List of top Questions asked in GATE CE

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

i	0	1	2
xi	1	2	3
f(xi)	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).

As per the International Civil Aviation Organization (ICAO), the basic runway length is increased by x (%) for every y (m) raise in elevation from the Mean Sea Level (MSL). The values of x and y, respectively, are

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

A soil sample was consolidated at a cell pressure of 20 kPa and a back pressure of 10 kPa for 24 hours during a consolidated undrained (CU) triaxial test. The cell pressure was increased to 30 kPa on the next day and it resulted in the development of pore water pressure of 1 kPa. The soil sample failed when the axial stress was gradually increased to 50 kPa. The pore water pressure at failure was recorded as 21 kPa. The value of Skempton's pore pressure parameter B for the soil sample is ______ (rounded off to 2 decimal places).

For assessing the compliance with the emissions standards of incineration plants, a correction needs to be applied to the measured concentrations of air pollutants. The emission standard (based on 11% Oxygen) for HCl is 50 mg/Nm³ and the measured concentrations of HCl and Oxygen in flue gas are 42 mg/Nm³ and 13%, respectively.
Assuming 21% Oxygen in air, the CORRECT statement is:

The return period of a large earthquake for a given region is 200 years. Assuming that earthquake occurrence follows Poisson's distribution, the probability that it will be exceeded at least once in 50 years is _____ % (rounded off to the nearest integer).

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

A flow velocity field \(\vec V:\vec V(x, y)\) for a fluid is represented by
\(\vec V = 3\hat i+ (5x)\hat j\)
In the context of the fluid and the flow, which one of the following statements is CORRECT?

An infinite slope is made up of cohesionless soil with seepage parallel to and up to the sloping surface. The angle of slope is 30° with respect to horizontal ground surface. The unit weights of the saturated soil and water are 20 kN/m³ and 10 kN/m³, respectively.
The minimum angle of shearing resistance of the soil (in degrees) for the critically stable condition of the slope is _____ (rounded off to the nearest integer).

A vector field \(\vec p\) and a scalar field \(r\) are given by
\(\vec p=(2x^2-3xy+z^2)\hat i+(2y^2−3yz+x^2)\hat j+(2z^2−3xz+x^2)\hat k\)
\(r=6x^2+4y^2 - z^2-9xyz - 2xy + 3xz-yz\)
Consider the statements P and Q.
P: Curl of the gradient of the scalar field r is a null vector.
Q: Divergence of curl of the vector field p is zero.
Which one of the following options is CORRECT?

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)

A spillway has unit discharge of 7.5 m³/s/m. The flow depth at the downstream horizontal apron is 0.5 m. The tail water depth (in meters) required to form a hydraulic jump is_____ (rounded off to 2 decimal places).

A slab panel with an effective depth of 250 mm is reinforced with 0.2% main reinforcement using 8 mm diameter steel bars. The uniform center-to-center spacing (in mm) at which the 8 mm diameter bars are placed in the slab panel is _____ (rounded off to the nearest integer).

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

The correct sequence of removing the Shores/Props is:

A 5m × 5m closed tank of 10 m height contains water and oil, and is connected to an overhead water reservoir as shown in the figure. Use \(γ_w=10\ kN/m^3\) and Specific gravity of oil = 0.8

The total force (in kN) due to pressure on the side PQR of the tank is _____ (rounded off to the nearest integer).

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).

The initial cost of an equipment is Rs. 1,00,000. Its salvage value at the end of accounting life of 5 years is Rs. 10,000. The difference in depreciation (in Rs.) computed using 'double-declining balance method' and 'straight line method' of depreciation in Year-2 is ____ (in positive integer).

A 2 m wide strip footing is founded at a depth of 1.5 m below the ground level in a homogeneous pure clay bed. The clay bed has unit cohesion of 40 kPa. Due to seasonal fluctuations of water table from peak summer to peak monsoon period, the net ultimate bearing capacity of the footing, as per Terzaghi's theory, will

An inverted T-shaped concrete beam (B₁) in the figure, with centroidal axis X - X, is subjected to an effective prestressing force of 1000 kN acting at the bottom kern point of the beam cross-section. Also consider an identical concrete beam (B₂) with the same grade of concrete but without any prestressing force.

The additional cracking moment (in kN. m) that can be carried by beam B₁ in comparison to beam B₂ is _____ (rounded off to the nearest integer).

Consider the statements P and Q.
P: Client's Preliminary Estimate is used for budgeting costs toward the end of planning and design phase.
Q: Client's Detailed Estimate is used for controlling costs during the execution of the project.
Which one of the following options is CORRECT?

The number of degrees of freedom for a natural open channel flow with a mobile bed is

The following table gives various components of Municipal Solid Waste (MSW) and a list of treatment/separation techniques.

Component of MSW	Treatment/separation technique
P - Ferrous metals	i - Incineration
Q - Aluminum and copper	ii - Rapid composting
R- Food waste	iii - Eddy current separator
S-Cardboard	iv - Magnetic separator

The CORRECT match is 

The free mean speed is 60 km/hr on a given road. The average space headway at jam density on this road is 8 m. For a linear speed-density relationship, the maximum flow (in veh/hr/lane) expected on the road is

A homogeneous shaft PQR with fixed supports at both ends is subjected to a torsional moment T at point Q, as shown in the figure. The polar moments of inertia of the portions PQ and QR of the shaft with circular cross-sections are \(J_1\) and \(J_2\), respectively. The torsional moment reactions at the supports P and R are \(T_p\) and \(T_R\), respectively.

If \(\frac {T_p}{T_R} = 4\) and \(\frac {J_1}{J_2} = 2\), the ratio of the lengths \(\frac {L_1}{L_2}\) is

Find the correct match between the plane stress states and the Mohr's circles.