In Geiger-Marsden experiment, the number of scattered $\alpha$-particles $N(\theta)$ is plotted as a function of scattering angle $\theta$. Which of the following options represents the correct plot? [Image Placeholder]

A ray of light with wavelength $\lambda$ is incident on three different photoelectric cells namely 1, 2 and 3. The threshold wavelength of these photoelectric cells are $\lambda_{1}$, $\lambda_{2},$ and $\lambda_{3,}$ respectively and the magnitude of stopping potentials of these cells are $V_{1}$, $V_{2}$ and $V_{3},$ respectively. The relation between $\lambda$ and threshold wavelengths are $\lambda_{1}\lambda$ and $\lambda_{3}>>\lambda$. The correct option is:

A protein undergoes reversible thermal denaturation from its initial state N to denatured state D according to $N \rightleftharpoons D$. At $60^{\circ}C$, the concentrations of both N and D are equal at equilibrium, and the standard enthalpy change of denaturation is $666~kJ~mol^{-1}$. The standard entropy change ($\Delta S^{\circ}$ in $kJ~K^{-1}~mol^{-1}$) of the protein upon denaturation at $60^{\circ}C$ is closest to

The green paramagnetic species formed by heating $KMnO_{4}$ at 513 K is

Consider a particle moving along a straight line, whose position as a function of time is given by $s(t)=\alpha t^{2}-\beta t+\gamma$, where $\alpha=1~ms^{-2}$ $\beta=6~ms^{-1}$ and $\gamma=5m.$ The average speed of the particle, in $ms^{-1}$ from $t=0$ to $t=6$ s is: