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Recent questions tagged numerical-answers

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GATE BT 2023 | Question: 23
Two fair six-sided dice are thrown. The probability of getting $12$ as the product of the numbers on the dice (rounded off to two decimal places) is __________.
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GATE BT 2023 | Question: 36
The following reaction represents biomass synthesis from hexadecane$\mathrm{C}_{16} \mathrm{H}_{34}+12.5 \mathrm{O}_2+2.13 \mathrm{NH}_3 \rightarrow 10.6 \mathrm{CH}_{1.6...
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GATE BT 2023 | Question: 37
Temperature of a reaction with an activation energy value of $15 \mathrm{kcal} \mathrm{mol}^{-1}$ is increased from $300 \mathrm{~K}$ to $310 \mathrm{~K}$. If the value o...
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GATE BT 2023 | Question: 38
E. coli is cultivated in a chemostat operated at a dilution rate of $0.2 h^{-1}$. The values of biomass yield due to oxygen consumption and the steady state biomass conce...
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GATE BT 2023 | Question: 39
Aqueous two-phase extraction is used to recover } \alpha \text {-amylase from a solution. A polypropylene glycol-dextran mixture is added and the solution separates into ...
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GATE BT 2023 | Question: 40
E. coli cultivated at $298 \mathrm{~K}$ uptakes an uncharged compound (A) by passive diffusion. The intracellular and extracellular concentrations of $\mathrm{A}$ are $0...
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GATE BT 2023 | Question: 41
If there are three unrooted trees for four protein sequences, the number of rooted trees for the same number of sequences is _______________.
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GATE BT 2023 | Question: 42
The number of different possible ways of forming five intramolecular disulfide bonds with ten cysteine residues of a protein is ______________.
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GATE BT 2023 | Question: 43
The following schematic diagram shows a chemostat with cell recyclewhere $\mathrm{F}_0$ and $\mathrm{F}_{\mathrm{r}}$ are the volumetric flow rates (in $L \cdot h^{-1}$ )...
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GATE BT 2023 | Question: 44
An enzyme (E) catalyzes the biochemical reaction $A \rightarrow B$ with $k_{c a t}$ equal to $500 s^{-1}$. If the initial reaction velocity $\left(V_{0}\right)$ is $10 \m...
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GATE BT 2023 | Question: 45
DNA sample collected from an unidentified bacterial species $(Y)$ contains $13 \%$ of adenine. The $G+C$ content (in percentage) of $Y$ is ____________.
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GATE BT 2023 | Question: 46
If $1000 \mathrm{bp}$ of a double-helical DNA weighs $1 \times 10^{-18} \mathrm{gm}$ and distance between two $\mathrm{bp}$ is $0.34 \mathrm{~nm}$, the total amount of DN...
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GATE BT 2023 | Question: 47
A protein has three identical sites arranged at the vertices of an equilateral triangle. If one site is filled with a dye (donor), the measured quantum yield $\left(\phi_...
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GATE BT 2023 | Question: 48
If $A=\left(\begin{array}{ll}1 & 2 \\ 3 & 5\end{array}\right)$, the value of $\left|A^{4}+3 A^{2}-5 A+6 I\right|$ is _____________.
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GATE BT 2023 | Question: 49
If $f(x)=\frac{\sin x+\cos x}{\sin x-\cos x}$, the value of $f^{\prime}(x)$ at $x=0$ is ___________.
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GATE BT 2023 | Question: 50
If $f(2)=5$ and $(f(x))(f(x+1))=3$ for all real values of $x$, the value of $f(10)$ is ____________.
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GATE BT 2023 | Question: 51
Ten playing cards numbered $1,2,3, \ldots, 10$ are placed face down on a table. One card is drawn at random, its number recorded, and then replaced face down. A card is d...
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GATE BT 2023 | Question: 52
The values of the consistency index ' $K$ ' and the flow behavior index ' $n$ ' of a dilatant fluid are 0.415 (in CGS units) and $1.23$, respectively. The value of the ap...
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GATE BT 2023 | Question: 53
An evaporator is insulated using glass wool material of $0.15 \mathrm{~m}$ thickness. The inner most surface and the outer surface of the insulation are at $700{ }^{\circ...
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GATE BT 2023 | Question: 54
A proportional controller is used to control the temperature of an autoclave from $60^{\circ} \mathrm{C}$ to $130^{\circ} \mathrm{C}$. If the proportional band setting of...
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GATE BT 2023 | Question: 55
A dNTP master-mix is prepared by combining $40 \mu L$ of each $20 \mathrm{mM}$ dNTP stock (dATP, dCTP, dGTP and dTTP). $4 \mu L$ of this dNTP master-mix is added to a PCR...
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GATE BT 2022 | Question: 1
What is the order of the differential equation given below?$\dfrac{d^{2}y}{dx^{2}} – 6x = 3x^{4} – 2x^{3} + 2$$1$$2$$3$$4$
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GATE BT 2022 | Question: 2
If the eigenvalues of a $2 \times 2$ matrix $P$ are $4$ and $2,$ then the eigenvalues of the matrix $P^{-1}$ are$0, 0$$0.0625, 0.25$$0.25, 0.5$$2, 4$
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GATE BT 2022 | Question: 3
For a double-pipe heat exchanger, the inside and outside heat transfer coefficients are $100$ and $200 \; \text{W m}^{-2} \text{K}^{-1},$ respectively. The thickness and ...
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GATE BT 2022 | Question: 5
The binding free energy of a ligand to its receptor protein is $-11.5 \; \text{kJ mol}^{-1}$ at $300 \; \text{K.}$ What is the value of the equilibrium binding constant?U...
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GATE BT 2022 | Question: 6
The overall stoichiometry for an aerobic cell growth is$3 \text{C}_{6} \text{H}_{12} \text{O}_{6} + 2.5 \text{NH}_{3} + \text{O}_{2} \rightarrow 1.5 \text{C}_{a} \text{H}...
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GATE BT 2022 | Question: 17
Assuming independent assortment and no recombination, the number of different combinations of maternal and paternal chromosomes in gametes of an organism with a diploid n...
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GATE BT 2022 | Question: 18
A microorganism is grown in a batch culture using glucose as a carbon source. The apparent growth yield is $0.5 \frac{\text{g biomass}}{\text{g substrate}}.$ The initial ...
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GATE BT 2022 | Question: 19
The degree of reduction of lactic acid $(\text{C}_{3} \text{H}_{6} \text{O}_{3})$ is __________.
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GATE BT 2022 | Question: 20
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 iteratio...
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GATE BT 2022 | Question: 21
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 _________.
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GATE BT 2022 | Question: 22
The maximum value of the function $f(x) = 3x^{2} – 2x^{3}$ for $x>0$ is ________.
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GATE BT 2022 | Question: 23
The specific growth rate of a yeast having a doubling time of $0.693 \; \text{h}$ (rounded off to nearest integer) is ________ $\text{h}^{-1}.$
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GATE BT 2022 | Question: 24
A fermentation broth of density $1000 \; \text{kg m}^{-3}$ and viscosity $10^{-3} \; \text{kg m}^{-1} \text{s}^{-1}$ is mixed in a $100\;\text{L}$ fermenter using a $0.1 ...
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GATE BT 2022 | Question: 25
For a pure species, the slope of the melting line$$\frac{dP}{dT} \; \text{at} \; -2 \; ^{\circ} \textrm{C} \; \text{is} -5.0665 \times 10^{6} \text{Pa K}^{-1}.$$The diff...
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GATE BT 2022 | Question: 29
A $2\times 2$ matrix $\textbf{P}$ has an eigen value $\lambda_{1}=2$ with eigenvector $x_{1}=\begin{pmatrix} 1 \\ 0 \end{pmatrix}$ and another eigenvalue $\lambda_{2}=5...
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GATE BT 2022 | Question: 47
Figure below depicts simplified metabolic and transport reactions taking place in the production of $\text{B}$ from $\text{A}$ in a cell. The subscript $ i\text{’}$ refer...
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GATE BT 2022 | Question: 48
The amount of biomass in a reactor at the end of the batch process is $50 \; \text{g}.$ Fed-batch operation is initiated by feeding the substrate solution at a constant r...
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GATE BT 2022 | Question: 49
An enzyme catalyzes the conversion of substrate $\text{A}$ into product $\text{B}.$ The rate equation for this reaction is$-r_{A}= \dfrac{\text{C}_{A}}{5+C_{A}} \text{mol...
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GATE BT 2022 | Question: 50
Liquid-phase mass transfer coefficient $(k_{L})$ is measured in a stirred tank vessel using steady-state method by sparging air. Oxygen uptake by the microorganism is mea...
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