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Q41. In a mineral with formula KAl3Si3O10(F0.5OHx), the value of ‘x’ is ________. (Round off to one decimal place)
In standard mica minerals like Muscovite, the chemical recipe always requires two spots filled by a combination of Fluorine (F) and Hydroxide (OH). If the formula says there is 0.5 of Fluorine already taking up space, the remaining space left to reach the total of 2 must be filled by Hydroxide (OH). So, 2.0 minus 0.5 equals 1.5.
Q42. The dips of the normal and overturned limbs of a horizontal-overturned antiform are 30⁰ and 70⁰, respectively. The interlimb angle of this fold is ________ degrees. (In integer)
Think of a rock layer folded completely over itself, like a wave crashing. Both sides (limbs) of the fold are slanted in the exact same direction. The gentler side tilts at 30 degrees, while the steeper, upside-down side tilts at 70 degrees. To find the angle completely wedged between these two sides, you simply subtract the smaller angle from the larger one: 70 minus 30 equals 40 degrees.
Q43. The vertical separation of a displaced horizontal stratum along a dip-slip reverse fault is 10 m when measured on a section perpendicular to the fault-strike. If the dip of the fault is 30⁰, the net slip of the fault will be ________ m. (In integer)
Imagine a block of rock sliding up a slanted ramp. The ramp is tilted at a 30-degree angle. The rock was pushed high enough to be lifted straight up vertically by 10 meters. Using basic right-angle triangle math (trigonometry), the sine of the 30-degree angle equals the vertical lift divided by the diagonal sliding distance (net slip). Solving this shows it must have slid diagonally 20 meters to get exactly 10 meters higher.
Q44. The value of φ (phi) of a sediment grain having a diameter of 0.125 mm is ________. (In integer)
Geologists use a special mathematical scale called the 'phi scale' to describe how big grains of sand or gravel are, using the formula: Phi = -log2(diameter in mm). If a sand grain is 0.125 mm wide (which is 1/8 of a millimeter, or 2 to the power of -3), the formula gives us a simple integer value of 3.
Q45. The Nd143 / Nd144 and Sm147 / Nd144 ratios of a rock are 0.516 and 0.389, respectively. The rock evolved as a closed system. As per the exact parent-daughter relationship equation, the Nd143 / Nd144 ratio of the rock 4.6 × 109 years ago was __________. (Round off to three decimal places) (Use decay constant for 147Sm = 6.54 × 10-12 y-1)
The correct answer is 0.502 to 0.506. This problem uses the radiometric dating formula to look backward in time to see what an isotope ratio used to be. By multiplying the parent ratio (0.389) by the decay factor over 4.6 billion years, we subtract that generated amount from the current 0.516 ratio. This reveals that the initial ratio was roughly 0.504.
Q46. If the angular aperture of a 20X objective is 46, the numerical aperture of the water immersion objective is __________. (Round off to two decimal places) (Use RI of water = 1.33)
The correct answer is 0.50 to 0.54. 'Numerical aperture' measures how much light a microscope lens can gather. The mathematical formula is: Refractive Index (RI) × sine(half of the angular aperture). Half of the 46-degree angle is 23 degrees. The sine of 23 degrees is about 0.39. Multiplying the water's RI (1.33) by 0.39 gives a numerical aperture of approximately 0.52.
Q47. A hillslope with an angle of 40 consists of soil having an internal friction angle of 30. The factor of safety of the hillslope is ________________. (Round off to two decimal places)
The correct answer is 0.65 to 0.75. The 'factor of safety' tells us if a hill is likely to collapse in a landslide. It is calculated by dividing the soil's resisting strength (tangent of its friction angle, 30°) by the sliding force of gravity (tangent of the hill's slope, 40°). The tangent of 30 is about 0.577, and the tangent of 40 is about 0.839. Dividing 0.577 by 0.839 gives roughly 0.69. Because this number is less than 1, the hill is unsafe.
Q48. A water flow transports spherical particles (diameter = 2 mm; density = 3 g/cm3) in suspension mode. If additional particles of density 2 g/cm3 are added into the flow, then the diameter of the particles that can be transported without a change in terminal fall velocity, using Stokes law, is ____________ mm. (Round off to two decimal places) (Use density of water = 1 g/cm3)
The correct answer is 2.80 to 2.84. Stokes' Law dictates how fast a particle sinks in water. For the two different particles to sink at the exact same speed, their diameter squared multiplied by their density difference must balance. The first particle has density minus water (3 - 1 = 2) and diameter squared (2² = 4), which multiplies to 8. The second particle has density minus water (2 - 1 = 1). To balance the equation to 8, its diameter squared must be 8, making its diameter the square root of 8, which is roughly 2.83 mm.
Q49. If the dip separation vector on a normal fault plane has an attitude 60 → 040 and a magnitude of 6 m, the heave on the fault is ___________ m. (In integer)
The correct answer is 3. When a fault slides, it moves diagonally downward. The total diagonal slide is 6 meters, plunging down at a 60-degree angle. The 'heave' is simply the horizontal stretch of this slide. Using basic trigonometry, we find the horizontal distance by multiplying the total slide (6) by the cosine of the angle (60 degrees). Since the cosine of 60 degrees is 0.5, multiplying 6 by 0.5 gives a heave of exactly 3 meters.
Q50. A metamorphic rock is composed of grossular garnet (Ca3Al2Si3O12), kyanite (Al2SiO5), anorthite (CaAl2Si2O8) and quartz (SiO2). If these minerals show an univariant reaction relationship, the number of components in this assemblage is ___________. (In integer)
The correct answer is 3. To build the chemical recipes for all four of these minerals, we need to count the minimum number of basic molecular ingredients (components). Looking at the formulas, we can build every single mineral listed simply by mixing Calcium oxide (CaO), Alumina (Al2O3), and Silica (SiO2). Because everything can be created from just these three distinct chemical building blocks, the number of components is 3.