List of practice Questions

Let \( M_{n \times p}(\mathbb{R}) \) be the subspace of \( M_{n \times p}(\mathbb{R}) \) defined by \[ V = \{ X \in M_{n \times p}(\mathbb{R}) : TX = 0 \}. \] Then the dimension of \( V \) is
The core and rim compositions of garnet are (Fe\(_{0.75}\)Ca\(_{0.90}\)Mn\(_{1.35}\))Al\(_2\)Si\(_3\)O\(_{12}\) and (Fe\(_{0.90}\)Ca\(_{1.35}\)Mn\(_{0.75}\))Al\(_2\)Si\(_3\)O\(_{12}\), respectively. The difference in mole fractions of spessertine between the core and the rim is _________ (answer in one decimal place).

The given P-T diagram shows the relative stability ranges of andalusite, sillimanite, and kyanite. The difference in degrees of freedom at points X and Y is _________. 

The difference between \(X_{\text{An}}\) and \(X_{\text{Ab}}\) in a feldspar represented by \(X\) in the given triangular diagram is _________ (answer in one decimal place). 

The geological map shows the contact between sandstone and limestone. The two dotted curves are the contours of 400 m and 500 m, respectively. The difference between the dip angles of the contact surface along the AB and AC directions is _________ degrees (rounded to two decimal places). 

In the given diagram, a 6 km high plateau is supported by a crustal root of thickness \(r\). The system is in isostatic equilibrium as per Airy’s hypothesis of isostasy. Densities of the crust and the mantle are 2800 kg/m\(^3\) and 3100 kg/m\(^3\), respectively. Assuming the acceleration due to gravity to be same throughout the region, the thickness of the root (\(r\)) is _________ km. 

The radii of \(A^{+2}\) and \(B^{-1}\) ions are 1.12 AA and 1.31AA respectively. The coordination number of \(A^{+2}\) in mineral AB\(_2\) is _________
 

Based on the given schematic ternary phase diagram, choose the correct statement(s). 

Match the metal deposits in Group I with the corresponding processes in Group II. 
Group I                       Group II 
P. Aluminum               1. Mechanical concentration 
Q. Iron                         2. Contact metasomatism 
R. Tungsten                 3. Residual concentration 
S. Thorium                   4. Chemical sedimentation 
 

Match the sedimentary structures in Group I with the corresponding processes in Group II. 
Group I                       Group II 
P. Stromatolite            1. Desiccation 
Q. Flute cast                2. Liquefaction 
R. Mud crack               3. Bioturbation 
S. Dish and pillar         4. Erosion 
 

Match the features in Group I with their characteristic rocks / rock suite in Group II. 

 

Match the fuels in Group I with corresponding areas of occurrence in Group II. 

 

Match the metamorphic rocks in Group I with corresponding parent rocks in Group II. 

Match the minerals in Group I with corresponding characteristic properties in Group II. 

 

Which of the following minerals exhibits the optic interference figure given below? 

The stereographic projection given below represents a 

Match the Precambrian lithounits in Group I with corresponding cratons in Group II. 

Figures X and Y show profile sections of folds traced by two cross-bedded sandstone beds. Which one of the following is the correct interpretation? 

The figure shows stereographic projections of the axial plane and the hinge line of a fold. Which one of the following folds is represented in the figure? 

Figures I, II and III are the outcrop patterns of three inclined beds P, Q and R on a flat ground. P is the oldest and R is the youngest amongst these beds. Identify the correct option that explains repetition of beds in the figures. 

Match the bivalves in Group I with their modes of life in Group II. 

 

Match the geomorphic features in Group I with corresponding environments in Group II. 

Group IGroup II
P. Eskers1. Beach
Q. Natural levee2. Volcanic
R. Chenier ridge3. Glacial
S. Plug dome4. Fluvial
A tabular ore body of 9 km\(^2\) area and an average thickness of 9 m has a density of 3000 kg/m\(^3\). The tonnage (in million tonnes) of the ore body is _________.
Assume that the orbit of the earth is a circle of radius 150 \(\times\) 10\(^6\) km. The gravitational constant and the earth’s orbital velocity are given as 6.7 \(\times\) 10\(^{-11}\) N·m\(^2\)/kg\(^2\) and 30 \(\times\) 10\(^3\) m/s, respectively. The calculated mass of the sun is _________ \(\times\) 10\(^30\) kg (rounded off to two decimal places).
Two vertical wells penetrating a confined aquifer are 200 m apart. The water surface elevations in these wells are 35 m and 40 m above a common reference datum. The discharge per unit area through the aquifer is 0.05 m/day. Using Darcy’s law, the coefficient of permeability is _________ m/day.