List of top Questions asked in GATE CE, GATE CY

A prismatic steel beam is shown in the figure.

The plastic moment, \( M_p \) calculated for the collapse mechanism using static method and kinematic method is

The smallest eigenvalue and the corresponding eigenvector of the matrix \( \begin{bmatrix} 2 & -2 \\ -1 & 6 \end{bmatrix} \) respectively are

A horizontal angle \( \theta \) is measured by four different surveyors multiple times and the values reported are given below.

\[ \begin{array}{|c|c|c|} \hline \text{Surveyor} & \text{Angle \( \theta \)} & \text{Number of observations} \\ \hline 1 & 36^\circ 30' & 4 \\ 2 & 36^\circ 00' & 3 \\ 3 & 35^\circ 30' & 8 \\ 4 & 36^\circ 30' & 4 \\ \hline \end{array} \]

The most probable value of the angle \( \theta \) (in degree, round off to two decimal places) is \(\underline{\hspace{1cm}}\).

Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].
Assertion [a]: One of the best ways to reduce the amount of solid wastes is to reduce the consumption of raw materials.
Reason [r]: Solid wastes are seldom generated when raw materials are converted to goods for consumption.

The rank of the matrix \( \begin{bmatrix} 5 & 0 & -5 & 0 \\ 0 & 2 & 0 & 1 \\ -5 & 0 & 5 & 0 \\ 0 & 1 & 0 & 2 \end{bmatrix} \) is:

The value of \( \lim_{x \to \infty} \dfrac{x \ln(x)}{1 + x^2} \) is:

The stopping sight distance (SSD) for a level highway is 140 m for the design speed of 90 km/h. The acceleration due to gravity and deceleration rate are 9.81 m/s\(^2\) and 3.5 m/s\(^2\), respectively. The perception/reaction time (in s, round off to two decimal places) used in the SSD calculation is \(\underline{\hspace{2cm}}\).

For a 2° curve on a high-speed Broad Gauge (BG) rail section, the maximum sanctioned speed is 100 km/h and the equilibrium speed is 80 km/h. Consider dynamic gauge of BG rail as 1750 mm. The degree of curve is defined as the angle subtended at its center by a 30.5 m arc. The cant deficiency for the curve (in mm, round off to integer) is \(\underline{\hspace{1cm}}\).

The void ratio of a clay soil sample M decreased from 0.575 to 0.510 when the applied pressure is increased from 120 kPa to 180 kPa. For the same increment in pressure, the void ratio of another clay soil sample N decreases from 0.600 to 0.550. If the ratio of hydraulic conductivity of sample M to sample N is 0.125, then the ratio of coefficient of consolidation of sample M to sample N (round off to three decimal places) is \(\underline{\hspace{1cm}}\).

A grit chamber of rectangular cross-section is to be designed to remove particles with diameter of 0.25 mm and specific gravity of 2.70. The terminal settling velocity of the particles is estimated as 2.5 cm/s. The chamber is having a width of 0.50 m and has to carry a peak wastewater flow of 9720 m\(^3\)/d giving the depth of flow as 0.75 m. If a flow-through velocity of 0.3 m/s has to be maintained using a proportional weir at the outlet end of the chamber, the minimum length of the chamber (in m, in integer) to remove 0.25 mm particles completely is \(\underline{\hspace{2cm}}\).

A reservoir with a live storage of 300 million cubic meters (1 hectare = \(10^4 \, \text{m}^2\)) of a crop with two fillings of the reservoir. If the base period of the crop is 120 days, the duty for this crop (in hectares per cumec, round off to integer) will then be \(\underline{\hspace{1cm}}\).

In an aggregate mix, the proportions of coarse aggregate, fine aggregate and mineral filler are 55%, 40% and 5%, respectively. The values of bulk specific gravity of the coarse aggregate, fine aggregate and mineral filler are 2.55, 2.65 and 2.70, respectively. The bulk specific gravity of the aggregate mix (round off to two decimal places) is \(\underline{\hspace{2cm}}\).

An equipment has been purchased at an initial cost of ₹160000 and has an estimated salvage value of ₹10000. The equipment has an estimated life of 5 years. The difference between the book values (in ₹, in integer) obtained at the end of the 4\(^\text{th}\) year using straight line method and sum of years digit method of depreciation is \(\underline{\hspace{1cm}}\).

Numerically integrate, \( f(x) = 10x - 20x^2 \) from lower limit \( a = 0 \) to upper limit \( b = 0.5 \). Use Trapezoidal rule with five equal subdivisions. The value (in units, round off to two decimal places) obtained is \(\underline{\hspace{2cm}}\).

A fire hose nozzle directs a steady stream of water of velocity 50 m/s at an angle of 45° above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and inviscid. Consider the density of air and the air friction as negligible, and assume the acceleration due to gravity as 9.81 m/s\(^2\). The maximum height (in m, round off to two decimal places) reached by the stream above the hose nozzle will then be \(\underline{\hspace{1cm}}\).

An elevated cylindrical water storage tank is shown in the figure. The tank has inner diameter of 1.5 m. It is supported on a solid steel circular column of diameter 75 mm and total height \( L \) of 4 m. Take, water density = 1000 kg/m\(^3\) and acceleration due to gravity = 10 m/s\(^2\). \includegraphics[width=0.25\linewidth]{image37.png} \[ \text{If elastic modulus (E) of steel is 200 GPa, ignoring self-weight of the tank, for the supporting steel column to remain unbuckled, the maximum depth (h) of the water permissible (in m, round off to one decimal place) is \(\underline{\hspace{1cm}}\).} \]