If $\tan A$ and $\tan B$ are the roots of the quadratic equation $x^2-px+q=0$,then $\sin^2(A+B)$ is equal to

The strength of an acid depends on its tendency to

The period of $f(x)=\cos \left(\frac{x}{3}\right)+\sin \left(\frac{x}{2}\right)$ is (in $\pi$)

Match the taxonomic categories given in column $I$ with their feature given in column $II$.

Column $I$	Column $II$
$A$. Taxon	$I$. Basic unit of classification
$B$. Species	$II$. $A$ taxonomic group of any rank
$C$. Phylum	$III$. Division is the same category in case of plants
$D$. Genus	$IV$. Identified based on a number of similar characters
$E$. Order	$V$. Group of related species having more characters in common with other species

Who proposed the binomial nomenclature system?

$A$ lead bullet at $27\,^oC$ just melts when stopped by an obstacle. Assuming that $25\%$ of the heat produced is absorbed by the obstacle,the velocity of the bullet at the time of striking is ........ $m/s$. (Melting point of lead $= 327\,^oC$,specific heat of lead $= 0.03\,cal/g\,^oC$,latent heat of fusion of lead $= 6\,cal/g$,and $J = 4.2\,J/cal$)