List of top Questions asked in GATE CE

A wide unlined channel carries sediment-free water. The depth of water is 1 m. The specific weight of water is 10 kN/m\(^3\). To prevent scouring, the maximum permissible tractive stress on bed is 10 N/m\(^2\). The maximum slope of the channel bed to prevent scouring is 1 in \(n\). The value of \(n\) is (in integer).

A bridge with an expected life of 50 years is designed for a flood of 10000 m\(^3\)/s corresponding to the return period of 100 years. The risk associated with this design is (rounded off to two decimal places).

A fully-penetrating well of 20 cm diameter is provided in an unconfined aquifer. The height of the ground water table is 30 m from the bottom of the aquifer. After a long period of pumping at a rate of 63 m\(^3\)/s, the drawdown in the observation wells at 10 m and 100 m from the pumped well is 12 m and 11 m, respectively. The transmissibility (in m\(^2\)/s) of the aquifer is (rounded off to one decimal place).

A homogenous, linearly elastic rod AB is connected to a linearly elastic spring BC in between the fixed supports at A and C, as shown in the figure. The cross-sectional area, modulus of elasticity, and the coefficient of thermal expansion of the rod AB are 500 mm\(^2\), \(60\times10^3\) MPa, and \(12\times10^{-6}\) per \(^{\circ}\)C, respectively. The stiffness (k) of spring BC is 2500 N/mm.

(Figure not to scale)
The internal force (in kN) that will develop in the spring BC when the temperature of rod AB is increased by \(100^{\circ}\)C is (rounded off to one decimal place).

An infinite slope with slope angle \(\beta = 22^{\circ}\) consists of soil with the following properties:
Unit weight \(\gamma = 15.72\) kN/m\(^3\)
Cohesion \(c' = 12\) kPa
Angle of internal friction \(\phi' = 15^{\circ}\)
The critical height of the slope (in m) is (rounded off to two decimal places).

Two identical blocks A and B are connected by a rigid rod. The blocks rest against vertical and horizontal planes, as shown in the figure. The coefficient of static friction at the vertical and horizontal planes is the same. If the sliding impends when \(\theta = 45^{\circ}\), the value of the coefficient of static friction is (rounded off to two decimal places).

Values of \(y\) for different values of \(x\) are tabulated below.

If a second-degree interpolating polynomial \(P_2(x)\) is used to represent \(y\), the value of \(P_2(0)\) is (rounded off to the nearest integer).

\[ f(x) = e^{-x} - x \]

Select ALL CORRECT option(s) which can be considered to check whether the flexural stresses in a prestressed concrete beam are within the allowable stresses at the transfer and the service stages.

The average sewage from a city is 90 million litres per day and the average 5-day Biochemical Oxygen Demand (BOD₅) is 300 mg/l. Average standard BOD₅ of the domestic sewage is 0.08 kg/day/person. The population equivalent of the city is

As per the Rankine's earth pressure theory, which of the following statements is/are FALSE?

Which of the following statements is/are TRUE in the context of the geometric design of highways?

A plane truss consists of two linearly elastic, homogeneous, identical members, namely PQ and QR. Both members have length (\(L\)), cross-sectional area (\(A\)), and modulus of elasticity (\(E\)). The members are inclined at \(45^{\circ}\) as shown in the figure. The truss has hinge supports at P and R. The translational degrees-of-freedom (\(u\) and \(v\)) are shown at joint Q.

(Figure not to scale)
After application of the boundary conditions, the stiffness matrix of the truss becomes:

In a laminar flow of a Newtonian fluid through a circular pipe of radius 5 cm, the maximum velocity is found to be 2 m/s. The velocity (in m/s) at a radial distance of 2.50 cm from the axis of the pipe is

The plane frame has a hinge and a roller support, and is loaded as shown in the figure. Both the columns have same height.

(Figure not to scale)
What is the absolute value of the maximum bending moment (in kN-m) in the frame?

Locations \(P\) and \(Q\) are separated by a wide valley. The difference in levels of locations \(P\) and \(Q\) measured by a levelling instrument stationed near \(P\) is 3.0 m. The same instrument stationed near \(Q\) measures the difference in levels of locations \(P\) and \(Q\) as \(-1.0\) m. Assume that the atmospheric refraction is the same during the measurements. The true difference in levels (in m) of locations \(P\) and \(Q\) is

A road is divided into four sections having varying widths as shown in the figure. Section-2 (S2) represents a capacity constrained condition with respect to the traffic flow passing through Section-1 (S1). Section-3 (S3) and Section-4 (S4) do not face any such capacity constraint with respect to the flow. A flow-density relationship for unconstrained and constrained flow conditions is shown in the figure.

If Section-1 observes density D2, the option representing the correct state of density in Sections 2, 3 and 4 is:

For a hydraulic jump formed in a rectangular horizontal channel, the sequent depth ratio is 2. The Froude number of supercritical stream is

An ordinary differential equation is given below.
\[ x^2\frac{d^2y}{dx^2} = 6y \]
Considering \(a\) and \(b\) as arbitrary constants, the general solution of the equation is

A 30 m long tape is standardized at \(25^{\circ}\text{C}\). It was used to measure the length of a line which came out to be 200 m. The temperature during the measurement was \(35^{\circ}\text{C}\). The coefficient of expansion of the tape was \(11 \times 10^{-6}\) per \(^{\circ}\text{C}\). The correction in the measured length (in mm) due to change in temperature is (in integer).

Let \(f(x)\) be a continuous function defined in \([0,2] \to \mathbb{R}\) and satisfying the equation
\[ \int_0^2 f(x)[x - f(x)]\,dx = \frac{2}{3} \]
The value of \(f(1)\) is

The height of the plane of collimation of a levelling instrument is 100.000 m from a datum. The levelling instrument measures a Back Sight of 1.500 m on a vertically held staff at a ground point \(P\). The reduced level (in m) of the ground point \(P\) with respect to the datum is (rounded off to three decimal places).

For a liquid, the permeability of a sandy soil having a void ratio of 0.60 was determined as 0.14 cm/s. Considering the same liquid and by using Taylor's equation, the permeability (in cm/s) of this soil corresponding to the void ratio of 0.80 is (rounded off to two decimal places).

To obtain an undisturbed clay soil sample, an Area Ratio of 10 % needs to be achieved for a thin walled sampling tube. If the outer diameter of the tube is 50.8 mm, the inner diameter (in mm) is (rounded off to one decimal place).

The travel times of three vehicles on a 2 km stretch of road are 4, 5, and 8 minutes. Assuming the speed of each vehicle to be constant in this stretch, the Space Mean Speed (in km/h) of the vehicles is (rounded off to two decimal places).