List of practice Questions

The state of stress in a deformable body is shown in the figure. Consider transformation of the stress from the \( x \)-\( y \) coordinate system to the \( X \)-\( Y \) coordinate system. The angle \( \theta \), locating the \( X \)-axis, is assumed to be positive when measured from the \( x \)-axis in counter-clockwise direction. 

 \[ \sigma_{xx} = 120 \, \text{MPa}, \sigma_{yy} = 40 \, \text{MPa}, \sigma_{xy} = 50 \, \text{MPa} \] The absolute magnitude of the shear stress component \( \sigma_{xy} \) (in MPa, rounded off to one decimal place) in the \( x \)-\( y \) coordinate system is \(\underline{\hspace{1cm}}\). 
 

The equation of deformation is derived to be \( y = x^2 - xL \) for a beam shown in the figure. 

A propped cantilever beam EF is subjected to a unit moving load as shown in the figure. The sign convention for positive shear force at the left and right sides of any section is also shown. 
 

The CORRECT qualitative nature of the influence line diagram for shear force at G is 

If \( P = \begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix}, \, Q = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \) then \( Q^T P^T \) is

The rank of matrix \( \begin{bmatrix} 1 & 2 & 2 & 3 \\ 3 & 4 & 2 & 5 \\ 5 & 6 & 2 & 7 \\ 7 & 8 & 2 & 9 \end{bmatrix} \) is

A secondary clarifier handles a total flow of 9600 m\(^3\)/d from the aeration tank of a conventional activated-sludge treatment system. The concentration of solids in the flow from the aeration tank is 3000 mg/L. The clarifier is required to thicken the solids to 12000 mg/L, and hence it is to be designed for a solid flux of \( 3.2 \, \frac{\text{kg}}{\text{m}^2 \cdot \text{h}} \). The surface area of the designed clarifier for thickening (in m\(^2\), in integer) is \(\underline{\hspace{1cm}}\).
Traversing is carried out for a closed traverse PQRS. The internal angles at vertices P, Q, R, and S are measured as 92°, 68°, 123°, and 77°, respectively. If fore bearing of line PQ is 27°, fore bearing of line RS (in degrees, in integer) is \(\underline{\hspace{1cm}}\).
Vehicular arrival at an isolated intersection follows the Poisson distribution. The mean vehicular arrival rate is 2 vehicles per minute. The probability (rounded off to two decimal places) that at least 2 vehicles will arrive in any given 1-minute interval is \(\underline{\hspace{1cm}}\).
A fluid flowing steadily in a circular pipe of radius \( R \) has a velocity that is everywhere parallel to the axis (centerline) of the pipe. The velocity distribution along the radial direction is \[ V_r = U \left( 1 - \frac{r^2}{R^2} \right) \] where \( r \) is the radial distance as measured from the pipe axis and \( U \) is the maximum velocity at \( r = 0 \). The average velocity of the fluid in the pipe is
Ammonia nitrogen is present in a given wastewater sample as the ammonium ion (\( \text{NH}_4^+ \)) and ammonia (\( \text{NH}_3 \)). If pH is the only deciding factor for the proportion of these two constituents, which of the following is a correct statement?
The cohesion (\( c \)), angle of internal friction (\( \phi \)) and unit weight (\( \gamma \)) of a soil are 15 kPa, 20°, and 17.5 kN/m\(^3\), respectively. The maximum depth of unsupported excavation in the soil (in m, rounded off to two decimal places) is \(\underline{\hspace{2cm}}\).
A signalized intersection operates in two phases. The lost time is 3 seconds per phase. The maximum ratios of approach flow to saturation flow for the two phases are 0.37 and 0.40. The optimum cycle length using the Webster's method (in seconds, round off to one decimal place) is \(\underline{\hspace{1cm}}\).
A 50 mL sample of industrial wastewater is taken into a silica crucible. The empty weight of the crucible is 54.352 g. The crucible with the sample is dried in a hot air oven at 104°C till a constant weight of 55.129 g. Thereafter, the crucible with the dried sample is fired at 600°C for 1 hour in a muffle furnace, and the weight of the crucible along with residue is determined as 54.783 g. The concentration of total volatile solids is \(\underline{\hspace{2cm}}\).
Which of the following is/are correct statement(s)?
Consider the limit: \[ \lim_{x \to 1} \left( \frac{1}{\ln x} - \frac{1}{x - 1} \right) \] The limit (correct up to one decimal place) is \(\underline{\hspace{2cm}}\).
The volume determined from \[ \int \int \int_V 8 x y z \, dV \text{for} V = [2, 3] \times [1, 2] \times [0, 1] \] will be (in integer) \(\underline{\hspace{1cm}}\).
Which one of the following statements is correct?
Which one of the following is correct?
The liquid forms of particulate air pollutants are
The shape of the most commonly designed highway vertical curve is
A highway designed for 80 km/h speed has a horizontal curve section with radius 250 m. If the design lateral friction is assumed to develop fully, the required super elevation is
Which of the following is NOT a correct statement?
Gypsum is typically added in cement to:
The direct and indirect costs estimated by a contractor for bidding a project are ₹160000 and ₹20000 respectively. If the mark-up applied is 10% of the bid price, the quoted price (in ₹) of the contractor is:
In an Oedometer apparatus, a specimen of fully saturated clay has been consolidated under a vertical pressure of 50 kN/m² and is presently at equilibrium. The effective stress and pore water pressure immediately on increasing the vertical stress to 150 kN/m², respectively, are: