The refractive index of the material of a double convex lens is $1.5$ and its focal length is $5 ~cm$. If the radii of curvature are equal,the value of the radius of curvature (in $cm$) is

$A$ sonometer wire resonates with a given tuning fork,forming standing waves with five antinodes between the two bridges when a mass of $9 \, kg$ is suspended from the wire. When this mass is replaced by a mass $M$,the wire resonates with the same tuning fork,forming three antinodes for the same positions of the bridges. The value of $M$ is .... $kg$.

$A$ disc of mass $M$ and radius $R$ rolls on a horizontal surface and then rolls up an inclined plane as shown in the figure. If the velocity of the disc is $v$,the height to which the disc will rise will be:

If $OA$ is equally inclined to $OX, OY$ and $OZ$ and if $A$ is $\sqrt{3}$ units from the origin,then $A$ is:

$A$ body of mass $6 ~kg$ is under a force which causes displacement in it given by $s = \frac{t^2}{4}$ metres,where $t$ is time. The work done by the force in $2$ seconds is: (in $~J$)

The maximum and minimum values of the function $f: R \rightarrow R$ defined by $f(x)=5 \cos x+3 \cos \left(x+\frac{\pi}{3}\right)+8$ for all $x \in R$,are respectively