The general formula of an amphibole mineral is A₀₋1B₂C₅T₃O₂₂(OH)₂, where A, B, C, and T are cationic sites with different co-ordination numbers as stated below: A=12, B=6-8, C=6, T=4. The amount of octahedral Al in an amphibole of composition Na₀.₆Ca₂Mg3.8Al₃Si₆O₂₂(OH)₂ is ......
General formula: A₀₋₁B₂C₅T₈O₂₂(OH)₂
Coordination numbers:
Given composition: Na₀.₆Ca₂Mg₃.₈Al₃.₀Si₆.₂O₂₂(OH)₂
Identifying cation sites:
T site (tetrahedral, 4-coordinated): Si and Al
C site (6-coordinated): Mg and Al(octahedral)
B site (6-8-coordinated): Ca
A site (12-coordinated): Na
Determining octahedral Al:
From the given composition:
T site (total = 8): $$\text{Si} + \text{Al(tetrahedral)} = 8$$ $$6.2 + \text{Al(tetrahedral)} = 8$$ $$\text{Al(tetrahedral)} = 1.8$$
C site (total = 5): $$\text{Mg} + \text{Al(octahedral)} = 5$$ $$3.8 + \text{Al(octahedral)} = 5$$ $$\text{Al(octahedral)} = 1.2$$
Answer: 1.2
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)