List of practice Questions

A uniform rod \( KJ \) of weight \( w \) shown in the figure rests against a frictionless vertical wall at the point \( K \) and a rough horizontal surface at point \( J \). It is given that \( w = 10 \, \text{kN} \), \( a = 4 \, \text{m} \), and \( b = 3 \, \text{m} \). The minimum coefficient of static friction that is required at the point \( J \) to hold the rod in equilibrium is _________ (round off to three decimal places).

The activities of a project are given in the following table along with their durations and dependency.

The total float of the activity \( E \) (in days) is _________ (in integer).

A group of total 16 piles are arranged in a square grid format. The center-to-center spacing (s) between adjacent piles is 3 m. The diameter (d) and length of embedment of each pile are 1 m and 20 m, respectively. The design capacity of each pile is 1000 kN in the vertical downward direction. The pile group efficiency \( \eta_g \) is given by: \[ \eta_g = 1 - \frac{\theta}{90} \left[ (n-1)m + (m-1)n \right] \frac{1}{mn} \] Where m and n are the number of rows and columns in the plan grid of pile arrangement, and \( \theta = \tan^{-1} \left( \frac{d}{s} \right) \). The design value of the pile group capacity (in kN) in the vertical downward direction is _________ \text{. (round off to the nearest integer)}

A saturated compressible clay layer of thickness h is sandwiched between two sand layers, as shown in the figure. Initially, the total vertical stress and pore water pressure at point P, which is located at the mid-depth of the clay layer, were 150 kPa and 25 kPa, respectively. Construction of a building caused an additional total vertical stress of 100 kPa at P. When the vertical effective stress at P is 175 kPa, the percentage of consolidation in the clay layer at P is _________ \text{. (in integer)}

A hydraulic jump takes place in a 6 m wide rectangular channel at a point where the upstream depth is 0.5 m (just before the jump). If the discharge in the channel is 30 m\(^3\)/s and the energy loss in the jump is 1.6 m, then the Froude number computed at the end of the jump is _________ (round off to two decimal places).

A pump with an efficiency of 80% is used to draw groundwater from a well for irrigating a flat field of area 108 hectares. The base period and delta for paddy crop on this field are 120 days and 144 cm, respectively. Water application efficiency in the field is 80%. The lowest level of water in the well is 10 m below the ground. The minimum required horse power (h.p.) of the pump is _________ (round off to two decimal places).

Two discrete spherical particles (P and Q) of equal mass density are independently released in water. Particle P and particle Q have diameters of 0.5 mm and 1.0 mm, respectively. Assume Stokes' law is valid. The drag force on particle Q will be _________ \text{ times the drag force on particle P.} (round off to the nearest integer)

At a municipal waste handling facility, 30 metric ton mixture of food waste, yard waste, and paper waste was available. The moisture content of this mixture was found to be 10%. The ideal moisture content for composting this mixture is 50%. The amount of water to be added to this mixture to bring its moisture content to the ideal condition is _________ \text{ metric ton.} (in integer)

A sewage treatment plant receives sewage at a flow rate of 5000 m\(^3\)/day. The total suspended solids (TSS) concentration in the sewage at the inlet of primary clarifier is 200 mg/L. After the primary treatment, the TSS concentration in sewage is reduced by 60 %. The sludge from the primary clarifier contains 2 % solids concentration. Subsequently, the sludge is subjected to gravity thickening process to achieve a solids concentration of 6 %. Assume that the density of sludge, before and after thickening, is 1000 kg/m\(^3\). The daily volume of the thickened sludge (in m\(^3\)/day) will be _________. (round off to the nearest integer)

Let \(y\) be a non-zero vector of size \(2022 \times 1\). Which of the following statement(s) is/are TRUE?

Which of the following statement(s) is/are correct?

Water is flowing in a horizontal, frictionless, rectangular channel. A smooth hump is built on the channel floor at a section and its height is gradually increased to reach choked condition in the channel. The depth of water at this section is \(y_2\) and that at its upstream section is \(y_1\). The correct statement(s) for the choked and unchoked conditions in the channel is/are

A pair of six-faced dice is rolled thrice. The probability that the sum of the outcomes in each roll equals 4 in exactly two of the three attempts is _________ (round off to three decimal places).

Consider two linearly elastic rods HI and IJ, each of length b, as shown in the figure. The rods are co-linear, and confined between two fixed supports at H and J. Both the rods are initially stress free. The coefficient of linear thermal expansion is \( \alpha = 10^{-6} \, \degree C^{-1} \), and the temperature of rod IJ is raised by \( \Delta T = 50 \degree C \, \text{, whereas the temperature of rod HI remains unchanged. An external horizontal force P is now applied at node I. It is given that the axial rigidities of the rods HI and IJ are 2AE and AE, respectively.

The linearly elastic planar structure shown in the figure is acted upon by two vertical concentrated forces. The horizontal beams UV and WX are connected with the help of the vertical linear spring with spring constant k = 20 kN/m. The fixed supports are provided at U and X. It is given that flexural rigidity \( EI = 10^5 \) kN-m², P = 100 kN, and a = 5 m. Force \( Q \) is applied at the center of beam WX such that the force in the spring VW becomes zero. The magnitude of force \( Q \) (in kN) is _________ \text{ kN}. (round off to the nearest integer)

A post-tensioned concrete member of span 15 m and cross-section of 450 mm $\times$ 450 mm is prestressed with three steel tendons, each of cross-sectional area 200 mm$^2$. The tendons are tensioned one after another to a stress of 1500 MPa. All the tendons are straight and located at 125 mm from the bottom of the member. Assume the prestress to be the same in all tendons and the modular ratio to be 6. The average loss of prestress, due to elastic deformation of concrete, considering all three tendons is

Match the following in Column X with Column Y:

A soil sample is underlying a water column of height \( h_1 \), as shown in the figure. The vertical effective stresses at points A, B, and C are \( \sigma_A' \), \( \sigma_B' \), and \( \sigma_C' \), respectively. Let \( \gamma_{sat} \) and \( \gamma' \) be the saturated and submerged unit weights of the soil sample, respectively, and \( \gamma_w \) be the unit weight of water. Which one of the following expressions correctly represents the sum \( (\sigma_A' + \sigma_B' + \sigma_C') \)?

A 100 mg of HNO$_3$ (strong acid) is added to water, bringing the final volume to 1.0 liter. Consider the atomic weights of H, N, and O, as 1 g/mol, 14 g/mol, and 16 g/mol, respectively. The final pH of this water is (Ignore the dissociation of water.)

In a city, the chemical formula of biodegradable fraction of municipal solid waste (MSW) is \( C_{100}H_{250}O_{80}N \). The waste has to be treated by forced-aeration composting process for which air requirement has to be estimated.
Assume oxygen in air (by weight) = 23%, and density of air = 1.3 kg/m$^3$. Atomic mass: \( C = 12 \), \( H = 1 \), \( O = 16 \), \( N = 14 \). C and H are oxidized completely whereas N is converted only into NH$_3$ during oxidation.
For oxidative degradation of 1 tonne of the waste, the required theoretical volume of air (in m$^3$/tonne) will be (round off to the nearest integer)

A single-lane highway has a traffic density of 40 vehicles/km. If the time-mean speed and space-mean speed are 40 kmph and 30 kmph, respectively, the average headway (in seconds) between the vehicles is:

The inside diameter of a sampler tube is 50 mm. The inside diameter of the cutting edge is kept such that the Inside Clearance Ratio (ICR) is 1.0% to minimize the friction on the sample as the sampler tube enters into the soil. The inside diameter (in mm) of the cutting edge is _________ (round off to two decimal places).

A concentrically loaded isolated square footing of size 2 m $\times$ 2 m carries a concentrated vertical load of 1000 kN. Considering Boussinesq’s theory of stress distribution, the maximum depth (in m) of the pressure bulb corresponding to 10% of the vertical load intensity will be _________ (round off to two decimal places).

In a triaxial unconsolidated undrained (UU) test on a saturated clay sample, the cell pressure was 100 kPa. If the deviatoric stress at failure was 150 kPa, then the undrained shear strength of the soil is _________ \text{ kPa}. (in integer)

A flood control structure having an expected life of n years is designed by considering a flood of return period T years. When T = n, and n \to \infty, the structure’s hydrologic risk of failure in percentage is} _________ %. (round off to one decimal place)