From the ground state electronic configuration of the elements given below,pick the one with the highest value of second ionisation energy.

If $\theta = \frac{\pi}{6}$,then the $10^{\text{th}}$ term of the series $1 + (\cos \theta + i \sin \theta)^1 + (\cos \theta + i \sin \theta)^2 + \dots$ is

In a meter bridge experiment,a resistance of $9 \Omega$ is connected in the left gap and an unknown resistance $x$ (where $x > 9 \Omega$) is connected in the right gap. If the resistances in the gaps are interchanged,the balancing point shifts by $10 \text{ cm}$. The value of the unknown resistance is: (in $\Omega$)

The period of oscillation of a simple pendulum of length $l$ suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination $\alpha$, is given by

If the coordinate axes are the bisectors of the angles between the pair of lines $ax^2 + 2hxy + by^2 = 0$ where $h^2 > ab$ and $a \neq b$,then