| List-I | List-II | ||
| (A) | Kinetic energy of Earth | (I) | $-\frac{GM_sM_e}{a}$ |
| (B) | Potential energy of Earth and Sun | (II) | $\frac{GM_sM_e}{2a}$ |
| (C) | Total energy of Earth and Sun | (III) | $\frac{GM_e}{ R}$ |
| (D) | Escape energy from surface of Earth per unit mass | (IV) | $\frac{GM_sM_e}{2a}$ |
In the given figure, the blocks $A$, $B$ and $C$ weigh $4\,\text{kg}$, $6\,\text{kg}$ and $8\,\text{kg}$ respectively. The coefficient of sliding friction between any two surfaces is $0.5$. The force $\vec{F}$ required to slide the block $C$ with constant speed is ___ N.
(Given: $g = 10\,\text{m s}^{-2}$) 
Let $\alpha,\beta\in\mathbb{R}$ be such that the function \[ f(x)= \begin{cases} 2\alpha(x^2-2)+2\beta x, & x<1 \\ (\alpha+3)x+(\alpha-\beta), & x\ge1 \end{cases} \] is differentiable at all $x\in\mathbb{R}$. Then $34(\alpha+\beta)$ is equal to}
