Which scientific term is used for a convenient category for the study of organisms like fish and mammals?

$P, Q, R$ and $S$ are four points with the position vectors $3i - 4j + 5k, 2i - j + 4k, -4i + 5j + k$ and $-3i + 4j + 3k$, respectively. Then, the line $PQ$ meets the line $RS$ at the point

The angle between a pair of tangents drawn from a point $P$ to the circle $x^{2}+y^{2}+4x-6y+9 \sin^{2} \alpha + 13 \cos^{2} \alpha = 0$ is $2 \alpha$. The equation of the locus of the point $P$ is

Match the following lists:

List-$I$	List-$II$
$A$. Ethane	$1$. $2$ $sp$ carbons
$B$. Ethylene	$2$. $6$ $sp^2$ carbons
$C$. Acetylene	$3$. $2$ $sp^3$ carbons
$D$. Benzene	$4$. $2$ $sp^2$ carbons
	$5$. $1$ $sp$ and $1$ $sp^2$ carbons

An inductance of $1 \ H$ is connected in series with an $AC$ source of $220 \ V$ and $50 \ Hz$. The inductive reactance (in ohm) is (in $\pi$)

Kepler's second law (law of areas) is nothing but a statement of