The number of subsets of $\{1, 2, 3, \ldots, 9\}$ containing at least one odd number is

$A$ small source of sound vibrating at a frequency $500 ~Hz$ is rotated along a circle of radius $\frac{100}{\pi} ~cm$ at a constant angular speed of $5 ~revolutions ~per ~second$. The minimum and maximum frequency of the sound observed by a listener situated in the plane of the circle is (speed of sound is $332 ~ms^{-1}$).

Which of the following statements is incorrect?

If the angles of a triangle are in the ratio $4:1:1,$ then the ratio of the longest side to the perimeter is

The heat evolved for the rise of water when one end of the capillary tube of radius $r$ is immersed vertically into water is (Assume surface tension $= T$ and density of water to be $\rho$)

The number of angular and radial nodes of $4d$ orbital respectively are