List of practice Questions

In a hypothetical rock, the Kd values of element E in minerals M1, M2, and M3 are 1.5, 1.0, and 0.5, respectively. The modal abundances of M1, M2, and M3 are 10%, 40%, and 50%, respectively. The bulk partition coefficient of element E in this rock is ________
A sediment core of 4 cm diameter and 35.81 cm height was collected. This core had an initial weight of 1000.00 g and upon drying the sediment, the weight decreased by 133.75 g. This core has a void ratio of 0.42857, where void ratio is defined as the ratio of volume of void to the volume of solid (Vv/Vs). The average density of the sediment in the core is ________\ g/cm\(^3\).
On a normal fault plane dipping 60° towards east, the measured heave and throw are 5 m and 12 m, respectively. If the strike-slip component of the fault is 13 m, the magnitude of true displacement of the fault is ________m.
A 3×3 image (Image A) has been linearly stretched to get the maximum contrast in an 8-bit display system. Digital Number (DN) values of the pixels in Image A are shown. The value of the pixel marked as '?' in the output Image B after linear stretching is ________
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An NMR spectrometer operating at proton resonance frequency \( \nu \) of 1 GHz will have a magnetic field strength of __________ Tesla (T). The gyromagnetic ratio for proton, \( \gamma = 2.675 \times 10^8 \, {T}^{-1} {s}^{-1} \). (Round off to one decimal place)
For the coupled reactions given below: Glucose 6-phosphate + H\(_2\)O → Glucose + Pi (Reaction 1)
ATP + Glucose → ADP + Glucose 6-phosphate (Reaction 2) The standard free energy change of ATP hydrolysis at 25 °C is __ kJ/mol. The equilibrium constants for Reaction 1 and Reaction 2 are 360 and 800, respectively; Gas constant \( R = 8.314 \, {J mol}^{-1} {K}^{-1} \). (Round off to two decimal places)
A watershed has an area of 74 km\(^2\). The stream network within this watershed consists of three different stream orders. The stream lengths in each order are as follows: Ist order streams: 3 km, 2.5 km, 4 km, 3 km, 2 km, 5 km
IInd order streams: 10 km, 15 km, 7 km
IIIrd order streams: 30 km
The drainage density of the watershed is _________km/km\(^2\) (Round off to two decimal places)
A sample contains 7 wt% CaO and 5 wt% MgO. The molar ratio of CaO to MgO in the sample is ________(Round off to two decimal places)
If the lowest Digital Number (DN) value in an image of 10-bit radiometric resolution is 0, then the maximum DN value of that image is ________
If one liter of water at pH 7 is mixed with one liter of water at pH 6, the resulting pH of the mixture is ____________
Two fair six-sided dice, with sides numbered 1 to 6, are thrown once. The probability of getting 7 as the sum of the numbers on the top side of the dice is ________. (Round off to two decimal places)
A binary mixture of benzene and toluene under vapour-liquid equilibrium at 80 \( ^\circ {C} \) follows ideal Raoult’s law. At this condition, the saturation pressures of benzene and toluene are 101 kPa and 40 kPa, respectively. If the mole fraction of benzene in the liquid phase is 0.6, the corresponding mole fraction of benzene in the vapour phase will be ________. (Round off to two decimal places)
In a fermentation process, each mole of glucose is converted to biomass (CH\(_1.8\)O\(_0.5\)N\(_0.2\)), with a biomass yield coefficient of 0.4 C-mol/C-mol, according to the unbalanced equation given below. \[ {C}_6{H}_{12}{O}_6 + {NH}_3 + {O}_2 \to {CH}_1.8{O}_0.5{N}_0.2 + {CO}_2 + {H}_2{O} \] The moles of oxygen consumption per mole of glucose consumed during fermentation is _. (Round off to two decimal places)
Let \( a_0 = 0 \) and define \( a_n = \frac{1}{2} (1 + a_{n-1}) \) for all positive integers \( n \geq 1 \). The least value of \( n \) for which \( |1 - a_n|<\frac{1}{2^{10}} \) is ______.
The percentage of light that would pass through a sample with an absorbance of 2 would be ________%. (Round off to the nearest integer)
A hot, freshly-sterilised fermentation medium is cooled in a double-pipe heat-exchanger. The medium enters the inner pipe of the exchanger at 95 \(^\circ C\) and leaves the exchanger at 40 \(^\circ C\). Cooling water, flowing counter-currently to the medium, enters the annulus of the exchanger at 15 \(^\circ C\) and leaves the exchanger at 45 \(^\circ C\). The overall heat transfer coefficient is 1350 W m\(^{-2}\) °C\(^{-1}\). The rate of heat transfer per unit area will be _________ W/m². (Round off to the nearest integer)
A 2 L bioreactor is being operated as a chemostat, at a flow rate of 0.8 L/h and sterile feed of 10 g/L substrate. The bacterial growth follows Monod kinetics at a maximum specific growth rate of 0.6 h\(^{-1}\) with a Monod constant of 0.5 g/L and a biomass yield coefficient of 0.4 g/g. The exit biomass concentration is _________ g/L. (Round off to one decimal place)
If the doubling time of a bacterial population is 3 hours, then its average specific growth rate during this period is ________ h\(^{-1}\). (Round off to two decimal places)
For a mechanically reversible isobaric process taking place in a closed system involving 5 moles of an ideal gas, the temperature increases from an initial value of 300 K to a final value of 450 K. If the specific heat capacity at constant volume (Cv) is given as 12.5 J mol\(^{-1}\) K\(^{-1}\) and gas constant is 8.314 J mol\(^{-1}\) K\(^{-1}\), the amount of heat transferred to the system will be _ J. (Round off to the nearest integer)
The allele associated with albinism in humans is recessive (c). The probability that an albino male (cc) and a carrier female (Cc) will have an offspring with normal skin pigmentation is _________.
The contour length of a B-DNA molecule that encodes a bacterial protein of 33 kDa is ________ nm. Consider the average molecular weight of an amino acid as 110 Da and helix rise per base pair for B-DNA as 0.34 nm.
Within the Michaelis-Menten framework, the ratio of \( v_0 / V_{{max}} \) when [S] = 20 × \( K_m \) is ________.
Consider a nonlinear algebraic equation, \( e^x - 2 = 0 \). Using the Newton-Raphson method, with the initial guess of \( x_0 = 1 \), the approximated value of the root of the equation after one iteration is ________.
The value of \( k \), for which the linear equations \( 2x + 3y = 6 \) and \( 4x + 6y = 3k \) have at least one solution, is ________. (Answer in integer)
The catalytic gas-phase reaction \( A \rightarrow {products} \) is carried out in an isothermal batch reactor of 10 L volume using 0.1 kg of a solid catalyst. The reaction is first-order with: \[ (-r_A) = k' a(t) C_A \] Where: - \( k' = \frac{1}{{kg catalyst} \cdot {h}} \) - \( C_A \) is the concentration of \( A \) in mol/L. The catalyst activity \( a(t) \) undergoes first-order decay with rate constant \( k_d = 0.01 \) per hour and \( a(0) = 1 \). The reactant conversion after 1 day of operation is __________ (rounded off to 2 decimal places).