$A$ uniform chain has a mass $m$ and length $l$. It is held on a frictionless table with one-sixth of its length hanging over the edge. The work done in just pulling the hanging part back on the table is

$A$ spherically symmetric gravitational system of particles has a mass density $\rho = \begin{cases} \rho_0 & \text{for } r \leq R \\ 0 & \text{for } r > R \end{cases}$ where $\rho_0$ is a constant. $A$ test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed $V$ as a function of distance $r$ $(0 < r < \infty)$ from the centre of the system is represented by:

Two charges $2 C$ and $6 C$ are separated by a finite distance. If a charge of $-4 C$ is added to each of them,the initial force of $12 \times 10^3 ~N$ will change to

The branched tree-like structure present in the cerebellum is known as:

The measurements of two quantities along with the precision of their respective measuring instruments are given as:
$A = 2.5 \, m/s \pm 0.5 \, m/s$
$B = 0.10 \, s \pm 0.01 \, s$
The value of $AB$ will be:

The metal used for the de-bromination reaction of $1, 2-dibromoethane$ is: