Identify $A$ in the given chemical reaction:

When aldehydes or ketones are treated with $C_6H_5-NH-NH_2$ (phenylhydrazine),the product formed is:

For the reduction of ketones to hydrocarbon,the appropriate agent is

Columns $1$,$2$,and $3$ contain starting materials,reaction conditions,and type of reactions,respectively.

$Column-1$	$Column-2$	$Column-3$
$(I)$ Toluene	$(i)$ $NaOH / Br_2$	$(P)$ Condensation
$(II)$ Acetophenone	$(ii)$ $Br_2 / h\nu$	$(Q)$ Carboxylation
$(III)$ Benzaldehyde	$(iii)$ $(CH_3CO)_2O / CH_3COOK$	$(R)$ Substitution
$(IV)$ Phenol	$(iv)$ $NaOH / CO_2$	$(S)$ Haloform

$(1)$ For the synthesis of benzoic acid,the only $CORRECT$ combination is
$[A] (III) (iv) (R)$ $[B] (IV) (ii) (P)$ $[C] (I) (iv) (Q)$ $[D] (II) (i) (S)$
$(2)$ The only $CORRECT$ combination in which the reaction proceeds through radical mechanism is
$[A] (I) (ii) (R)$ $[B] (II) (iii) (R)$ $[C] (III) (ii) (P)$ $[D] (IV) (i) (Q)$
$(3)$ The only $CORRECT$ combination that gives two different carboxylic acids is
$[A] (IV) (iii) (Q)$ $[B] (III) (iii) (P)$ $[C] (II) (iv) (R)$ $[D] (I) (i) (S)$

Acetaldehyde reacts with $C_2H_5MgCl$. The final product is

Grignard's reagent reacts with ethanal (acetaldehyde) and propanone to give: