# Surveying Questions and Answers – Survey Adjustments and Errors Theory – Laws of Weights

This set of Surveying Multiple Choice Questions & Answers (MCQs) focuses on “Survey Adjustments and Errors Theory – Laws of Weights”.

1. The laws of weight are established on the basis of____________
a) Observed equation
b) Normal equation
c) Least squares
d) Probability equation

Explanation: The laws of weight are established based on the method of least squares in which it describes the true value among the list of possible errors. It consists of the sum of squares with a minimum residual error.

2. In the laws of weight, weight is inversely proportional to length.
a) True
b) False

Explanation: In the laws of weight, it is described that weight is inversely proportional to the length which makes length of various routes level.

3. Weight of the equation remains unchanged even when the signs in the equation are changed.
a) True
b) False

Explanation: The laws of weight include certain cases off which the weight of the equation doesn’t change even though the sign of the equation changes. It indicates that the sig of the equation is independent of the weight applied.

4. Find the arithmetic mean if the angles and their weights were given as 20˚42ꞌ3ꞌꞌ, 20˚42ꞌ4ꞌꞌ, 20˚42ꞌ6ꞌꞌ and 2, 2, 2 respectively.
a) 20˚42ꞌ6.3ꞌꞌ
b) 20˚42ꞌ5.3ꞌꞌ
c) 20˚42ꞌ1.3ꞌꞌ
d) 20˚42ꞌ4.3ꞌꞌ

Explanation: The arithmetic mean can be calculated as,
Mean = 20˚42ꞌ + (1/3)*(3ꞌꞌ + 4ꞌꞌ + 6ꞌꞌ)
Mean = 20˚42ꞌ4.3ꞌꞌ.

5. Determine the weight of the weighted arithmetic mean if the angles and their weights are given as 40˚56ꞌ2ꞌꞌ, 40˚56ꞌ7ꞌꞌ, 40˚56ꞌ12ꞌꞌ and 5, 4, 9 respectively.
a) 13
b) 18
c) 81
d) 10

Explanation: The weight of the weighted arithmetic mean can be calculated by summation of the individual weights. So,
Weight of the arithmetic mean = 5+ 4+ 9 = 18.
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6. Find the weight of the algebraic sum of the two quantities given as 21˚43ꞌ10ꞌꞌ, 54˚32ꞌ20ꞌꞌ, having weights 5, 7 respectively.
a) 13*35
b) 13/35
c) 35/13
d) 48

Explanation: From the given, it is clear that we can use sum of reciprocals of individual weights i.e.
Summation = 1/5 + 1/7 = 13 / 35.
Weight of α+ β = (76˚15ꞌ30ꞌꞌ) = 1/ (13/35) = 35 /13.

7. If the angle α = 54˚32ꞌ12ꞌꞌ, having weight 7, is multiplied by a factor 5 then find the resulting weight of that angle.
a) 7/25
b) 25/7
c) 175
d) 571

Explanation: The weight of the angle can be found out by dividing the square of that factor with the given weight.
5α = (272˚41ꞌ) = 7 / 52 = 7 / 25.

8. Find the weight of the equation α+ β = 23˚45ꞌ20ꞌꞌ if it is multiplied by its own weight. Weight of the equation is given as 2.
a) 2
b) 1/2
c) 4
d) 5

Explanation: If the equation is multiplied by its own weight then the resulting weight will be equal to reciprocal of the original weight.
2*(α+ β) = 47˚30ꞌ40ꞌꞌ, weight = 12.

9. Determine the weight of the quantity β = 21˚54ꞌ13ꞌꞌ if it is divides by a factor 3. Its original weight is 8.
a) 9/8
b) 8/9
c) 27
d) 72

Explanation: If a quantity is divided a factor then the weight can be obtained by multiplying with square of that factor to the original weight.
β/3 = 7˚18ꞌ4.3ꞌꞌ = 8*(32) = 72.

10. What will be the value of weight if the equation α+ β = 32˚18ꞌ7ꞌꞌ having weight 5 is subtracted by 180˚?
a) 3
b) 5/3
c) 5
d) 2

Explanation: If the equation is subtracted from a constant, the weight of the equation remains unchanged. So,
180˚- 32˚18ꞌ7ꞌꞌ = 147˚41ꞌ53ꞌꞌ, weight of the equation = 5.

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