Jee Main Jan 30 Shift 1 Mathematics - Question8

Answer: (3)

Solution:

$-1 \leq\left|\frac{2-|x|}{4}\right| \leq 1$

$\Rightarrow\left|\frac{2-|x|}{4}\right| \leq 1$

$\Rightarrow-1 \leq \frac{2-|x|}{4} \leq 1$

$-4 \leq 2-|x| \leq 4$

$-6 \leq-|x| \leq 2$

$-2 \leq|x| \leq 6$

$|x| \leq 6$

$\Rightarrow x \in[-6,6]$

Now, $3-x \neq 1$

And $x \neq 2$

and $3-x>0$

$x<3$

From (1), (2) and (3)

$\Rightarrow x \in[-6,3]-{2}$

$\alpha=6$

$\beta=3$

$\gamma=2$

$\alpha+\beta+\gamma=11$