List of top Questions asked in GATE Civil Engineering- 2024

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 g/cm³ and 1.3 g/cm³, respectively. Assume the specific gravity of sand as 2.7.
The relative density index of the in-situ sand is ______ (rounded off to 2 decimal places).

A map is prepared with a scale of 1:1000 and a contour interval of 1 m. If the distance between two adjacent contours on the map is 10 mm, the slope of the ground between the adjacent contours is

Using the following data, the spatial resolution of a push-broom sensor is _________ m (in integer). 
Data: 
Orbital altitude (above earth surface) = 1000 km 
Number of spectral bands = 5 
Number of detectors/CCDs (charged coupled devices) in a row = 4000 
Ground swath = 20 km

In a sample of 100 heart patients, each patient has 80% chance of having a heart attack without medicine X. It is clinically known that medicine X reduces the probability of having a heart attack by 50%. Medicine X is taken by 50 of these 100 patients. The probability that a randomly selected patient, out of the 100 patients, takes medicine X and has a heart attack is

Find the odd one out in the set: {19, 37, 21, 17, 23, 29, 31, 11}

The beam shown in the figure is subjected to a uniformly distributed downward load of intensity q between supports A and B.

Considering the upward reactions as positive, the support reactions are

A water treatment plant treats 25 MLD water with a natural alkalinity of 4.0 mg/L (as CaCO₃). It is estimated that, during coagulation of this water, 450 kg/day of calcium bicarbonate (Ca(HCO₃)₂) is required based on the alum dosage.
Consider the atomic weights as: Ca-40, H-1, C-12, O-16.
The quantity of pure quick lime, CaO (in kg) required for this process per day is _____ (rounded off to 2 decimal places).

A four-band multispectral image with pixel size of 50 m x 50 m covers a ground area of 20 km × 20 km. If the radiometric resolution of the satellite data is 8 bits, then the uncompressed satellite image contains _______ kilobytes (kB) of data (in integer).

A partial differential equation
\(\frac{∂^2T}{∂x^2}+\frac{∂^2T}{∂y^2}=0\)
is defined for the two-dimensional field T: T(x, y), inside a planar square domain of size 2 m x 2 m. Three boundary edges of the square domain are maintained at value T = 50, whereas the fourth boundary edge is maintained T = 100.
The value of T at the center of the domain is

The plane frame shown in the figure has fixed support at joint A, hinge support at joint F, and roller support at joint I. In the figure, A to I indicate joints of the frame.

If the axial deformations are neglected, the degree of kinematic indeterminacy is ____ . (in integer).

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 particles should settle forming three layers: coarse anthracite particles at the top of the bed, silica sand in the middle, and small ilmenite sand particles at the bottom of the bed.
Assume
(i) Slow discrete settling (Stoke's law is applicable)
(ii) All particles are spherical
(iii) Diameter of silica sand particles is 0.20 mm
The CORRECT option fulfilling the diameter requirements for this filter media is

A 30 cm diameter well fully penetrates an unconfined aquifer of saturated thickness 20 m with hydraulic conductivity of 10 m/day. Under the steady pumping rate for a long time, the drawdowns in two observation wells located at 10 m and 100 m from the pumping well are 5 m and 1 m, respectively. The corresponding pumping rate (in m³/day) from the well is _____ . (rounded off to 2 decimal places)

If the plotting accuracy of a map is 0.25 mm and the scale of the same map is 1:100000, what will be the minimum ground distance that can be plotted on the map?

The consolidated data of a spot speed study for a certain stretch of a highway is given in the table.

Speed Range (kmph)	Number of observations
0-10	7
10-20	31
20-30	76
30-40	129
40-50	104
50-60	78
60-70	29
70-80	24
80-90	13
90-100	9

The "upper speed limit" (in kmph) for the traffic sign is

A horizontal curve of radius 1080 m (with transition curves on either side) in a Broad Gauge railway track is designed and constructed for an equilibrium speed of 70 kmph. However, a few years after construction, the Railway Authorities decided to run express trains on this track. The maximum allowable cant deficiency is 10 cm.
The maximum restricted speed (in kmph) of the express trains running on this track is __________ (rounded off to the nearest integer).

A 2 m × 1.5 m tank of 6 m height is provided with a 100 mm diameter orifice at the center of its base. The orifice is plugged and the tank is filled up to 5 m height. Consider the average value of discharge coefficient as 0.6 and acceleration due to gravity (g) as 10 m/s². After unplugging the orifice, the time (in seconds) taken for the water level to drop from 5 m to 3.5 m under free discharge condition is _________ (rounded off to 2 decimal places).

To reduce the slope distance (S) to an equivalent horizontal distance (H) as shown in the figure given below, the following independent observations were taken.
\(S = 29.95 m ± 0.01 m; \theta = 4°30' ± 10' \)
The required precision of computed horizontal distance is ± 0.005 m. Assume a "balanced accuracy" where the contribution to precision of the horizontal distance comes equally from the slope distance and angle measurements. The minimum number of angle observations to achieve the desired precision is 
(Given 1 radian = 206265 seconds) 

Independent angles AOB, BOC and AOC were observed as shown in figure. The standard error of all observations is same. The adjusted values of these angles using the least squares adjustment are

A 2m × 2m tank of 3 m height has inflow, outflow and stirring mechanisms. Initially, the tank was half-filled with fresh water. At t = 0, an inflow of a salt solution of concentration 5 g/m³ at the rate of 2 litre/s and an outflow of the well stirred mixture at the rate of 1 litre/s are initiated. This process can be modelled using the following differential equation:
\(\frac {dm}{dt}+\frac {m}{6000+t}=0.01\)
where m is the mass (grams) of the salt at time t (seconds). The mass of the salt (in grams) in the tank at 75% of its capacity is _____ (rounded off to 2 decimal places).

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 P and Q.
P : It is economically advisable to complete the activity early by crashing, if the indirect cost of the project is Rs. 8,500 per day.
Q : It is economically advisable to complete the activity early by crashing, if the indirect cost of the project is Rs. 10,000 per day.
Which one of the following options is CORRECT ?

Consider two matrices \(A=\begin{bmatrix} 2 & 1 & 4 \\ 1 & 0 & 3 \end{bmatrix}\) and \(B=\begin{bmatrix} -1 & 0 \\ 2 & 3 \\ 1 & 4 \end{bmatrix}\)
The determinant of the matrix AB is _____ (in integer).

If the number of sides resulting in a closed traverse is increased from three to four, the sum of the interior angles increases by

A drained triaxial test was conducted on a saturated sand specimen using a stress-path triaxial testing system. The specimen failed when the axial stress reached a value of 100 kN/m² from an initial confining pressure of 300 kN/m².
The angle of shearing plane (in degrees) with respect to horizontal is _______ (rounded off to the nearest integer).

A 500 m long water distribution pipeline P with diameter 1.0 m, is used to convey 0.1 m³/s of flow. A new pipeline Q, with the same length and flow rate, is to replace P. The friction factors for P and Q are 0.04 and 0.01, respectively. The diameter of the pipeline Q (in meters) is ______ (rounded off to 2 decimal places).

A rectangular channel is 4.0 m wide and carries a discharge of 2.0 m³/s with a depth of 0.4 m. The channel transitions to a maximum width contraction at a downstream location, without influencing the upstream flow conditions. The width (in meters) at the maximum contraction is ______ (rounded off to 2 decimal places).