# Fundamental Concepts of Surveying

 Question 1
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)
 A 0.25 B 0.4 C 0.67 D 0.83
GATE CE 2022 SET-2   Geometics Engineering
Question 1 Explanation:
\begin{aligned} r&=5 \\ e_r&=\frac{0.2}{100} \times 5=0.01cm \\ A&=\pi r^2 \\ e_A&=2 \pi r.e_r \end{aligned}
Absolute perecentage error in computed area
\begin{aligned} &=\frac{e_A}{A} \times 100 \\ &=\frac{2 \pi r.e_r}{\pi r^2} \times 100\\ &=2 \times \left ( \frac{e_r}{r} \times 100 \right )\\ &=2 \times 0.2=0.4 \end{aligned}
 Question 2
A line between stations P and Q laid on a slope of 1 in 5 was measured as 350 m using a 50 m tape. The tape is known to be short by 0.1 m.
The corrected horizontal length (in m) of the line PQ will be
 A 342.52 B 349.3 C 356.2 D 350.7
GATE CE 2022 SET-1   Geometics Engineering
Question 2 Explanation: Horizontal distance of line
$PQ=350 \cos \theta =\frac{350 \times 5}{\sqrt{26}}=343.20m$
Tape is 0.1 m short.
Nominal length of tape,$l = 50 m$
Actual length of tape, $l' = 50 - 0.1 = 49.9 m$
Corrected horizontal length of line PQ
\begin{aligned} &=\left ( \frac{l'}{l} \right ) \times 343.2\\ &=\left ( \frac{49.9}{50} \right )\times 343.2\\ &=342.517\simeq 342.52m \end{aligned}
 Question 3
In general, the CORRECT sequence of surveying operations is
 A Field observations$\rightarrow$ Reconnaissance$\rightarrow$ Data analysis$\rightarrow$ Map making B Data analysis$\rightarrow$ Reconnaissance$\rightarrow$ Field observations $\rightarrow$ Map making C Reconnaissance$\rightarrow$ Field observations $\rightarrow$ Data analysis $\rightarrow$ Map making D Reconnaissance$\rightarrow$ Data analysis $\rightarrow$ Field observations $\rightarrow$ Map making
GATE CE 2021 SET-2   Geometics Engineering
Question 3 Explanation:
Reconnaissance$\rightarrow$Field observations$\rightarrow$Data analysis$\rightarrow$Map making
 Question 4
Which of the following is/are correct statement(s)?
 A Back Bearing of a line is equal to Fore Bearing $\pm 180^{\circ}$ B If the whole circle bearing of a line is $270^{\circ}$, its reduced bearing is $90^{\circ} \mathrm{NW}$ C The boundary of water of a calm water pond will represent contour line D In the case of fixed hair stadia tachometry, the staff intercept will be larger, when the staff is held nearer to the observation point
GATE CE 2021 SET-1   Geometics Engineering
Question 4 Explanation:
The principal of fixed hair tacheometry is that distances are proportional to staff intercept.
As distance increase, staff intercept also increases.
 Question 5
In a survey work, three independent angle, X, Y and Z were observed with weight $W_{X},W_{Y},W_{Z}$ respectively. The weight of the sum of angles X, Y and Z is given by:
 A $1/(\frac{1}{W_{X}}+\frac{1}{W_{Y}}+\frac{1}{W_{Z}})$ B $(\frac{1}{W_{X}}+\frac{1}{W_{Y}}+\frac{1}{W_{Z}})$ C $W_{X}+W_{Y}+W_{Z}$ D $W_{X}^{2}+W_{Y}^{2}+W_{Z}^{2}$
GATE CE 2015 SET-1   Geomatics Engineering
 Question 6
Which of the following statements is FALSE?
 A Plumb line is along the direction of gravity B Mean Sea Level (MSL) is used as a reference surface for establishing the horizontal control C Mean Sea Level (MSL) is a simplification of Geoid D Geoid is an equi-potential surface of gravity
GATE CE 2015 SET-1   Geomatics Engineering
Question 6 Explanation:
Mean sea level (MSL) is used as a reference surface for establishing the vertical control.
 Question 7
The survey carried out to delineate natural features,such as hills, rivers, forests and manmade features, suchas towns, villages, buildings, roads, transmission lines and canals is classified as
 A engineering survey B geological survey C land survey D topographic survey
GATE CE 2014 SET-2   Geomatics Engineering
Question 7 Explanation:
Tropographic survey is done to determine the natural features of a country such as rivers, strains, lakes, wood, hills etc. and artificial features such as roads, railways, canals, towns and villages.
 Question 8
The plan of a survey plotted to a scale of 10 m to 1 cm is reduced in such a way that a line originally 10 cm long now measures 9 cm. The area of the reduced plan is measured as 81 $cm^{2}$. The actual area ($m^{2}$) of the survey is
 A 10000 B 6561 C 1000 D 656
GATE CE 2008   Geomatics Engineering
Question 8 Explanation:
Shrinking factor $= \frac{9}{10}=0.9$
Reduced plan area $=(\text { Shrinkage factor })^{2}$
$\times$ Actual plan area
$\Rightarrow \quad 81=(0.9)^{2} \times$ Actual plan area
$\Rightarrow$ Actual plan area $=100 \mathrm{cm}^{2}$
$\therefore \quad$
Actual area of survey in $\mathrm{m}^{2}$
\begin{aligned} &=100 \times(10)^{2} \\ &=10000 \end{aligned}
 Question 9
The type of surveying in which the curvature of the earth is taken into account is called
 A Geodetic surveying B Plane surveying C Preliminary surveying D Topographical surveying
GATE CE 2008   Geomatics Engineering
Question 9 Explanation:
Geodetic surveying is that type of surveying in which the shape of the earth is taken into account. Geodetic surveying involves spherical trigonometry.
 Question 10
The plan of a map was photo copied to a reduced size such that a line originally 100 mm, measures 90 mm. The original scale of the plan was 1:1000. The revised scale is
 A 1:900 B 1:1111 C 1:1121 D 1:1221
GATE CE 2007   Geomatics Engineering
Question 10 Explanation:
\begin{aligned} \text { Reduction factor }&=\frac{90}{100}=0.9 \\ \text { Revised scale }&=\text { Original scale }\\ &\times \text { Reduction factor }\\ =\frac{1}{1000} \times 0.9&=\frac{1}{1000 / 0.9}=\frac{1}{1111} \end{aligned}
There are 10 questions to complete.