List of top Civil Engineering Questions asked in GATE CE

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).

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 \(2 \text{ m} \times 2 \text{ m}\) 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).

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}

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. \includegraphics[width=0.5\linewidth]{34image.png} \text{ If \( T_P / T_R = 4 \) and \( J_1 / J_2 = 2 \), the ratio of the lengths \( L_1 / L_2 \) is:}

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?}

What are the eigenvalues of the matrix \[ \begin{bmatrix} 2 & 1 & 1
1 & 4 & 1
1 & 1 & 2 \end{bmatrix} \] ?

Consider the data of \( f(x) \) given in the table. \[ \begin{array}{|c|c|c|c|} \hline i & 0 & 1 & 2
\hline x_i & 1 & 2 & 3
\hline f(x_i) & 0 & 0.3010 & 0.4771
\hline \end{array} \] The value of \( f(1.5) \) estimated using second-order Newton's interpolation formula is \_\_\_\_\_\_\_\_ \textit{(rounded off to 2 decimal places).}

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. \includegraphics[width=0.5\linewidth]{45image.png} \ If the axial deformations are neglected, the degree of kinematic indeterminacy is \_\_\_\_\_\_ \textit{(in integer).}

An embankment is constructed with soil by maintaining the degree of saturation as 75\% during compaction. The specific gravity of soil is 2.68 and the moisture content is 17\% during compaction. Consider the unit weight of water as 10 kN/m\(^3\). The dry unit weight (in kN/m\(^3\)) of the compacted soil is \_\_\_\_\_\_\_\_\_\_ \textit{(rounded off to 2 decimal places).}

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 m\(^3\)/day) from the well is \_\_\_\_\_\_\_\_\_\_ \textit{(rounded off to 2 decimal places).}

For the following partial differential equation, \[ x \frac{\partial^2 f}{\partial x^2} + y \frac{\partial^2 f}{\partial y^2} = \frac{x^2 + y^2}{2} \] which of the following option(s) is/are CORRECT?