If $x = 2^{1/3} - 2^{-1/3}$,then $2x^3 + 6x = $

$A$ gramophone record is revolving with an angular velocity $\omega$. $A$ coin is placed at a distance $R$ from the centre of the record. The static coefficient of friction is $\mu$. The coin will revolve with the record if

$A$ body is thrown vertically upwards and reaches its maximum height in $t$ seconds. The total time from the time of projection to reach a point at half of its maximum height while returning (in seconds) is:

Two spherical soap bubbles of radii $r_1$ and $r_2$ in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to:

$A$ proton, a deuteron, and an $\alpha -$ particle enter a region of perpendicular magnetic field (to their velocities) with the same kinetic energy. If $r_p, r_d,$ and $r_{\alpha}$ are the radii of the circular paths of these particles, then:

When a system is taken from state $i$ to state $f$ along the path $iaf,$ it is found that $Q = 50 \, cal$ and $W = 20 \, cal$. Along the path $ibf$,$Q = 36 \, cal$. Work done along the path $ibf$ will be ........... $cal$.