List of practice Questions

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)
The base length of the runway at the mean sea level (MSL) is 1500 m. If the runway is located at an altitude of 300 m above the MSL, the actual length (in m) of the runway to be provided is _________ (round off to the nearest integer).
Consider the polynomial \( f(x) = x^3 - 6x^2 + 11x - 6 \) on the domain \( S \) given by \( 1 \leq x \leq 3 \). The first and second derivatives are \( f'(x) \) and \( f''(x) \).
Consider the following statements:
I. The given polynomial is zero at the boundary points \( x = 1 \text{ and } x = 3. \)
II. There exists one local maxima of \( f(x) \text{ within the domain } S. \)
III. The second derivative \( f''(x)>0 \text{ throughout the domain } S. \)
IV. There exists one local minima of \( f(x) \text{ within the domain } S. \)
The correct option is:
An undamped spring-mass system with mass \( m \) and spring stiffness \( k \) is shown in the figure. The natural frequency and natural period of this system are \( \omega \) rad/s and \( T \) s, respectively. If the stiffness of the spring is doubled and the mass is halved, then the natural frequency and the natural period of the modified system, respectively, are
For the square steel beam cross-section shown in the figure, the shape factor about \(z - z\) axis is \(S\) and the plastic moment capacity is \(M_P\). Consider yield stress \(f_y = 250 \, \text{MPa}\) and \(a = 100 \, \text{mm}\). The values of \(S\) and \(M_P\) (rounded-off to one decimal place) are:
If the magnetic bearing of the Sun at a place at noon is \( S 2^\circ E \), the magnetic declination (in degrees) at that place is
P and Q are two square matrices of the same order. Which of the following statement(s) is/are correct?
In a solid waste handling facility, the moisture contents (MC) of food waste, paper waste, and glass waste were found to be MCf, MCp, and MCg, respectively. Similarly, the energy contents (EC) of plastic waste, food waste, and glass waste were found to be ECpp, ECf, and ECg, respectively. Which of the following statement(s) is/are correct?
To design an optimum municipal solid waste collection route, which of the following is/are NOT desired:
For a traffic stream, $v$ is the space mean speed, $k$ is the density, $q$ is the flow, $v_f$ is the free flow speed, and $k_j$ is the jam density. Assume that the speed decreases linearly with density.
Which of the following relation(s) is/are correct?
The error in measuring the radius of a 5 cm circular rod was 0.2%. If the cross-sectional area of the rod was calculated using this measurement, then the resulting absolute percentage error in the computed area is _________ % . (round off to two decimal places).
The components of pure shear strain in a sheared material are given in the matrix form:
\[ \epsilon = \begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix} \] Here, \(\text{Trace}(\epsilon) = 0\). Given, P = \text{Trace}(\epsilon^8) and Q = \text{Trace}(\epsilon^{11}). \text{The numerical value of} (P + Q) \text{ is} _________ \text{. (in integer)}.
Stresses acting on an infinitesimal soil element are shown in the figure (with \( \sigma_z>\sigma_x \)). The major and minor principal stresses are \( \sigma_1 \) and \( \sigma_3 \), respectively. Considering the compressive stresses as positive, which one of the following expressions correctly represents the angle between the major principal stress plane and the horizontal plane?
Match Column X with Column Y:
Which one of the following combinations is correct?
In a certain month, the reference crop evapotranspiration at a location is 6 mm/day. If the crop coefficient and soil coefficient are 1.2 and 0.8, respectively, the actual evapotranspiration in mm/day is
The dimension of dynamic viscosity is: