If ${}^n{P_4} : {}^n{P_5} = 1 : 2$,then $n = $

If $A = \{2, 4, 5\}$ and $B = \{7, 8, 9\}$,then $n(A \times B)$ is equal to:

The locus of the poles of focal chords of the parabola $y^2 = 4ax$ is

The potential energy of a particle of mass $1\, kg$ in motion along the $x-$axis is given by $U = 4(1 - \cos 2x)$,where $x$ is in $meters$. The period of small oscillation (in $seconds$) is

$A$ Zener diode,having a breakdown voltage equal to $15 \, V$,is used in a voltage regulator circuit as shown in the figure. The current through the diode is ..... $mA$.

The incentre of the triangle with vertices $(1, \sqrt{3})$,$(0, 0)$ and $(2, 0)$ is