What is the value of linear velocity,if $\vec \omega = 3\hat i - 4\hat j + \hat k$ and $\vec r = 5\hat i - 6\hat j + 6\hat k$?

If the lines $4x + 3y - 1 = 0$,$x - y + 5 = 0$ and $kx + 5y - 3 = 0$ are concurrent,then $k$ is equal to:

The difference between the radii of $n^{\text{th}}$ and $(n+1)^{\text{th}}$ orbits of a hydrogen atom is equal to the radius of the $(n-1)^{\text{th}}$ orbit of hydrogen. The angular momentum of the electron in the $n^{\text{th}}$ orbit is . . . . . . ($h$ is Planck's constant).

Reproducing new plants by cells instead of seeds is known as

$A$ car $P$ approaching a crossing at a speed of $10 \, m/s$ sounds a horn of frequency $700 \, Hz$ when $40 \, m$ in front of the crossing. The speed of sound in air is $340 \, m/s$. Another car $Q$ is at rest on a road which is perpendicular to the road on which car $P$ is reaching the crossing. The driver of car $Q$ hears the sound of the horn of car $P$ when he is $30 \, m$ in front of the crossing. The apparent frequency heard by the driver of car $Q$ is ...... $Hz$.

$A$ sodium atom is in one of the states labeled 'Lowest excited levels'. It remains in that state for an average time of $10^{-8} \ s$,before it makes a transition back to a ground state. What is the uncertainty in energy of that excited state?