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 ____________.

Consider a water tank as shown in the figure. It's cross-sectional area is 0.4 m². The tank has an opening B near the bottom whose cross-section area is 1 cm². A load of 24 kg is applied on the water at the top when the height of the water level is 40 cm above the bottom, the velocity of water coming out the opening B is v ms^-1.

The value of v, to the nearest integer, is ___________. [Take value of g to be 10 ms^-2]