Engineering Mathematics - Common Section - Geomatics Engineering Previous Year Questions

1

2024 · Geomatics Engineering · Common Section · Engineering Mathematics

Geomatics Engineering (GE) 2024

Which of the following options best describes the “uncertainty” in a measurement?

A

It includes both random and gross errors

B

It includes only systematic errors

C

It includes both systematic and gross errors

D

It includes both random and systematic errors

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2

2024 · Geomatics Engineering · Common Section · Engineering Mathematics

Geomatics Engineering (GE) 2024

Which of the following options describes the CORRECT relationship for a Gaussian distributed random error?

A

Probable error < Average error < Standard error < 90% error

B

Standard error < Average error < Probable error < 90% error

C

Average error < Probable error < 90% error < Standard error

D

Probable error < 90% error < Average error < Standard error

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3

2024 · Geomatics Engineering · Common Section · Engineering Mathematics

Geomatics Engineering (GE) 2024

The Chi-square distribution is used for comparing the

A

population variance with the sample variance for a given degree of freedom

B

population mean with the sample mean for a given degree of freedom

C

population median with the sample median for a given degree of freedom

D

population mean and standard deviation with the sample mean and standard deviation for a given degree of freedom

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4

2024 · Geomatics Engineering · Common Section · Engineering Mathematics

Geomatics Engineering (GE) 2024

The standard error of a unit weight for a set of angle observations is 10". The minimum number of observations required to reduce the standard error of the mean for this set of observations to 2" is ______ (in integer).

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5

2024 · Geomatics Engineering · Common Section · Engineering Mathematics

Geomatics Engineering (GE) 2024

In the figure, \(d_1\), \(d_2\), \(d_3\) are three independently measured distances for estimating the unknown distances \(x\) and \(y\). The correlation coefficient between the unknown estimates approximately equals to
\(d_1 = 100\text{ m} \pm 1\text{ cm}\)
\(d_3 = 150\text{ m} \pm 2\text{ cm}\)
\(d_2 = 175\text{ m} \pm 3\text{ cm}\)

A

+0.325

B

−0.496

C

+0.755

D

−0.592

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6

2024 · Geomatics Engineering · Common Section · Engineering Mathematics

Geomatics Engineering (GE) 2024

Find the best match between Column A and Column B

A

P–5, Q–4, R–3, S–1

B

P–5, Q–4, R–2, S–3

C

P–3, Q–1, R–2, S–4

D

P–2, Q–3, R–4, S–1

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7

2025 · Geomatics Engineering · Common Section · Engineering Mathematics

Geomatics Engineering (GE) 2025

For a sample drawn from normally distributed population, the statistic \( Y = \frac{(n-1)s^2}{\sigma^2} \), where \( n \) = sample size, \( \sigma \) = population standard deviation, \( s \) = sample standard deviation, has

A

Chi-square distribution with \((n-1) \) degrees of freedom

B

Chi-square distribution with \(n \) degrees of freedom

C

Chi-square distribution with \((n+1) \) degrees of freedom

D

Gaussian distribution with \(n \) degrees of freedom

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8

2025 · Geomatics Engineering · Common Section · Engineering Mathematics

Geomatics Engineering (GE) 2025

If the absolute temperature (greater than 0 K) of a body is doubled, it would emit ______ times more radiation.

A

2

B

4

C

8

D

16

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9

2025 · Geomatics Engineering · Common Section · Engineering Mathematics

Geomatics Engineering (GE) 2025

For the weighted least squares adjustment, which of the following statements is/are correct?

A

Weighted sum of the squares of the residuals is minimized

B

The expected value of the residuals is equal to zero

C

Redundancy of observations is maximized

D

Weights are taken inversely proportional to the variance of the observations

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10

2025 · Geomatics Engineering · Common Section · Engineering Mathematics

Geomatics Engineering (GE) 2025

For a given set of observations for distance measurements, the standard error was computed as ± 2.5 cm. Assuming that the observations conform to normal error distribution theory, the probable error will be given by ± ______ cm (rounded off to 2 decimal places).

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11

2025 · Geomatics Engineering · Common Section · Engineering Mathematics

Geomatics Engineering (GE) 2025

The covariance matrix, Σ, for the planar coordinates of a surveyed point is given as: \[ \Sigma = \begin{bmatrix} 25 \text{ mm}^2 & 0.500 \text{ mm}^2 \\ 0.500 \text{ mm}^2 & 100 \text{ mm}^2 \end{bmatrix} \] The coefficient of correlation is ______ (rounded off to 2 decimal places).

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12

2025 · Geomatics Engineering · Common Section · Engineering Mathematics

Geomatics Engineering (GE) 2025

In a given weighted graph shown below, what is the value of the expression \((p + d)^2\)
where,
i. Alphabets A, B, C, D, E and F denote the nodes
ii. Numbers 1 to 6 denote the weights between two nodes
iii. \(d\) = shortest distance between node A and node E
iv. \(p\) = number of paths with distance \(d\)

A

100

B

64

C

81

D

121

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13

2025 · Geomatics Engineering · Common Section · Engineering Mathematics

Geomatics Engineering (GE) 2025

Two adjacent angles \(A\) and \(B\) have been observed with the following mean values and correlation matrix, \(\rho\).
\(\bar{A} = 10^\circ20'10'' \pm 10''\)
\(\bar{B} = 25^\circ35'15'' \pm 20''\) \(\rho = \begin{bmatrix} 1.0 & 0.6 \\ 0.6 & 1.0 \end{bmatrix}\)
The standard deviation of the sum of the estimated angles \(\bar{A}\) and \(\bar{B}\) will be __________ (in arcseconds) (rounded off to 2 decimal places).

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14

2025 · Geomatics Engineering · Common Section · Engineering Mathematics

Geomatics Engineering (GE) 2025

The residual error in a measurement comprises a bias of + 0.08 m and a random component given by the following density function:
\(f(x) = \frac{1}{0.15} \exp\left(\frac{-x^2}{0.0072}\right)\) m
For this system, the mean square error (MSE) is __________ m. (rounded off to 2 decimal places)

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15

2025 · Geomatics Engineering · Common Section · Engineering Mathematics

Geomatics Engineering (GE) 2025

For the following ten angle observations, the standard error of the mean angle is given as __________ arcsecond (rounded off to 2 decimal places).
25°40'12'' 25°40'14'' 25°40'16'' 25°40'18'' 25°40'09''
25°40'15'' 25°40'10'' 25°40'13'' 25°40'15'' 25°40'18''

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16

2025 · Geomatics Engineering · Common Section · Engineering Mathematics

Geomatics Engineering (GE) 2025

The velocity (\(V\)) of a satellite moving in a circular orbit at a height of 1000 km above earth surface is __________ km s⁻¹ (rounded off to 2 decimal places).
\(G = 6.67 \times 10^{-11}\) m³ kg⁻¹ s⁻², \(M_e = 5.972 \times 10^{24}\) kg and \(r_e = 6378\) km

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17

2025 · Geomatics Engineering · Common Section · Engineering Mathematics

Geomatics Engineering (GE) 2025

Energy carried by a part of short-wave infrared ray at 1000 nm wavelength is __________ eV (rounded off to 2 decimal places).
\(h = 6.626 \times 10^{-34}\) J s, 1 J = \(6.242 \times 10^{18}\) eV, \(c = 3 \times 10^8\) m s⁻¹

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18

2025 · Geomatics Engineering · Common Section · Engineering Mathematics

Geomatics Engineering (GE) 2025

A point is specified along the Greenwich Meridian at 60° N latitude on an ellipsoid. The parameters of the ellipsoid are semi-major axis a=6378137 m and flattening factor f=1/298.224. The volume of the ellipsoid is given by 4πa²b/3, where b is the semi-minor axis. The latitude of the point on the sphere whose volume is the same as the volume of the ellipsoid of reference is ______° N (rounded off to 2 decimal places).

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19

2022 · Geomatics Engineering · Common Section · Engineering Mathematics

Geomatics Engineering (GE) 2022

For the following observation equation
\[2\alpha = 124^{\circ} 52' 22'' \quad \text{weight } 4,\]
the weight of \(\left(\frac{\alpha}{3}\right)\) is ____ (in integer).

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20

2022 · Geomatics Engineering · Common Section · Engineering Mathematics

Geomatics Engineering (GE) 2022

Following observation equations are obtained in a survey task.
\(x + y = 3\)
\(2x + y = 6\)
\(x + 2y = 4\)
Using least square method, the most probable values of x and y will be

A

x = 2.10, y = 0.90

B

x = 2.64, y = 0.64

C

x = 2.51, y = 0.51

D

x = 2.75, y = 0.75

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