Methanogens belong to $..........$.

The transformed equation of $x^2+6xy+8y^2=10$ when the axes are rotated through an angle $\frac{\pi}{4}$ is:

$A$ double slit experiment is immersed in water of refractive index $1.33$. The slit separation is $1 ~mm$ and the distance between the slit and the screen is $1.33 ~m$. The slits are illuminated by light of wavelength $6300 ~Å$. The fringe width is:

One litre of oxygen at a pressure of $1 ~atm$ and two litres of nitrogen at a pressure of $0.5 ~atm$ are introduced into a vessel of volume $1 ~L$. If there is no change in temperature,the final pressure of the mixture of gas (in $atm$) is

Mass $M$ is divided into two parts $xM$ and $(1-x)M$. For a given separation,the value of $x$ for which the gravitational attraction between the two pieces becomes maximum is

If $[2,6]$ is divided into four intervals of equal length, then the approximate value of $\int_2^6 \frac{1}{x^2-x} dx$ using Simpson's rule is