The number of radial nodes of $3s$ and $2p$ orbitals respectively are

If $\tan \theta + \cot \theta = 2$,then $\sin \theta$ is equal to

If the angular velocity of a disc depends on the angle rotated $\theta$ as $\omega = \theta^2 + 2\theta$,then its angular acceleration $\alpha$ at $\theta = 1 \ rad$ is ......... $rad/sec^2$.

The part of the fallopian tube closest to the ovary is -

If $\omega$ is a complex cube root of unity,then $\sin \left\{\left(\omega^{10}+\omega^{23}\right) \pi-\frac{\pi}{4}\right\}$ is equal to

$A$ mass $M$,attached to a horizontal spring,executes $S.H.M.$ with amplitude $A_1$. When the mass $M$ passes through its mean position,a smaller mass $m$ is placed over it and both of them move together with amplitude $A_2$. The ratio of $\left( \frac{A_1}{A_2} \right)$ is