Recent questions tagged numerical-answers

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 $...

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 __________.

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}...

Consider the growth of $\textit{S. cerevisiae}$ under aerobic condition in a bioreactor and the specific growth rate of yeast is $0.5\; \text{h}^{-1}.$ The overall reacti...

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...

A circular plasmid has three different but unique restriction sites for enzymes $‘\text{a'}, ‘\text{b'}$ and $‘\text{c'}.$ When enzymes $‘\text{a'}$ and $‘\text{b'}$ are ...

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 unrooted trees in a phylogeny of five sequences is$3$$15$$105$$945$

Under standard temperature $(T)$ and pressure $(P)$ conditions, $128 \: g$ of an ideal has molecule $A$ occupies a volume of $1 \: L$. The gas molecule $A$ obeys the rela...

The sum of the infinite geometric series $1 + 1/3 + 1/3^2+ 1/3^3+ \dots$ (rounded off to one decimal place) is ___________

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 trans...

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 ___________

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

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...

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...

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. col...

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 _________

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....

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 on...

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 __________.

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^...

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 ...

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...

Calculate the following integral $\int \limits_0^{\pi^2/4} \sin \sqrt{x} dx =$____________.

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 mo...

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 att...

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 satur...

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 $50 \: \mu L$ pur...

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 (rounde...

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...

The solution of $ \underset{x\rightarrow 8 }\lim\left ( \dfrac{x^{2}-64}{x-8} \right )$ is _____________.

The median value for the dataset $\left ( 12, 10,16,8,90,50,30,24 \right )$ is ______________.

The degree of reduction for acetic acid $\left ( C_{2} H_{4}O_{2}\right )$ is ____________.

The mass of $1$ $kmol$ of oxygen molecules is ___________$g$ (rounded off to the nearest integer).

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...

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...

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...

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...