Which of the following reacts with $KMnO_4$ but does not react with $AgNO_3$?

Given below are two statements:
Statement-$I$:
$trans$-But-$2$-ene upon treatment with $Br_2$ in $CCl_4$ gives the following product:
(Image provided)
Statement-$II$:
$cis$-But-$2$-ene upon treatment with alkaline $KMnO_4$ gives the following product:
(Image provided)
In the light of the above statements, choose the most appropriate answer from the options given below.

Alkene $(A)$ will be:
$\mathop A\limits_{(\text{alkene})} \xrightarrow{RCO_3H, H_2O} \text{Racemic mixture}$
$\mathop A\limits_{(\text{alkene})} \xrightarrow{\text{Cold dil. } KMnO_4} \text{Meso-compound}$

On catalytic reduction $(H_2/Pt)$,how many alkenes will give $2-$methylbutane?

What is the product formed by the reaction of propene with $Br_2$ in $CCl_4$?

Name the alkene with molecular formula $C_{10}H_{20}$.