$\begin{array}{1 1}(A)\;780\\(B)\;782\\(C)\;784\\(D)\;786\end{array} $

- $C(n,r)=\large\frac{n!}{r!(n-r)!}$

No of questions in part I=6

No of questions in part II=6

The different ways of doing the questions are

$\Rightarrow (6C_3\times 6C_4)+(6C_4\times 6C_3)+(6C_2\times 6C_5)+(6C_5\times 6C_2)$

$6C_3=\large\frac{6!}{3!\times 3!}$

$\Rightarrow \large\frac{6\times 5\times 4\times 3\times 2\times 1}{3\times 2\times 1\times 3\times 2\times 1}$

$\Rightarrow 20$

$6C_4=\large\frac{6!}{4!\times 2!}$

$\Rightarrow \large\frac{6\times 5\times 4\times 3\times 2\times 1}{4\times 3\times 2\times 1\times 2\times 1}$

$\Rightarrow 15$

$6C_2=\large\frac{6!}{2!\times 4!}$

$\Rightarrow \large\frac{6\times 5\times 4!}{2\times 4!}$

$\Rightarrow 15$

$6C_5=\large\frac{6!}{5!}$

$\Rightarrow \large\frac{6\times 5!}{5!}$

$\Rightarrow 6$

$\Rightarrow (20\times 15)+(15\times 20)+(15\times 6)+(6\times 15)$

$\Rightarrow 300+300+90+90$

$\Rightarrow 780$

Hence (A) is the correct answer.

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