In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes $$x$$ times its initial resonant frequency $$\omega_0$$. The value of $$x$$ is :

A car is moving with a constant speed of 20 m/s in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take g = 10 m/s$$^2$$)

If $$\overrightarrow P = 3\widehat i + \sqrt 3 \widehat j + 2\widehat k$$ and $$\overrightarrow Q = 4\widehat i + \sqrt 3 \widehat j + 2.5\widehat k$$ then, the unit vector in the direction of $$\overrightarrow P \times \overrightarrow Q $$ is $${1 \over x}\left( {\sqrt 3 \widehat i + \widehat j - 2\sqrt 3 \widehat k} \right)$$. The value of $$x$$ is _________.

$$\mathrm{I_{CM}}$$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. $$\mathrm{I_{AB}}$$ is it's moment of inertia about an axis AB perpendicular to plane and parallel to axis CM at a distance $$\frac{2}{3}$$R from center. Where R is the radius of the disc. The ratio of $$\mathrm{I_{AB}}$$ and $$\mathrm{I_{CM}}$$ is $$x:9$$. The value of $$x$$ is _____________.