$A$ pair of substances which gives the same products on reaction with water is

Match the common name given in column $I$ with their taxonomic category order given in column $II$ and choose the correct combination from the options given below.

Column-$I$ (Common name)	Column-$II$ (Taxonomic category-Order)
$A$. Wheat	$I$. Primata
$B$. Mango	$II$. Diptera
$C$. Housefly	$III$. Sapindales
$D$. Man	$IV$. Poales

$A$ transverse sinusoidal wave moves along a string in the positive $x-$ direction at a speed of $10\, cm/s$. The wavelength of the wave is $0.5\, m$ and its amplitude is $10\, cm$. At a particular time $t$,the snapshot of the wave is shown in the figure. The velocity of point $P$ when its displacement is $5\, cm$ is:

$ABC$ is a triangular plate of uniform thickness. Its sides are as shown in the figure. If $I_{AB}$,$I_{BC}$,and $I_{CA}$ are the moments of inertia of the plate about axes $AB$,$BC$,and $CA$ respectively,then which of the following relations is correct?

Which of the following statements is correct for any thermodynamic system?

Given $\lambda \in [0, 20]$,find the number of integral values of $\lambda$ for which the function $f(x) = x^3 - 12x + \lambda$ has a point of local maxima.