Which of the following is a micronutrient for plants?

$\lim _{x \rightarrow 0} \left( \frac{x \cdot 10^x - x}{1 - \cos x} \right)$ is equal to

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 $A$ and $B$ are two events such that $A \subset B$ and $P(B) \neq 0$,then which of the following is correct?

The technique used to make numerous copies of a specific segment of $DNA$ quickly and accurately is

Two concentric coils of $10$ turns each are placed in the same plane. Their radii are $20 \ cm$ and $40 \ cm$ and carry $0.2 \ A$ and $0.3 \ A$ current respectively in opposite directions. The magnetic induction (in $T$) at the centre is