There are two section and the candidates has to answer at least $2$ question from each section with total of $6$ questions.

So, there are three followign ways.

$(i)$ no of ways $\Rightarrow$ selecting $2$ questions from section $A$ and $4$ questions from sections $B$

$\Rightarrow^5 C _2 \times{ }^5 C _4 \Rightarrow 10 \times 5 \Rightarrow 50$

$(ii)$ no. of ways $\Rightarrow$ selecting $3$ questions from each section.

$\Rightarrow^5 C _3 \times^5 C _3 \Rightarrow 10 \times 19=100$

$(iii)$ no. of ways $\Rightarrow$ selecting 4 from section $A$ and $2$ from section $B$

$\Rightarrow^5 C _4 \times{ }^5 C _2 \Rightarrow 5 \times 10 \Rightarrow 50$

$\therefore$ Total no. of ways $=50+100+50=200$.