$A$ 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

$A$ transformer works on the principle of

$A$ railway line is taken round a circular arc of radius $1000 \ m$,and is banked by raising the outer rail $h \ m$ above the inner rail. If the lateral force on the inner rail when a train travels round the curve at $10 \ ms^{-1}$ is equal to the lateral force on the outer rail when the train's speed is $20 \ ms^{-1}$,the value of $4g \tan \theta$ is equal to: (The distance between the rails is $1.5 \ m$).

$Fe_2Cr_2O_4 + Na_2CO_3 + O_2$ $\xrightarrow{\text{Fusion}} [X]$ $\xrightarrow[H_2O]{H^+} [Y]$ $\xrightarrow{H_2O_2/H^+} [Z]$
Which of the following statements is true for the compounds $[X], [Y]$ and $[Z]$?

If the extremities of a diagonal of a square are $(1, -2, 3)$ and $(2, -3, 5)$,then the length of its side is

$A$ proton, a deuteron, and an $\alpha$-particle having the same momentum enter a region of uniform electric field between the parallel plates of a capacitor. The electric field is perpendicular to the initial path of the particles. The ratio of deflections suffered by them is