$\begin{array}{1 1}(A)\;\text{True}\\(B)\;\text{False}\end{array} $

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Total no of questions =12

Questions required to Ans =7

Two groups $\rightarrow 6-6$

No of ways =$6C_5\times 6C_2+6C_2\times 6C_5+6C_3\times 6C_4+6C_4\times 6C_3$

$6C_5=\large\frac{6!}{5!1!}$$=6$

$6C_2=\large\frac{6!}{2!4!}=\frac{6\times 5}{2}$$=15$

$6C_3=\large\frac{6!}{3!3!}=\frac{6\times 5\times 4\times 3!}{3!\times 3\times 2}$$=20$

$6C_4=\large\frac{6!}{4!2!}=\frac{6\times 5\times 4!}{4!\times 2}$$=15$

No of ways =$6\times 15+15\times 6+20\times 15+15\times 20$

$\Rightarrow 90+90+300+300$

$\Rightarrow 180+600$

$\Rightarrow 780$ ways

Hence the given statement is false

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