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Recent questions tagged numerical-answers
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41
GATE BT 2021 | Question: 47
A sedimentation tank of height $100 \textit{ cm}$ is used in a conventional activated sludge process to separate a suspension of spherical shaped granular sludge biomass of $0.5 \textit{ mm}$ diameter. The viscosity of the liquid is ... their terminal velocity instantaneously, the biomass settling time in $\textit{min}$ (rounded off to two decimal places) is ___________
A sedimentation tank of height $100 \textit{ cm}$ is used in a conventional activated sludge process to separate a suspension of spherical shaped granular sludge biomass ...
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42
GATE BT 2021 | Question: 48
In a random mating population, $Y$ and $y$ are dominant and recessive alleles, respectively. If the frequency of $Y$ allele in both sperm and egg is $0.70$, then the frequency $Y/y$ heterozygotes (rounded off to two decimal places) is ___________.
In a random mating population, $Y$ and $y$ are dominant and recessive alleles, respectively. If the frequency of $Y$ allele in both sperm and egg is $0.70$, then the freq...
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43
GATE BT 2021 | Question: 55
A bacterium produces acetic acid from ethanol as per the following reaction $2CH_3CH_2OH+2O_2 \rightarrow 2CH_3COOH+2H_2O$ The thermodynamic maximum yield of acetic acid from ethanol in $g \: g^{-1}$ (rounded off to two decimal places) is ___________
A bacterium produces acetic acid from ethanol as per the following reaction $$2CH_3CH_2OH+2O_2 \rightarrow 2CH_3COOH+2H_2O$$ The thermodynamic maximum yield of acetic aci...
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44
GATE2019: 21
The solution of $ \underset{x\rightarrow 8 }\lim\left ( \dfrac{x^{2}-64}{x-8} \right )$ is _____________.
The solution of $ \underset{x\rightarrow 8 }\lim\left ( \dfrac{x^{2}-64}{x-8} \right )$ is _____________.
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Calculus
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numerical-answers
calculus
limits
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45
GATE2019: 22
The median value for the dataset $\left ( 12, 10,16,8,90,50,30,24 \right )$ is ______________.
The median value for the dataset $\left ( 12, 10,16,8,90,50,30,24 \right )$ is ______________.
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Probability and Statistics
gate2019
numerical-answers
probability-and-statistics
statistics
median
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46
GATE2019: 23
The degree of reduction for acetic acid $\left ( C_{2} H_{4}O_{2}\right )$ is ____________.
The degree of reduction for acetic acid $\left ( C_{2} H_{4}O_{2}\right )$ is ____________.
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47
GATE2019: 24
The mass of $1$ $kmol$ of oxygen molecules is ___________$g$ (rounded off to the nearest integer).
The mass of $1$ $kmol$ of oxygen molecules is ___________$g$ (rounded off to the nearest integer).
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48
GATE2019: 25
Protein concentration of a crude enzyme preparation was $10\:mg\:mL^{-1}$. $10\:\mu L$ of this sample gave an activity of $5\:\mu mol\:min^{-1}$ under standard assay conditions. The specific activity of this crude enzyme preparation is ____________ units $mg^{-1}$.
Protein concentration of a crude enzyme preparation was $10\:mg\:mL^{-1}$. $10\:\mu L$ of this sample gave an activity of $5\:\mu mol\:min^{-1}$ under standard assay cond...
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49
GATE2019: 45
A UV-visible spectrophotometer has a minimum detectable absorbance of $0.02$. The minimum concentration of a protein sample that can be measured reliably in this instrument with a cuvette of $1cm$ path length is _________$\mu M$ . The molar extinction coefficient of the protein is $10,000\;L\:mol^{-1}\:cm^{-1}$.
A UV-visible spectrophotometer has a minimum detectable absorbance of $0.02$. The minimum concentration of a protein sample that can be measured reliably in this instrume...
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50
GATE2019: 46
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). $(R =1.987\:cal\:mol^{-1}\:K^{-1},\:T=37 \;^{\circ}C)$
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...
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51
GATE2019: 47
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 these parents will have purple flowers is ____________ (rounded off to $2$ decimal places).
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 fl...
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52
GATE2019: 48
The molecular mass of a protein is $22\:kDa$. The size of the $\text{cDNA}$ (excluding the untranslated regions) that codes for this protein is __________ $kb$ (rounded off to $1$ decimal place).
The molecular mass of a protein is $22\:kDa$. The size of the $\text{cDNA}$ (excluding the untranslated regions) that codes for this protein is __________ $kb$ (rounded o...
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53
GATE2019: 49
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 $(X)$ ... $\sigma$) for the casino payout is Rs. _____________ (rounded off to the nearest integer).
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...
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54
GATE2019: 50
$\int _{-1}^{1}\:f\left ( x \right )dx$ calculated using trapezoidal rule for the values given in the table is ______ (rounded off to $2$ ...
$\int _{-1}^{1}\:f\left ( x \right )dx$ calculated using trapezoidal rule for the values given in the table is ______ (rounded off to $2$ decimal places).$$\begin{array}{...
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Numerical Methods
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numerical-answers
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
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55
GATE2019: 51
Yeast biomass $\left ( C_{6}H_{10}O_{3}N \right )$ grown on glucose is described by the stoichiometric equation given below: $C_{6}H_{12}O_{6}+0.48\:NH_{3}+3\:O_{2} \to 0.48\:C_{6}H_{10}O_{3}N+3.12\:CO_{2}+4.32\:H_{2}O$ The amount of glucose ... $1,00,000$ $L$ is __________ $kg$ (rounded off to the nearest integer).
Yeast biomass $\left ( C_{6}H_{10}O_{3}N \right )$ grown on glucose is described by the stoichiometric equation given below:$$C_{6}H_{12}O_{6}+0.48\:NH_{3}+3\:O_{2} \to 0...
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56
GATE2019: 52
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 $10\:ppm$ ... 'chemostat' mode, the working volume require for this process is _____________ $L$ (rounded off to the nearest integer).
Phenolic wastewater discharged from an industry was treated with Pseudomonas $sp$. in an aerobic bioreactor. The influent and effluent concentrations of phenol were $10,0...
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57
GATE2019: 53
In a cross-flow filtration process, the pressure drop $\left ( \Delta P \right )$ driving the fluid flow is $2$ atm, inlet feed pressure $\left ( P_{i} \right )$ is $3$ atm and filtrate pressure $\left ( P_{f} \right )$ is equal to atmospheric pressure. The average transmembrane pressure drop $\left ( \Delta P_{m} \right )$ is ___________ atm.
In a cross-flow filtration process, the pressure drop $\left ( \Delta P \right )$ driving the fluid flow is $2$ atm, inlet feed pressure $\left ( P_{i} \right )$ is $3$ a...
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58
GATE2019: 54
An industrial fermentor containing $10,000\:L$ of medium needs to be sterilized. The initial spore concentration in the medium is $10^{6}$ spores $mL^{-1}$. The desired probability of contamination after sterilization is $10^{-3}$. The ... cell death during heating and cooling phases. The holding time of the sterilization process is___________ min (rounded off to the nearest integer).
An industrial fermentor containing $10,000\:L$ of medium needs to be sterilized. The initial spore concentration in the medium is $10^{6}$ spores $mL^{-1}$. The desired ...
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59
GATE2019: 55
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 = $0.3$ ... the agitator in the larger reactor is ___________ rpm. Assume that the scale-up factor is the cube root of the ratio of fermentor volumes.
The dimensions and operating condition of a lab-scale fermentor are as follows:Volume = $1\:L$Diameter = $20$ cmAgitator speed = $600$ rpmRatio of impeller diameter to fe...
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60
GATE2020: 21
The number of molecules of a nucleotide of molecular weight $300\:g$/mol present in $10$ picomoles is ____________ $\times10^{12}$ (round off to $2$ decimal places).
The number of molecules of a nucleotide of molecular weight $300\:g$/mol present in $10$ picomoles is ____________ $\times10^{12}$ (round off to $2$ decimal places).
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61
GATE2020: 22
To facilitate mass transfer from a gas to a liquid phase, a gas bubble of radius $r$ is introduced into the liquid. The gas bubble then breaks into $8$ bubbles of equal radius. Upon this change, the ratio of the interfacial surface area to the gas phase volume for the system changes from $3/r$ to $3n/r$. The value of $n$ is _____________________.
To facilitate mass transfer from a gas to a liquid phase, a gas bubble of radius $r$ is introduced into the liquid. The gas bubble then breaks into $8$ bubbles of equal r...
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62
GATE2020: 23
The largest eigenvalue of the matrix $\begin{bmatrix} 4 &1 \\ -2& 1 \end{bmatrix}$ is ______________.
The largest eigenvalue of the matrix $\begin{bmatrix} 4 &1 \\ -2& 1 \end{bmatrix}$ is ______________.
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Linear Algebra
gate2020
numerical-answers
linear-algebra
matrices
eigen-values
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63
GATE2020: 24
A normal random variable has mean equal to $0$, and standard deviation equal to $3$. The probability that on a random draw the value of this random variable is greater than $0$ is __________ (round off to $2$ decimal places).
A normal random variable has mean equal to $0$, and standard deviation equal to $3$. The probability that on a random draw the value of this random variable is greater th...
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Probability and Statistics
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numerical-answers
probability-and-statistics
probability
mean-and-standard-deviation
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64
GATE2020: 25
A variable $Y$ is a function of $t$. Given that $Y\left ( t=0 \right )=1$ and $Y\left ( t=1 \right )=2,\dfrac{dY}{dt}$ in the interval $t=\left [ 0,1 \right ]$ can be approximated as _________________.
A variable $Y$ is a function of $t$. Given that $Y\left ( t=0 \right )=1$ and $Y\left ( t=1 \right )=2,\dfrac{dY}{dt}$ in the interval $t=\left [ 0,1 \right ]$ can be ap...
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65
GATE2020: 43
The sequence of a $1$ $Mb$ long $DNA$ is random. This $DNA$ has all four bases occurring in equal proportion. The number of nucleotides, on average, between two successive $EcoRI$ recognition site $GAATTC$ is ____________.
The sequence of a $1$ $Mb$ long $DNA$ is random. This $DNA$ has all four bases occurring in equal proportion. The number of nucleotides, on average, between two successiv...
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66
GATE2020: 44
$E$ coli was grown in $^{15}N$ medium for several generations. Cells were then transferred to $^{14}N$ medium, allowed to grow for $4$ generations and $DNA$ was isolated immediately. The proportion of total $DNA$ with intermediate density is ___________ (round off to $2$ decimal places).
$E$ coli was grown in $^{15}N$ medium for several generations. Cells were then transferred to $^{14}N$ medium, allowed to grow for $4$ generations and $DNA$ was isolated ...
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67
GATE2020: 45
A batch reactor is inoculated with $1 \:g/L$ biomass. Under these conditions, cells exhibit a lag phase of $30$ min. If the specific growth rate in the log phase is $0.00417\;min^{-1}$, the time taken for the biomass to increase to $8 \:g/L$ is ________________ min (round off to $2$ decimal places).
A batch reactor is inoculated with $1 \:g/L$ biomass. Under these conditions, cells exhibit a lag phase of $30$ min. If the specific growth rate in the log phase is $0.00...
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68
GATE2020: 46
The system of linear equations $cx+y=5$ $3x+3y=6$ has no solution when $c$ is equal to _______________________.
The system of linear equations$$cx+y=5$$$$3x+3y=6$$has no solution when $c$ is equal to _______________________.
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Linear Algebra
gate2020
numerical-answers
linear-algebra
system-of-equations
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69
GATE2020: 47
The amino acid sequence of a peptide is $Phe-Leu-lle-Met-Ser-Leu$. The number of codons that encode the amino acids present in this peptide is given below: Phe: $2$ codons Leu: $6$ codons Ile: $3$ codons Met: $1$ codon Ser: $4$ codons The number of unique $DNA$ sequences that can encode this peptide is ___________.
The amino acid sequence of a peptide is $Phe-Leu-lle-Met-Ser-Leu$. The number of codons that encode the amino acids present in this peptide is given below:Phe: $2$ codons...
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70
GATE2020: 48
Assume that a cell culture was started with five human fibroblast cells. Two cells did not divide even once whereas the other three cells completed three rounds of cell division. At this stage, the total number of kinetochores in all the cells put together is ___________________.
Assume that a cell culture was started with five human fibroblast cells. Two cells did not divide even once whereas the other three cells completed three rounds of cell d...
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71
GATE2020: 49
Growth of an organism on glucose in a chemostat is characterized by Monod model with specific growth rate = $0.45 \:h^{-1}$ and $K_{s}= 0.5 \:g/L$. Biomass from the substrate is generated as $Y_{XS}=0.4 \:g/g$. The chemostat volume is $0.9\:L$ ... at $1\:L/h$ and contains $20 \:g/L$ of glucose. At steady state, the concentration of biomass in the chemostat is _________________ $g/L$.
Growth of an organism on glucose in a chemostat is characterized by Monod model with specific growth rate = $0.45 \:h^{-1}$ and $K_{s}= 0.5 \:g/L$. Biomass from the subst...
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72
GATE2020: 50
A function $f$ is given as : $f(X)=4X-X^{2}$ The function $f$ is maximized when $X$ is equal to _________________.
A function $f$ is given as :$$f(X)=4X-X^{2}$$The function $f$ is maximized when $X$ is equal to _________________.
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Calculus
gate2020
numerical-answers
calculus
maxima-minima
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0
answers
73
GATE2020: 51
An infinite series $S$ is given as: $S=1+2/3+3/9+4/27+5/81+\:.\dots$ (to infinity) The value of $S$ is ______________________ (round off to $2$ decimal places).
An infinite series $S$ is given as:$S=1+2/3+3/9+4/27+5/81+\:.\dots$ (to infinity)The value of $S$ is ______________________ (round off to $2$ decimal places).
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Calculus
gate2020
numerical-answers
calculus
sequences-and-series
infinite-series
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0
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74
GATE2020: 52
Protein $A$ and protein $B$ form a covalent complex. Gel filtration chromatography of this complex showed a peak corresponding to $200 \:kDa$. $SDS-PAGE$ analysis of this complex, with and without beta-mercaptoethanol, showed a single band corresponding to molecular ... the molecular weight of protein $A$ is $25 \:kDa$, the molecular weight of protein $B$ is ________________ $kDa$.
Protein $A$ and protein $B$ form a covalent complex. Gel filtration chromatography of this complex showed a peak corresponding to $200 \:kDa$. $SDS-PAGE$ analysis of this...
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75
GATE2020: 53
The concentrations of $ATP$, $ADP$ and inorganic phosphate in a cell are $2.59, \:0.73$ and $2.72 \:mM$, respectively. Under these conditions, free energy change for the synthesis of $ATP$ at $37^{\circ}C$ is $kJ$/mol (round off to $2$ decimal places). Given: free energy change for $ATP$ hydrolysis under standard conditions is $-30.5$ $kJ$/mol and $R=8.315$ $kJ/mol.K$
The concentrations of $ATP$, $ADP$ and inorganic phosphate in a cell are $2.59, \:0.73$ and $2.72 \:mM$, respectively. Under these conditions, free energy change for the ...
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76
GATE2020: 54
An algorithm was designed to find globins in protein sequence databases. A database which has $78$ globin sequences was searched using this algorithm. The algorithm retrieved $72$ sequences of which only $65$ were globins. The sensitivity of this algorithm is ___________ $\%$ (round off to $2$ decimal places).
An algorithm was designed to find globins in protein sequence databases. A database which has $78$ globin sequences was searched using this algorithm. The algorithm retri...
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77
GATE2020: 55
The mitochondrial electron transfer chain oxidizes $NADH$ with oxygen being the terminal electron acceptor. The redox potentials for the two half-reactions are given below: $NAD^{+}+H^{+}+2e^{-}\rightarrow NADH,E^{0}{}'=-0.32V$ ... electrons from $NADH$ to $O_{2}$ is _________________ $kJ/mol$ (round off to $2$ decimal places). Given: $F=96500\:C$/mol.
The mitochondrial electron transfer chain oxidizes $NADH$ with oxygen being the terminal electron acceptor. The redox potentials for the two half-reactions are given belo...
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78
GATE2020: 17
A function $f$ is as follows: $f(x) = \begin{cases} 15 & \text{if }x<1 \\ cx& \text{if } x\geq 1 \end{cases}$ The function $f$ is a continuous function when $c$ is equal to ____________________ (answer in an integer).
A function $f$ is as follows:$$f(x) = \begin{cases} 15 & \text{if }x<1 \\ cx& \text{if } x\geq 1 \end{cases}$$The function $f$ is a continuous function when $c$ is equal ...
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Calculus
gate2020
numerical-answers
calculus
continuity
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0
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79
GATE2020: 18
Given that $Z=X^{2}+Y^{2}$, the value of $\dfrac{\partial Z}{\partial X}$ for $X=1$ and $Y=0$ is ________________ (answer is an integer).
Given that $Z=X^{2}+Y^{2}$, the value of $\dfrac{\partial Z}{\partial X}$ for $X=1$ and $Y=0$ is ________________ (answer is an integer).
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Others
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numerical-answers
differential-equations
partial-differential-equation
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0
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80
GATE2020: 20
Solvents $A$ and $B$ are completely immiscible. Solute $S$ is soluble in both these solvents. $100\: g$ of $S$ was added to a container which has $2\: kg$ each of $A$ and $B$. The solute is $1.5$ times more soluble in ... thoroughly and allowed to reach equilibrium. Assuming that the solute has completely dissolved, the amount of solute in solvent $A$ phase is _____________ $g$.
Solvents $A$ and $B$ are completely immiscible. Solute $S$ is soluble in both these solvents. $100\: g$ of $S$ was added to a container which has $2\: kg$ each of $A$ and...
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