Surveying

The following vertical circle readings were taken by a theodolite set up at station A to observe targets located at P and Q. Find the vertical angle . 

Which of the following triangles are well conditioned and may be suitable for control establishment using triangulation? 

The bearing of the line from North is and angle measured in clockwise direction is . The bearing of line in Quadrantal Bearing System is ____________

For a profile given in the figure in the form of three steps A, B and C, the following information is available:
Height of step A ( ) with respect to a reference line = 10 m (known and error free)
Difference in height between step A and step B ( ) = 5 m 2 mm
Difference in height between step B and step C ( ) = 8 m 3 mm
and are the unknown heights of step B and C, respectively. The step B is higher than step C and D.
The coefficient of correlation, , between the height differences = 0.25
The coefficient of correlation between estimated heights of points B and C ( ) will be ............................. (Rounded off to 2 decimal places).

As shown in the following figure, let denote three uncorrelated clockwise directions, observed at point with equal standard errors for each direction, i.e., . Let and be two included angles formed by these three directions. The covariance matrix (in arcsecond ) for these included angles will be given as: 
 

Here, the covariance matrix would typically be presented in a LaTeX format, but for now we are using a placeholder.

In the following figure, A and B are fixed points with known plane rectangular coordinates. C and D are the new points in the control survey whose coordinates are to be determined. For this network, the surveyor has measured all 8 internal angles (1 to 8) and 5 sides BC, CD, DA, AC and BD. The value of redundancy (r) for the given figure will be equal to ................. (In integer). 

A perfectly adjusted tacheometer is set at a point A having Reduced Level (RL) of 80.50 m and the following readings are taken to the staff held at point B having RL of 80.10 m.

The height of the instrument from the ground above point A is \underline{\hspace{1.8cm}} m (Rounded off to 2 decimal places).

Following is the page of a field book used for levelling. Few readings marked with ‘-’ are illegible. The Reduced Level (RL) of the Temporary Bench Mark (TBM) is ................. m (Rounded off to 2 decimal places). All the readings are in m.