Recent questions tagged numerical-answers

In a group of students, $10$ students like Mathematics, $12$ students like English, $4$ students like both Mathematics and English, and $6$ students like neither Mathemat...

As shown in the figure, circle $C_{1}$ with center $O_{1}$ and radius $r_{1}$ touches the square $V W X Y$ at points $P$ and $Q$ while circle $C_{2}$ with center $O_{2}$ ...

Consider the two functions $f_{1}(x)=\dfrac{x^{2}-4}{x-2}$ and $f_{2}(x)=x^{2}-2 x+2$. Which of the following is the value of $\left(f_{1}(x)+f_{2}(x)\right)$ as $x \righ...

Which of the following is one of the eigenvalues for the matrix given below?\[\left[\begin{array}{cc}3 & 4 \\4 & -3\end{array}\right]\]$1$$3$$5$$7$

The equation $\dfrac{d^{2} y}{d x^{2}}-y=0$ has a solution of the form $y=e^{A x}$. The value(s) of $A$ satisfying this is/are:$0$$1$$-1$$-\infty$

You are characterizing a new enzyme isolated and purified in the laboratory. If the maximum velocity of the enzyme is $1800 ~\mu$ moles $\mathrm{L}^{-1} \mathrm{~min}^{-1...

To determine the viable cell count of a bacterial culture, you have plated $50 ~\mu \mathrm{~L}$ of a $100$ -fold diluted sample of the culture on a nutrient agar plate a...

Given below is the Gibbs free energy change ( $\Delta \mathrm{G}$ ) in kilo Joules per electron equivalent ( $\mathrm{kJ} \mathrm{e}^{-} \mathrm{eq}^{-1}$ ) at pH $7.0$, ...

You have purified an enzyme using a series of chromatographic methods. It was observed that a $10 ~\mu \mathrm{g} \mathrm{~mL}^{-1}$ of this purified enzyme converted $10...

In the open-loop process shown in the figure, the input $U(s)$, the transfer function $G_{p}(s)$ and the output $Y(s)$ are given in the Laplace domain in terms of the Lap...

By elemental analysis of a biomass sample, it was found that the cells in the given sample are composed of (by weight) $\mathrm{C}=50 \%, \mathrm{H}=8 \%, \mathrm{O}=20 \...

Consider the equation $\dfrac{d y}{d x}=\dfrac{1}{x}$The value of the integral $\int_{1}^{2} d y$ using trapezoidal method and interval $h=0.25$ is $\_\_\_\_$. (rounded o...

If the straight lines given by the following two equations are parallel to each other, the value of $\boldsymbol{a}$ is $\_\_\_\_$. (answer in integer)\[4 x+7 y=6 ; \quad...

A straight line $y=x-1$ intersects a circle with center at $x=1, y=1$ and radius of magnitude $1$ at two points. The length of the chord formed by this intersection is $\...

A heat exchanger during operation in a bioprocess has a steady temperature of $90^{\circ} \mathrm{C}$. After completion of its operation, it was shut down and it was obse...

A $\text{CSTR}$ with a volume of $100 \mathrm{~m}^{3}$ is operated in cell recycle mode. At a volumetric flow rate of $10 \mathrm{~m}^{3}$ day ${ }^{-1}$ and effluent bio...

The electron equivalent per liter (e-eq $\mathrm{L}^{-1}$ ) of acetate ion solution of concentration $10 \mathrm{~g} \mathrm{~L}^{-1}$ is $\_\_\_\_$ $\mathrm{e}^{-} \math...

From the following plot of $\dfrac{d y}{d x}$ versus $x$ and if $y(2)=5$, the value of $y(3)$ is $\_\_\_\_$. (rounded off to one decimal place) 

A batch sterilizer is being operated at $121^{\circ} \mathrm{C}$ for sterilizing a medium containing microbial cells. Assume that the thermal deactivation of cells is a f...

A substrate is consumed in a zero order reaction such that its concentration falls from $42 \mathrm{~g} \mathrm{~L}^{-1}$ to $14 \mathrm{~g} \mathrm{~L}^{-1}$ in $4$ hour...

A microbe that follows Monod growth kinetics on a limiting substrate (maximum specific growth rate of $0.5 \mathrm{~h}^{-1}$ and Monod constant of $0.1 ~\mathrm{mg} \math...

It is desired to cultivate $150$ mg (dry weight) microbial cells with an empirical formula of $\mathrm{C}_{5} \mathrm{H}_{7} \mathrm{O}_{2} \mathrm{~N}$. If the phosphoru...

In the process of generating a clonal mammalian cell line, a single cell was seeded in a well of a cell culture plate. After the first $48$ hours, one of the progeny cell...

A disease-associated allele shows $\text{X}$-linked recessive inheritance. If the mother is a carrier of the disease, the father is genetically normal and the child born ...

A packed bed bioreactor with length $1 \text{~m}$ and inside diameter $10 \text{~cm}$ has liquid flowing at an interstitial velocity of $1 \mathrm{~cm} \mathrm{~s}^{-1}$....

​​​​​The sum of the following infinite series is:$$ \frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}+\frac{1}{5!}+\cdots $$$\pi$$1+e$$e-1$$e$

​​​​The minimum value of the function$$ f(x)=x+\frac{4}{x} $$for $x>0$ is$1$$2$$3$$4$

​​​Which of the following compounds have the same degree of reduction per carbon-mole?GlucoseLactic acidAcetic acidFormic acid

For a mechanically reversible isobaric process taking place in a closed system involving $5$ moles of an ideal gas, the temperature increases from an initial value of $30...

The contour length of a B-DNA molecule that encodes a bacterial protein of $33 \: \text{kDa}$ is $\_\_\_\_$ $\mathrm{ nm}$.Consider the average molecular weight of an ami...

Within the Michaelis-Menten framework, the ratio of $v_{0} / V_{\max }$ when $[\mathrm{S}]=20 \times K_{\mathrm{m}}$ is $\_\_\_\_\_$(Round off to two decimal places)

Consider a nonlinear algebraic equation, $e^{x}-2=0$. Using the Newton-Raphson method, with the initial guess of $x_{0}=1$, the approximated value of the root of the equa...

The value of $k$, for which the linear equations $2 x+3 y=6$ and $4 x+6 y=3 k$ have at least one solution, is $\_\_\_\_\_$ (Answer in integer)

Two fair six-sided dice, with sides numbered $1$ to $6$ , are thrown once. The probability of getting $7$ as the sum of the numbers on the top side of the dice is $\_\_\_...