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).

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).

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).

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).

The President, along with the Council of Ministers, ............. to visit India next week.

Eigenvalue question: \[\begin{pmatrix} 6 & 8 \\ 4 & 2 \end{pmatrix} \quad \text{Eigenvalue options:} \quad \text{(i) 1, (ii) 2, (iii) 3, (iv) 4}\]

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 $.

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

Runway length after elevation and temperature correction is 700 m. The effective gradient is 1%. Find the final corrected length.

Solve the cubic equation: \[ x^3 - \frac{15}{2} x^2 + 18x + 20 = 0 \]

Given the following values, calculate the required properties: \[ S = 0.67, \quad e = 0.6, \quad w = 0.15, \quad G = 2.67, \quad \gamma_w = 9.81 \, \text{kN/m}^3, \quad V = 5 \, \text{m}^3 \]

Solve the second-order differential equation: \[ y'' + 0.8 y' + 0.16 y = 0, \quad y(0) = 3, \quad y'(0) = 4.5 \]

Match the following processes to their corresponding descriptions: Sintering, Fouling , Positioning , Coking

Find the order and degree of the following differential equation: \[ \frac{d^3 y}{dx^3} + \frac{d^2 y}{dx^2} + \frac{dy}{dx} + y = 0 \]

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

Given the bearing N30°W, determine the corresponding Whole Circle Bearing (WCB). \

Given: - Bearing = N30°W - Find WCB

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 $

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

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).

Consider the data of f (x) given in the table.

i	0	1	2
x_i	1	2	3
f(x_i)	0	0.3010	0.4771

The value of ƒ(1.5) estimated using second-order Newton's interpolation formula is ____ . (rounded off to 2 decimal places).

Which one of the given options is a possible value of $ x $ in the following sequence? \[ 3, 7, 15, x, 63, 127, 255 \]

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?

The chart below compares the Installed Capacity (MW) of four power generation technologies, T1, T2, T3, and T4, and their Electricity Generation (MWh) in a time of 1000 hours (h).

The Capacity Factor of a power generation technology is defined as: \[ \text{Capacity Factor} = \frac{\text{Electricity Generation (MWh)}}{\text{Installed Capacity (MW)} \times 1000 \, \text{(h)}} \] Which one of the given technologies has the highest Capacity Factor?

In the $ 4 \times 4 $ array shown below, each cell of the first three columns has either a cross (X) or a number, as per the given rule.
A number equals the count of crosses in its 8 neighboring cells (left, right, top, bottom, and diagonals). The fourth column is empty. As per this rule, the maximum number of crosses possible in the empty column is

During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be $89.85^\circ$, the ratio of the Earth-Sun and Earth-Moon distances is closest to: