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Recent questions tagged numerical-answers

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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 number of $12$ is __________.
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: 19
The degree of reduction of lactic acid $(\text{C}_{3} \text{H}_{6} \text{O}_{3})$ is __________.
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 iteration (rounded off to one decimal place) 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 iterat...
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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 _________.
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 ________.
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 ________ $\text{h}^{-1}.$
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: 25
For a pure species, the slope of the melting line $\frac{dP}{dT} \; \text{at} \; -2 \; ^{\circ} \textrm{C} \; \text{is} -5.0665 \times 10^{6} \text{Pa K}^{-1}.$ ... $\text{J} \; \text{mol}^{-1}.$
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: 45
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 __________.
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 $...
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GATE BT 2022 | Question: 46
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 __________.
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 __________.
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GATE BT 2022 | Question: 52
Consider the growth of $\textit{S. cerevisiae}$ under aerobic condition in a bioreactor and the specific growth rate of yeast is $0.5\; \text{h}^{-1}.$ ... $\text{kL mol}^{-1}\text{h}^{-1}.$
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...
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GATE BT 2021 | Question: 20
The sum of the infinite geometric series $1 + 1/3 + 1/3^2+ 1/3^3+ \dots$ (rounded off to one decimal place) is ___________
The sum of the infinite geometric series $1 + 1/3 + 1/3^2+ 1/3^3+ \dots$ (rounded off to one decimal place) is ___________
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GATE BT 2021 | Question: 21
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 transfer of the balls to the box $A$ in the same order (rounded off to two decimal places) 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...
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GATE BT 2021 | Question: 22
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 ___________
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 ___________...
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GATE BT 2021 | Question: 23
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 value of $\underset{x \to 0} \lim \left [ \dfrac{x- \sin 2x}{x-\sin 5x} \right]$ (rounded off to two decimal places) is __________
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GATE BT 2021 | Question: 25
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 required starch concentration $mM$ (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...
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GATE BT 2021 | Question: 41
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 _________
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 _________
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GATE BT 2021 | Question: 43
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 one decimal place) is ________.
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...
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GATE BT 2021 | Question: 44
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 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 __________.
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GATE BT 2021 | Question: 46
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 $33\: g L^{-1}$, the cell concentration in $g \: L^{-1}$ (rounded off to the nearest integer) at $24 \: h$ 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^...
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GATE BT 2021 | Question: 49
Calculate the following integral $\int \limits_0^{\pi^2/4} \sin \sqrt{x} dx =$____________.
Calculate the following integral $\int \limits_0^{\pi^2/4} \sin \sqrt{x} dx =$____________.
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GATE BT 2021 | Question: 54
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 (rounded off to the nearest integer) is _________
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...
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