List of top Questions asked in GATE CE

A smooth vertical retaining wall supporting layered soils is shown in the figure. According to Rankine's earth pressure theory, the lateral active earth pressure acting at the base of the wall is \underline{\hspace{2cm} kPa (rounded off to one decimal place).} \includegraphics[width=0.5\linewidth]{image125.png}

Which of the following options match the test reporting conventions with the given material tests in the table? \includegraphics[width=0.75\linewidth]{image24.png}

The infinitesimal element shown in the figure (not to scale) represents the state of stress at a point in a body. What is the magnitude of the maximum principal stress (in N/mm², in integer) at the point? \includegraphics[width=0.5\linewidth]{image7.png}

An idealised bridge truss is shown in the figure. The force in Member U2L3 is \underline{\hspace{2cm} kN (round off to one decimal place).} \includegraphics[width=0.5\linewidth]{image95.png}

In the following table, identify the correct set of associations between the entries in Column-1 and Column-2.\[\begin{array}{|c|c|} \hline Column-1 & Column-2 \\ \hline \text{P: Reverse Osmosis} & \text{I: Ponding} \\ \hline \text{Q: Trickling Filter} & \text{II: Freundlich Isotherm} \\ \hline \text{R: Coagulation} & \text{III: Concentration Polarization} \\ \hline \text{S: Adsorption} & \text{IV: Charge Neutralization} \\ \hline \end{array}\]

A plot of speed-density relationship (linear) of two roads (Road A and Road B) is shown in the figure. If the capacity of Road A is \(C_A\) and the capacity of Road B is \(C_B\), what is \(\frac{C_A}{C_B}\)? \includegraphics[width=0.5\linewidth]{image9.png}

For the matrix \[ [A] = \begin{bmatrix} 1 & 2 & 3 \\ 3 & 2 & 1 \\ 3 & 1 & 2 \end{bmatrix} \\ which of the following statements is/are TRUE?

For the function \( f(x) = e^x |\sin x|, \; x \in \mathbb{R, \) which of the following statements is/are TRUE?}

Consider the beam shown in the figure (not to scale), on a hinge support at end A and a roller support at end B. The beam has a constant flexural rigidity and is subjected to the external moments of magnitude \( M \) at one-third spans, as shown in the figure. Which of the following statements is/are TRUE? \includegraphics[width=0.5\linewidth]{image8.png}

Which of the following statements is/are TRUE in relation to the Maximum Mixing Depth (or Height) $D_{\text{max}$ in the atmosphere?}

Consider the horizontal axis passing through the centroid of the steel beam cross-section shown (a symmetric "plus" of arm width $b$). What is the shape factor (rounded off to one decimal place) for the cross-section? \includegraphics[width=0.5\linewidth]{image77.png}

Consider the pin-jointed truss shown (not to scale). All members have the same axial rigidity, $AE$. Members $QR,\;RS,\;ST$ have the same length $L$. Angles $QBT,\;RCT,\;SDT$ are $90^\circ$ and angles $BQT,\;CRT,\;DST$ are $30^\circ$. A vertical load $P$ acts at joint $T$. If the vertical deflection of joint $T$ is $ \displaystyle \Delta_T=k\,\frac{PL}{AE}$, what is the value of $k$? \includegraphics[width=0.35\linewidth]{image88.png}

Consider that a force \( P \) is acting on the surface of a half-space (Boussinesq's problem). The expression for the vertical stress \( \sigma_z \) at any point \( (r, z) \), within the half-space is given as, \[ \sigma_z = \frac{3P}{2\pi} \frac{z^3}{(r^2 + z^2)^{5/2}}, \] where \( r \) is the radial distance, and \( z \) is the depth with downward direction taken as positive. At any given \( r \), there is a variation of \( \sigma_z \) along \( z \), and at a specific \( z \), the value of \( \sigma_z \) will be maximum. What is the locus of the maximum \( \sigma_z \)?

A square footing of size $2.5\,\text{m\times2.5\,\text{m}$ is placed $1.0\,\text{m}$ below the ground surface on a cohesionless soil. The water table is at the base of the footing. Above and below the water table, $\gamma=18$ and $\gamma_{\text{sat}}=20~\text{kN/m}^3$ (thus $\gamma' = 20-10 = 10~\text{kN/m}^3$). Given $N_q=58$, the net ultimate bearing capacity for the soil is $q_{nu}=1706~\text{kPa}$. Earlier, a plate load test with a circular plate of diameter $0.30$ m was carried out in the same pit during dry season (WT below influence zone). Using Terzaghi's formulation, find the ultimate bearing capacity of the plate (in kPa).}

A very wide rectangular channel carries a discharge $Q=70~\mathrm{m^3/s$ per meter width. Its bed slope changes from $S_0=0.0001$ to $S_0=0.0009$ at a point $P$ (not to scale). The Manning's roughness coefficient is $n=0.01$. What water-surface profile(s) exist(s) near the point $P$?} \includegraphics[width=0.5\linewidth]{image99.png}

Consider the fillet-welded lap joint shown in the figure (not to scale). The length of the weld shown is the effective length. The welded surfaces meet at right angle. The weld size is 8 mm, and the permissible stress in the weld is 120 MPa. What is the safe load $P$ (in kN, rounded off to one decimal place) that can be transmitted by this welded joint? \includegraphics[width=0.5\linewidth]{image66.png}

A drained direct shear test was carried out on a sandy soil. Under a normal stress of 50 kPa, the test specimen failed at a shear stress of 35 kPa. The angle of internal friction of the sample is \underline{\hspace{3cm} degree (round off to the nearest integer).}

A canal supplies water to an area growing wheat over 100 hectares. The duration between the first and last watering is 120 days, and the total depth of water required by the crop is 35 cm. The most intense watering is required over a period of 30 days and requires a total depth of water equal to 12 cm. Assuming precipitation to be negligible and neglecting all losses, the minimum discharge (in m\(^3\)/s, rounded off to three decimal places) in the canal to satisfy the crop requirement is \underline{\hspace{2cm}.}

The ordinates of a one-hour unit hydrograph (1-hr UH) for a catchment are:
\includegraphics[width=1.0\linewidth]{image55.png} Using superposition, a $D$-hour unit hydrograph is derived. Its ordinates are found to be $3\ \text{m}^3\!/\text{s}$ at $t=1$ hour and $10\ \text{m}^3\!/\text{s}$ at $t=2$ hour. Find the value of $D$ (integer).

A function $f(x)$, that is smooth and convex-shaped (concave downward) on the interval $(x_l,x_u)$ is shown. The function is observed at an odd number of regularly spaced points. If the area under the function is computed numerically, then \underline{\hspace{1cm}.} \includegraphics[width=0.5\linewidth]{image44.png}