GATE BT kind:question PYQs & Answers — Page 52 — Exam Papers

Questions 511–520 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 52 of 65

The difference in concentrations of an uncharged solute between two compartments is 1.6-fold. The energy required for active transport of the solute across the membrane separating the two compartments is ______ cal mol⁻¹ (rounded off to the nearest integer). (R = 1.987 cal mol⁻¹ K⁻¹, T = 37 °C)

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In pea plants, purple color of flowers is determined by the dominant allele while white color is determined by the recessive allele. A genetic cross between two purple flower-bearing plants results in an offspring with white flowers. The probability that the third offspring from the parents will have purple flowers is ______ (rounded off to 2 decimal places).

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The molecular mass of a protein is 22 kDa. The size of the cDNA (excluding the untranslated regions) that codes for this protein is ______ kb (rounded off to 1 decimal place).

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A new game is being introduced in a casino. A player can lose Rs. 100, break even, win Rs. 100, or win Rs. 500. The probabilities (P(X)) of each of these outcomes (X) are given in the following table:

X (in Rs.)	-100	0	100	500
P(X)	0.25	0.5	0.2	0.05

The standard deviation (σ) for the casino payout is Rs. ______ (rounded off to the nearest integer).

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∫ from −1 to 1 f(x) dx calculated using trapezoid rule for the values given in the table is ______ (rounded off to 2 decimal places).

x	−1	−2/3	−1/3	0	1/3	2/3	1
f(x)	0.37	0.51	0.71	1.0	1.40	1.95	2.71

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Yeast biomass (C₆H₁₀O₃N) grown on glucose is described by the stoichiometric equation given below: C₆H₁₂O₆ + 0.48 NH₃ + 3 O₂ → 0.48 C₆H₁₀O₃N + 3.12 CO₂ + 4.32 H₂O

The amount of glucose needed for the production of 50 g L⁻¹ of yeast biomass in a batch reactor with a working volume of 1,00,000 L is ______ kg (rounded off to the nearest integer).

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Phenolic wastewater discharged from an industry was treated with Pseudomonas sp. in an aerobic bioreactor. The influent and effluent concentrations of phenol were 10,000 and 10 ppm, respectively. The inlet feed rate of wastewater was 80 L h⁻¹. The kinetic properties of the organism are as follows: Maximum specific growth rate (μₘ) = 1 h⁻¹ Saturation constant (Kₛ) = 100 mg L⁻¹ Cell death rate (k_d) = 0.01 h⁻¹ Assuming that the bioreactor operates under ‘chemostat’ mode, the working volume required for this process is ______ L (rounded off to the nearest integer).

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In a cross-flow filtration process, the pressure drop (ΔP) driving the fluid flow is 2 atm, inlet feed pressure (Pᵢ) is 3 atm and filtrate pressure (P_f) is equal to atmospheric pressure. The average transmembrane pressure drop (ΔPₘ) is ______ atm.

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An industrial fermentor containing 10,000 L of medium needs to be sterilized. The initial spore concentration in the medium is 10⁶ spores mL⁻¹. The desired probability of contamination after sterilization is 10⁻³. The death rate of spores at 121 °C is 4 min⁻¹. Assume that there is no cell death during heating and cooling phases. The holding time of the sterilization process is ______ min (rounded off to the nearest integer).

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The dimensions and operating condition of a lab-scale fermentor are as follows: Volume = 1 L Diameter = 20 cm Agitator speed = 600 rpm Ratio of impeller diameter to fermentor diameter = 0.3 This fermentor needs to be scaled up to 8,000 L for a large scale industrial application. If the scale-up is based on constant impeller tip speed, the speed of the agitator in the larger reactor is ______ rpm. Assume that the scale-up factor is the cube root of the ratio of fermentor volumes.

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