The equation of the pair of straight lines parallel to the $X$-axis and touching the circle $x^2+y^2-6x-4y-12=0$ is:

If the series limit of the Lyman series for a Hydrogen atom is equal to the series limit of the Balmer series for a hydrogen-like atom,then the atomic number of this hydrogen-like atom will be:

If $x$ is real,then the minimum value of $y = \frac{x^2-x+1}{x^2+x+1}$ is

If $x_1, x_2, \ldots, x_n$ are $n$ observations such that $\sum_{i=1}^n x_i^2 = 400$ and $\sum_{i=1}^n x_i = 80$,then the least value of $n$ is

$A$ particle performs linear $SHM$. At a particular instant,the velocity of the particle is $u$ and acceleration is $\alpha$ (both having the same direction). At another instant,the velocity is $v$ and acceleration is $\beta$ $(0 < \alpha < \beta)$ (both in opposite directions to each other). The distance between the two positions is

The total work done on a particle is equal to the change in its kinetic energy. This is applicable: