List of top Questions asked in GATE CE

A two-phase signalized intersection is designed with a cycle time of 100 s. The amber and red times for each phase are 4 s and 50 s, respectively. If the total lost time per phase due to start-up and clearance is 2 s, the effective green time of each phase is \(\underline{\hspace{2cm}}\) s. (in integer)

A reinforced concrete beam with rectangular cross section (width = 300 mm, effective depth = 580 mm) is made of M30 grade concrete. It has 1% longitudinal tension reinforcement of Fe 415 grade steel. The design shear strength for this beam is 0.66 N/mm\(^2\). The beam has to resist a factored shear force of 440 kN. The spacing of two-legged, 10 mm diameter vertical stirrups of Fe 415 grade steel is \(\underline{\hspace{2cm}}\) mm. (round off to the nearest integer)

A square concrete pile of 10 m length is driven into a deep layer of uniform homogeneous clay. Average unconfined compressive strength of the clay, determined through laboratory tests on undisturbed samples extracted from the clay layer, is 100 kPa. If the ultimate compressive load capacity of the driven pile is 632 kN, the required width of the pile is \(\underline{\hspace{2cm}}\) mm. (in integer)
(Bearing capacity factor \( N_c = 9 \), adhesion factor \( \alpha = 0.7 \))

A raft foundation of \( 30 \, \text{m} \times 25 \, \text{m} \) is proposed to be constructed at a depth of 8 m in a sand layer. A 25 mm thick saturated clay layer exists 2 m below the base of the raft foundation. Below the clay layer, a dense sand layer exists at the site. A 25 mm thick undisturbed sample was collected from the mid-depth of the clay layer and tested in a laboratory oedometer under double drainage condition. It was found that the soil sample had undergone 50 % consolidation settlement in 10 minutes.
The time (in days) required for 25 % consolidation settlement of the raft foundation will be \(\underline{\hspace{2cm}}\). (round off to the nearest integer)

A two-hour duration storm event with uniform excess rainfall of 3 cm occurred on a watershed. The ordinates of streamflow hydrograph resulting from this event are given in the table. \[ \begin{array}{|c|c|} \hline \text{Time (hours)} & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \text{Streamflow (m}^3/\text{s}) & 10 & 16 & 34 & 40 & 31 & 25 & 16 & 10 \\ \hline \end{array} \] Considering a constant baseflow of 10 m\(^3\)/s, the peak flow ordinate (in m\(^3\)/s) of the one-hour unit hydrograph for the watershed is \(\underline{\hspace{2cm}}\). (in integer)

A 2 % sewage sample (in distilled water) was incubated for 3 days at 27 °C temperature. After incubation, a dissolved oxygen depletion of 10 mg/L was recorded. The biochemical oxygen demand (BOD) rate constant at 27 °C was found to be 0.23 day\(^{-1}\) (at base e).
The ultimate BOD (in mg/L) of the sewage will be \(\underline{\hspace{2cm}}\) . (round off to the nearest integer)

Consider the differential equation \[ \frac{dy}{dx} = 4(x + 2) - y \] For the initial condition \( y = 3 \) at \( x = 1 \), the value of \( y \) at \( x = 1.4 \) obtained using Euler's method with a step-size of 0.2 is \(\underline{\hspace{2cm}}\) . (round off to one decimal place)

A set of observations of independent variable \( x \) and the corresponding dependent variable \( y \) is given below. \[ \begin{array}{|c|c|} \hline x & y \\ \hline 5 & 16 \\ 2 & 10 \\ 4 & 13 \\ 3 & 12 \\ \hline \end{array} \] Based on the data, the coefficient \( a \) of the linear regression model \[ y = a + bx \] is estimated as 6.1. The coefficient \( b \) is \(\underline{\hspace{2cm}}\) . (round off to one decimal place)

Consider the linearly elastic plane frame shown in the figure. Members HF, FK, and FG are welded together at joint F. Joints K, G, and H are fixed supports. A counter-clockwise moment \( M \) is applied at joint F. Consider flexural rigidity \( EI = 10^5 \, \text{kN-m}^2 \) for each member and neglect axial deformations. \includegraphics[width=0.35\linewidth]{image51.png} If the magnitude (absolute value) of the support moment at H is 10 kN-m, the magnitude (absolute value) of the applied moment \( M \) (in kN-m) to maintain static equilibrium is \(\underline{\hspace{1cm}}\) (round off to the nearest integer).

Consider a simply supported beam PQ as shown in the figure. A truck having 100 kN on the front axle and 200 kN on the rear axle, moves from left to right. The spacing between the axles is 3 m. The maximum bending moment at point R is \(\underline{\hspace{2cm}}\) kNm. (in integer)
\includegraphics[width=0.5\linewidth]{image52.png}

As per Rankine's theory of earth pressure, the inclination of failure planes is \[ \left( 45^\circ + \frac{\phi}{2} \right) \] with respect to the direction of the minor principal stress. The above statement is correct for which one of the following options?

In a water sample, the concentrations of Ca\(^{2+}\), Mg\(^{2+}\) and HCO\(_3^-\) are 100 mg/L, 36 mg/L and 122 mg/L, respectively. The atomic masses of various elements are: Ca = 40, Mg = 24, H = 1, C = 12, O = 16.
The total hardness and the temporary hardness in the water sample (in mg/L as CaCO\(_3\)) will

An uncompacted heap of soil has a volume of 10000 m\(^3\) and void ratio of 1. If the soil is compacted to a volume of 7500 m\(^3\), then the corresponding void ratio of the compacted soil is \(\underline{\hspace{2cm}}\) (round off to one decimal place).

A concentrated vertical load of 3000 kN is applied on a horizontal ground surface. Points P and Q are at depths 1 m and 2 m below the ground, respectively, along the line of application of the load. Considering the ground to be a linearly elastic, isotropic, semi-infinite medium, the ratio of the increase in vertical stress at P to the increase in vertical stress at Q is \(\underline{\hspace{2cm}}\) (in integer).

At a site, Static Cone Penetration Test was carried out. The measured point (tip) resistance \( q_c \) was 1000 kPa at a certain depth. The friction ratio (\( f_r \)) was estimated as 1 % at the same depth.
The value of sleeve (side) friction (in kPa) at that depth was \(\underline{\hspace{2cm}}\) . (in integer)

During a particular stage of the growth of a crop, the consumptive use of water is 2.8 mm/day. The amount of water available in the soil is 50 % of the maximum depth of available water in the root zone. Consider the maximum root zone depth of the crop as 80 mm and the irrigation efficiency as 70 %.
The interval between irrigation (in days) will be \(\underline{\hspace{2cm}}\) . (round off to the nearest integer)

The bearing of a survey line is N31°17′W. Its azimuth observed from north is \(\underline{\hspace{2cm}}\) degrees. (round off to two decimal places)

The matrix \( M \) is defined as \[ M = \begin{bmatrix} 1 & 3 \\ 4 & 2 \end{bmatrix} \] and has eigenvalues 5 and -2. The matrix \( Q \) is formed as \[ Q = M^3 - 4M^2 - 2M \] Which of the following is/are the eigenvalue(s) of matrix \( Q \)? \\