Recent questions tagged numerical-answers

For a discrete random variable $X$, $\textit{ran}(X)=\{0,1,2,3\}$ and the cumulative probability $F(X )$ is shown below: $$\begin{array}{|c|c|c|c|c|} \hline X & 0 & 1 & ...

Oxygen transfer was measured in a stirred tank bioreactor using dynamic method. The dissolved oxygen tension was found to be $80 \%$ air saturation under steady state con...

Plasmid DNA $(0.5 \: \mu g)$ containing an ampicillin resistance marker was added to $200 \: \mu l$ of competent cells. The transformed competent cells were diluted $10,0...

$\textit{Saccharomyces cerevisiae}$ produces ethanol by fermentation. The theoretical yield of ethanol from $2.5$ g of glucose is _________ g.

The diameters of a large and a small vessel are $1.62$ m and $16.2$ cm. ,respectively. The vessels are geometrically similar and operated under similar volumetric agitate...

Consider the following multiple sequence alignment of four DNA sequences.$$\begin{array}{cccc} A & C & T & A \\ A & C & T & G \\ A & G & T & C \\ A & G & C & T \end{arra...

The $K_i$ of a novel competitive inhibitor designed against an enzyme is $2.5 \: \mu M$. The enzyme was assayed in the absence or presence of the inhibitor $(5 \: \mu M)$...

A heterozygous tall plant $(Tt)$ was crossed with a homozygous dwarf plant $(tt)$. The resultant seeds were collected. If five seeds are chosen at random, then the probab...

Assuming random distribution of nucleotides, the average number of fragments generated upon digestion of a circular DNA of size $4.3 \times 10^5$ bp with $\textit{Alu}I (...

A synchronous culture containing $1.8 \times 10^5$ monkey kidney cells was seeded into three identical flasks. The doubling time of these cells is $24$ h. After $24$ h, t...

The standard free energy change $(\Delta G' ^\circ)$ for ATP hydrolysis is $-30 kJ \cdot \text{mole}^{-1}$. The $\textit{in vivo}$ concentrations of ATP, ADP and $P_i$ in...

In a fed-batch culture, $200 \text{ g . L}^{-1}$ glucose solution is added at a flow rate of $50 \text{ L . h}^{-1}$ . The initial culture volume (at quasi steady state) ...

Samples of bacterial culture taken at $5$ PM and then the next day at $5$ AM were found to have $10^4$ and $10^7$ cells.mL${-1}$, respectively. Assuming that both the sam...

Biomass is being produced in a continuous stirred tank bioreactor of $750$ L capacity. The sterile feed containing $8 \: g \cdot L^{-1}$ glucose as substrate was fed at a...

In any given year, the probability of an earthquake greater than Magnitude $6$ occurring in the Garhwal Himalayas is $0.04$. The average time between successive occurrenc...

$10\%$ of the population in a town is HIV+. A new diagnostic kit for HIV detection is available; this kit correctly identifies HIV+ individuals 95% of the time, and HIV i...

If an unbiased coin is tossed $10$ times, the probability that all outcomes are same will be_______ $ \times 10^{-5}$

The limit of the function $e^{-2t}\sin (t)$ as t $\rightarrow\infty$ so, is

The degree of reduction of ethanol is_______

A bacterium belonging to cocci group has a diameter of $2\:\mu m.$ The numerical value of the ratio of its surface area to volume (in $\mu m^{-1}$) is _______.

A T- ask is seeded with $10^5$ anchorage-dependent cells. The available area of the T- ask is $25\: cm^2$ and the volume of the medium is $25\: ml$. Assume that the cells...

Consider a continuous culture provided with a sterile feed containing $10$ mM glucose. The steady state cell density and substrate concentration at three different diluti...

Triose phosphate isomerase converts dihydroxy acetone phosphate $(DHAP)$ to glyceraldehyde-3-phosphate $(G-3-P)$ in a reversible reaction. At $\text{298 K and pH 7.0,}$ t...

Topological Winding number of a $\text{2.0 kb}$ covalently closed circular DNA was found to be $191$ with a writhing number of $-4$. Hence, its $\text{LINKING NUMBER}$ an...

Consider a population of $10,000$ individuals, of which $2500$ are homozygotes (PP) and $3000$ are heterozygotes (Pp) genotype. The frequency of allele p in the populatio...

In a mouse genome, the numbers of functional $V\alpha, J\alpha, V\beta, D\beta, J\beta$ gene segments are $\text{79, 38, 21, 2 and 11,}$ respectively. The total number of...

In an affine gap penalty model, if the gap opening penalty $-20$, gap extension penalty is $-4$ and gap length is $8$, the gap score is__________.

The length of the minimum unique stretch of DNA sequence that can be found only once in a $3$ billion base pairs long genome is$14$$15$$16$$18$

What is the holding period (min) at a $K$ value of $\text{3.36min}^{-1}?$$10.6$$9.5$$8.4$$7.2$

A solution was prepared by dissolving $\text{100 mg}$ of protein $X$ in $\text{100 ml}$ of water. Molecular weight of protein $X$ is $\text{15,000 Da};$ Avogadro’s number...

During sterilization of a fermentation medium in a given bioreactor $\nabla_{heaing}=12.56, \nabla_{cooling}= 7.48$ and the total value of $\nabla$ required for whole ste...

One percent of the cars manufactured by a company are defective. What is the probability (upto four decimals) that more than two cars are defective, if $100$ cars are pro...

In a genetic study, $80$ people were found to have alleles for polydactyly. Only $36$ of them were polydactylous. What is the extent of penetrance percentage? ___________...

The maximum cell concentration $(\text{g l}^{-1})$ expected in a bioreactor with initial cell concentration of $\text{1.75 g l}^{-1}$ and an initial glucose concentration...

The total number of fragments generated by the complete and sequential cleavage of the polypeptide given below by Trypsin followed by $CNBr$ is __________.$Phe-Trp-Met-Gl...

In a batch culture, the specific rate of substrate utilization is $\text{0.25 g (g cell mass)}$$^{-1} h^{-1}$ and specific rate of product formation is $\text{0.215 g (g ...

Calculate the percentage sequence identity for the pairwise alignment given below. ______________$\text{HELLO-}$$\text{YELLOW}$

A callus of $\text{5 g}$ dry weight was inoculated on semi-solid medium for growth. The dry weight of the callus was found to increase by $1.5$ fold after $10$ days of in...