A capacitor of $$10 \mu \mathrm{F}$$ capacitance whose plates are separated by $$10 \mathrm{~mm}$$ through air and each plate has area $$4 \mathrm{~cm}^2$$ is now filled equally with two dielectric media of $$K_1=2, K_2=3$$ respectively as shown in figure. If new force between the plates is $$8 \mathrm{~N}$$. The supply voltage is ________ V.

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 $$=333 \mathrm{~m} / \mathrm{s}$$)