Recent questions tagged numerical-answers

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...

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...

$\int _{-1}^{1}\:f\left ( x \right )dx$ calculated using trapezoidal rule for the values given in the table is ______ (rounded off to $2$ decimal places).$$\begin{array}{...

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...

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...

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...

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...

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).

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...

The largest eigenvalue of the matrix $\begin{bmatrix} 4 &1 \\ -2& 1 \end{bmatrix}$ is ______________.

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...

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...

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...

$E$ 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 ...

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...

The system of linear equations$$cx+y=5$$$$3x+3y=6$$has no solution when $c$ is equal to _______________________.

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...

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...

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...

A function $f$ is given as :$$f(X)=4X-X^{2}$$The function $f$ is maximized when $X$ is equal to _________________.

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).

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...

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 ...

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...

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...

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 ...

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).

The elemental composition of dry biomass of a yeast species is $CH_{1.6}O_{0.4}N_{0.2}S_{0.0024}P_{0.017}$. The contribution of carbon to the dry biomass is _________ $\%...

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...

The number of possible rooted trees in a phylogeny of three species is ______.

Matrix $A=\begin{bmatrix} 0&6 \\ p&0 \end{bmatrix}$ will be skew-symmetric when $p$= ____.

The power required for agitation of non-aerated medium in fermentation is ___________kW.Operating conditions are as follows:Fermentor diameter $= 3$ mNumber of impellers ...

Runs scored by a batsman in five one-day matches are $55$, $75$, $67$, $88$ and $15$. The standard deviation is _________

The positive Eigen value of the following matrix is __________. $$\begin{bmatrix} 2 & 1 \\ 5 & -2 \end{bmatrix}$$

The value of the integral $\displaystyle \int_0^{0.9} \dfrac{dx}{(1-x)(2-x)}$ is ____________

A crossing was performed between the genotypes $\textit{DdEeFfgg}$ and $\textit{ddEeFfGg}$. Assuming that the allelic pairs of all genes assort independently, the proport...

The equilibrium potential of a biological membrane for $Na^+$ is $55$ mV at $37^\circ$ C. Concentration of $Na^+$ inside the cell is $20$ mM. Assuming the membrane is per...

In an assay of the type II dehydroquinase of molecular mass $18$ kDa, it is found that the $V_{\text{max}}$ of the enzyme is $0.0134 \: \mu \text{ mol} \cdot \text{min}^{...

The molar extinction coeffcients of Trp and Tyr at $280$ nm are $5690$ and $1280 \: M^{-1} \cdot cm^{-1}$, respectively. The polypeptide chain of yeast alcohol dehydrogen...