If $(2, -1, 3)$ is the foot of the perpendicular drawn from the origin to a plane, then the equation of that plane is

The chemical reaction that involves the roasting process is

$A$ 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

$A$ smooth sphere $A$ is moving on a frictionless horizontal plane with an angular velocity $\omega$ and a linear velocity $v$ of its center of mass. It undergoes an elastic head-on collision with an identical sphere $B$ which is at rest. If there is no friction anywhere,then after the collision,their angular speeds are $\omega_A$ and $\omega_B$ respectively. Then:

$A$ circle of radius $4$,drawn on a chord of the parabola $y^2 = 8x$ as diameter,touches the axis of the parabola. Then,the slope of the chord is

$A$ reaction,$3 X_{(g)} \rightarrow 2 Y_{(g)} + Z_{(g)}$,takes place in a closed vessel. What is the rate of formation of $Y$ (in $mol \ L^{-1} \ s^{-1}$) if the rate of disappearance of $X$ is $7.2 \times 10^{-3} \ mol \ L^{-1} \ s^{-1}$?