List of top Questions asked in GATE CE

The real variables x, y, z, and the real constants p, q, r satisfy.
\( \frac{x}{pq-r^2} = \frac{y}{qr-p^2} = \frac{ z}{rp - q^2}\)
Given that the denominators are non-zero, the value of \(px +qy+rz\) is

The number of trains and their corresponding speeds for a curved Broad Gauge section with 437 m radius, are 20 trains travel at a speed of 40 km/hr 15 trains travel at a speed of 50 km/hr 12 trains travel at a speed of 60 km/hr 8 trains travel at a speed of 70 km/hr 3 trains travel at a speed of 80 km/hr If the gauge (center-to-center distance between the rail heads) is taken as 1750 mm, the required equilibrium cant (in mm) will be ______ (rounded off to the nearest integer).

The figure presents the trajectories of six vehicles within a time-space domain. The number in the parentheses represents unique identification of each vehicle. \includegraphics[width=0.5\linewidth]{78image.png} The mean speed (in km/hr) of the vehicles in the entire time-space domain is __ (rounded off to the nearest integer).

The following data is obtained from an axle load survey at a site: Average rear axle load = 12000 kg Number of commercial vehicles = 800 per day The pavement at this site would be reconstructed over a period of 5 years from the date of survey. The design life of the reconstructed pavement is 15 years. Use the standard axle load as 8160 kg and the annual average vehicle growth rate as 4.0\%. Assume that Equivalent Wheel Load Factor (EWLF) and Vehicle Damage Factor (VDF) are equal. The cumulative standard axle (in msa) for the pavement design is \_\_\_\_ (rounded off to 2 decimal places).

A bird is resting on a point P at a height of 8 m above the Mean Sea Level (MSL). Upon hearing a loud noise, the bird flies parallel to the ground surface and reaches a point Q which is located at a height of 3 m above MSL. The ground surface has a falling gradient of 1 in 2. Ignoring the effects of curvature and refraction, the horizontal distance (in meters) between points P and Q is \_\_\_\_\_ (in integer).

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 total primary consolidation settlement (\(S_c\)) of a building constructed on a 10 m thick saturated clay layer is estimated to be 50 mm. After 300 days of the construction of the building, primary consolidation settlement was reported as 10 mm. The additional time (in days) required to achieve 50\% of \(S_c\) will be \_\_\_\_\_\_ (rounded off to the nearest integer).

An infinite slope is made up of cohesionless soil with seepage parallel to and up to the sloping surface. The angle of slope is \(30^\circ\) with respect to horizontal ground surface. The unit weights of the saturated soil and water are \(20 \text{ kN/m}^3\) and \(10 \text{ kN/m}^3\), 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 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).

The ordinates of a 1-hour unit hydrograph (UH) are given below: \includegraphics[width=0.5\linewidth]{66image.png} These ordinates are used to derive a 3-hour UH. The peak discharge (in m$^3$/s) for the derived 3-hour UH is ______ (rounded off to the nearest integer).

A standard round bottom triangular canal section as shown in the figure has a bed slope of 1 in 200. Consider the Chezy's coefficient as 150 m$^{1/2}$/s. \includegraphics[width=0.5\linewidth]{89image.png} The normal depth of flow, \( y \) (in meters), for carrying a discharge of 20 m$^3$/s is __ (rounded off to 2 decimal places).

A spillway has unit discharge of \(7.5 \text{ m}^3/\text{s/m}\). The flow depth at the downstream horizontal apron is \(0.5 \text{ m}\). The tail water depth (in meters) required to form a hydraulic jump is ______ (rounded {off to 2 decimal places).}

A \(5 \text{ m} \times 5 \text{ m}\) closed tank of \(10 \text{ m}\) height contains water and oil, and is connected to an overhead water reservoir as shown in the figure. Use \(\gamma_w = 10 \text{ kN/m}^3\) and Specific gravity of oil = 0.8. \includegraphics[width=0.5\linewidth]{99image.png} The total force (in kN) due to pressure on the side \(PQR\) of the tank is __ (rounded off to the nearest integer).

Activated carbon is used to remove a pollutant from wastewater in a mixed batch reactor, which follows first-order reaction kinetics. At a reaction rate of \(0.38 \text{/day}\), the time (in days) required to remove the pollutant by 95\% is ______ (rounded off to 1 decimal place).

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).

A \(2 \text{ m} \times 2 \text{ m}\) tank of \(3 \text{ m}\) 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 \(5 \text{ g/m}^3\) at the rate of \(2 \text{ litres/s}\) and an outflow of the well stirred mixture at the rate of \(1 \text{ litre/s}\) 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 the tank at 75\% of its capacity is \_\_\_\_ grams (rounded off to 2 decimal places).

The plane truss shown in the figure has 13 joints and 22 members. The truss is made of a homogeneous, prismatic, linearly elastic material. All members have identical axial rigidity. Joints A to M indicate the joints of the truss. The truss has pin supports at joints A and L and roller support at joint K. The truss is subjected to a 10 kN vertically downward force at joint H and a 10 kN horizontal force in the rightward direction at joint B as shown. \includegraphics[width=0.5\linewidth]{67image.png} The magnitude of the reaction (in kN) at the pin support L is ______ (rounded off to 1 decimal place).

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. \includegraphics[width=0.5\linewidth]{87image.png} 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).

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 vector field \( \vec{p} \) and a scalar field \( r \) are given by \[ \vec{p} = \left( 2x^2 - 3xy + z^2 \right) \hat{i} + \left( 2y^2 - 3yz + x^2 \right) \hat{j} + \left( 2z^2 - 3xz + x^2 \right) \hat{k} \] \[ r = 6x^2 + 4y^2 - z^2 - 9xyz - 2xy + 3xz - yz \] 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 \( \vec{p} \) is zero. Which one of the following options is CORRECT?

Find the correct match between the plane stress states and the Mohr’s circles. \includegraphics[width=0.5\linewidth]{55image.png}

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: \includegraphics[width=0.5\linewidth]{70image.png}