List of practice Questions

When a supercritical stream enters a mild-sloped (M) channel section, the type of flow profile would become 

The probabilities of occurrences of two independent events \( A \) and \( B \) are 0.5 and 0.8, respectively. What is the probability of occurrence of at least \( A \) or \( B \) (rounded off to one decimal place)?

A group of 9 friction piles are arranged in a square grid maintaining equal spacing in all directions. Each pile is of diameter 300 mm and length 7 m. Assume that the soil is cohesionless with effective friction angle \(\phi' = 32^\circ\). What is the center-to-center spacing of the piles (in m) for the pile group efficiency of 60%?

A possible slope failure is shown in the figure. Three soil samples are taken from different locations (I, II and III) of the potential failure plane. Which is the most appropriate shear strength test for each sample to identify the failure mechanism? 

P: Triaxial compression test 
Q: Triaxial extension test 
R: Direct shear (shear box) test 
S: Vane shear test 

The specific gravity of a soil is 2.60. The soil is at 50% degree of saturation with a water content of 15%. The void ratio of the soil is 

In cement concrete mix design, with the increase in water-cement ratio, which one of the following statements is TRUE?

A singly reinforced concrete beam of balanced section is made of M20 grade concrete and Fe415 grade steel bars. The magnitudes of the maximum compressive strain in concrete and the tensile strain in the bars at ultimate state under flexure, as per IS 456: 2000 are

In the differential equation $\dfrac{dy}{dx} + \alpha x y = 0$, $\alpha$ is a positive constant. If $y=1.0$ at $x=0.0$, and $y=0.8$ at $x=1.0$, the value of $\alpha$ is  (rounded off to three decimal places). 

Consider the fillet-welded lap joint shown in the figure (not to scale). The length of the weld shown is the effective length. The welded surfaces meet at right angle. The weld size is 8 mm, and the permissible stress in the weld is 120 MPa. What is the safe load $P$ (in kN, rounded off to one decimal place) that can be transmitted by this welded joint? 

A drained direct shear test was carried out on a sandy soil. Under a normal stress of 50 kPa, the test specimen failed at a shear stress of 35 kPa. The angle of internal friction of the sample is

A canal supplies water to an area growing wheat over 100 hectares. The duration between the first and last watering is 120 days, and the total depth of water required by the crop is 35 cm. The most intense watering is required over a period of 30 days and requires a total depth of water equal to 12 cm. Assuming precipitation to be negligible and neglecting all losses, the minimum discharge (in m\(^3\)/s, rounded off to three decimal places) in the canal to satisfy the crop requirement is 

The ordinates of a one-hour unit hydrograph (1-hr UH) for a catchment are:
 Using superposition, a $D$-hour unit hydrograph is derived. Its ordinates are found to be $3\ \text{m}^3\!/\text{s}$ at $t=1$ hour and $10\ \text{m}^3\!/\text{s}$ at $t=2$ hour. Find the value of $D$ (integer).

For a horizontal curve, the radius of a circular curve is 300 m with the design speed 15 m/s. If the allowable jerk is 0.75 m/s$^3$, what is the minimum length (in m, integer) of the transition curve?

A function $f(x)$, that is smooth and convex-shaped (concave downward) on the interval $(x_l,x_u)$ is shown. The function is observed at an odd number of regularly spaced points. If the area under the function is computed numerically, then 

Consider a doubly reinforced RCC beam with the option of using either Fe250 plain bars or Fe500 deformed bars in the compression zone. The modulus of elasticity of steel is \( 2 \times 10^5 \, \text{N/mm}^2 \). As per IS456:2000, in which type(s) of the bars, the stress in the compression steel \( (f_{sc}) \) can reach the design strength (0.87 \( f_y \)) at the limit state of collapse?

Consider the horizontal axis passing through the centroid of the steel beam cross-section shown (a symmetric "plus" of arm width $b$). What is the shape factor (rounded off to one decimal place) for the cross-section?

In the following table, identify the correct set of associations between the entries in Column-1 and Column-2. \[ \begin{array}{|c|c|} \hline \textbf{Column-1} & \textbf{Column-2} \\ \hline \text{P: Reverse Osmosis} & \text{I: Ponding} \\ \hline \text{Q: Trickling Filter} & \text{II: Freundlich Isotherm} \\ \hline \text{R: Coagulation} & \text{III: Concentration Polarization} \\ \hline \text{S: Adsorption} & \text{IV: Charge Neutralization} \\ \hline \end{array} \]

A plot of speed-density relationship (linear) of two roads (Road A and Road B) is shown in the figure. If the capacity of Road A is \(C_A\) and the capacity of Road B is \(C_B\), what is \(\frac{C_A}{C_B}\)? 

For the matrix \[ [A] = \begin{bmatrix} 1 & 2 & 3 \\ 3 & 2 & 1 \\ 3 & 1 & 2 \end{bmatrix} \] which of the following statements is/are TRUE? 

For the function \( f(x) = e^x |\sin x|, \; x \in \mathbb{R}, \) which of the following statements is/are TRUE?}

Consider the beam shown in the figure (not to scale), on a hinge support at end A and a roller support at end B. The beam has a constant flexural rigidity and is subjected to the external moments of magnitude \( M \) at one-third spans, as shown in the figure. Which of the following statements is/are TRUE? 

Which of the following statements is/are TRUE in relation to the Maximum Mixing Depth (or Height) ${Dmax}$ in the atmosphere?}

Which of the following options match the test reporting conventions with the given material tests in the table?

The differential equation \(\dfrac{du}{dt} + 2tu^{2} = 1\) is solved by a backward difference scheme. At the \((n-1)\)-th time step, \(u_{n-1}=1.75\) and \(t_{n-1}=3.14\,\text{s}\). With \(\Delta t=0.01\,\text{s}\), find \(u_n-u_{n-1}\) (round off to three decimals).

The infinitesimal element shown in the figure (not to scale) represents the state of stress at a point in a body. What is the magnitude of the maximum principal stress (in N/mm², in integer) at the point?