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GATE CE
List of top Questions asked in GATE CE
On a two-lane highway, a horizontal curve of radius 300 m is provided. The design speed is 80 km/h.
If the longest wheelbase of vehicle expected on this highway is 7 m, then the extra widening required (in m) is .......... (round off to two decimal places).
GATE CE - 2025
GATE CE
Engineering Graphics
Horizontal and vertical curves
A 60 cm diameter well completely penetrates a confined aquifer of permeability \( 5 \times 10^{-4} \, {m/s} \). The length of the strainer (spanning the entire thickness of the aquifer) is 10 m. The drawdown at the well under steady state pumping is 1.0 m. Assume that the radius of influence for this pumping is 300 m.
The discharge from the well (in litres per minute) is ......... (round off to the nearest integer).
GATE CE - 2025
GATE CE
Soil Mechanics and Foundation Engineering
Well Hydraulics
A community generates 1 million litres/day (MLD) of wastewater. This wastewater is treated using activated sludge process (ASP). The working volume of the aeration tank of the ASP is 250 m\(^3\), and the biomass concentration in the tank is 3000 mg/L. Analyses results showed that a biomass concentration of 10 mg/L is present in the treated effluent from the secondary sedimentation tank of the ASP. Sludge wastage from the system is at a rate of 5000 L/day with a biomass concentration of 10000 mg/L. The system is in steady state condition.
The biological sludge residence time (BSRT) of the system (in days) is ......... (round off to one decimal place).
GATE CE - 2025
GATE CE
Environmental Engineering
Quantity of Domestic Wastewater
A designer used plate load test to obtain the value of the bearing capacity factor \( N_t \). A circular plate of 1 m diameter was placed on the surface of a dry sand layer extending very deep beneath the ground. The unit weight of the sand is 16.66 kN/m\(^3\). The plate is loaded to failure at a pressure of 1500 kPa.
Considering Terzaghi's bearing capacity theory, the bearing capacity factor \( N_t \) is ......... (round off to the nearest integer).
GATE CE - 2025
GATE CE
Soil Mechanics and Foundation Engineering
Bearing Capacity
The President, along with the Council of Ministers, ............. to visit India next week.
GATE CE - 2025
GATE CE
General Aptitude
Subject Verb Agreement
Eigenvalue question:
\[\begin{pmatrix} 6 & 8 \\ 4 & 2 \end{pmatrix} \quad \text{Eigenvalue options:} \quad \text{(i) 1, (ii) 2, (iii) 3, (iv) 4}\]
GATE CE - 2025
GATE CE
Engineering Mathematics
Linear Algebra
Given the matrix equation:
\[A = \begin{pmatrix} 2 & 3 & 4 \\ 1 & 4 & 5 \\ 4 & 3 & 2 \end{pmatrix} \quad A \cdot X = B\]
Where \( A \) is the matrix, \( X \) is the unknown vector, and \( B \) is a constant vector. Solve for \( X \).
GATE CE - 2025
GATE CE
Engineering Mathematics
Linear Algebra
Given the following conditions, determine the value of the 15-minute Peak Hourly Factor (PHF):
Given:
- Vehicles in the peak hour come in 10-minute intervals
- Find the value of the 15-minute PHF
GATE CE - 2025
GATE CE
Transportation Engineering
Concept of airport runway length
Runway length after elevation and temperature correction is 700 m. The effective gradient is 1%. Find the final corrected length.
GATE CE - 2025
GATE CE
Transportation Engineering
Concept of airport runway length
Solve the cubic equation:
\[ x^3 - \frac{15}{2} x^2 + 18x + 20 = 0 \]
GATE CE - 2025
GATE CE
Engineering Mathematics
Algebra
Solve the second-order differential equation:
\[ y'' + 0.8 y' + 0.16 y = 0, \quad y(0) = 3, \quad y'(0) = 4.5 \]
GATE CE - 2025
GATE CE
Engineering Mathematics
Calculus
Given the following values, calculate the required properties:
\[ S = 0.67, \quad e = 0.6, \quad w = 0.15, \quad G = 2.67, \quad \gamma_w = 9.81 \, \text{kN/m}^3, \quad V = 5 \, \text{m}^3 \]
GATE CE - 2025
GATE CE
Geomatics Engineering
Soil Mechanics
Match the following processes to their corresponding descriptions: Sintering, Fouling , Positioning , Coking
GATE CE - 2025
GATE CE
Chemical Engineering
Material Science
Find the order and degree of the following differential equation:
\[ \frac{d^3 y}{dx^3} + \frac{d^2 y}{dx^2} + \frac{dy}{dx} + y = 0 \]
GATE CE - 2025
GATE CE
Engineering Mathematics
Calculus
Given the following staff readings at two levels, determine the Reduced Level (RL) of B.
Given: - RL of A = 150 m - Find RL of B
GATE CE - 2025
GATE CE
Geophysics
Surveying and Levelling
Given the bearing N30°W, determine the corresponding Whole Circle Bearing (WCB).
\
Given: - Bearing = N30°W - Find WCB
GATE CE - 2025
GATE CE
Geophysics
Surveying and Levelling
Given the following data, determine the final water content \( W_2 \):
Given: - \( W_1 = 18\% \) - \( G_p = 2.74 \) - \( S_1 = 0.65 \) - \( S_2 = 0.852 \) - Find \( W_2 \)
GATE CE - 2025
GATE CE
Civil Engineering
Soil Mechanics
Given the following data for a hydraulic jump, determine the power loss (in kW):
Given: - \( B = 5 \, \text{m} \) - \( Q = 15 \, \text{m}^3/\text{sec} \) - \( y_1 = 0.5 \, \text{m} \) - \( g = 9.81 \, \text{m/s}^2 \) - \( \rho_w = 1000 \, \text{kg/m}^3 \) - \( \alpha = 1.0 \) - Find Power loss in kW
GATE CE - 2025
GATE CE
Civil Engineering
Fluid Mechanics
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
GATE CE - 2024
GATE CE
Structural Engineering
Statically determinate and indeterminate structures by force/ energy methods
A linearly elastic beam of length 2l with flexural rigidity EI has negligible mass. A massless spring with a spring constant k and a rigid block of mass m are attached to the beam as shown in the figure.
The natural frequency of this system is
GATE CE - 2024
GATE CE
Structural Engineering
Analysis of beams
A water treatment plant treats 25 MLD water with a natural alkalinity of 4.0 mg/L (as CaCO
3
). It is estimated that, during coagulation of this water, 450 kg/day of calcium bicarbonate (Ca(HCO
3
)
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).
GATE CE - 2024
GATE CE
Environmental Engineering
Wastewater management
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)
GATE CE - 2024
GATE CE
Geomatics Engineering
Distance and angle measurement
Concrete of characteristic strength 30 MPa is required. If 40 specimens of concrete cubes are to be tested, the minimum number of specimens having at least 30 MPa strength should be
GATE CE - 2024
GATE CE
Structural Engineering
Concrete
The following figure shows the arrangement of formwork for casting a cantilever RC beam.
The correct sequence of removing the Shores/Props is:
GATE CE - 2024
GATE CE
Structural Engineering
Construction Management
The statements P and Q are related to matrices A and B, which are conformable for both addition and multiplication.
P : (A + B)
T
= A
T
+ B
T
Q: (AB)
T
= A
T
B
T
Which one of the following options is CORRECT ?
GATE CE - 2024
GATE CE
Mathematics
Matrix Algebra
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