Recent questions tagged numerical-answers

​​​​A thermometer measuring body temperature follows a first-order response with a time constant of $40$ seconds. The instrument will reach $95 \%$ of its steady-state ou...

​​​​If the function$$ f(x)=\left\{\begin{array}{ll}\sin 2 x, & \text { for } x>0 \\a+b x, & \text { for } x \leq 0\end{array}\right.$$where $a$ and $b$ are constants, is ...

In a fermentation process, each mole of glucose is converted to biomass $\left(\mathrm{CH}_{1.8} \mathrm{O}_{0.5} \mathrm{~N}_{0.2}\right)$, with a biomass yield coeffici...

Let $a_{0}=0$ and define $a_{n}=\frac{1}{2}\left(1+a_{n-1}\right)$ for all positive integers $n \geq 1$. The least value of $n$ for which $\left|1-a_{n}\right|<\frac{1}{2...

The percentage of light that would pass through a sample with an absorbance of $2$ would be $\_\_\_\_\_$ $\%$ .(Round off to the nearest integer)

Let $A=\left(\begin{array}{ccc}1 & 0 & 1 \\ 0 & k & 0 \\ 3 & 0 & -1\end{array}\right)$. If the eigenvalues of $A$ are $-2,1$, and $2$ , then the value of $k$ is $\_\_\_\_...

An NMR spectrometer operating at proton resonance frequency $(v)$ of $1 \: \mathrm{GHz}$ will have a magnetic field strength of $\_\_\_\_$ Tesla (T).The gyromagnetic rati...

For the coupled reactions given below\[\begin{array}{ll}\text { Glucose 6-phosphate }+\mathrm{H}_{2} \mathrm{O} \rightarrow \text { Glucose }+\mathrm{Pi} & \text { (React...

A value of $k$ for which the linear equations $(k-1) x+3 y=0$ and $2 x+k y=0$ have a non-zero solution is $\_\_\_\_\_\_\_$.$1$$2$$3$$4$

The solution of the differential equation $\frac{d y}{d x}=y+e^{-x}$ that satisfies $y(0)=-\frac{1}{2}$ is $\_\_\_\_\_\_\_$.$-\frac{1}{2} e^{-\frac{x}{2}}$$-\frac{1}{2} e...

The six faces of a cube (die) are numbered as $1,2,3,4,5$ and $6$, and it is rolled once. An outcome is the observed number on the top face. If the probability of getting...

Aspergillus niger is grown in a $10,000$ L stirred batch bioreactor under aerated conditions to produce citric acid. At steady state oxygen transfer conditions, the speci...

Ethanol is produced in a $10,000$ L stirred bioreactor using an impeller of diameter $1 \mathrm{~m}$. The density and viscosity of fermentation broth are $1000 \mathrm{~k...

The free energy change of ATP hydrolysis at $25^{\circ} \mathrm{C}$ is $-32.2 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The free energy change for hydrolysis of $\alpha$-glycerop...

A fermentor is filled with medium at a rate of $1 \mathrm{~L} \mathrm{~min}^{-1}$. A leak develops at the bottom of the fermentor when the medium in the fermentor reaches...

Consider scale-up of fungal fermentation from a $20 \mathrm{~L}$ model-type to $20,000 \mathrm{~L}$ prototype stirred tank reactor. The model-type and prototype have the ...

The value of the limit $\lim _{x \rightarrow \infty} \frac{x}{2} \ln \left(1+\frac{2024}{x}\right)$ is $\_\_\_\_\_\_\_\_$.

Let $y(x)=x^2 \ln x$ for $x>0$, be a solution of $x^2 \frac{d^2 y}{d x^2}+4 y=\alpha x \frac{d y}{d x}$. Then the value of $\alpha$ is $\_\_\_\_\_\_\_\_\_$.

The absolute relative error in evaluating the integral $\int_0^1 x^2 d x$ by the trapezoidal rule with the step size $0.25$ is $\%$ $\_\_\_\_\_\_\_\_$ (rounded off to $2$...

The pie chart presents the percentage contribution of different macronutrients to a typical $2,000$ $\mathrm{kcal}$ diet of a person.The typical energy density $(\mathrm{...

A rectangular paper of $20 \mathrm{~cm} \times 8 \mathrm{~cm}$ is folded $3$ times. Each fold is made along the line of symmetry, which is perpendicular to its long edge....

Fabry disease in humans is a X-linked disease. The probability (in percentage) for a phenotypically normal father and a carrier mother to have a son with Fabry disease is...

The value of $\lim _{x \rightarrow 0}\left[\frac{\cos 2 x-\cos 4 x}{x^{2}}\right]$ is ___________.

If $7^{3 x}=216$, the value of $7^{-x}$ (rounded off to three decimal places) is _____________.