The radius of the sphere $x^2+y^2+z^2=12x+4y+3z$ is

$A$ small mass $m$ is attached to a massless string whose other end is fixed at $P$ as shown in the figure. The mass is undergoing circular motion in the $x-y$ plane with center $O$ and constant angular speed $\omega$. If the angular momentum of the system,calculated about $O$ and $P$ is denoted by $\vec L_o$ and $\vec L_p$ respectively,then:

In an experiment,four quantities $a, b, c$ and $d$ are measured with percentage errors of $1\%, 2\%, 3\%$ and $4\%$ respectively. Quantity $P$ is calculated as $P = \frac{a^3 b^2}{cd}$. The percentage error in the measurement of $P$ is .......... $\%$

The correct stability order of the given tautomers is:

If the distance $s$ travelled by a particle in time $t$ is given by $s=t^2-2t+5$, then its acceleration is

If $\cos A = \frac{3}{4}$,then $32 \sin \left(\frac{A}{2}\right) \sin \left(\frac{5A}{2}\right) = $