The shortest distance between the line $y - x = 1$ and the curve $x = y^2$ is:

If $A(1,2,3), B(3,7,-2), C(6,7,7)$ and $D(-1,0,-1)$ are points in a plane, then the vector equation of the line passing through the centroids of $\triangle ABD$ and $\triangle ACD$ is

$A$ uniform rod of mass $m$ and length $l$ is moving with velocity $u$ in a direction perpendicular to its length. $A$ blow of impulse $J$ is given perpendicular to its length at a distance $\frac{l}{4}$ from its centre at point $P$ such that the instantaneous velocity of point $P$ becomes $2u$. Then the velocity of its centre of mass will be:

$A$ glass capillary tube of inner diameter $0.28 \ mm$ is lowered vertically into water in a vessel. The pressure to be applied on the water in the capillary tube so that the water level in the tube is the same as that in the vessel (in $N/m^2$) is:
(Surface tension of water $= 0.07 \ N/m$,Atmospheric pressure $= 10^5 \ N/m^2$)

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

The human gene $Dystrophin$ contains how many million bases?