The bob of a pendulum was released from a horizontal position. The length of the pendulum is $$10 \mathrm{~m}$$. If it dissipates $$10 \%$$ of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is:

[Use, $$\mathrm{g}: 10 \mathrm{~ms}^{-2}$$]

$$N$$ moles of a polyatomic gas $$(f=6)$$ must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of $$N$$ is :

In Young's double slit experiment, light from two identical sources are superimposing on a screen. The path difference between the two lights reaching at a point on the screen is $$7 \lambda / 4$$. The ratio of intensity of fringe at this point with respect to the maximum intensity of the fringe is :

Given below are two statements:

Statement I : Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons revolve around it, is Rutherford's model.

Statement II : An atom is a spherical cloud of positive charges with electrons embedded in it, is a special case of Rutherford's model.

In the light of the above statements, choose the most appropriate from the options given below