A projectile is thrown from a point O on the ground at an angle 45$$^\circ$$ from the vertical and with a speed 5$$\sqrt 2 $$ m/s. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, 0.5 s after the splitting. The other part, t seconds after splitting, falls to the ground at a distance x meters from the point O. The acceleration due to gravity g = 10 m/s².

The value of x is _______________.

In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q₁ $$\mu$$C. Then S is switched to position Q. After a long time, the charge on the capacitor is q₂ $$\mu$$C.



The magnitude of q₁ is ________________.

In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q₁ $$\mu$$C. Then S is switched to position Q. After a long time, the charge on the capacitor is q₂ $$\mu$$C.



The magnitude of q₂ is ________________.

Two point charges $$-$$Q and +Q/$$\sqrt 3 $$ are placed in the xy-plane at the origin (0, 0) and a point (2, 0), respectively, as shown in the figure. This results in an equipotential circle of radius R and potential V = 0 in the xy-plane with its center at (b, 0). All lengths are measured in meters.



The value of R is __________ meter.