List of practice Questions

The solid cylinder of length 80 cm and mass M has a radius of 20 cm. Calculate the density of the material used if the moment of inertia of the cylinder about an axis CD parallel to AB as shown in figure is 2.7 kg m\(^2\). 

 

The angle between vector \( (\vec{A}) \) and \( (\vec{A} - \vec{B}) \) is: 

 

A lake has a maximum depth of 60 m. If the mean atmospheric pressure in the lake region is 91 kPa and the unit weight of the lake water is 9790 N/m\(^3\), the absolute pressure (in kPa, round off to two decimal places) at the maximum depth of the lake is \(\underline{\hspace{2cm}}\).
A 12-hour unit hydrograph (of 1 cm excess rainfall) of a catchment is of a triangular shape with a base width of 144 hour and a peak discharge of 23 m\(^3\)/s. The area of the catchment (in km\(^2\), round off to the nearest integer) is \(\underline{\hspace{2cm}}\).

Match List - I with List - II : 

Choose the most appropriate answer from the options given below : 
 

The internal \(d_i\) and external \(d_o\) diameters of a Shelby sampler are 48 mm and 52 mm, respectively. The area ratio (\(A_r\)) of the sampler (in %, round off to two decimal places) is _______________

A propped cantilever beam XY, with an internal hinge at the middle, is carrying a uniformly distributed load of 10 kN/m, as shown in the figure. 

The vertical reaction at support X (in kN, in integer) is \(\underline{\hspace{1cm}}\)

A solid circular torsional member OPQ is subjected to torsional moments as shown in the figure (not to scale). The yield shear strength of the constituent material is 160 MPa.
 

The absolute maximum shear stress in the member (in MPa, round off to one decimal place) is \(\underline{\hspace{1cm}}\).

The value (round off to one decimal place) of \[ \int_{-1}^1 x e^{|x|} \, dx \text{ is \(\underline{\hspace{1cm}}\).} \]
Which of the following statement(s) is/are correct?
The softening point of bitumen has the same unit as that of
The hardness of a water sample is measured directly by titration with 0.01 M solution of ethylenediamine tetraacetic acid (EDTA) using eriochrome black T (EBT) as an indicator. The EBT reacts and forms complexes with divalent metallic cations present in the water. During titration, the EDTA replaces the EBT in the complex. When the replacement of EBT is complete at the end point of the titration, the colour of the solution changes from
Relationship between traffic speed and density is described using a negatively sloped straight line. If \( v_f \) is the free-flow speed, then the speed at which the maximum flow occurs is:
The most appropriate triaxial test to assess the long-term stability of an excavated clay slope is
In case of bids in Two-Envelope System, the correct option is
Seasoning of timber for use in construction is done essentially to

A single story building model is shown in the figure. The rigid bar of mass \( m \) is supported by three massless elastic columns whose ends are fixed against rotation. For each of the columns, the applied lateral force (P) and corresponding moment (M) are also shown in the figure. The lateral deflection (\( \delta \)) of the bar is given by \( \delta = \dfrac{PL^3}{12EI} \) where \( L \) is the effective length of the column, \( E \) is the Young's modulus of elasticity and \( I \) is the area moment of inertia of the column cross-section with respect to its neutral axis. 
For the lateral deflection profile of the columns as shown in the figure, the natural frequency of the system for horizontal oscillation is 

Strain hardening of structural steel means
In general, the CORRECT sequence of surveying operations is
If A is a square matrix then orthogonality property mandates
In an equilateral triangle PQR, side PQ is divided into four equal parts, side QR is divided into six equal parts and side PR is divided into eight equal parts. The length of each subdivided part in cm is an integer. The minimum area of the triangle PQR possible, in cm², is
1. Some football players play cricket.
2. All cricket players play hockey.
Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is:

In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q. The probability that any point picked randomly within the square falls in the shaded area is 

The author said, "Musicians rehearse before their concerts. Actors rehearse their roles before the opening of a new play. On the other hand, I find it strange that many public speakers think they can just walk on to the stage and start speaking. In my opinion, it is no less important for public speakers to rehearse their talks." Based on the above passage, which one of the following is TRUE?
On a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such that you arrive at a point that is 6 units East of point O. Next, you travelled in the North-West direction, so that you arrive at point Q that is 8 units North of point P. The distance of point Q to point O, in the same units, should be \(\underline{\hspace{2cm}}\)