A cyclist starts from the point $$P$$ of a circular ground of radius $$2 \mathrm{~km}$$ and travels along its circumference to the point $$\mathrm{S}$$. The displacement of a cyclist is:

A body of $$m \mathrm{~kg}$$ slides from rest along the curve of vertical circle from point $$A$$ to $$B$$ in friction less path. The velocity of the body at $$B$$ is:

(given, $$R=14 \mathrm{~m}, g=10 \mathrm{~m} / \mathrm{s}^2$$ and $$\sqrt{2}=1.4$$)

The width of one of the two slits in a Young's double slit experiment is 4 times that of the other slit. The ratio of the maximum of the minimum intensity in the interference pattern is:

The translational degrees of freedom $$\left(f_t\right)$$ and rotational degrees of freedom $$\left(f_r\right)$$ of $$\mathrm{CH}_4$$ molecule are: