A particle moves in a straight line so that its displacement $$x$$ at any time $$t$$ is given by $$x^2=1+t^2$$. Its acceleration at any time $$\mathrm{t}$$ is $$x^{-\mathrm{n}}$$ where $$\mathrm{n}=$$ _________.

Two coherent monochromatic light beams of intensities I and $$4 \mathrm{~I}$$ are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is $$x \mathrm{~I}$$. The value of $$x$$ is __________.

Two open organ pipes of lengths $$60 \mathrm{~cm}$$ and $$90 \mathrm{~cm}$$ resonate at $$6^{\text {th }}$$ and $$5^{\text {th }}$$ harmonics respectively. The difference of frequencies for the given modes is _________ $$\mathrm{Hz}$$. (Velocity of sound in air $$=333 \mathrm{~m} / \mathrm{s}$$)

In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at $$10.2 \mathrm{~V}$$. The wavelength of light emitted by hydrogen atom when excited to the first excitation level is ________ nm. (Given hc $$=1245 \mathrm{~eV} \mathrm{~nm}, \mathrm{e}=1.6 \times 10^{-19} \mathrm{C}$$).