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Recent questions tagged numerical-answers

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82
GATE2019: 19
The number of possible rooted trees in a phylogeny of three species is ______.
The number of possible rooted trees in a phylogeny of three species is ______.
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83
GATE2019: 20
Matrix $A=\begin{bmatrix} 0&6 \\ p&0 \end{bmatrix}$ will be skew-symmetric when $p$= ____.
Matrix $A=\begin{bmatrix} 0&6 \\ p&0 \end{bmatrix}$ will be skew-symmetric when $p$= ____.
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85
GATE2016-22
Runs scored by a batsman in five one-day matches are $55$, $75$, $67$, $88$ and $15$. The standard deviation is _________
Runs scored by a batsman in five one-day matches are $55$, $75$, $67$, $88$ and $15$. The standard deviation is _________
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86
GATE2016-23
The positive Eigen value of the following matrix is __________. $\begin{bmatrix} 2 & 1 \\ 5 & -2 \end{bmatrix}$
The positive Eigen value of the following matrix is __________. $$\begin{bmatrix} 2 & 1 \\ 5 & -2 \end{bmatrix}$$
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87
GATE2016-25
The value of the integral $\displaystyle \int_0^{0.9} \dfrac{dx}{(1-x)(2-x)}$ is ____________
The value of the integral $\displaystyle \int_0^{0.9} \dfrac{dx}{(1-x)(2-x)}$ is ____________
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88
GATE2016-34
A crossing was performed between the genotypes $\textit{DdEeFfgg}$ and $\textit{ddEeFfGg}$. Assuming that the allelic pairs of all genes assort independently, the proportion of progeny having the genotype $\textit{ddeeffgg}$ is expected to be _______ $\%$
A crossing was performed between the genotypes $\textit{DdEeFfgg}$ and $\textit{ddEeFfGg}$. Assuming that the allelic pairs of all genes assort independently, the proport...
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95
GATE2016-53
$\dfrac{d^2y}{dx^2}-y=0$. The conditions for this second order homogeneous differential equation are $y(0)=1$ and $\dfrac{dy}{dx}=3$ at $x=0$. The value of $y$ when $x = 2$ is __________
$\dfrac{d^2y}{dx^2}-y=0$. The conditions for this second order homogeneous differential equation are $y(0)=1$ and $\dfrac{dy}{dx}=3$ at $x=0$. The value of $y$ when $x = ...
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96
GATE2016-54
The value of determinant $A$ given below is ________. $A = \begin{pmatrix} 5 & 16 & 81 \\ 0 & 2 & 2 \\ 0 & 0 & 16 \end{pmatrix}$
The value of determinant $A$ given below is ________.$A = \begin{pmatrix} 5 & 16 & 81 \\ 0 & 2 & 2 \\ 0 & 0 & 16 \end{pmatrix}$
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97
GATE2016-55
Consider the equation $V=\dfrac{aS}{b+S+\dfrac{S^2}{c}}$ Given $a = 4$, $b = 1$ and $c = 9$, the positive value of $S$ at which $V$ is maximum, will be _________
Consider the equation$V=\dfrac{aS}{b+S+\dfrac{S^2}{c}}$Given $a = 4$, $b = 1$ and $c = 9$, the positive value of $S$ at which $V$ is maximum, will be _________
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98
GATE2017-4
The surface area (in $m^2$) of the largest sphere that can fit into a hollow cube with edges of length $1$ meter is ______ Given data: $\pi=3.14$
The surface area (in $m^2$) of the largest sphere that can fit into a hollow cube with edges of length $1$ meter is ______Given data: $\pi=3.14$
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99
GATE2017-5
In a thin layer chromatography experiment using a silica gel plate, a compound showed migration of $12.5$ cm and the solvent front showed migration of $18$ cm. The $R_f$ value for the compound is ______
In a thin layer chromatography experiment using a silica gel plate, a compound showed migration of $12.5$ cm and the solvent front showed migration of $18$ cm. The $R_f$ ...
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100
GATE2017-6
$\underset{x \to 0}{\lim} \dfrac{\sin(x)}{x}$ is ________
$\underset{x \to 0}{\lim} \dfrac{\sin(x)}{x}$ is ________
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101
GATE2017-14
If a protein contains four cysteine residues, the number of different ways they can simultaneously form two intra-molecular disulphide bonds is __________.
If a protein contains four cysteine residues, the number of different ways they can simultaneously form two intra-molecular disulphide bonds is __________.
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102
GATE2017-16
For $y=f(x)$, if $\dfrac{d^2y}{dx^2}=0$, $\dfrac{dy}{dx}=0$ at $x=0$, and $y=1$ at $x=1$, the value of $y$ at $x=2$ is __________
For $y=f(x)$, if $\dfrac{d^2y}{dx^2}=0$, $\dfrac{dy}{dx}=0$ at $x=0$, and $y=1$ at $x=1$, the value of $y$ at $x=2$ is __________
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104
GATE2017-25
At the transcription start site of a gene, any of the four nucleotides can occur with equal probability $p$. The Shannon Entropy $S$, given by $S= – \Sigma_{i=1}^4 p_i \ln p_i$, for this start site is _________
At the transcription start site of a gene, any of the four nucleotides can occur with equal probability $p$. The Shannon Entropy $S$, given by $S= – \Sigma_{i=1}^4 p_i ...
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105
GATE2017-28
The angle (in degrees) between the vectors $\overrightarrow{x}= \hat{i}-\hat{j}+2 \hat{k}$ and $\overrightarrow{y} = 2 \hat{i} – \hat{j}-1.5 \hat{k}$ is _________
The angle (in degrees) between the vectors $\overrightarrow{x}= \hat{i}-\hat{j}+2 \hat{k}$ and $\overrightarrow{y} = 2 \hat{i} – \hat{j}-1.5 \hat{k}$ is _________
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107
GATE2017-34
The concentration (in micromolar) of NADH in a solution with $A_{340}=0.50$ is _________ Given data: Path length $=1$ cm; Molar extinction coefficient of NADH $\varepsilon_{340}= 6220 M^{-1}cm^{-1}$
The concentration (in micromolar) of NADH in a solution with $A_{340}=0.50$ is _________Given data: Path length $=1$ cm; Molar extinction coefficient of NADH $\varepsilon...
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108
GATE2017-35
The specific activity of an enzyme in a crude extract of $\textit{E.coli}$ is $9.5$ units/mg of protein. The specific activity increased to $68$ units/mg of protein upon ion-exchange chromatography. The fold purification is ________
The specific activity of an enzyme in a crude extract of $\textit{E.coli}$ is $9.5$ units/mg of protein. The specific activity increased to $68$ units/mg of protein upon ...
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109
GATE2017-37
The value of $c$ for which the following system of linear equations has an infinite number of solutions is ________ $\begin{bmatrix}1 & 2 \\ 1 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} c \\ 4 \end{bmatrix}$
The value of $c$ for which the following system of linear equations has an infinite number of solutions is ________ $$\begin{bmatrix}1 & 2 \\ 1 & 2 \end{bmatrix} \begin{b...
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111
GATE2017-46
If the chemical composition of proteins in an organism is $CH_{1.5}O_{0.3}N_{0.3}S_{0.004}$, the mass percentage of carbon in the protein is __________ Given data: Atomic weights $(Da)$ of $C=12, H=1, O=16, N=14$, and $S=32$.
If the chemical composition of proteins in an organism is $CH_{1.5}O_{0.3}N_{0.3}S_{0.004}$, the mass percentage of carbon in the protein is __________Given data: Atomic ...
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112
GATE2017-47
For the probability density $P(x) = 0.5e^{-0.5x}$, the integral $\displaystyle \int_0^{\infty}P(x)dx =$ __________
For the probability density $P(x) = 0.5e^{-0.5x}$, the integral $\displaystyle \int_0^{\infty}P(x)dx =$ __________
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113
GATE2017-49
A zero-order liquid phase reaction $A \xrightarrow{k} B$ is being carried out in a batch reactor with $k=10^{-3}$ mol/min. If the starting concentration of $A$ is $0.1$ moles/liter, the time (in minutes) taken by the system before $A$ is exhausted in a $100$ liter reactor is _________
A zero-order liquid phase reaction $A \xrightarrow{k} B$ is being carried out in a batch reactor with $k=10^{-3}$ mol/min. If the starting concentration of $A$ is $0.1$ m...
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114
GATE2017-52
A DNA strand of length $25$ nm wraps diametrically around the circumference of a spherical histone-octamer once. The radius (nm) of the histone-octamer is _______ Given data: $\pi = 3.14$
A DNA strand of length $25$ nm wraps diametrically around the circumference of a spherical histone-octamer once. The radius (nm) of the histone-octamer is _______Given da...
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116
GATE2017-54
During anaerobic growth, an organism converts glucose $(P)$ into biomass $(Q)$, ethanol $(R)$, acetaldehyde $(S)$, and glycerol $(T)$ ... , the ethanol produced (in grams) is ________ Given data: Atomic weights (Da) of $C=12, H=1, O=16$, and $N=14$
During anaerobic growth, an organism converts glucose $(P)$ into biomass $(Q)$, ethanol $(R)$, acetaldehyde $(S)$, and glycerol $(T)$. Every mole of carbon present in glu...
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118
GATE2015-19
A single subunit enzyme converts $420$ $\mu$moles of substrate to product in one minute. The activity of the enzyme is ________ $\times 10^{-6}$ Kalal.
A single subunit enzyme converts $420$ $\mu$moles of substrate to product in one minute. The activity of the enzyme is ________ $\times 10^{-6}$ Kalal.
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119
GATE2015-22
The determinant of the matrix $\begin{bmatrix} 3 & 0 & 0 \\ 2 & 5 & 0 \\ 6 & -8 & -4 \end{bmatrix}$ is __________
The determinant of the matrix $\begin{bmatrix} 3 & 0 & 0 \\ 2 & 5 & 0 \\ 6 & -8 & -4 \end{bmatrix}$ is __________
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120
GATE2015-33
Consider the following infinite series: $1+ r+r^2 +r^3+ \dots \dots \infty$ If $r = 0.3$, then the sum of this infinite series is ____________
Consider the following infinite series:$$1+ r+r^2 +r^3+ \dots \dots \infty$$ If $r = 0.3$, then the sum of this infinite series is ____________
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