If \(x_1\) be the size of the magnified image and \(x_2\) the size of the diminished image in Lens Displacement Method, then the size of the object is :

The point of intersection of tangents at the ends of the latus-rectum of the parabola $y^2 = 4x$ is

$y=A e^x+B e^{2 x}+C e^{3 x}$ satisfies the differential equation

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

Two wires $A$ and $B$ are of the same material. Their lengths are in the ratio $1:2$ and their diameters are in the ratio $2:1$. When stretched by forces $F_A$ and $F_B$ respectively,they experience an equal increase in their lengths. Then the ratio $F_A/F_B$ is:

$A$ geostationary satellite is revolving around the earth. To make it escape from the gravitational field of the earth,its velocity must be increased by ........ $\%$