kPa. If the ultimate compressive load capacity of the driven pile is 632 kN, the required width of the pile is \(\underline{\hspace{2cm}}\) mm. (in integer)
(Bearing capacity factor \( N_c = 9 \), adhesion factor \( \alpha = 0.7 \))
A raft foundation of \( 30 \, \text{m} \times 25 \, \text{m} \) is proposed to be constructed at a depth of 8 m in a sand layer. A 25 mm thick saturated clay layer exists 2 m below the base of the raft foundation. Below the clay layer, a dense sand layer exists at the site. A 25 mm thick undisturbed sample was collected from the mid-depth of the clay layer and tested in a laboratory oedometer under double drainage condition. It was found that the soil sample had undergone 50 % consolidation settlement in 10 minutes.
The time (in days) required for 25 % consolidation settlement of the raft foundation will be \(\underline{\hspace{2cm}}\). (round off to the nearest integer)
A two-hour duration storm event with uniform excess rainfall of 3 cm occurred on a watershed. The ordinates of streamflow hydrograph resulting from this event are given in the table. \[ \begin{array}{|c|c|} \hline \text{Time (hours)} & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \text{Streamflow (m}^3/\text{s}) & 10 & 16 & 34 & 40 & 31 & 25 & 16 & 10 \\ \hline \end{array} \] Considering a constant baseflow of 10 m\(^3\)/s, the peak flow ordinate (in m\(^3\)/s) of the one-hour unit hydrograph for the watershed is \(\underline{\hspace{2cm}}\). (in integer)
Depth of water flowing in a 3 m wide rectangular channel is 2 m. The channel carries a discharge of 12 m\(^3\)/s. Take \( g = 9.8 \, \text{m/s}^2 \). The bed width (in m) at contraction, which just causes the critical flow, is \(\underline{\hspace{1cm}}\) without changing the upstream water level. (round off to two decimal places)
A wastewater sample contains two nitrogen species, namely ammonia and nitrate. Consider the atomic weight of N, H, and O as 14 g/mol, 1 g/mol, and 16 g/mol, respectively. In this wastewater, the concentration of ammonia is 34 mg NH\(_3\)/liter and that of nitrate is 6.2 mg NO\(_3^-\)/liter. The total nitrogen concentration in this wastewater is \(\underline{\hspace{1cm}}\) milligrams nitrogen per liter. (round off to one decimal place)
A 2 % sewage sample (in distilled water) was incubated for 3 days at 27 °C temperature. After incubation, a dissolved oxygen depletion of 10 mg/L was recorded. The biochemical oxygen demand (BOD) rate constant at 27 °C was found to be 0.23 day\(^{-1}\) (at base e).
The ultimate BOD (in mg/L) of the sewage will be \(\underline{\hspace{2cm}}\) . (round off to the nearest integer)
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