Choose the incorrect order of the given properties.

The value of $\cot \left(\sum_{n=1}^{23} \cot ^{-1}\left(1+\sum_{k=1}^n 2 k\right)\right)$ is

If $\vec F$ is the force acting on a particle having position vector $\vec r$ and $\vec \tau$ is the torque of this force about the origin,then:

$A$ satellite is launched into a circular orbit of radius $R$ around the Earth,while a second satellite is launched into an orbit of radius $1.02 R$. The percentage difference in the time periods of the two satellites is ......... $\%$

From a disc of mass $M$ and radius $R$,a circular hole of diameter $R$ is cut such that its rim passes through the center of the disc. The moment of inertia of the remaining part of the disc about a perpendicular axis passing through the center of the original disc is

$KO_2$ exhibits paramagnetic behaviour. This is due to the paramagnetic nature of