List of top Questions asked in GATE CE

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

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

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

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

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

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 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

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).

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) 

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

The following figure shows the arrangement of formwork for casting a cantilever RC beam.

The correct sequence of removing the Shores/Props is:

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^TB^T
Which one of the following options is CORRECT ?

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).

The second-order differential equation in an unknown function u: u(x, y) is defined as:\(\frac{\partial^2u }{\partial x^2 } =2\)
Assuming g: g(x), f: f(y), and h: h(y), the general solution of the above differential equation is

What is the CORRECT match between the survey instruments/parts of instruments shown in the table and the operations carried out with them ?

Instruments/Parts of instruments		Operations
P	Bubble tube	i	Tacheometry
Q	Plumb bob	ii	Minor movements
R	Tangent screw	iii	Centering
S	Stadia cross-wire	iv	Levelling

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).

A 3 m long, horizontal, rigid, uniform beam PQ has negligible mass. The beam is subjected to a 3 kN concentrated vertically downward force at 1 m from P, as shown in the figure. The beam is resting on vertical linear springs at the ends P and Q. For the spring at the end P, the spring constant K_p 100 kN/m.

If the beam DOES NOT rotate under the application of the force and displaces only vertically, the value of the spring constant KQ (in kN/m) for the spring at the end Q is