Step 1: Understanding the deposition rate.
The shale sequence has a thickness of 10 m, and it was deposited over 10,000 years, implying a uniform rate of deposition. The rate of deposition is:
\[
\text{Deposition rate} = \frac{10 \, \text{m}}{10000 \, \text{years}} = 0.001 \, \text{m/year}
\]
Step 2: Calculating the number of samples.
To collect samples every 500 years, we need to calculate the number of 500-year intervals in the 10,000-year period:
\[
\text{Number of samples} = \frac{10000 \, \text{years}}{500 \, \text{years/sample}} = 20 \, \text{samples}
\]
Step 3: Conclusion.
The number of samples that must be collected is 20.
In the given schematic diagram, cross beds are exposed on a vertical rock face. The feature XY (bold line) represents a/an:

The schematic diagram represents thin section of a carbonate rock. The type of cement formed by large calcite crystals is known as:

Match the following structures in Group I with the corresponding environment of deposition in Group II: 
A magma having density of 2900 kg m\(^-3\) just reaches the surface through a two-layered crust as shown in the figure below. Assuming isostatic equilibrium, its depth of melting is .......... km. (Round off to one decimal place) 
Two boreholes A and B, both inclined towards 270°, penetrate a dipping coal bed at the same point and pass through it entirely in the sub-surface as shown in the figure below. The bed dips towards 270°. The thickness of the coal bed, measured along the borehole A is 10 m and along borehole B is 8 m. The angle between the two boreholes is 20°. The orthogonal thickness \( x \) of the coal bed is ........ m. (Round off to one decimal place) 
A well-developed succession of laminated shale is bound by two volcanic ash beds that were precisely dated as shown in the schematic diagram given below. Assuming a constant sedimentation rate, the age of the fossiliferous limestone bed 65 m above the basal volcanic ash bed is ............ Ma. (Round off to nearest integer) 
The data tabulated below are for flooding events in the last 400 years.
The probability of a large flood accompanied by a glacial lake outburst flood (GLOF) in 2025 is ........... \(\times 10^{-3}\). (Round off to one decimal place)
| Year | Flood Size | Magnitude rank |
|---|---|---|
| 1625 | Large | 2 |
| 1658 | Large + GLOF | 1 |
| 1692 | Small | 4 |
| 1704 | Large | 2 |
| 1767 | Large | 2 |
| 1806 | Small | 4 |
| 1872 | Large + GLOF | 1 |
| 1909 | Large | 2 |
| 1932 | Large | 2 |
| 1966 | Medium | 3 |
| 2023 | Large + GLOF | 1 |
A satellite launching vehicle is carrying a lander for Moon mapping.
As shown in the figure below, P is the position where the gravitational forces exerted by Earth and Moon on the vehicle balance out.
The distance \( P \) from the center of the Earth is ........... \(\times 10^5\) km. (Round off to two decimal places)