The work done by a force $\vec F = (-6x^3 \hat i) \text{ N}$,in displacing a particle from $x = 4 \text{ m}$ to $x = -2 \text{ m}$ is .............. $J$.

If $S_n = 1^3 + 2^3 + \ldots + n^3$ and $T_n = 1 + 2 + \ldots + n$,then

$A$ particle of charge $q$ and mass $m$ moves in a circular orbit of radius $r$ with angular speed $\omega$. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on

The $V-Q$ graph is shown below. What does the area of $\Delta OAB$ represent in this graph?

If $A=\left[\begin{array}{rr}i & -i \\ -i & i\end{array}\right]$ and $B=\left[\begin{array}{rr}1 & -1 \\ -1 & 1\end{array}\right]$,then find $A^8$. (in $B$)

$A$ proton and an $\alpha$-particle are accelerated through a potential difference of $100 \ V$. The ratio of the wavelength associated with the proton to that associated with an $\alpha$-particle is