List of practice Questions

The power consumption readings (in watt) by an instrument at fixed intervals of time (in seconds) are tabulated below:

\[ \begin{array}{|c|c|} \hline \text{Time (s)} & \text{Power consumption (W)} \\ \hline 0.0 & 8.6 \\ 0.6 & 9.2 \\ 1.2 & 7.8 \\ 1.8 & 6.4 \\ 2.4 & 7.2 \\ 3.0 & 8.6 \\ 3.6 & 11.2 \\ \hline \end{array} \]
Using Simpson's 1/3rd rule, the energy expenditure of the instrument in joules is _____.[Round off to two decimal places]

An engine develops 42 kW brake power when it runs with B20 fuel (80% biodiesel and 20% diesel by volume) with a brake thermal efficiency of 24%. The heating value of the fuel is 46.15 MJ kg$^{-1}$ and its density is 0.845 kg L$^{-1}$. The fuel consumption of the engine in L h$^{-1}$ will be _____.$ \textit{[Round off to two decimal places]}$

The root mean square acceleration for mechanical vibration of a tractor is 3.15 m s$^{-2}$ and its frequency is 80 Hz. The root mean square amplitude of the vibration in µm is _____. $\textit{[Round off to two decimal places]}$

A sprinkler irrigation system with an irrigation efficiency of 70% is used to irrigate 16 ha of maize crop. The crop evapotranspiration of 6 mm day$^{-1}$ is used for estimating the irrigation depth. If the irrigation system is operated 20 hours per day for 10 days, the system capacity in L s$^{-1}$ is _____. $\textit{[Round off to two decimal places]}$

The degree of reduction of lactic acid (C₃H₆O₃) is _________.

Consider a nonlinear algebraic equation, $x\ln x + x - 1 = 0$. Using the Newton–Raphson method, with the initial guess of $x_{0}=3$, the value of $x$ after one iteration (rounded off to one decimal place) is _________.

The probability density function of a random variable $ X $ is $ p(x) = 2e^{-2x} $. The probability $ P(1 \leq X \leq 2) $ (rounded off to two decimal places) is _________ .

The specific growth rate of a yeast having a doubling time of 0.693 h (rounded off to nearest integer) is _________ h^-1.

A fermentation broth of density 1000 kg m^-3 and viscosity 10^-3 kg m^-1 s^-1 is mixed in a 100 L fermenter using a 0.1 m diameter impeller, rotating at a speed of 2 s^-1. The impeller Reynolds number is _________.

For a pure species, the slope of the melting line $\dfrac{dP}{dT}$ at $-2^{\circ}$C is $-5.0665\times 10^{6}$ Pa K$^{-1}$. The difference between the molar volumes of the liquid and solid phase at $-2^{\circ}$C is $-4.5\times 10^{-6}$ m$^{3}$ mol$^{-1}$. The value of the latent heat of fusion (rounded off to nearest integer) is _________ J mol$^{-1}$.

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 _________.

Figure below depicts simplified metabolic and transport reactions taking place in the production of B from A in a cell. The subscript ‘i’ refers to intracellular metabolites. $r_j$ is the $j^{\text{th}}$ reaction flux in $\frac{g}{(g\;dry\;mass)\;h}$. Under pseudo–steady–state condition, the following reaction fluxes are available: $r_1 = 4,\; r_3 = 1,\; r_6 = 1$. The transport flux of B, $r_4$, is _________ $\frac{g}{(g\;dry\;mass)\;h}$.

Liquid-phase mass transfer coefficient ($k_L$) is measured in a stirred tank vessel using $\textit{steady-state method}$ by sparging air. Oxygen uptake by the microorganism is measured. The bulk concentration of O$_2$ is $10^{-4}$ mol L$^{-1}$. Solubility of O$_2$ in water at 25$^\circ$C is $10^{-3}$ mol L$^{-1}$. If the oxygen consumption rate is $9\times10^{-4}$ mol L$^{-1}$ s$^{-1}$, and interfacial area is 100 m$^2$/m$^3$, the value of $k_L$ is _________ cm s$^{-1}$.

Consider the growth of S. cerevisiae under aerobic condition in a bioreactor and the specific growth rate of yeast is 0.5 h$^{-1}$. The overall reaction of the process is \[ 2C_6H_{12}O_6 + 0.2 NH_3 + 10.35 O_2 \to CH_{1.8} O_{0.5} N_{0.2} + 0.2 C_2 H_6 O + 10.6 CO_2 + 10.8 H_2 O \] The heat of combustion values for different compounds are tabulated below with reference to CO$_2$, H$_2$O, O$_2$, and N$_2$ at standard conditions. Heat of Combustion

Compound	Heat of combustion (kJ mol^-1)
C₆H₁₂O₆	2802
NH₃	383
CH_1.8O_0.5N_0.2	560
C₂H₆O	1366

The specific rate of heat production (rounded off to the nearest integer) is _________ kJ mol$^{-1}$ h$^{-1}$.

A pilot sterilization was carried out in a vessel containing 100 m³ medium with an initial spore concentration of 10⁸ spores/ml. The accepted level of contamination after sterilization is 1 spore in the entire vessel. The specific death rate constant for the spore is 2 min^-1 at 121°C. Assuming no death takes place during the heating and cooling cycles, the holding time at 121°C (rounded off to nearest integer) is _________ min.

A circular plasmid has three different but unique restriction sites for enzymes 'a', 'b' and 'c.' When enzymes 'a' and 'b' are used together, two fragments of equal size are generated. Enzyme 'c' creates fragments of equal size only from one of the fragments generated by those cleaved by 'a' and 'b'. The plasmid is treated with a mixture of 'a', 'b' and 'c' and analysed by agarose gel electrophoresis. The number of bands observed in the gel is _________.

A bacterial strain is grown in nutrient medium at 37$^\circ$C under aerobic conditions. The medium is inoculated with $ 10^2 $ cells from a seed culture. If the number of cells in the culture is $ 10^5 $ after 10 hours of growth, the doubling time of the strain (rounded off to the nearest integer) is _________ h.

Which of the following statement(s) regarding trafficking in eukaryotic cells is(are) CORRECT?

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 $Y$ (rounded off to one decimal place) is _________.

A fed-batch operation is initiated by feeding substrate solution at 1 L h\textsuperscript{-1 containing 50 g L\textsuperscript{-1} substrate. The reactor initially contains 50 g biomass. The biomass yield $Y_{X/S}^{M}$ is 0.4 $\frac{g\;biomass}{g\;substrate}$. Assuming quasi-steady state, the maximum biomass after 5 h of feeding is _________ g.}

An enzyme catalyzes the conversion of substrate A into product B. The rate equation for this reaction is \[ -r_A = \frac{C_A}{5 + C_A} \;\; \text{mol L}^{-1}\text{min}^{-1} \] Substrate A at an initial concentration of 10 mol L$^{-1$ enters an ideal mixed flow reactor (MFR) at a flow rate of 10 L min$^{-1}$. The volume of the MFR required for 50% conversion of substrate to product is _________ L.}

Consider a piston–cylinder assembly as shown. The cylinder contains 1 mole of an ideal gas at 300 K, initially held at position $z_1$. After the stopper is removed, the piston rises suddenly against atmospheric pressure ($1.013\times10^{5}$ Pa) to a new position $z_2$. The cylinder walls are insulated. The heat capacity at constant volume $(C_V)$ is 12.5 J mol\textsuperscript{-1 K\textsuperscript{-1}. The cross-sectional area of the cylinder is $10^{-3}$ m\textsuperscript{2}. Assume the piston is weightless and frictionless. If $z_2 - z_1 = 1$ m, the final temperature of the gas (rounded to nearest integer) is _________ K.}