A sinusoidal voltage of peak value 250 V is applied to a series LCR circuit, in which R = 8$$\Omega$$, L = 24 mH and C = 60 $$\mu$$F. The value of power dissipated at resonant condition is 'x' kW. The value of x to the nearest integer is ____________.

In the logic circuit shown in the figure, if input A and B are 0 to 1 respectively, the output at Y would be 'x'.

The value of x is ____________.

A ball of mass 10 kg moving with a velocity $$10\sqrt 3 $$ m s^$$-$$1 along X-axis, hits another ball of mass 20 kg which is at rest. After collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along Y-axis at a speed of 10 m/s. The second piece starts moving at a speed of 20 m/s at an angle $$\theta$$ (degree) with respect to the X-axis.

The configuration of pieces after collision is shown in the figure.

The value of $$\theta$$ to the nearest integer is ____________.

The first three spectral lines of H-atom in the Balmer series are
given $$\lambda$$₁, $$\lambda$$₂, $$\lambda$$₃ considering the Bohr atomic model, the wave lengths of first and third spectral lines $$\left( \frac{\lambda_{1} }{\lambda_{3} } \right) $$ are related by a factor of approximately 'x' $$\times$$ 10^$$-$$1.

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