Two solutions of $KNO_3$ and $CH_3COOH$ are prepared separately. The molarity of both is $0.1 \ M$ and their osmotic pressures are $P_1$ and $P_2$ respectively. The correct relationship between the osmotic pressures is:

$A$ uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. $A$ block of mass $m_2$ is attached to the free end of the rope. $A$ transverse pulse of wavelength $\lambda_1$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $\lambda_2$. The ratio $\lambda_2/\lambda_1$ is

The molecule having one unpaired electron is

Heterogametic male condition does not occur in

$\int(x+1)^2 e^x d x$ is equal to

If $C_p$ and $C_v$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively,then