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

If the pair of straight lines given by $A x^2+2 H x y+B y^2=0$,where $(H^2 > A B)$,forms an equilateral triangle with the line $a x+b y+c=0$,then $(A+3 B)(3 A+B)=$ (in $H^2$)

Find the equation of the circle passing through the point $(1, 1)$ and the intersection points of the circles $x^2 + y^2 = 6$ and $x^2 + y^2 - 6x + 8 = 0$.

$\cos A \cos 2 A \cos 4 A \ldots \cos 2^{n-1} A$ equals

Four smooth steel balls of equal mass at rest are free to move along a straight line without friction. The first ball is given a velocity of $0.4 \, m/s$. It collides head-on with the second elastically,the second one similarly with the third,and so on. The velocity of the last ball is .......... $m/s$.

If $\theta = \frac{\pi}{6}$,then the $10^{th}$ term of the series $1 + (\cos \theta + i \sin \theta) + (\cos \theta + i \sin \theta)^2 + (\cos \theta + i \sin \theta)^3 + \dots$ is equal to: