Changes in $GnRH$ pulse frequency in females is controlled by circulating levels of

If a polygon of $n$ sides has $275$ diagonals,then $n$ is equal to

$A$ particle of mass $M$ is situated at the centre of a spherical shell of same mass $M$ and radius $a$. The gravitational potential at a point situated at a distance of $\frac{a}{2}$ from the centre will be:

$\int \tan ^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right) d x$ is equal to

The total number of nitrogenous bases in the human genome is estimated to be about

If the lines $x^2+2xy-35y^2-4x+44y-12=0$ and $5x+\lambda y-8=0$ are concurrent,then $\lambda$ equals