A double convex lens made of glass of refractive index 1.5 and radii of curvature of the curved surfaces 20 cm each is immersed in a liquid of refractive index n_L. The correct plot showing the variation of the power, in the units of diopter (D), as a function of n_L is :

Consider a hydrogen atom with $v_k, r_k,$ and $K_k$ denoting the velocity, orbital radius and kinetic energy of the electron in the $k^{{th}}$ orbit, respectively. The electron undergoes a transition from the $n^{{th}}$ orbit, emitting radiation corresponding to the Lyman series. Considering $h$ to be the Planck’s constant and $ ho_0$ the permittivity of the free space, the correct statement(s) is/are:

A particle is thrown with a speed v from a point O at an angle θ with the horizontal plane such that it passes through the point P at a height of 1 m and horizontal distance of 5 m from O, as shown in the figure. If acceleration due to gravity is g $\text{ms}^{-2}$, then the correct statement(s) is/are:

A quasi-static cycle of a monoatomic ideal gas contains an isothermal process $(ab)$, followed by an isochoric process $(bc)$ and an adiabatic process $(ca)$ as shown in the figure. The volumes of the gas are $V_1$ and $V_2$ at $a$ and $b$, respectively. If the cycle has heat input $Q_{\mathrm{in}}$ and output $Q_{\mathrm{out}}$, then the efficiency of the cycle is defined as $$\eta = \frac{Q_{\mathrm{in}} - Q_{\mathrm{out}}}{Q_{\mathrm{in}}}.$$ The correct statement(s) is/are:

[Given: $\ln 2 \approx 0.7$]