Which one of the following minerals has isolated (SiO$_4$)$^{4-}$ tetrahedra linked by divalent cations in octahedral coordination?
Step 1: Understanding the question.
The question asks about a mineral that has isolated tetrahedra of SiO$_4$ linked by divalent cations in octahedral coordination. This is characteristic of the mineral olivine.
Step 2: Analyzing the options.
(A) Muscovite: Muscovite is a type of mica, with a different structure from olivine.
(B) Quartz: Quartz consists of SiO$_2$ where the tetrahedra are not isolated, but form a continuous chain or framework.
(C) Beryl: Beryl is a silicate mineral with a hexagonal crystal structure, not isolated tetrahedra.
(D) Olivine: This is the correct answer. Olivine has isolated SiO$_4$ tetrahedra linked by divalent cations in octahedral coordination.
Step 3: Conclusion.
The correct answer is (D) Olivine because it matches the description of the mineral with isolated SiO$_4$ tetrahedra.
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)