The total work done on a particle is equal to the change in its kinetic energy. This is applicable

If $\frac{(x - 1)^2}{x^3 + x} = \frac{A}{x} + \frac{Bx + C}{x^2 + 1}$,then

$A$ cell is connected between the points $A$ and $C$ of a circular conductor $ABCD$ of centre $O$ with angle $AOC = 60^{\circ}$. If $B_1$ and $B_2$ are the magnitudes of the magnetic fields at $O$ due to the currents in $ABC$ and $ADC$ respectively,the ratio $\frac{B_1}{B_2}$ is

$A$ uniform chain of length $2\, m$ is kept on a table such that a length of $60\, cm$ hangs freely from the edge of the table. The total mass of the chain is $4\, kg$. What is the work done in pulling the entire chain on the table? ................ $J$

$A$ rocket of mass $M$ is launched vertically from the surface of the earth with an initial speed $V$. Assuming the radius of the earth to be $R$ and negligible air resistance,the maximum height attained by the rocket above the surface of the earth is

Give the correct order of initials $T$ or $F$ for the following statements. Use $T$ if the statement is true and $F$ if it is false.
$(I)$ Sulphide ions react with $Na_2[Fe(CN)_5(NO)]$ to form a purple-coloured compound $Na_4[Fe(CN)_5(NOS)]$. In the reaction,the oxidation state of iron changes.
$(II)$ $Pt(IV)$ compounds are relatively more stable than $Ni(IV)$ compounds.
$(III)$ The welding of magnesium can be done in an atmosphere of Helium.
$(IV)$ $LiAlH_4$ on hydrolysis will give $H_2$.