List of top Engineering Mathematics Questions asked in GATE Geomatics Engineering

For the following ten angle observations, the standard error of the mean angle is given as 2cm arcsecond (rounded off to 2 decimal places).

25$^\circ$40'12''	25$^\circ$40'14''	25$^\circ$40'16''	25$^\circ$40'18''	25$^\circ$40'09''
25$^\circ$40'15''	25$^\circ$40'10''	25$^\circ$40'13''	25$^\circ$40'15''	25$^\circ$40'18''

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

Two adjacent angles $ A $ and $ B $ have been observed with the following mean values and correlation matrix $ \rho $:

\[ \bar{A} = 10^\circ 20'10'' \pm 10'', \quad \bar{B} = 25^\circ 35'15'' \pm 20'' \]
\[ \rho = \begin{bmatrix} 1.0 & 0.6 \\ 0.6 & 1.0 \end{bmatrix} \]

The standard deviation of the sum of the estimated angles $ A + B $ will be 2cm arcseconds (rounded off to 2 decimal places).

Consider the nodes of a square grid A, B, C and D (shown in figure below), where a certain parameter is measured. The distances between the points is also indicated in the same figure. For example, the value observed at point A is 120 and is indicated as A (120), and the distance between points A and B is 1.0 units. The value at point ‘X’ computed using bilinear interpolation, using the values at points A, B, C and D is _________

The covariance matrix, $ \Sigma $, for the planar coordinates of a surveyed point is given as:

\[ \Sigma = \begin{bmatrix} 25 & 0.500 \\ 0.500 & 100 \end{bmatrix} \quad \text{(in mm}^2\text{)} \] The coefficient of correlation is __________ (rounded off to 2 decimal places).

In a two-dimensional coordinate system, it is proposed to determine the size and shape of a triangle ABC in addition to its location and orientation. For this, all the internal angles and sides of the triangle were observed. Further, the planar coordinates of point A and bearing/azimuth of line AB were known. The redundancy ($ r $) for the above system will be equal to _________ (Answer in integer).

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

Which one of the following image processing methods employs standard deviation?

For a given set of observations for distance measurements, the standard error was computed as $ \pm 2.5 \, {cm} $. Assuming that the observations conform to normal error distribution theory, the probable error will be given by $ \pm \, \underline{{1.5cm}} \, {cm} $ (rounded off to 2 decimal places).