Recent questions tagged numerical-answers

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1

GATE BT 2022 | Question: 17
Assuming independent assortment and no recombination, the number of different combinations of maternal and paternal chromosomes in gametes of an organism with a diploid number of $12$ is __________.

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2

GATE BT 2022 | Question: 18
A microorganism is grown in a batch culture using glucose as a carbon source. The apparent growth yield is $0.5 \frac{\text{g biomass}}{\text{g substrate}}.$ ... that there is no endogenous metabolism, the maximum biomass concentration that can be achieved is _________ $ \text{g L}^{-1}.$

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3

GATE BT 2022 | Question: 19
The degree of reduction of lactic acid $(\text{C}_{3} \text{H}_{6} \text{O}_{3})$ is __________.

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4

GATE BT 2022 | Question: 20
Consider a nonlinear algebraic equation, $x\ln x + x – 1 = 0.$ Using the Newton-Raphson method, with the initial guess of $x_{0} = 3,$ the value of $x$ after one iteration (rounded off to one decimal place) is ___________.

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5

GATE BT 2022 | Question: 21
The probability density function of a random variable $X$ is $p(x) = 2e^{-2x}.$ The probability $P(1 \leq X \leq 2)$ (rounded off to two decimal places) is _________.

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6

GATE BT 2022 | Question: 22
The maximum value of the function $f(x) = 3x^{2} – 2x^{3}$ for $x>0$ is ________.

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7

GATE BT 2022 | Question: 23
The specific growth rate of a yeast having a doubling time of $0.693 \; \text{h}$ (rounded off to nearest integer) is ________ $\text{h}^{-1}.$

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8

GATE BT 2022 | Question: 24
A fermentation broth of density $1000 \; \text{kg m}^{-3}$ and viscosity $10^{-3} \; \text{kg m}^{-1} \text{s}^{-1}$ is mixed in a $100\;\text{L}$ fermenter using a $0.1 \; \text{m}$ diameter impeller, rotating at a speed of $2 \; \text{s}^{-1}.$ The impeller Reynolds number is _________.

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9

GATE BT 2022 | Question: 25
For a pure species, the slope of the melting line $\frac{dP}{dT} \; \text{at} \; -2 \; ^{\circ} \textrm{C} \; \text{is} -5.0665 \times 10^{6} \text{Pa K}^{-1}.$ ... $\text{J} \; \text{mol}^{-1}.$

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10

GATE BT 2022 | Question: 45
Consider a random variable $X$ with mean $\mu_{x}=0.1$ and variance $\sigma_{x}^{2}=0.2.$ A new random variable $Y=2X+1$ is defined. The variance of the random variable $Y$ (rounded off to one decimal place) is __________.

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11

GATE BT 2022 | Question: 46
For $x_{1}>0$ and $x_{2}>0,$ the value of $\displaystyle{}\lim_{x_{1} \to x_{2}}\frac{x_{1}-x_{2}}{x_{2}\ln\left(\frac{x_{1}}{x_{2}}\right)}$ is __________.

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12

GATE BT 2022 | Question: 47
Figure below depicts simplified metabolic and transport reactions taking place in the production of $\text{B}$ from $\text{A}$ in a cell. The subscript $`i\text{'}$ refers to intracellular metabolites. $r_{j}$ is the $j^{\text{th}}$ ... $\text{B}, \; r_{4}$ is ___________$\frac{g}{(\text{g dry mass)h}}.$

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13

GATE BT 2022 | Question: 48
The amount of biomass in a reactor at the end of the batch process is $50 \; \text{g}.$ Fed-batch operation is initiated by feeding the substrate solution at a constant rate of $1 \; \text{L h}^{-1}.$ The concentration of substrate in the feed is ... system is at quasi-steady state, the maximum amount of biomass after $5 \; \text{h}$ of feeding is __________ $\text{g}.$

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14

GATE BT 2022 | Question: 49
An enzyme catalyzes the conversion of substrate $\text{A}$ into product $\text{B}.$ The rate equation for this reaction is $-r_{A}= \dfrac{\text{C}_{A}}{5+C_{A}} \text{mol} \; \text{L}^{-1} \text{min}^{-1}$ Substrate $\text{A}$ at an ... $\text{MFR}$ required for $50\%$ conversion of substrate to product is __________ $\text{L}.$

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15

GATE BT 2022 | Question: 50
Liquid-phase mass transfer coefficient $(k_{L})$ is measured in a stirred tank vessel using steady-state method by sparging air. Oxygen uptake by the microorganism is measured. The bulk concentration of $\text{O}_{2}$ is $10^{-4} \text{mol L}^{-1}.$ ... $100\; \text{m}^{2}/\text{m}^{3},$ the value of $k_{L}$ is ___________ $\text{cm s}^{-1}.$

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16

GATE BT 2022 | Question: 51
Consider a piston-cylinder assembly shown in the figure below. The walls of the cylinder are insulated. The cylinder contains $1$ mole of an ideal gas at $300 \; \text{K}$ and the piston is held initially at the position $\text{z}_{1}$ using a stopper. ... $\text{K}.$

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17

GATE BT 2022 | Question: 52
Consider the growth of $\textit{S. cerevisiae}$ under aerobic condition in a bioreactor and the specific growth rate of yeast is $0.5\; \text{h}^{-1}.$ ... $\text{kL mol}^{-1}\text{h}^{-1}.$

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18

GATE BT 2022 | Question: 53
A pilot sterilization was carried out in a vessel containing $1000\; \text{m}^{3}$ medium with an initial spore concentration of $10^{8} \;\text{spores/ml.}$ The accepted level of contamination after sterilization is $1$ spore in the entire vessel. The ... cycles, the holding time at $121^{\circ}\text{C}.$ (rounded off to nearest integer) is _________ $\text{min}.$

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19

GATE BT 2022 | Question: 54
A circular plasmid has three different but unique restriction sites for enzymes $ \text{a'}, \text{b'}$ and $ \text{c'}.$ When enzymes $ \text{a'}$ and $ \text{b'}$ ... $ \text{c'}$ and analysed by agarose gel electrophoresis. The number of bands observed in the gel is _________.

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20

GATE BT 2022 | Question: 55
A bacterial strain is grown in nutrient medium at $37^{\circ}\text{C}$ under aerobic conditions. The medium is inoculated with $10^{2}$ cells from a seed culture. If the number of cells in the culture is $10^{5}$ after $10$ hours of growth, the doubling time of the strain (rounded off to nearest integer) is ___________ $\text{h}.$

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21

GATE BT 2021 | Question: 20
The sum of the infinite geometric series $1 + 1/3 + 1/3^2+ 1/3^3+ \dots$ (rounded off to one decimal place) is ___________

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22

GATE BT 2021 | Question: 21
Three balls, colored in blue, green and red, are successively transferred from box $A$ to box $B$ in the order $\text{BLUE-GREEN-RED.}$ The probability of a reverse transfer of the balls to the box $A$ in the same order (rounded off to two decimal places) is ____________

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23

GATE BT 2021 | Question: 22
Decimal reduction time of a bacterial strain is $20 \textit{ min}$. Specific death rate constant in $\textit{min}^{-1}$ (rounded off to two decimal places) is ___________

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24

GATE BT 2021 | Question: 23
The value of $\underset{x \to 0} \lim \left [ \dfrac{x- \sin 2x}{x-\sin 5x} \right]$ (rounded off to two decimal places) is __________

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25

GATE BT 2021 | Question: 24
A system consists of two reactors, connected by a valve. The first reactor $(R1)$ contains an ideal gas $A$ of volume $5\: L$ and the second reactor $(R2)$ has an ideal gas $B$ of volume $10\: L$. Initially, the valve is ... If the temperature $T$ of both the reactors is maintained constant, the final equilibrium pressure in $\textit{atm}$ of the system is _____________

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26

GATE BT 2021 | Question: 25
The enzyme $\alpha$-amylase used in starch hydrolysis has an affinity constant $(K_m)$ value of $0.005 \: M$. To achieve one-fourth of the maximum rate of hydrolysis, the required starch concentration $mM$ (rounded off to two decimal places) is ____________

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27

GATE BT 2021 | Question: 39
In a Mendel’s dilhybrid experiment, a homozygous pea plant with round yellow seeds was crossed with a homozygous plant with wrinkled green seeds. $F_1$ intercross produced $560 \: F_2$ progency. The number of $F_2$ progency having both dominant traits (round and yellow) is ____________

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28

GATE BT 2021 | Question: 40
A $0.1 \textit{ mL}$ aliquot of a bacteriophage stock having a concentration of $4 \times 10^9 \textit{ phages mL}^{-1}$ is added to $0.5 \textit{ mL}$ of $\textit{E. coli}$ culture having a concentration of $2 \times 10^8 \textit{ cells mL}^{-1}$. The multiplicity of infection is ________

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29

GATE BT 2021 | Question: 41
If the area of a triangle with the vertices $(k,0), (2,0)$ and $(0, -2)$ is $2$ square units, the value of $k$ is _________

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30

GATE BT 2021 | Question: 42
In a chemostat with a dilution rate of $0.8$ $h^{-1}$, the steady state biomass concentration and the specific product formation rate are $8 \textit{ mol m}^{-3}$ and $0.2 \;(\textit{mol product}) (\textit{mol biomass})^{-1} \: h^{-1}$, respectively. The steady state product concentration in $\textit{mol m}^{-3}$ is ___________

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31

GATE BT 2021 | Question: 43
If the values of two random variables $(X,Y)$ are $(121, 360)$, $(242, 364)$ and $(363, 362)$, the value of correlation coefficient between $X$ and $Y$ (rounded off to one decimal place) is ________.

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32

GATE BT 2021 | Question: 44
The determinant of matrix $A = \begin{pmatrix} 1 & 1& 1 & 1 \\ -1 & 1 & 1 & 1 \\ -1 & -1 & 1 & 1 \\ 1 & 1 & 1 & 3 \end{pmatrix}$ is __________.

go_editor asked in Linear Algebra Mar 1, 2021

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33

GATE BT 2021 | Question: 45
It is desired to scale-up a fermentation from $1L$ to $1000L$ vessel by maintaining a constant power-to-volume ratio. The small fermenter is operated at an agitator speed of $300$ rotations per minute $(\textit{rpm})$. If the value of scale up factor is $10$, agitator speed in $\textit{rpm}$ (rounded off to the nearest integer) for the large fermenter is _________.

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34

GATE BT 2021 | Question: 46
The specific growth rate of a mold during exponential phase of its growth in a batch cultivation is $0.15 \: h^{-1}$. If the cell concentration at $30 \: h$ is $33\: g L^{-1}$, the cell concentration in $g \: L^{-1}$ (rounded off to the nearest integer) at $24 \: h$ is ________.

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35

GATE BT 2021 | Question: 49
Calculate the following integral $\int \limits_0^{\pi^2/4} \sin \sqrt{x} dx =$____________.

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36

GATE BT 2021 | Question: 50
A feed stream $(F_1)$ containing components $A$ and $B$ is processed in a system comprising of separation unit and a mixer as shown below in the schematic diagram. The mole fractions of the components $A$ and $B$ are $x_A$ and $x_B$, respectively. If $F_1+F_2=100 \textit{ kg h}^{-1}$, the degrees of freedom of the system is _________.

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37

GATE BT 2021 | Question: 51
A batch cultivation of $\textit{E. coli}$ follows zeroth order Monod's growth kinetics. The cell growth is terminated when the residual dissolved oxygen concentration attains $10\%$ of its saturation value and oxygen mass transfer coefficient $(k_La)$ reaches its ... (rounded off to two decimal places) at the end of the batch cultivation is __________

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38

GATE BT 2021 | Question: 52
Milk flowing through a stainless steel inner tube ($40 \textit{ mm}$ inner diameter) of double tube-type heater is to be heated from $10^\circ C$ to $85^\circ C$ by saturated steam condensing at $120^\circ C$ on the outer surface of the inner tube. Total ... -2} $^\circ C^{-1}$. The total length of the heating tube in $m$ (rounded off to one decimal place) is __________

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39

GATE BT 2021 | Question: 53
A $\text{DNA}$ solution of $50 \: \mu g \: mL^{-1}$ concentration gives an absorbance of $1.0$ at $260 \textit{ nm}$. An aliquot of $20 \: \mu L$ from a $50 \: \mu L$ purified plasmid solution is diluted with distilled water to a total ... $\mu g \: \mu L^{-1}$ (rounded off to two decimal places) is ________.

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40

GATE BT 2021 | Question: 54
The possible number of $\textit{Sal}\text{I}$ restriction sites in a $9\text{ kb}$ double-stranded $\text{DNA}$, with all four bases occurring in equal proportion (rounded off to the nearest integer) is _________

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