Beats are produced by two waves $y_1 = a \sin(1000\pi t)$ and $y_2 = a \sin(998\pi t)$. The number of beats heard per second is:

Which one of the following is not a functional unit of an ecosystem?

For a first order reaction at $27^{\circ} C$,the ratio of time required for $75 \%$ completion to $25 \%$ completion of reaction is

Solution $X$ contains $Na_2CO_3$ and $NaHCO_3$. $20 \ mL$ of $X$ when titrated using methyl orange indicator consumed $60 \ mL$ of $0.1 \ M$ $HCl$ solution. In another experiment,$20 \ mL$ of $X$ solution when titrated using phenolphthalein consumed $20 \ mL$ of $0.1 \ M$ $HCl$ solution. The concentrations (in $mol \ L^{-1}$) of $Na_2CO_3$ and $NaHCO_3$ in $X$ are respectively:

The length of the subtangent at $(2,2)$ to the curve $x^5=2y^4$ is

The evolutionary history of an organism is known as .......