Numericals
The given section with uniform lithology and sedimentation rate records two ash layers dated at 77 Ma and 76 Ma, respectively. An index fossil species present in the lower part of the section becomes extinct at a horizon 7m above the base. The estimated age of the extinction event is ………….. Ma. (Answer in integer).
From the given diagram we can say that increase in height by 1m causes decrease in age with 0.5 Ma.
So, age at height 7m is 74 Ma Ans.
A hollow discoid (cylindrical) microfossil has an outer diameter of 20 µm, height 10 µm and wall thickness 1 µm. The internal volume that can be occupied by the organism is …………..µm3. (use π = 3.14) (Round off to one decimal place).
Given microfossil is like a cylinder as in the image,
where, outer radius (R) = 20/2 =10µm
height (h) = 10µm, π = 3.14
wall thickness =1µm
inner radius (r) = inner diameter/2 = (20-2)/2=9µm
Internal volume = volume of the hollow part
= πr2h
=3.14*81*10
=2543.4 Ans.
In the following isobaric temperature-composition diagram, the number of common phases in all the invariant points is ……………... (Answer in integer)
There are two invarient points in the system one is peritectic point where “melt + A+ C” is present.
Another invarient point is eutectic point where “melt + C + B” is present
so the common phases are melt & C
number of common phases = 2 Ans.
A muscovite has the following composition in which iron is ferrous. The amount of ‘Al’ in the tetrahedral site is …………….. (per formula unit). (Round off to two decimal places). Muscovite composition: KAl2.50Fe0.25Si3.25O10(OH)2
At the tetrahedral site there are total 4 sites of Al & Si
As given Si occupies 3.25 tetrahedral sites remaining tetrahedral 0.75 site is occupied by Al Ans.
The density of a 200 g gabbro sample, cut in the form of a cube, is 3125 kg/m3. The length of the sample is ……………… mm. (Answer in integer).
Given, mass of gabbro (m) = 200g = 0.2kg
density = 3125 kg/m3
volume of gabbro = mass/ density = 0.2/3125 = 6.4*10-5 m3
Gabbro is now converted into a cube, we can apply the formula of cube volume
V= (side or length of cube)3
6.4*10-5 = a3
a = 0.04 m = 40mm Ans.
A drill run of 3 m was carried out in a coalfield site, where rock core samples were recovered only for a cumulative length of 255 cm. The core loss in percentage is equal to …………. (Answer in integer).
Given, total drill = 3m = 300cm
recovered sample = 255cm
core loss % = (loss/total drill)*100
core loss % = (45/300)*100
= 15 % Ans.
During concretionary growth of a spherical grain of radius 2 Å, the rate of change of surface area with respect to change in radius of the grain is ………….*10−8 cm (use π = 3.14) (Round off to two decimal places).
Surface area of sphere (S)= 4πr2
the rate of change of surface area with respect of change in radius of grain = dS/dr
As S=4πr2
on differentiation wit respect to r, dS/dr = 4π*2r
dS/dr = 4*3.14*2*2
dS/dr = 50.24 Å = 50.24*10-8 cm Ans.
The weight loss during the conversion of 1 mole of gypsum to anhydrite is …………..% (atomic weights of Ca = 40.0, S = 32.0, O = 16.0, H = 1.0). (Round off to two decimal places).
Gypsum = CaSO4.2H2O, Anhydrite = CaSO4
When gypsum is converted into anhydrite the water will be removed from the gypsum
weight loss in % = ( weight removed/initial weight )*100
where, weight removed = molecular weight of water
= 2(1*2 + 16) = 36
initial weight = molecular weight of CaSO4.2H2O
= (40 + 32 + 16*4) + 2(1*2 + 16) = 172
Weight loss in % = (36/172)*100
=20.93 % Ans.
A bed with an attitude 020°, 30° NW is rotated 55° counter-clockwise (looking northerly) along its strike line. The dip of the bed after rotation will be ………………° NW. (Answer in integer).
The width of the outcrop of a fault zone on a flat surface is 100 m as shown in the figure. A vertical borehole through the fault zone measured its vertical thickness to be 100 m. The true thickness of the fault zone is ……………… m. (Round off to two decimal places).
In an oblique slip fault with an attitude 000, 30° E, the net slip vector has a length of 20 m and a rake of 30° S on the fault plane. The displacement of a horizontal bed along the fault trace in a plane perpendicular to the strike of the fault is ………………….. m. (Answer in integer).
as you can see in the diagram a triangle is given which denotes net slip, strike-slip and dip slip components.
and angle is 300
according to question we have to find out trace which is perpendicular to the strike (dip slip component)
Dip slip = sin 300 * net slip
Dip slip = (1/2)*20 = 10m Ans.
If the activity of a radioactive mineral falls from 800 counts/s to 500 counts/s in 80 minutes, half-life of the mineral is …………………….. minutes. (Round off to two decimal places).
According to the radioactive equation – N/N0 = e-λt
or log (N/N0 ) = -λt
log (500/800) = -λ*80
log(5/8) = -λ*80
λ = -0.47/-80 , λ = 0.005875
half life = 0.693/λ = 117.96 Ans.
In a laboratory experiment, water discharge through a porous rock sample in 2 hours was 10 cm3 . The cylindrical rock sample is 10 cm long and has a diameter of 50 mm. If the discharge occurred at a constant head of 300 cm, the coefficient of permeability of the rock sample is ………..*10−6 cm/s. (Round off to two decimal places).
According to the Darcy law , Q = KIA
Q = 10cm3/2hr = 5 cm3/hr = 5/60*60 cm3/sec
I = hydraulic gradient = dh/dl = 300/10 = 30
A = cross section area = 3.14*r2 = 3.14*(25/10)cm2
= 3.14*2.5*2.5 = 19.625 cm2
K= Q/IA
K = 5/60*60*30*19.625
K = 2.35 cm/sec Ans.
The following diagram represents a binary phase diagram for the system A–B at atmospheric pressure. If ‘X’ is the initial composition of melt, then the amount of melt that converts to solid when the magma cools from 1400 °C to 1250 °C is ……………….. %. (Round off to two decimal places)
Liquid at 14000C = (20/30)*100
= 66.66 %
Liquid at 12500C = (5/50)*100 = 10%
Liquid that is converted to solid = 66.66-10 = 56.66 % Ans.
The following table shows modal abundance and mineral composition data of a plutonic igneous rock. The amount of SiO2 in bulk composition of the rock is ……………….. %. (Round off to two decimal places).
Total SiO2 = (wt.% of SiO2 in Olivine)*(olivine mode) + (wt.% of SiO2 in clinopyroxene)*(pyroxene mode) + (wt.% of SiO2 in Orthopyroxene)*(orthopyroxene mode)
Total SiO2 = 0.34*45 + 0.55*35 + 0.58*20 = 46.15 % Ans.
Refer to the schematic sketch given (not to scale). Assume average saturated density of oceanic crustal rocks = 3200 kg/m3 , density of ocean water = 1000 kg/m3 , and acceleration due to gravity = 10 m/s2. The overburden pressure at a point (P) located 2 km below seabed and 4 km below the ocean surface is ………………………… MPa. (Answer in integer).
The overburden pressure = pressure by surface + pressure by sea bed
pressure = rho*g*h
overburden = 1000*10*2 + 3200*10*2
overburden = 20000 + 64000
overburden = 84000 KPa (as density in kg/m3)
overburden = 84 MPa Ans.
If the indices of refraction of a uniaxial section are ɛ = 1.653 and ω = 1.544, and the retardation between the two rays is 550 nm, then the thickness of the section is ……..µm. (Round off to two decimal places).
retardation = 550nm = 550*10-3µm
birefringence = ɛ – ω = 1.653 – 1.544
= 0.109
The formula is , retardation = birefringence * thickness
thickness = retardation / birefringence
t = 550*10-3 / 0.109
t = 5.045µm Ans.
A crystal has lattice parameters of a : 4.26 Å, b : 10 Å and c : 3.44 Å, respectively. A plane intercepts on the a, b and c axes at 2.13 Å, 10 Å and 1.72 Å, respectively. The Miller Indices for the plane, written as an integer, is …………….(Answer in integer).
intercept at axis a = 2.13/4.26 = 1/2 unit length
intercept at axis b = 10/10 = 1 unit length
intercept at axis c = 1.72/3.44 = 1/2 unit length
miller indices is the reciprocal of the intercepts –
miller indices = 2 1 2 Ans.
In the uvarovite garnet (Ca3 +2Cr2 +3Si3 +4O12), Ca is in cubic coordination, Cr is in octahedral coordination and Si is in tetrahedral coordination. The electrostatic bond strength of the Ca2+ central ion is ……………….. (Round off to two decimal places)
Bond strength = charge on the cation / CN of the cation
As given Ca is in cubic coordination so CN for Ca = 8
Bond strength = 2/8 = 0.25 Ans.
In a structurally controlled fluvial setting, an asymmetric flight of river terraces T1, T2, T3 shown in the figure was sampled at location L1. The age of the sample at L1 was 30 ka (kiloyears). Assuming that the terraces were formed entirely due to deformation related uplift, the average uplift rate in the past 30 ka in the region was…………….. mm/yr. (Answer in integer)
average uplift rate = total length / time taken for uplift
average uplift = (400-100) / 30*1000
average uplift = 300/30000
average uplift = 1m/100yr = 10mm/yr Ans.
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