Two wires of same length and thickness having specific resistances 6$$\Omega$$ cm and 3$$\Omega$$ cm respectively are connected in parallel. The effective resistivity is $$\rho$$$$\Omega$$ cm. The value of $$\rho$$, to the nearest integer, is ____________.

Consider a 72 cm long wire AB as shown in the figure. The galvanometer jockey is placed at P on AB at a distance x cm from A. The galvanometer shows zero deflection.


The value of x, to the nearest integer, is ___________.

A galaxy is moving away from the earth at a speed of 286 kms^$$-$$1. The shift in the wavelength of a redline at 630 nm is x $$\times$$ 10^$$-$$10 m. The value of x, to the nearest integer, is ____________. [Take the value of speed of light c, as 3 $$\times$$ 10⁸ ms^$$-$$1]

A ball of mass 4 kg, moving with a velocity of 10 ms^$$-$$1, collides with a spring of length 8 m and force constant 100 Nm^$$-$$1. The length of the compressed spring is x m. The value of x, to the nearest integer, is ____________.