Surveying Question Paper on “Survey Adjustments and Errors Theory – Most Probable Values Determination”.
1. Most probable value can be found by using a ______________
a) Normal equation
b) Probability law
c) Probability curve
d) Algebraic coefficients
Answer: a
Clarification: From the unknowns, normal equations are found out. These are further used in identifying the most probable values if the number of unknowns is equal to the most probable value.
2. Most probable value is not used in the determination of which of the following?
a) Observations by conditions
b) Indirect readings from unequal weights
c) Observations from equal weights
d) Probability curve
Answer: d
Clarification: The most probable value obtained from the unknowns of the normal equation helps in the determination of direct observations from equal and unequal weights, indirect readings from equal and unequal weights, observations accompanied by condition equation.
3. If A = 57028ꞌ42ꞌꞌ, 4A = 88015ꞌ59ꞌꞌ, 5A = 143057ꞌ31ꞌꞌ. Find the most probable value of A.
a) A = 26045ꞌ46ꞌꞌ
b) A = 26054ꞌ64ꞌꞌ
c) A = 26054ꞌ46ꞌꞌ
d) A = 62054ꞌ46ꞌꞌ
Answer: c
Clarification: The coefficients of A are given as 1, 4, 5. By multiplying these we get, A = 57028ꞌ42ꞌꞌ, 16A = 3530ꞌ56ꞌꞌ, 25A = 7190ꞌ35ꞌꞌ on adding we get, 42A = 1130020ꞌ13ꞌꞌ and A = 26054ꞌ46ꞌꞌ.
4. The Most probable value found by normal equation involves the usage of known values.
a) True
b) False
Answer: b
Clarification: From the normal equations found, the most probable value can be determined. The normal equations involve the usage of unknowns which help in the determination of most probable value but the number of unknowns must be known to us.
5. It is necessary for the observed equations to be accompanied with condition equation.
a) True
b) False
Answer: b
Clarification: It is not necessary for an observed equation to be accompanied with condition equation. It indicates a certain case in the most probable values. If so, the condition equation is reduced to observed equation which will give an unknown. It is preferable than the method of correlates.
6. Most probable value determines certain observations. Which among them will give accurate value?
a) Direct observation with unequal weights
b) Indirect observation with weights
c) Direct observation with weights
d) Observation with condition equation
Answer: d
Clarification: Since the usage of condition equation is done and it is been reduced to an observed equation, this involves more accuracy in the process. The observed equation obtained can be determined by method of correlates too.
7. Find the most probable value with the observations 2.76, 4.32, 9.87, 8.83 having equal weights.
a) 6.45
b) 6.54
c) 4.65
d) 5.46
Answer: a
Clarification: The value of most probable value can be obtained by using the formula,
M = (V1 + V2 + V3 +V4) / n. On substitution, we get
M = (2.76 + 4.32 + 9.87 + 8.83) / 4
M = 6.45.
8. From which of the following cases, the value of most probable value can be easily determined?
a) Indirect method
b) Direct method
c) Method of correlates
d) From observations
Answer: c
Clarification: Among the methods available, the method of correlates is capable of providing accurate values in every step. Due to its accuracy, it is adopted in solving complex problems.
9. Determine the most probable value of B from the equations B = 65˚21ꞌ40ꞌꞌ weighing 3 and 2B = 132˚40ꞌ20ꞌꞌ weighing 2.
a) 141˚18ꞌ52.7ꞌꞌ
b) 114˚18ꞌ52.7ꞌꞌ
c) 114˚8ꞌ52.7ꞌꞌ
d) 411˚18ꞌ52.7ꞌꞌ
Answer: b
Clarification: The M.P.V of B can be found by multiplying the coefficient with the corresponding weight i.e.,
3*B = 196˚5ꞌ and similarly 8B = 1061˚22ꞌ40ꞌꞌ. On addition, we get
11B = 1257˚27ꞌ40ꞌꞌ
B = 114˚18ꞌ52.7ꞌꞌ.
10. From the set of observations (1.87+ 9.73+ 9.22), find the most probable value. The weights of the observations are given as 4, 7, 9 respectively.
a) 2.97
b) 9.72
c) 7.92
d) 7.29
Answer: c
Clarification: If the weights are unequal then the most probable vale can be given as,
M = (V1 + V2 + V3) / (w1 + w2 + w3). On substitution, we get
M = (4*1.87 + 7 * 9.73 + 9*9.22) / (4 + 7 + 9)
M = 7.92.
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